Bacterial Communication and Cooperation: From Understanding to Applications. Anand Pai. Department of Biomedical Engineering Duke University

Transcription

1 Bacterial Communication and Cooperation: From Understanding to Applications by Anand Pai Department of Biomedical Engineering Duke University Date: Approved: Lingchong You, Supervisor George Truskey Henry Greenside Margarethe Kuehn Jingdong Tian Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2013

2 ABSTRACT Bacterial Communication and Cooperation: From Understanding to Applications by Anand Pai Department of Biomedical Engineering Duke University Date: Approved: Lingchong You, Supervisor George Truskey Henry Greenside Margarethe Kuehn Jingdong Tian An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2013

3 Copyright by Anand Pai 2013

4 Abstract While they are single- celled organisms, most bacteria have been shown to communicate and cooperate at the population level. Bacterial cell- cell communication is termed quorum sensing (QS) wherein individual cells sense their population s density and modulate the expression of specific target genes accordingly. These QS- regulated target genes are responsible for a variety of cooperative actions such as the secretion of beneficial enzymes into the environment. Thus, bacteria regulate their cooperative actions in a density- dependent manner through QS. In my research, I investigated the fundamental principles that underlie QS and cooperation across diverse bacterial species and showed how these social characteristics enable bacterial proliferation. I first examined the underlying reaction- diffusion and biochemical mechanisms across bacterial QS systems. I found that cutting across the diversity within QS systems is a simple, universally conserved, signaling module that comprises of signal synthesis, transport, detection, and degradation as the fundamental parameters. Exploiting this core module s universality, I developed a single summary metric, sensing potential (v) that captures the dominant activation properties of a QS system. v quantifies the ability of bacteria to sense their confinement and conveniently captures the kinetic properties of diverse QS systems. iv

5 How does QS- mediated regulation of cooperation benefit bacteria? To address this question, I then designed and implemented an engineered system in Escherichia coli where cells can be induced to synthesize and secrete a costly but beneficial public- good exoenzyme using different regulation strategies. Combining mathematical modeling with quantitative experiments using the engineered system, I showed that exoenzyme production is overall advantageous to bacteria only if initiated at a sufficiently high density. It is this property that sets the potential advantage for QS- mediated regulation when initial cell density is low. I also demonstrated that this advantage of QS- mediated regulation is robust to varying initial cell densities and growth durations and is particularly striking when bacteria face uncertainty, such as from stochastic dispersal during their lifecycle. Furthermore, I showed that for QS to be optimal, its activation properties must be appropriately tuned - neither too late, nor too early. Lastly, QS- mediated cooperation has been shown to be critical for the virulence and proliferation of bacterial pathogens, providing an important new target for anti- bacterial therapies. Here, I combined mathematical modeling and engineered gene circuits to examine the long- term effects of inhibition therapies directed at QS and cooperation. I showed that inhibiting QS can lead to the selection of more cooperative bacterial variants. As a result, such treatment can counter- intuitively increase the virulence of the overall population. In contrast, directly inhibiting the public good can destabilize bacterial cooperation and reduce virulence in the overall population. v

6 Overall, my research has (1) elucidated the core components of cell- cell communication across bacteria, (2) explained how communication and cooperation advantage bacterial growth, and (3) opened up the important application of this research in devising novel antibacterial therapies. vi

7 To my family and friends for their unconditional and reliable love. vii

8 Contents Abstract... iv List of Tables... xii List of Figures... xiii Acknowledgements... xv 1. Bacterial communication through quorum sensing The diversity of quorum sensing systems in bacteria QS signal production and transport Detection of QS signals Target functions controlled by QS A mathematical framework for QS What is sensing potential v and what does it convey? Estimating the sensing potential of QS bacteria The biochemical and physical parameters of QS Modulation of sensing potential Mapping signal concentration based activation to population density dependent response A case study: QS- mediated regulation of exoenzyme secretion QS- control for a general effector Discussion: The core model for QS reveals universal sensing characteristics QS- based control of cooperation in bacteria Introduction: why coordinate to cooperate? viii

9 2.2 Engineering a synthetic system for exoenzyme production Engineering the QS- activated public- good exoproduct Essential characteristics of the engineered circuit The plasmids that constitute the engineered circuit General materials and methods Mathematical model of exoenzyme dynamics Population growth Exoenzyme synthesis and secretion: Growth and the effect of cell density under different control strategies Elucidating the characteristics of QS as a control system using an engineered circuit Density dependence of exoenzyme production benefit QS provides an appropriate density- dependent control strategy QS- mediated regulation is robust to stochastic dispersal events QS kinetics need to be appropriately tuned for optimal regulation Evolution of QS characteristics and the presence of cheaters Conclusion Inhibiting QS- mediated cooperation as antibacterial therapy Introduction: Disrupting social behavior as an alternative to traditional antibiotics Cheaters in a cooperative population and implication for anti- bacterial therapy targeting QS Modeling a population of QS cooperators and cheaters ix

10 3.4 Effect of inhibition on total population growth Effect of inhibition on cheater invasion How is cooperation maintained as a trait despite the presence of cheaters? How is the evolutionary maintenance of cooperation affected by inhibition? Simulation methods for population growth and inhibition Population growth Inhibition Evolutionary maintenance of cooperation by population structuring Experimentally examining inhibition strategies Plasmids and strains for cheaters and cooperators Method for measuring cooperator or cheater frequency in a mixed population Preliminary data: effect of inhibition on population growth and cheater invasion Appendix A A.1 A general modeling framework for QS signaling across bacteria A.1.1 Uniform concentration A.1.2 Transport across the membrane is rate limiting A.1.3 Effect of bacterial periplasm is negligible A.1.4 Modeling positive feedback A.1.5 Type Ia and Type IIa sensing: A.2 Modeling the target (Effector) A.3 Optimal regulation strategy x

11 A.4 Generality of cost- benefit analysis results Appendix B B.1 Construction of plasmids for QS- mediated cooperation B.1.1 pexo B.1.2 pexoi B.1.3 prtransp B.2 Testing enzyme secretion and function B.3 Testing QS- mediated activation B.4 Estimating 3OC6HSL concentration in QS population at high density B.5 Stochastic variation in initial density B.6 The optimal control strategy for controlling exoproduct production B.7 QS advantage across different initial densities and lifecycle times B.8 Parameter values for modeling QS- mediated exoenzyme production Appendix C: Long- term monitoring of bacterial growth and plasmid segregation C.1 Plasmids, strains and growth conditions C.2 Long- term monitoring of bacterial growth and reporter expression References Biography xi

12 List of Tables Table 1: Well- studied QS systems in bacteria Table 2: Parameters for estimating sensing potential Table 3: Plasmids used in our study Table 4: Modeling parameters for QS- mediated exoproduct activation xii

13 List of Figures Figure 1: Cell- cell signaling and density- dependent action in bacteria Figure 2: General framework for bacterial QS Figure 3: Calculated and observed sensing potentials for 15 well- characterized QS systems Figure 4: Sensing potential observed and calculated with error bounds Figure 5: Sensing potential plotted as a function of β and δ Figure 6: Optimal control of effector activation by QS Figure 7: QS- mediated activation of target functions Figure 8: A synthetic gene circuit that implements three strategies to control exoenzyme production Figure 9: Schematic of BlaMs construction Figure 10: Strategies for activating production of exoproducts Figure 11: Population density determines benefit of exoenzyme production Figure 12: Density- dependent activation through QS Figure 13: QS- control is advantageous irrespective of initial density Figure 14: QS based control is robust to stochasticity caused by dispersal Figure 15: Optimal tuning of QS to maximize bacterial growth Figure 16: Cost of LuxI production under IPTG is negligible compared to cost of exoproduct synthesis and cheater invasion in public goods scenario Figure 17: QS controlled cooperation in bacteria Figure 18: Schematic of bacterial cooperation machinery Figure 19: Simulations of population growth and cheater invasion xiii

14 Figure 20: Effect of inhibition strategies on cooperator growth and frequency Figure 21: Population structuring provides evolutionary selection for cooperation despite cheater invasion Figure 22: Effect of inhibition on long- term evolutionary selection for cooperation Figure 23: Experimental results on inhibition strategies Figure 24: Signal diffusion across bacterial periplasm Figure 25: Optimal exoenzyme synthesis strategy ( E ) during growth Figure 26: Cost- benefit scenario for bacterium in enclosure of unchanging Ve Figure 27: Cytoplasmic BlaMs (unlike wildtype periplasmic Bla) does not prevent cell wall damage from beta- lactam antibiotics Figure 28: Liquid phase test of BlaMs secretion by hlyb- hlyd transporter Figure 29: Density- dependent activation under QS control through AHL based signaling Figure 30: Growth dynamics under poisson dilution Figure 31: Comparing different QS systems across stress levels Figure 32: Plasmid segregation during bacterial growth Figure 33: Trapping and imaging E. coli in microfluidic device Figure 34: Long- term observation of plasmid expression dynamics in a microfluidic device Figure 35: Quantitative observations from microscopy opt xiv

15 Acknowledgements I am deeply indebted to Dr. Lingchong You for accepting me into his lab at Duke and for his consistent guidance since then. Under him, I have gained tremendously in scientific thought and critical analysis, but, above all, I have learned to never dismiss an idea without thought. Without his support for my ideas and research, I would not have made it this far. My colleagues in the You lab have been essential to my sanity through graduate school. Needless to say, and as everyone in the lab knows, I am joined at the hip to Yu Tanouchi as a friend, roommate, colleague, co- investigator, and often as co- conspirator. I credit Jeffrey Wong for never failing to bring me back to earth with his dismissive remarks about bacterial research. Anoop Sadanandan and Bruno Borges, beyond their friendship, taught me to appreciate the art that is political science. I would also like to thank my committee members: George Truskey, Henry Greenside, Margarethe Kuehn and Jingdong Tian for their continued guidance. In particular, I learned a lot from my discussions with Henry Greenside, often coming away with questions I had never considered. I am glad to have had the opportunity to learn from him and feel privileged to have his advice and support. I also thank Margarethe Kuehn for always being willing to discuss my projects and for helping me look beyond E. coli. xv

16 A special thanks to Shishi Luo for an inordinate number of things, starting with the sheer joy she brings to my life. She manages to patiently nod and wait for me to reach a conclusion she has already reached an eon ago. The famous words...no man is an island, entire of itself by John Donne holds more than just true for my work; they represent my work and me. xvi

17 1. Bacterial communication through quorum sensing Quorum sensing (QS) is the mechanism by which bacteria modulate their gene expression depending on changes in population density. This modulation is accomplished by the production and sensing of small signal molecules that, at a sufficiently high concentration, activate specific target functions (1, 2) (Figure 1). A QS system can be divided into a sensor module that houses the signal synthesis, secretion and detection systems and an effector module that carries out the targeted function when induced. Figure 1: Cell- cell signaling and density- dependent action in bacteria. In QS, individual bacteria produce signal molecules (orange circles) that are secreted or diffuse into the environment. This signal s concentration acts as a proxy for population density in the environment. At sufficiently high population density, receptor (R) bound to signal activates expression of target genes. Orange and green colors represent QS system and target machinery respectively. 1

18 1.1 The diversity of quorum sensing systems in bacteria QS signal production and transport For sensors, a wide variety of signal molecules have been identified. Gram- negative bacteria often use acyl homoserine lactones (AHLs) as signals (1, 3). These AHLs are typically synthesized by LuxI- type enzymes from fatty acids, where LuxI is the canonical AHL synthase from bacterium Vibrio fischeri. Gram- positive bacteria often use small peptides as QS signals (4, 5). These peptides differ in size and in the complexity of post- translational modifications. In all QS sensors, signals are produced intracellularly and transported to the extracellular environment. Small AHLs diffuse freely across bacterial cell membranes (6) while large AHLs appear to be actively transported by pumps such as the multidrug efflux (mex) pumps in Pseudomonas aeruginosa (7). Peptides are typically too large for diffusion across membranes and are transported by dedicated ATP- binding cassette (ABC) transporters (5, 8) Detection of QS signals Different strategies are in place to detect these signals. AHL signals often lead to activation of cytoplasmic regulator proteins such as LuxR in V. fischeri (3, 6), which then activates target gene expression. Peptide signals and also some AHLs, are typically sensed by membrane- associated receptors to initiate a phosphorylation cascade that leads to target gene expression (4, 5). In Vibrio harveyi, an AHL (HAI- 1) and a furanone 2

19 (AI- 2) are detected by different surface receptors (LuxN and LuxP/Q respectively) (9). An additional level of complexity arises in that bacteria often house multiple QS systems. In V. harveyi three QS sensors work in parallel to control luminescence (9). In V. fischeri two AHL based QS systems, ain and lux, are involved in the control of luminescence and symbiotic growth in the squid host (10, 11) but in the ain system the extracellular AHL signal is detected by a membrane based sensor while in the lux system the receptor (LuxR) is cytoplasmic Target functions controlled by QS The list of bacterial functions under QS control has expanded tremendously from its initial discovery for bioluminescence in V. harveyi (12) and competence regulation in Streptococcus pneumoniae (13) to diverse functions such as exoenzyme secretion in P. aeruginosa and various plant pathogens (14, 15), conjugation in Agrobacterium tumefaciencs (16), sporulation control in Myxococcus xanthus (17), virulence in Staphylococcus aureus (18) and eukaryote host detection in Enterococcus faecalis (19). The QS systems behind these functions are all drastically different and as such the link between QS characteristics and the function regulated in terms of benefit to the host bacterium is unclear (20, 21). Here we show that despite the diversity in structure and function, the essential properties of QS can be captured by a simple generic metric, sensing potential. The metric is based on a universally conserved core signaling module that consists of signal 3

20 synthesis, transport, detection, and degradation as the fundamental parameters; one that appears across diverse QS systems. We exploit its universality to model this core module and derive sensing potential as a general measure of QS. This sensing potential conveys the ability of a QS bacterium to measure the size of its enclosure. We validate our model using experimental observations of diverse QS bacteria reported in literature. In doing so, we also provide a comprehensive survey of the available quantitative information on the kinetics of these QS systems. We find that, in addition to providing a concise, integrated description of the sensing property of a QS module, sensing potential captures the dominant trend of sensing characteristics of different QS systems. Capitalizing on these properties, we focus on the effector modules under QS regulation and study how QS characteristics affect effector regulation. 1.2 A mathematical framework for QS We note that every QS sensor falls into one of two categories (which we refer to as Type I or Type II) of the core module depending on where the signal concentration (A) is detected. In a Type I system (Figure 2A), the extracellular signal concentration is sensed while in a Type II system, the intracellular signal concentration is sensed (Figure 2B). To describe the dynamics of each Type of sensing, we assume that the signal (A) is synthesized at a constant rate k inside the bacterium (of volume Vc) and is lost by degradation and transport to its microenvironment (of volume Ve). The signal concentration inside the cell (Ai) and that outside (Ae) is assumed to be uniform and 4

21 transport across the bacterial membrane is assumed to be rate limiting (see Appendix A). In the microenvironment, the exported signal is diluted by a factor of V V c e and is again subject to degradation. We model the signaling dynamics by accounting for the signal synthesis, transport, and degradation (Figure 2A and B). We assume that: (1) signal transport (D, hr - 1 ) and degradation (da, hr - 1 ) are proportional to the signal concentration (A nm); (2) the signal is synthesized at a constant rate (k, nm hr - 1 ). For a Type I system (Figure 2A), the rate of change of the intracellular and extracellular signal respectively is given by da i dt = k DA i d a A i (1.1) da dt e V = DAi V c e d a A e (1.2) For Type II systems (Figure 2B), we have: dai dt da dt e = k D = D ( Ai Ae ) d a Ai V V c ( Ai Ae ) da Ae e (1.3) (1.4) where D ( ) A i A e now accounts for the two way transport. Here, Ve represents the volume of the bacterial microenvironment and Vc represents the cell volume of an average bacterium. 5

22 Figure 2: General framework for bacterial QS. (A) Type I: the extracellular signal concentration (Ae, red box) is sensed. (B) Type II: the intracellular concentration (Ai, red box) is sensed. Arrows represent reactions. Stippled arrows represent transport. (C) The steady- state signal concentration (A, orange) decreases with Ve. The parameters of the lux system of V. fischeri are used to plot the curve. At a sufficiently small Ve, A will exceed the threshold level K (50 nm) to elicit effector response. Inset: By definition, K is the signal concentration to induce an effector. A QS system often displays a graded response (green curve) and K is determined as the half- activation signal concentration. 6

23 For Type I, Eqs. 1.1 and 1.2 are solved simultaneously to get the steady state Ae as a function of Ve: A e = V e V c Dk 2 ( d + Dd ) a a (1.5) For Type II, Eqs. 1.3 and 1.4 give: A i = V e k D + da V c Ve Ve Dd a + D da + V V c c d 2 a (1.6) According to Eqs. 1.5 and 1.6, both Ae and Ai increase with decreasing Ve (Figure 2C). The critical Ve,c and hence the sensing potential v, for which Ae (Type I) and Ai (Type II) cross the threshold K is calculated by solving Eqs. 1.5 & 1.6 for v at Ae, Ai = K Dk δβ respectively. For Type 1 we get: v = = where β = k and 2 K( d a + Dd a ) 1+ δ Kd a δ = D d a Dk DKd a 1 1. For Type II, we get: v = =. d a ( k DK Kd a ) β 1 δ 1 For both Type I and Type II systems, Ai and Ae increase with a decreasing Ve (Figure 2C). For a sufficiently small Ve (<Ve,c), the signal concentration would exceed a threshold (K) required for phenotypic expression (Figure 2C). 7

24 1.3 What is sensing potential v and what does it convey? We define the dimensionless ratio Ve,c/Vc as the sensing potential (v) of the sensor for the host bacterium. v is determined by the key QS parameters signal synthesis rate (k), activation threshold of a target function (K), and rate constants for degradation (da), and transport (D). These parameters can be rearranged into two dimensionless variables k D by appropriately scaling with respect to da: β = and δ =. These dimensionless Kd a d a forms were chosen such that δ conveys how fast a signal is transported from a cell once it is made at rate conveyed in β. As the ratio of signal synthesis rate to the activation threshold and signal degradation rate constant, β quantifies the efficiency of signal synthesis. δ is the ratio of the transport rate constant and degradation rate constant. As such, 1/δ is analogous to the Thiele modulus seen in reaction- diffusion processes (22, 23) and developmental processes involving diffusion (24), where it measures the relative rates of reactive and diffusive processes. The above analysis can be readily generalized to account for variations, such as feedback, two way signal transport in the Type I case (Type Ia), and the use of specialized pumps for signal transport (Type IIa) (see Appendix A). By definition v conveys the size of the microenvironment required for effector activation, in multiples of the bacterium volume. To interpret sensing potential we note that v is 0 for a QS system that is never activated. In contrast, v approaches infinity if target function is always active, as under a constitutive promoter. 8

25 As an analogy, consider the following; under appropriate assumptions, the kinetic theory of gases gives rise to a simple gas law that relates different gas properties (state variables), pressure (P), volume (V), and temperature (T). A real gas would still have the pressure property P, though its dependence on T would be more complex, depending on the specific molecular properties of the real gas. Extending this analogy a little further, the microscopic movement of individual molecules averages to a mean free path for collisions and leads to the combined gas pressure (23). Similarly, for a population of cells (n) in a large volume (V), Ve represents the average enclosure volume (Ve =V/n) for each cell. Here, signal sensing by individual cells averages to a critical enclosure size Ve,c for activation that corresponds to their sensing potential. 1.4 Estimating the sensing potential of QS bacteria In population- level experiments, Ve,c can be approximately calculated as 1/dcrit where dcrit is the population density observed to trigger a QS phenotype(9). Thus, the observed sensing potential vobserved is 1/(dcritVc). This vobserved reflects the phenotype (potential) of the actual QS system, comprising of all its regulatory interactions in addition to the core module while vcalculated represents the estimated potential based only on the core module. To test the applicability of our framework, we compare the sensing potential calculated (vcalculated) using our framework with vobserved (Figure 3 and Figure 4). Several factors affect this comparison, in addition to the uncertainty in measurements of biological parameters. The first is the estimation of a threshold K. The 9

26 experimental measurement of K as A at half maximal activation is an approximation for when phenotypic expression can be considered ON (Figure 2C inset). Second, for lack of reliable data to quantify positive feedback, we do not include this effect while estimating vcalculated. Positive feedback increases v (see Appendix A) and many, but not all, of the QS systems considered here display this regulatory phenomenon. Thus, vcalculated will likely under predict vobserved. Third, vobserved is calculated from continuously growing cultures where species concentrations may differ from steady state values. Despite these issues, we find a strong correlation between vcalculated and vobserved (n=15, p < 0.05) indicating that vcalculated captures the dominant characteristics of the diverse QS systems listed. A linear regression of vcalculated against vobserved gives a slope slightly greater than one ( 1.1± 0.05 ), which is consistent with our expectation that vcalculated would tend to under predict vobserved. Additionally, six of the sensor modules shown in Figure 3 occur together in pairs in QS bacteria, where they form a hierarchical structure of phenotypic activation. For each of the three pairs from V. fischeri (ain, lux) (25), V. harveyi (HAI- 1, luxs) (9), and Pseudomonas aeruginosa (las, rhl) (26), vcalculated correctly predicts the order of activation. 10

27 Figure 3: Calculated and observed sensing potentials for 15 well- characterized QS systems. Squares represent Type I sensing; triangles Type II. Each dot represents a different module. Details of the parameters and equations to estimate vcalculated as well as the calculation of vobserved from experimental observations are provided in Appendix A.1. See Tables 1 and 2 for a synopsis of the data used to plot this figure. 11

28 Table 1: Well- studied QS systems in bacteria Host Bacterium QS sensor S. aureus agr B. subtilis Comx, CSF S. pneumoniae CSP P. aeruginosa rhl, las V. fischeri ain, lux S. meliloti sin R. leguminosarum cin V. harveyi HAI- 1, luxs E. carotovora car A. tumefaciens tra V. cholerae CAI- 1, luxs* S. mutans CSP* B. cepacia cep Note: V. cholerae, S. mutans, B. cepacia are additional data points not plotted in Figure 3 for lack of clear information on parameters. 12

29 Log 10 (v) v calculated v observed Rhl Car Lux Las Cin Tra Cep Ain Sin HAI-1 Log 10 (v) v calculated v observed Agr Comx CSF2 CAI-1 CSP LuxS* CSP* LuxS CSF1 Figure 4: Sensing potential observed and calculated with error bounds. Bar- chart comparing vcalculated and vobserved with the respective bounds generated by either uncertainty in parameter estimation (see Table 2) for vcalculated or range reporter in literature for vobserved. Top and bottom panels carry all the AHL and non- AHL based systems respectively. In both panels data is arranged in increasing order of vobserved. To prevent confusion, * indicates systems with the same name in different host bacteria. 1.5 The biochemical and physical parameters of QS The parameters below (Table 2) were either taken directly from literature or estimated from literature. A detailed description for each parameter, its source, and its estimation, can be found in the Supplementary Text 2 associated with publication (27). vcalculated is obtained using the appropriate equations for sensing potential. The 13

30 experimentally observed critical cell density for phenotypic expression is typically reported as a range. Log(vobserved) shown is the mean of the logarithm of the observed sensing potential for the range. For the Type IIa case, the signal import rate constant is calculated to be 100 min - 1. The correlation test on Log(vobserved) and Log(vcalculated) is performed with a null hypothesis that the two are uncorrelated with 13 (n- 2) degrees of freedom. The last four data points are additional (some parameters are unknown and were guessed) and not included in Figure 3 nor while calculating the correlation. Table 2: Parameters for estimating sensing potential QS sensor K nm/hr da hr - 1 D hr - 1 K nm Log(vcalculated) Log(vobserved) agr comx CSF CSF CSP rhl las ain lux sin cin

31 HAI luxs car tra CAI luxs* CSP* cep Modulation of sensing potential We use the model to study the interplay between signal synthesis, its transport and sensing and its effect on activation by looking at the effect of β and δ on v. In Type I sensing, where the extracellular signal is detected, an increase in δ helps speed up the extracellular signal accumulation leading to an increase in v (Figure 5 A). This increase however is limited by β representing the amount of signal being made (Figure 5A). Thus in Type I sensing, v increases with both β and δ but the increase in v with δ saturates at a level depending on β. 15

32 A 10 3 Type I sensing B 10 4 Type II sensing β=500 β=500 v 10 2 β=100 v Self Activation β= β= M β= δ" Q R δ" Figure 5: Sensing potential plotted as a function of β and δ. (A) Type I sensing where the extracellular signal is detected. Thus an increase in δ increases extracellular signal accumulation leading to an increase in v. The increase is limited by the amount of signal being made given by β. (B) Type II sensing where the intracellular signal is sensed. Faster export (larger δ ) removes the intracellular signal leading to reduction in v. Since signal is produced intracellularly, low signal transport δ in comparison to the signal production β could lead to intracellular signal accumulation to above threshold levels, irrespective of v. This appears as steep rise in v (v à ) for particular combinations of β and δ and represents self- activation of the QS host. The interplay of β and δ leading to self- activation can be seen as follows; for β =10, the vertical line Q marks a critical δ (= β - 1), below which v approaches infinity (effector self- activation). Line R does the same for β = 100. Consider point M on β =10 and low v. If β is increased to 100 while keeping δ constant, the change results in self- activation. In Type II sensing, gene expression is triggered by the intracellular signal. While increasing β increases v, faster export (larger δ ) tends to remove the intracellular signal and reduce v (Figure 5 B). The dependence of the two Types of sensing on δ is hence opposite. Importantly, since the signal is both produced and detected intracellularly in Type II systems, for a given δ, transport across the bacterial membrane places an upper limit on β (Figure 5 B). An increase in β beyond this limit results in a discontinuity in v ( v ). To restate, if signal synthesis is fast (large β) and its export rate is sufficiently 16

33 small (small δ), its intracellular concentration would always exceed the activation threshold (K), regardless of the microenvironment size. This can also been seen mathematically by considering the case where Ve à so that the extracellular signal is infinitely diluted, Ae à 0. Putting Ae = 0 in equation Eq 1.3 shows that Ai can still exceed the threshold K if synthesis k is sufficiently large, and/or D+da is sufficiently small. Hence, fast signal synthesis or slow signal turnover, or both, could lead to self- activation of the effector (irrespective of Ve). This predicted Type II self- activation appears to occur in nature under appropriate conditions. In P. aeruginosa, starvation can cause increased signal synthesis leading to effector activation irrespective of cell- density (28). In A. tumefaciens, TraM sequesters TraR from the TraR- 3OC8- HSL complex(29, 30). Since, TraR induces the QS phenotype on binding with 3OC8- HSL, deletion of TraM can give rise to a lower K (higher β) such that v leading to constitutive activation (29, 30). As in Type I, v becomes insensitive to δ in Type II systems for sufficiently fast transport, and is limited by β (Figure 5 B). 1.6 Mapping signal concentration based activation to population density dependent response. In QS, the signal concentration acts a proxy for population density. Here we map the relation between the underlying biochemical, signal- mediated, target gene activation and the observed phenotype of population density dependent response. Experimentally, 17

34 18 the dose- dependent activation (E) of a target gene by the QS signal is well described by a Hill function(31, 32):, (1.7) where A is the sensed signal concentration for Type I ( ) or Type II ( ) systems and a is the hill coefficient. To analyze benefits of QS regulation independent of the type of sensing we derive the inducing function (Eq. 1.7) in terms of v. In other words, we seek to map ( ). For Type I, substituting Eq. 1.5 for Ae in Eq. 1.7 gives:. Rearranging terms gives: Simplifying further using the equation for v we get: a a a A K A E E + = max A e A = A i A = ( ) Vc Ve v E A K E,, ( ) ( ) a a a c e a a a a c e Dd d V V Dk K Dd d V V Dk E E = 2 2 max ( ) ( ) a c e a a a a a a c e V V Dd d K Dk Dd d K Dk E V V v E = 2 2 max,

35 19 (1.8) Hence for the Type I case, maps to. For a Type II system, additional analysis is required. As Ai does not go to zero (whereas in Eq. 1.5, ). Instead,. In other words, there is always a basal level of signal in the cell (for non- zero k) causing a constant low level of induction. Since as a function, displays the property, as, does not map exactly to for large Ve. Instead goes to a low but non- zero basal value for large Ve. However, the majority of QS sensors considered lie in the region with <10 4 where deviation is relatively small. We thus use Eq. 1.8 for effector induction by sensor without making a distinction between Type I and II but note that the equation underestimates the low basal activation at low population densities. a c e a a c e V V v v E V V v E + = max, a e a a e p A K A E E + =,max a a c e a v V V v E E + = max V e 0 A e a i d D k A + a a c e a v V V v E E + = max 0 E V e a i a a i p A K A E E + =,max a a c e a v V V v E E + = max a i a a i p A K A E E + =,max e V c V /

36 1.7 A case study: QS-mediated regulation of exoenzyme secretion As an integrated measure of QS characteristics, v represents a collective QS phenotype, irrespective of the parameters that lead to it. For example, two QS systems could have the same potential v but resulting from different synthesis and transport rate parameters. This framework can then be conveniently applied to study the phenotypic consequences of differing QS characteristics. For this, we first define a QS- associated change in host fitness ( Δ f ) as the benefit gained minus the cost incurred upon effector activation by QS. Assuming the cost of sensor operation to be negligible compared to effector cost (33), we examine Δf due to effector activation by different sensors with varying v values. We note that effector activation (E) by QS for a bacterium in an enclosure of size Ve can be approximately modeled with eq. 1.8: E E = ( V / V e v a max a c ) + v a, where a is the Hill coefficient and Emax represents maximal activation. The cost and benefit of the effector (which are functions of E) then determine whether QS regulation is beneficial to the host bacterium in a given scenario and, if so, how tuning v affects host fitness. To elucidate this, we model a common biological target function regulated by QS: the secretion of exoenzymes (15, 20, 34). Here, QS controls the synthesis of the enzyme (P), which is secreted to the extracellular microenvironment. In this context, E represents the synthesis rate of P. In the microenvironment, P degrades a substrate (S) to 20

37 produce a nutrient N. We assume that diffusion of enzymes across the cell membrane is negligible due to their large size and that they are actively secreted by pumps. Furthermore, we assume that diffusion and mixing in the environment are much faster than cell growth so that all species (enzyme and generated nutrient) are uniformly distributed in the microenvironment (See Appendix A for modeling details). Consider a batch culture where, starting from a low density, the bacteria grow in number (n) for a time span (T) in a constant culture volume V with unlimited S. The cost of effector activation to each individual cell depends on E, while the benefit depends on the amount of N reaching the cell. Both in turn depend on the per cell enclosure volume Ve (Ve=V/n). With this extended model, we first derive Δ f for the host cell as a function of E and Ve. By further assuming that the bacterial growth rate g is an increasing function of Δ f (35, 36), we can analyze the overall benefit of QS- mediated effector regulation during T. 21

38 A v= Fitness Δf Early Late V e /V 4 5 c 10 6 B Cell density n T cells/ml Late secretion v opt v Early secretion Cell density n T cells/ml C Optimum Late Induction v opt Early Induction v Figure 6: Optimal control of effector activation by QS. (A) Fitness increase ( Δ f ) for effector activation controlled by QS sensors with distinct sensing potentials. Shown are results from typical early (large v), intermediate and late (small v) inducing sensors. (B) Collective fitness nt as a function v. vopt here marks the sensing potential for maximum nt. Colored circles mark nt values for corresponding fitness curves for the three sensors shown in A. Note that nt under QS regulation (finite positive v) is greater than with effector shut off (v=0) and effector constitutively activated (v à ) showing QS regulation is advantageous. (C) Optimal QS characteristics (vopt) for a general beneficial effector. nt calculated for one parameter set of the general benefit function is shown for the case where QS regulation is beneficial. Typical QS activation characteristics corresponding to cell density (early or late induction) are marked. nt from QS regulation is higher than with effector shutoff (nt at v=0) or constitutive activation (nt at và ) and is maximal at a unique finite vopt. Inset: collective fitness curves for other parameter sets where QS proves advantageous. The vopt for each curve is determined by the effector characteristics. 22

39 First, two trivial scenarios emerge where regulation of exoenzyme synthesis is unnecessary. If the cell density during T is never sufficient for benefit to outweigh the cost of synthesis and secretion ( Δ f <0), the best strategy is not to activate the effector (v = 0). On the other hand if the benefit always overwhelms the cost during T, the best strategy is constitutive enzyme synthesis at the maximal rate (v à ). Excluding these two scenarios, QS regulation of exoenzyme synthesis is advantageous and needs to be optimally tuned to maximize bacterial fitness. As bacteria grow in the culture, there is gradual reduction in the average enclosure volume Ve per bacterium from V n 0V c to V, where n0 and nt are the numbers of bacteria at t = 0 n t V c and t T, respectively. This leads to an increase in E by QS controlled activation. Overall, this results in a continual change in Δf and its path depends on the sensor s v (Figure 6 A). The best QS strategy, such as early activation (with large v) or late activation (with small v) of enzyme production during growth can be determined by the accrued Δf during T. This collective fitness can be measured by nt, the final number of bacteria at the end of T. Numerical calculation indicates that nt is a biphasic function of v (Figure 6 B) with a distinct potential (vopt) at which nt is maximal. vopt represents the optimal QS sensor characteristics for each set of physical and biological parameters that define this cost- benefit scenario. A detailed analysis along with simulations is included in Appendix A

40 1.8 QS-control for a general effector The previous analysis shows that: (a) the cost and benefit of exoenzyme secretion determines whether QS regulation is advantageous to the host in a given scenario, and (b) when advantageous, a unique tuning of the QS characteristics (vopt) provides the maximum nt (see Figure 6B). How applicable are these results for other QS regulated target functions? To address this question, we extend the analysis to a general effector that is costly but beneficial. Again, nt depends on the specific cost (C) and benefit (B) functions for the effector. C used in exoenzyme analysis is based on measurements of the effect of gene expression on growth rate (35) and can be assumed to remain qualitatively unchanged for different effectors. Learning from the exoenzyme study, B will depend on the extent of effector activation E and enclosure volume Ve. In particular, we note that B can be assumed to be an increasing but saturating function in terms of E and 1/Ve (Eq. A.24), which can capture the effects of a wide range of effectors. Similar to exoenzyme regulation, QS regulation is unnecessary when either the cost or benefit of effector activation overwhelms the other. When cost of effector activation is much larger than its benefit, the best strategy is to keep the cost minimal by shutting off the effector (v = 0). On the other hand, if benefit from effector activation is overwhelming, the best strategy is to simply maximize possible benefit (and hence Δf) by always operating the effector at full activation (v à ). Both scenarios require no 24

41 regulation. Otherwise, QS regulation is advantageous over constitutive effector control and its characteristics need to be uniquely tuned (vopt) to maximize nt (Figure 6C). A large vopt indicates that early activation during growth is optimal, whereas a small vopt indicates that activation at a high density is optimal. vopt in each case is uniquely determined by the parameters of the effector (Figure 6C inset). This result shows that distinct functions require QS systems with appropriately tuned characteristics for optimal regulation (Additional details in Appendix A.1.8). 1.9 Discussion: The core model for QS reveals universal sensing characteristics. Here we developed a simple metric sensing potential to quantify the ability of a bacterium to sense the confinement of its microenvironment. The metric emerges from a core module seen in all QS systems so that it is a generic measure; v can be measured for any given QS system. We have made a number of simplifying assumptions in our analysis based on experimental observations of QS signal diffusion and mathematical analysis (see Appendix A). They allow us to reduce the complex nature of QS regulated activation, which typically involves multiple steps and many regulatory species (30, 37), down to four fundamental measurable parameters governing signal synthesis, transport, degradation and detection. Despite the simplicity of the metric, our analysis indicates that v of the core module can capture the dominant trend of sensing properties across the highly diverse QS systems (Figure 3). The same analysis also shows cases of deviations between the 25

42 actual potential of a QS system (vobserved) and the estimated potential (vcalculated) that is based on the simple core module. This deviation indicates additional regulatory interactions that act over and above that captured by the minimal core module. For example, positive feedback on signal synthesis positive feedback was not included in the estimations in Figure 3- would increase vcalculated (methods) and could account for many of the deviations. In addition to providing an intuitive classification of QS modules (Figure 2), the framework also helps reveal the commonality and difference between Type I and Type II sensing. For sufficiently fast signal transport (δ à ), the sensing potential for both types is uniquely determined by and approximately proportional to β, suggesting a common strategy to modulate sensing potential (Figure 5). We see several examples of this strategy. In the plant pathogen A. tumefaciens, plant produced compounds called opines act as primary regulators of the tra QS (Type II) system by controlling signal synthesis (38, 39). Without opines, transcription of the signal synthase trai is repressed to a low basal level (low v since β is low), whereas the presence of opines, indicating the presence of the plant host, relieves the repression and leads to normal expression of trai and virulence at high density. However, when δ is small, it has opposite, significant effects for the two types: increasing δ decreases v in Type II systems (Figure 5B) but increases v in Type I systems (Figure 5A). Dependence of v on δ (for small δ ) is complex in Type II sensing. As δ 26

43 approaches a critical threshold (β - 1), v drastically increases to approach infinity. Below the threshold, a Type II system can activate its effector irrespective of cell density (Figure 5B), which is impossible in Type I systems. This control strategy appears to be adopted by some bacteria. In P. aeruginosa (28), starvation causes faster signal synthesis in both the las and rhl QS systems. In A. tumefaciens (30), deletion of a repressor element in the tra system lowers the signal sensing threshold. In both cases, the change in biochemical parameters causes a large increase in β driving v to infinity (Figure 5B), leading to activation of the QS- regulated effector independent of cell density. Thus, Type II systems appear to have an additional layer of effector control over QS so as to subvert it under certain scenarios. Sensing potential provides a concise, integrated description of the sensing characteristics of a QS module, even if its underlying mechanism is more complex than the core module. Thus, v can be used as a single modulated (reduced) variable to study how QS characteristics affect downstream regulation. To illustrate its application, we use our framework to study the scenarios in which QS regulation of functions proves advantageous. This additionally provides an insight into the evolution of QS as a regulation strategy, as seen in the analysis of other evolutionary strategies (40-42). By modeling exoenzyme control and then generalizing the conclusion to other effectors, we show that QS regulation is advantageous when the cost of effector synthesis is comparable to its resulting benefit (Figure 6B). A closer look reveals that an 27

44 underlying requirement is that the benefit from such an effector s activation depends on the environment size (Figure 6C). For enzyme secretion, benefit decreases with increased dilution of the enzyme in the microenvironment. In this case, QS regulation allows effector synthesis to be kept low for large Ve, where benefit is low compared to cost, and increases it gradually with Ve, hence providing optimal control. In the absence of such benefit dependence on Ve, QS regulation, regardless of any cost- benefit parameter combination, will likely not be advantageous. This conclusion is quite general as many QS controlled effectors display similar (Ve dependent) benefit function, wherein benefit is an increasing but saturating function of effector activation and density. Overall, sensing potential provides an intuitive and measurable connection between an individual QS cell and the population level phenotype. Additionally, the benefit of QS regulation emerges naturally by analyzing effector controlled by sensors of different potentials (Figure 6). Taken together, our analysis combines sensing with regulation benefit so that it can be understood and quantified in terms of both a single QS cell and a population of QS cells. 28

45 2. QS-based control of cooperation in bacteria 2.1 Introduction: why coordinate to cooperate? The target functions controlled by QS include a range of cooperative actions such as the secretion of nutrient- foraging enzymes, virulence toxins, and biofilm- forming compounds (14, 34, 43-46). These exoproducts are costly to produce but once released into the environment they act as beneficial public goods available to all bacteria in the vicinity (Figure 7). How does QS- mediated control of public good production benefit bacteria? As an example, consider an exoproduct that provides benefit by degrading a stress- causing agent in the environment (Figure 7). For a fixed per- cell production rate of the exoproduct, the cost per cell is fixed. However, the benefit of the exoproduct, reflected in any reduction of the stress- causing agent s concentration, should increase with exoproduct concentration, which in turn increases with the cell density. At a high cell density, the secreted exoproduct would be at a sufficiently high concentration to remove the stress within a short time. In contrast, with a low- density population, the concentration of the exoproduct in the environment is low, which will prolong the stress removal period. Intuitively, undertaking the cost of production under stress would only be advantageous if the cell density is above a sufficiently high critical density. This notion captures the potential advantage of sensing cell density: to delay production of costly exoproducts until an appropriately high density is reached where 29

46 the benefit of exoproducts can outweigh cost of their production (Figure 7). Of particular relevance in this regard is the recent work from Darch et al (47) based on the model QS bacterium Pseudomonas aeruginosa. Using a QS mutant where density- dependent activation was abolished, the study demonstrated that the benefit of producing an exoproduct (one that is typically produced under QS- mediated control) increased in a density- dependent manner while the benefit of a private intracellular good did not. Figure 7: QS- mediated activation of target functions. QS controls a variety of target functions including cooperative actions such as the secretion of exoproducts. Individual cells undertake the cost of producing and secreting these exoproducts. Once secreted, the actions of the exoproducts benefit the entire population, in this case by degrading or inhibiting the stress- causing agent. However, this benefit depends on the concentration of the exoproducts, which in turn depends on the population density. Blunt arrow (blue) indicates inhibition. 30

47 Knowing that exoproduct benefit is density- dependent (47, 48), and that QS provides a density- sensing mechanism (49), raises several fundamental questions on QS as a general control strategy to regulate production of exoproducts in bacteria. How much delay is advantageous and what are the QS characteristics to achieve this? What happens when production is activated earlier or later? When critical bacterial- lifecycle events, such as the advent of stress and population dispersal (transition from high to low density), occur stochastically, is QS still beneficial and, if so, to what extent? In a particular environment, how do signaling parameters of the QS machinery affect the overall benefit? 2.2 Engineering a synthetic system for exoenzyme production The above listed questions can be answered using a biological system where the result of different activation strategies (differing in the timing of activation) can be consistently compared based on the specific impact of exoenzyme production. Here we take a synthetic- biology approach (50-52) wherein a synthetic circuit provides a well- defined system to study its corresponding natural counterpart with a focus on the key, fundamental, parameters. We designed and implemented a system (53) in Escherichia coli where cells can be induced to synthesize and secrete a costly but beneficial public- good exoenzyme using different control strategies (Figure 8). We considered three control strategies that span a wide range of control in regulating a costly but beneficial exoenzyme in engineered 31

48 Escherichia coli. The first strategy is not to produce the exoenzyme (OFF), whereby cells avoid the cost of production but grow slower under stress. The second is to produce the exoenzyme always at a high rate (ON). With this strategy, cells incur high production cost but the secreted exoproduct can provide benefit by actively relieving the stress. The third is QS- mediated control where cells only produce the exoenzyme at a sufficiently high density Engineering the QS-activated public-good exoproduct We implemented the three control strategies in a common synthetic gene circuit (Figure 8) using the well- characterized LuxR/LuxI QS system of Vibrio fischeri. Circuit carrying cells, when induced, can produce and secrete BlaMs (Figure 9), a modified beta- lactamase exoenzyme that degrades a beta- lactam antibiotic in the culture, 6- aminopenicillanic acid (6- APA) (54), which mimics stress. Exogenously added acyl- homoserine lactone (AHL) can bind to and activate LuxR, which in turn activates BlaMs production from the PLuxI promoter. Expression of transporter genes hlyb and hlyd enables extracellular secretion of BlaMs (54). Here, the AHL- induced circuit realizes the ON strategy; the uninduced circuit realizes the OFF strategy. For QS- mediated control, AHL can be autonomously produced by the cells via LuxI, the expression of which is controlled by IPTG. Under QS, AHL concentration increases with cell density and will activate expression of BlaMs only at a sufficiently high density. Expression of LuxR and the Hly transporter proteins is regulated in the same way for all three strategies. 32

49 Figure 8: A synthetic gene circuit that implements three strategies to control exoenzyme production. LuxR and hemolysin transporters HlyB and HlyD are constitutively produced in the circuit. The signal AHL (orange circles) can bind to cytoplasmic LuxR and activate BlaMs production. BlaMs is cytoplasmic until secreted into the environment by the HlyB- HlyD transport machinery where it provides benefit by degrading 6- APA. For the OFF case, no AHL is added. For the ON case, AHL is added exogenously. For the QS case, IPTG at appropriate concentration is added. IPTG drives expression of LuxI that catalyzes AHL synthesis. At a low cell density, AHL concentration is low both inside and outside the cells. A sufficiently high cell density leads to sufficient accumulation of intracellular AHL, leading to exoenzyme production. 33

50 Figure 9: Schematic of BlaMs construction. BlaM is the mature cytoplasmic form of wildtype Bla without its N- terminal periplasmic signal peptide. BlaMs is formed by the fusion of BlaM and HlyAs, the C- terminal transport signal sequence from the hemolysin HlyA. The transporter genes hlyb and hlyd, when expressed, enable the secretion of a protein carrying the HlyAs signal into the extracellular environment Essential characteristics of the engineered circuit The following characteristics of our system are critical to address the questions on QS control: (1) The specific circuit configuration and the ability to chemically induce the desired control strategy (ON, OFF, or QS) allow multiple strategies to be compared based on the specific impact of exoenzyme production. (2) The exoenzyme BlaMs acts as an inducible public- good exoproduct. When secreted into the environment it degrades beta- lactams such as 6- APA but provides no protection when within cells. (3) The cell density at which exoproduct synthesis is initiated by QS can be modulated allowing comparison across a spectrum of strategies, all within the same system. (4) By adjusting 34

51 the 6- APA concentration, the relative ratio of cost to benefit can be changed and the role and importance of appropriate activation timing can be observed (5) High temporal resolution measurement of bacterial growth provides an insight into the reaction and transport dynamics of exoproduct and its impact over the bacterial lifecycle The plasmids that constitute the engineered circuit A two- plasmid system was designed and implemented for our study. pexoi (p15a, Kan R ) is responsible for IPTG- inducible production of LuxI and BlaMs (under PLuxI) inducible by AHL- bound LuxR. prtrans (ColE1, Cm R ) expresses LuxR and the transporter genes under an anhydrotetracycline (atc) inducible promoter. It also constitutively expresses the TetR repressor for low, tightly controlled expression. The transporter gene cassette was derived from plasmid pvdl9.3 and 25 ng/µμl of atc was added to the media for expression of LuxR and the transporter. See Table 3 in Appendix B for list of strains and plasmids used in our study. Further details of the contructions of the plasmid based circuits is provided in Appendix B. Principle strains used was: JM109 (enda1 glnv44 thi- 1 rela1 gyra96 reca1 mcrb + Δ(lac- proab) e14 - [F'ʹ trad36 proab + laciq laczδm15] hsdr17(rk - mk + )) General materials and methods Cells were grown in TBK media (10 g tryptone, 7 g KCl, buffered with 100 mm 3- (N- morpholino) propanesulfonic acid, MOPS) at 30ºC with ph was balanced to 7.0 using KOH. Cells transformed with circuit carrying plasmids (pexoi and prtrans) were 35

52 grown from single clones overnight for 14 hrs. Plasmids were maintained with 100 µμg/ml of chloramphenicol and 50 µμg/ml of kanamycin. 1 ml overnight culture was spun down, washed and suspended in 1 ml distilled water. Washed cells were diluted ranging from 300 fold (lowest dilution, highest initial density) to fold (3 fold dilution series, 5 levels) into prepared media with 25 ng/µμl atc to induce production of LuxR and transporter. To induce LuxI for QS, 2 mm IPTG (in water) or appropriate dilution was used. Equivalent amount of water was added as control in the absence of IPTG. TBK media supplemented with 0.1% Arabinose and 25 ng/µμl atc was used for all comparisons of QS, ON and OFF populations. 3OC6AHL (Sigma, K3007) was prepared as a stock solution of 20 mm by adding 4.5 mg to 1 ml of ethyl acetate. This was subsequently diluted by adding 5 µμl of stock solution to 995 µμl of media giving 100 µμm final concentration. Lower concentrations were prepared using serial dilutions in media. 6- APA solution was freshly prepared for each experiment by dissolving 50 mg 6- APA (Sigma, A70909) powder in 1 M HCl. Subsequent dilutions was made in water such that effective HCl solution concentration was always 0.1 M. As control, 0.1 M HCl was added to wells where no 6- APA was added. 200 µμl of the prepared cultures were laid out in triplicates in 96- well microplates (Corning). 50 µμl of mineral oil was added to prevent evaporation and the plate was incubated in plate reader (Victor3, Perkin- Elmer) at 30 C. Readings of absorbance at

53 nm (OD) and GFP fluorescence (when applicable) were taken every 10 minutes with periodic shaking (5s orbital followed by 5s pause). 2.3 Mathematical model of exoenzyme dynamics We developed a mathematical model for this system that, at its core, accounts for the combined effect of the cost and benefit of exoenzyme production; exoenzyme cost is incorporated through a reduction in growth rate proportional to the extent of maximal activation, while its benefit is indirectly accounted for by the increase in growth rate when secreted exoenzyme degrades antibiotic. We have neglected the cost of QS per se, as this is much less than that due to production of exoproducts (33, 34). This assumption is also consistent with measurements with our synthetic system Population growth. We model bacterial growth using the logistic equation: dn dt = gn ( 1 N), (2.1) where N is cell density C(cells/ml) normalized to the carrying capacity of the medium NM (cells/ml), and g the specific growth rate (hr - 1 ). Bacterial growth is affected by both the presence of antibiotic and the cost of exoenzyme synthesis. Here, we consider a simplistic relationship: g = Benefit Cost (2.2) 37

54 We model benefit as the increase in growth rate due to degradation of the antibiotic: Benefit = b 0 b m b m + Ab, (2.3) b 0 is the maximum growth rate in the absence of any antibiotic and with no enzyme production, b m the antibiotic concentration at which growth rate is half maximal, and Ab the antibiotic concentration. [ ] We assume cost to increase directly with activation E (where E 0,1 is the fraction of maximal activation) of exoenzyme production: Cost = c p E. (2.4) Here, growth rate is reduced by both, antibiotic presence and production cost and we assume an additive relationship between them Exoenzyme synthesis and secretion: Consider a single cell of intracellular volume Vc in the population of density C with maximal exoenzyme production rate kp. We assume that passive diffusion of enzymes across the cell membrane is negligible and that they are actively secreted by pumps with first order rate constant Dp. For simplicity, we assume the exoenzyme degrades with a rate d p in both the intracellular and extracellular environments. Assuming a well- mixed system, the equations for exoenzyme P can be written as 38

55 dp i dt = k pe D p P i d p P i (2.5) dp e dt = D pp i 1 CV c d p P e, (2.6) where i and e indicate exoenzyme concentrations inside the cell and in the microenvironment respectively. Dp is the exoenzyme transport rate constant. 1 CV c captures the dilution of the exoenzyme concentration ( D p P i ) once secreted. Antibiotic Ab degradation is modeled as follows: dab dt = d Ab, p P e Ab d Ab Ab (2.7) d Ab, p is the rate constant for active degradation of antibiotic by exoenzyme. We model that the antibiotic itself degrades with a low first order rate constant. d Ab Density- dependent activation of exoenzyme synthesis under the control of a QS system with potential v can be written as v a E =! 1 $ # &+ v a " CV c %, (2.8) where a is the cooperativity of the activation system. v conveys, in multiples of the bacterium volume V c, the size of the per- cell microenvironment required for half- maximal QS- based activation. 39

56 2.3.3 Growth and the effect of cell density under different control strategies. To compare growth of ON and OFF populations, we numerically solved equations (2.1)- (2.7) by setting activation at E =1 for ON and E = 0 for OFF with all other parameters kept the same. To compare QS, ON and OFF strategies simultaneously, we numerically solved equations (2.1)- (2.8) by setting v =10 4 for QS, v = 0 for OFF, and v = for ON. The simulations were repeated at varying initial densities and at each time point the cell density ratio of QS against OFF or ON (whichever was higher) was plotted for comparison. The parameters used in the simulations are described in Appendix B and listed in Table Elucidating the characteristics of QS as a control system using an engineered circuit Density dependence of exoenzyme production benefit We simulated growth of ON and OFF populations (Figure 10 A) starting from the same initial density in the presence of stress. We first compared their growth when their initial density was high (Figure 10 B). Initially, the ON population grows slower than the OFF population. Due to the cost of producing the exoenzyme and the inherent delay between exoenzyme production and antibiotic degradation, the collective benefit does not instantly exceed the cost of production. As the exoenzyme degrades the antibiotic, the growth rate of the ON population gradually increases and eventually 40

57 exceeds that of the OFF population. After sufficient time (Tcross), the ON population reaches and outgrows the OFF population, making ON an advantageous strategy. Experimentally, we monitored the growth of ON and OFF populations when a sub- lethal concentration of 6- APA was applied at a high initial density (300- fold dilution of an overnight culture to ~ cells/ml). Consistent with simulation, the ON population eventually recovered from an initial delay to exceed the OFF population (Figure 10 C, Tcross ~ 10 hours). If the initial density is sufficiently low, however, simulation shows that the ON population will never win during the growth period despite its ability to actively degrade the antibiotic (Figure 10 B). Higher dilution of the secreted exoenzyme results in little benefit for the ON cells, but the exoenzyme synthesis incurs the same cost as earlier. As such, eventual benefit from exoenzyme production cannot make up its initial growth disadvantage in comparison to the OFF population, making OFF the advantageous strategy. Again, consistent with simulations, when 6- APA at the same concentration as before was applied at a low initial density ( fold dilution of an overnight culture to ~ cells/ml), the ON population was unable to outgrow the OFF population during the growth period (Figure 10 C). 41

58 Figure 10: Strategies for activating production of exoproducts. (A) Under QS control, production is activated in a density- dependent manner: OFF at low densities and activated to ON at sufficiently high densities. Cell density is shown scaled to the carrying capacity NM of the bacterial environment. (B) Simulated growth of ON and OFF populations starting from either high or low initial cell density in the presence of antibiotic. (C) Measured growth dynamics starting at high and low initial density in the presence of 25 µμg/ml 6- APA. Absorbance (OD) readings below are not reliably detectable. ON and OFF cultures were split from the same dilution and hence had the same initial density. Also see Figure 11 for rescaling that highlights crossover of ON and OFF at high initial density. 42

59 The dependence of accrued benefit per cost invested on cell density results in Tcross increasing rapidly as the initial density is decreased and approaching the entire growth period observed during which the ON population cannot outgrow the OFF population (Figure 11). Thus, whether the production of a costly exoenzyme can eventually benefit the population depends on both the initial cell density and duration of growth: both must be sufficiently large for production to become beneficial at the population level. This suggests that a critical intermediate density (Ncrit) exists as a transition point at which production becomes advantageous in the bacterial lifecycle. For a population starting growth at a low density (below the transition point), a control mechanism that only activates production (OFF to ON) after this critical density would be advantageous. QS is an implementation of such a control strategy (see Appendix B). 43

60 Figure 11: Population density determines benefit of exoenzyme production. (A) Rescaled versions (for clarity) of Figure 10 B and C for comparison of ON and OFF growth starting at high initial density. On the right, the data is shown in log scale (top, smaller density range than originally shown) and linear scale (bottom). Each dot represents the average from three technical replicates and shaded area spans the standard deviation. Corresponding simulation results are shown on the left. (B) Measured Tcross for different initial densities. At each initial density, Tcross indicates the time when the means of ON and OFF growth curves crossed over. At the lowest initial densities, no crossover was observed during the growth period. The shading from pink to blue indicates the transition from a low initial density region at which ON cannot outgrow OFF to a high density one where ON can outgrow OFF given time Tcross. We mark Ncrit in this approximate transition region. Initial densities (OD) values were calculated from the OD measurement of the overnight culture and the dilution level. 44

61 2.4.2 QS provides an appropriate density-dependent control strategy. To examine the effectiveness of QS as an optimal control strategy, we simulated growth of three populations starting from a low initial density in the presence of the stress (Figure 12A). We chose a QS system that activates production at a sufficiently high density (reaching half- maximal activation at 10-1 NM where NM is the carrying capacity; see Figure 10 A). For the same low initial density as before, the ON population cannot outgrow the OFF population. The QS population initially grows similarly to the OFF population, as neither incurs significant cost of exoenzyme production. At a sufficiently high density, however, the QS population can trigger expression of the exoenzyme. At this high density, the net benefit of the exoenzyme will exceed its production cost (with a brief time delay, during which the QS population was losing slightly to the OFF population). The overall benefit of the exoenzyme enables the QS population to outgrow the OFF population. To test this prediction experimentally, we compared growth of three bacterial populations starting at the same low initial density (~4x10 3 cells/ml) in the presence of 25 µμg/ml 6- APA, with BlaMs synthesis OFF, always ON, or controlled by QS. For the ON population, the concentration of the exogenously added AHL was comparable to the AHL concentration measured in the QS culture at a high density (~9 nm). Again, due to the low initial starting density, the OFF population always outgrew the ON population. 45

62 As predicted by modeling, the QS population initially grew similarly as the OFF population but outgrew the latter at high density (Figure 12C, top left panel). Figure 12: Density- dependent activation through QS. (A) Simulated growth of QS, ON, and OFF populations starting from a low initial density in the presence of stress. (B) Simulations of QS, ON and OFF populations were carried out over a range of initial densities (onset of stress) and the densities of all three 46

63 were compared at each time point. The color intensity at each dot in the grid ( data points) represents the ratio of cell density of QS against the greater of ON or OFF at the corresponding time. Colored lines are shown to help demarcate the regions where a particular strategy is best. To demarcate the regions a difference of 1% in cell- density at any point was considered significant. Moving vertically from any initial density, the red line indicates transition from QS=OFF (before QS activation) to OFF> QS (pink region, immediately following QS activation). The next transition occurs at the green line where QS>OFF following the benefit of exoproduct action at high density. Orange line marks Tcross where ON outgrows OFF. (C and D) Growth of QS, ON, and OFF populations starting from low (C) and high (D) initial densities in the presence of 25 µμg/ml 6- APA. Insets in the panels show the corresponding results in linear scale to highlight the crossover of ON and OFF. Each data point is the average of four replicates and shaded area spans the standard deviation. Initial densities (cells/ml) were estimated from the dilution level and density of the overnight culture. Vertical stippled line marks 20 hour point where the three are compared below. Bar graph at the bottom compares growth of QS, ON, and OFF, at 20 hour point. * over a bar indicates significant difference from each of the others (one way ANOVA and Tukey- Kramer method multiple comparison with alpha=0.01). In general, stress can occur at variable densities and the subsequent growth duration can also vary. Given such variability, is QS still advantageous? To address this, we simulated QS, ON and OFF populations starting at varying initial densities and compared them all throughout their growth period (Figure 12B). When starting at low initial densities (below 10-4 NM), growth of the QS population largely follows that of the OFF population until a sufficiently high density, where QS- mediated activation allows the QS population to overtake OFF. At these low initial densities, ON is always the losing strategy, never being able to overtake OFF or QS during the growth period. Starting from high initial densities (above 10-3 NM), exoenzyme synthesis is beneficial and the ON population grows slower than OFF (below orange curve) for a short period before overtaking it (above orange curve). Here, QS activates exoenzyme synthesis 47

64 within a short period of initiating growth and overtakes both ON and OFF populations. Thus, OFF is the losing strategy for a high initial density (region above orange curve). Regardless of the initial density, however, QS only loses to OFF for a brief period following activation (pink region). This region is an inherent feature reflecting the dynamics of the enzymatic process: while cost is incurred immediately during production, the beneficial reduction in antibiotic requires the dynamical processes of transport and enzymatic reaction (see Appendix B for more detailed analysis on where QS would not be the best strategy). Overall, it emerges that QS is advantageous, or at least non- losing, for all combinations of initial densities and growth periods (also see Appendix B for QS comparison across varying stress levels and activation densities). This predicted property was confirmed experimentally (Figure 12 C and D and Figure 13) by comparing the three populations over different initial densities during the growth period. As expected, in the absence of the 6- APA OFF was always advantageous regardless of initial density (Figure 13). In the presence of 6- APA, QS emerged as the winning strategy over majority of the observed growth period, regardless of initial density, and was never the losing strategy (Figure 12 C and D and Figure 13). At low initial densities (below ~10 4 cells/ml), as before, ON was the losing strategy while QS was the best strategy (Figure 12C). At high initial densities (above ~10 5 cells/ml), 48

65 exoenzyme production by both QS and ON is beneficial with OFF as the losing strategy (Figure 12D). Figure 13: QS- control is advantageous irrespective of initial density. (Top panels) QS- mediated regulation is advantageous in the presence of 6- APA regardless of initial density. Growth of QS, ON, and OFF populations starting from the 49

66 indicated low (left) and high (right) initial densities in the presence of 25 µμg/ml 6- APA. Insets show the corresponding results in linear scale to highlight the crossover of ON and OFF indicated by the vertical stippled line. Each data point is the average of four replicates and shaded area spans the standard deviation. Initial densities (cells/ml) were estimated from the dilution level and density of the overnight culture. (Bottom panels) QS- mediated regulation is not advantageous in the absence of 6- APA. Figures show growth of QS, ON, and OFF populations (as discussed in the top panel). In the absence of any stress, OFF is always the best strategy while ON is always the loosing strategy QS-mediated regulation is robust to stochastic dispersal events. We have shown that QS is an advantageous control strategy when considering a single bacterial population starting growth from a defined initial density. However, an event such as dispersal, that restarts the growth cycle (Figure 14A) from low cell numbers after reaching a high cell density (biofilm formation, fruiting body development or sporulation) can result in variable initial densities (2). Consequently, the post- dispersal global population will consist of subpopulations with a large spread in the distribution of their initial densities (Figure 14B). Aside from being implicated in the dispersal event (55, 56), QS is suggested to be critical during initiation of growth from low numbers following dispersal (2). To examine whether and to what extent QS remains advantageous in such an event, we mimicked dispersal through extreme dilution (51). High dilution ( fold) of an overnight culture into a 96- well plate resulted in high stochastic variability in the seeding density of individual wells with about 2-3 cells per well (estimated from the number of empty wells, see ref. (51) and Appendix B.5). Here, each well acted as a subpopulation with a variable initial density. We exploited this variability to examine whether QS, which is driven by the kinetics of 50

67 signal production, diffusion, and sensing, and could hence be sensitive to environmental fluctuations, would remain effective as a controller. Consistent with simulations (Figure 14 C) we found that despite the stochasticity in the initial density, the overall QS population outgrew the overall OFF population (Figure 14D), akin to that seen earlier in the absence of variability in seeding. We note however that the stochasticity we generate is not a universal number and biologically its magnitude may vary from that generated experimentally (Figure 14 B). In lieu of this, we investigated how the extent of variability in initial density affects QS. Using simulations, we compared the growth of two QS populations starting at the same mean initial density, but with different degrees of variability in the densities of their subpopulations (Figure 14E). Experimentally, we similarly compared two QS populations by using the dilution level to manipulate the degree of variability in subpopulation densities (Figure 14B; also see Appendix B.5). 51

68 Figure 14: QS based control is robust to stochasticity caused by dispersal. (A) Schematic showing stochastic dispersal of a high- density population generating sub- populations with a wide distribution of initial seeding densities. (B) Histogram showing the typical distributions generated experimentally within the wells of 96- well plate after extreme dilution of an overnight culture. Note that higher dilution (green, fold of overnight culture) results in higher spread than the lower dilution (orange, fold of overnight culture) (C) Simulation results showing growth QS and OFF populations after dispersal event. Initial densities for 200 subpopulations were chosen from a Poisson distribution (a Poisson parameter λ of 2 was used with 52

69 population mean shifted to 10-4 ) (D) Combined growth dynamics of QS and OFF populations following high dilution in the presence of 25 µμg/ml 6- APA demonstrates that QS remains advantageous. Each dot is OD averaged over 48 wells (subpopulations) and shaded area spans the standard deviation. (E) Simulation results showing growth of QS populations with high and low spread after dispersal event. Simulations were performed as described in C. To compare the difference between populations with high (green) and low (orange) initial spreads, λ values of 2 and 20 were chosen to capture the 10- fold difference in experimental dilution. A shorter time span (15-30 hours) is used so that the differences in growth are more visible. (F) Combined QS population growth in the presence of 25 µμg/ml 6- APA comparing the cases of high or low spread in the initial density across subpopulations. Each dot is OD averaged over 48 wells (subpopulations) and shaded area spans the standard deviation. Surprisingly, both simulations (Figure 14E) and experiments (Figure 14F) showed the high- spread population significantly outgrew the low- spread population for a large period. The reason behind this counterintuitive result lies in the particular way by which QS operates: starting from a sufficiently low initial density, target gene activation is solely dependent on a critical cell density. During growth under stress, a high- spread population will have more subpopulations at higher and lower density than the low spread one (Figure 14B). As such, after a sufficiently long growth period, the higher density subpopulations will be the first to reach a density at which exoenzyme synthesis would be beneficial and hence the first to exploit the benefit of exoenzyme secretion. Thus, beyond demonstrating that QS- control is advantageous and robust over the bacterial lifecycle, our results show that the benefit of QS- control in only enhanced by the variability in initial density generated by stochasticity in dispersal. 53

70 2.4.4 QS kinetics need to be appropriately tuned for optimal regulation. Lastly, we note that QS systems in nature are tremendously diverse, in terms of both their molecular implementations and their activation properties. For instance, the density at which QS triggers its target gene can span four orders of magnitude (Figure 3). This diversity raises another fundamental, unaddressed question with regard to the advantage of QS control: how do two distinct QS systems compare when one activates production at a lower density than the other? In chapter 1, we developed the metric sensing potential (v) that uniquely captures the dominant activation properties of QS. The larger the value of v, the lower the density at which a QS system activates (Figure 15 A). At the extreme, an infinitely large v represents a system that is always activated (ON) and v = 0 represents one that is always inactive (OFF). Thus, using v as a metric allows us to examine a continuous range of QS systems. In the absence of stress, simulations predict growth to be a decreasing function of v (Figure 15 B left, grey). This decrease reflects the corresponding increase in cost accrued with early activation during growth in the absence of any benefit. In contrast, in the presence of stress, simulations predict growth to be a biphasic function of v (Figure 15B left, green) with a finite potential (vopt) at which growth is maximal. This biphasic function results from the opposing roles of cost, which increases with early activation, and benefit, which increases with late activation. vopt represents the density- dependent activation path (Figure 15A) during the lifecycle that is closest to the theoretical optimal 54

71 path and can be realized through QS (see Appendix B.6 for derivation of optimal control strategy). To examine this experimentally, we modulated the strength of QS using IPTG. Increasing IPTG leads to faster AHL production and shifts QS activation to lower density, which corresponds to a higher sensing potential (see Appendix B.3). We then compared growth of QS populations under different levels of IPTG in the presence and absence of antibiotic. Consistent with simulation results, biphasic growth dependence was seen only in the presence of 6- APA and an intermediate level of QS strength (0.5 mm IPTG) proved optimal. In the absence of 6- APA, growth decreased monotonically with increasing IPTG reflecting the accrued cost without benefits (Figure 15 B right). Noting that the optimal sensing potential (vopt ) represents a trade- off between the costliness of early activation and the loss of obtainable benefit in late activation, we examined the interplay between the level of stress and QS characteristics. In simulations (Figure 15C left panels) and experiments (Figure 15C right panels), we used cell densities to define the growth landscape. In the absence of stress, growth initially does not change significantly with increasing IPTG (Figure 15C top right), as reflected by the relatively flat growth landscape (until 12 hours or OD<0.05). This indicates that the cost of LuxI production through IPTG is small compared with the cost of exoenzyme synthesis and secretion as assumed in our model (Figure 15C top left). After this period, growth starts to decrease with IPTG and the steepness of the decline increases with time. 55

72 This reflects the cost of exoenzyme synthesis and secretion following the onset of QS controlled activation in the absence of any benefit - increasing IPTG leads to earlier activation and hence higher accrued cost with time. In the presence of stress, however, the growth landscape becomes biphasic and its shape changes predictably with the level of stress (Figure 15C panels with antibiotic). With increasing stress, the biphasic peak of the landscape (which determines the optimal QS characteristics) becomes increasingly sharp and shifts towards higher v; earlier activation is favored with higher stress. These landscape changes demonstrate that the optimal QS characteristics, as determined by the overall benefit of late versus early activation, depend on the specific parameters of the stress- response scenario. When stress onset is stochastic in timing and magnitude, v for the species may not be exactly at the optimal level for the specific case and its position on the landscape would determine the overall advantage of QS. This scenario is relevant where QS inhibition is being examined as an alternative intervention strategy against QS bacterial pathogens (57-59). Given the biphasic relationship between growth and v, inhibition of signaling, which reduces v, may counter- intuitively increase overall growth (Figure 15 B, for example from 2 mm to 0.25 mm IPTG in the presence of 6- APA). Depending on factors such as stress level and extent of signal disruption, this could similarly occur when an in hibitor that targets signal production is used as an antibacterial treatment, and may lead to misinterpretation of the effects of the intervention strategy. 56

73 Figure 15: Optimal tuning of QS to maximize bacterial growth. 57

74 (A) Density- dependent activation of production governed by the potential v of a QS system. QS systems that activate early (high v), at an intermediate density, and late (low v), during growth are shown. (B) Optimal QS potential in the presence of antibiotic as predicted by simulation (left) and measured experimentally (right). Cell densities (normalized to the highest value) at 22.5 hours were used to compare the different potentials in the presence (green) and absence (grey) of stress. (C) Simulated (left panels) and experimentally observed (right panels) bacterial growth starting from a low initial density over a range of v and for increasing stress (from top to bottom). Both simulations and experiments demonstrate biphasic dependence of growth on v in the presence of stress. Bracketed values indicate the level of stress (for simulation) and corresponding concentration of 6- APA used in the experiment. Horizontal arrow at 22.5 hours indicates the point in time at which growth was compared in B. Increasing 6- APA increases the benefit per cost of exoenzyme production Evolution of QS characteristics and the presence of cheaters. With stress that is constant in magnitude and regular over bacterial lifecycles, the biphasic function (Figure 15B) defines the landscape for the evolutionary tuning of QS characteristics (35). Here, QS characteristics would be directed toward vopt with which overall growth during the lifecycle is maximal (Figure 15 B and C). This notion has been speculated based on the observation that natural QS systems appear to be tuned for their specialized niches (60, 61). Several bacteria carry multiple QS systems controlling different functions. In P. aeruginosa, the las and rhl systems display distinct potentials and are activated hierarchically during growth and control elastase and rhamnolipid secretion respectively (27, 62). Similarly, Bacillus subtilis uses two distinct QS systems (27, 63) with vastly different potentials to tightly regulate competence development and sporulation, consistent with the notion that each one is best adapted to its function. Our results demonstrate the cost- effectiveness, robustness, and tuning of QS, as a control strategy for a clonal population (relatedness r=1 (64, 65)) and can provide the 58

75 minimal requirement for adaptive evolution of QS in bacteria (45, 64). However, additional mechanisms such as kin selection and population structure would be required to maintain QS and public- good based cooperation in heterogeneous populations containing cheater cells that do not produce exoproducts but benefit from them (34, 51, 65-67). Indeed, events such as dispersal (Figure 14) have been shown to provide the scenarios for QS and QS- mediated cooperation to be maintained (2, 34, 51, 64). In chapter 3, we discuss the maintenance of QS and cooperation in more detail. To capture the presence of cheaters in a QS population, we replaced LuxR in prtrans with reporter GFPmut3 making the cells incapable of responding to AHL and producing exoenzyme, while simultaneously enabling us to identify cheater cells from QS cells using flow cytometry. These cheaters represent the commonly found cheaters among QS bacteria with mutations in the LuxR- type regulator (signal- blind(34, 64)) or the exoproduct genes themselves(68). In our system, the cost of signaling through LuxI- based AHL production is small compared to the cost of exoenzyme synthesis (Figure 16A, B and Figure 15C, No 6- APA panels). 59

76 Figure 16: Cost of LuxI production under IPTG is negligible compared to cost of exoproduct synthesis and cheater invasion in public goods scenario. (A and B) Growth curves of QS (A) and cheater cells (B) grown separately under indicated IPTG levels in the absence of 6- APA are shown. Cheater cells lack LuxR 60

77 (carrying pgfptrans instead of prtrans) but are otherwise similar to QS cells; both QS and cheater cells carry IPTG inducible LuxI. Increasing IPTG in the absence of 6- APA reduces growth for QS cells, which incur cost of exoenzyme synthesis when activated at sufficiently high density but get no benefit. IPTG has no effect on the cheater cells. Each dot is averaged over four replicates and shaded area spans the standard deviation.(c and D) Growth of pure QS (green) and cheater (magenta) population in the absence (C) and presence (D) of 6- APA. (E) Typical flow cytometry results used for estimating proportion of QS and cheaters before and after growth. (F) Invasion of QS cells by cheaters. Percentage of QS cells in mixture of QS and cheaters measured before the start of experiment, and after 24 hours of growth under 25 µμg/ml 6- APA. Error bars shown are from 5 replicates. We first examined the growth of pure QS and cheater cells in the presence or absence of 6- APA. Overnight grown QS and cheater cells were both diluted fold (overnight ODs were indistinguishable) in fresh TBK growth media. In the absence of 6- APA, cheater cells initially grew alongside QS cells but eventually outgrew them at high density following activation of enzyme synthesis at high density (Figure 16C). This reflects the cost accrued by QS cells following activation at sufficiently high density as discussed in Figure 15 (No 6- APA case). In the presence of 6- APA, however, QS- controlled production of enzyme was beneficial and QS cells outgrow cheaters (Figure 16D). To confirm the invasion of a QS population by cheaters based on the public- good scenario, we measured initial and final ratios following growth of a mixed population in the presence of 6- APA. Using the GFP expression of Cheaters cheater proportion was measured by flow cytometry of 10,000 cells (Figure 16E) using a FACSCantoII (BD Biosciences) flow cytometer and visualized in FACSDIVA (BD Biosciences). Total cell 61

78 count was gated based on forward and side scatter and the number of GFP- positive events (gating on FITC pulse height) was measured. Mixture proportions were measured and after 24 hour growth in plate. In each case, 50 ml of the cell mixture to be analyzed was diluted 100- fold and regrown in TBK media for 6 hours along with 50 ng/µμl atc for 3 hours before fixing in 1% formaldehyde. To ensure that the experimental growth does not change our measurement of GFP- positive cells by somehow affecting GFP expression, pure cheater cells were studied using the same procedure. About 4% of 10,000 events were classified under flow cytometry dark (false negative) but this fraction remained unchanged before and after growth (in the presence of 6- APA) with no visible difference in the expression level of GFP. Growth of mixed culture of QS and cheater cells showed a clear increase in cheater fraction (>10%) after 24 hours of growth in 6- APA (Figure 16 E and F). Taken together, these results (Figure 16 C- F) demonstrate the expected effect of public- good secretion in the presence of cheaters - cheater cells that do not undertake the cost of exoenzyme synthesis fare worse under stress when by themselves but, in a heterogeneous population, are able to take advantage of QS cells that invest in exoenzyme secretion. 2.5 Conclusion Overall, combining growth measurements with high temporal resolution and with mathematical modeling, we show that: 62

79 1. QS- mediated regulation of exoproduct synthesis is robust and overall advantageous over varying initial cell densities and growth durations (Figure 12). 2. The advantage of QS- control is particularly striking when bacteria face uncertainty, such as from stochastic dispersal over their lifecycle (Figure 14). 3. For QS to be optimal, its kinetic properties must be appropriately tuned such that the activation density is neither too early nor too late, as determined by the cost- benefit parameters of the exoproduct scenario (Figure 15). These results go significantly beyond demonstrating the density- dependence of exoproduct benefit. They provide novel, fundamental advances in the understanding of the benefit of QS as a general control strategy seen across bacteria. 63

80 3. Inhibiting QS-mediated cooperation as antibacterial therapy 3.1 Introduction: Disrupting social behavior as an alternative to traditional antibiotics. Antibiotics against bacteria typically target DNA replication, RNA synthesis, protein production and peptidoglycan biosynthesis (69). However, the mode of their action tends to select for growth of mutants with resistance to them (69, 70). Therefore, there exists a vital need for developing new approaches to combat pathogens that can minimize the chance of resistance development. Disruption of quorum sensing (QS), the cell- cell signaling mechanism that modulates bacterial virulence, has been proposed as one alternative (59, 71-75). However, the evolutionary consequence of such inhibition strategies remains unclear there is evidence that it can lead to undesirable, long- term consequences (76, 77). 3.2 Cheaters in a cooperative population and implication for anti-bacterial therapy targeting QS. As discussed in chapters 1 and 2, the target functions of QS regulation often involve the cooperative production of public- good exoproducts. This QS- mediated cooperation is commonly exploited by cheaters invading the cooperative population (Figure 17)(78, 79); cheaters do not produce public goods (and hence do not incur any production costs) but benefit from the exoproducts. Despite cheater invasion being universal, mechanisms such as kin selection or population structure are shown to select 64

81 for cooperative traits in the long term (34, 51, 65-67, 80). Crucially, because cheaters do not produce exoproducts that are virulence factors, the presence of cheaters in a population has been linked to reduced overall virulence (79, 81-84). Thus, inhibition strategies aimed at QS must be examined for their efficacy in reducing bacterial virulence as well as their impact on the evolutionary selection for cooperation. Figure 17: QS controlled cooperation in bacteria. Cooperative QS bacteria (grey) monitor their cell density during the growth through the production and sensing of small signal molecules (orange circles). At sufficiently high density, high signal concentration triggers production of public- good exoproducts (green ovals). These exoproducts are costly to produce but, once secreted into the environment, benefit the entire population. Cheaters (red) that emerge during growth do not produce exoproducts but benefit from them 65

82 To achieve this, we divide the bacterial machinery into two broad classes for targeted interference, the QS signaling components for density- dependent initiation of cooperation, and the exoproduct based components for secretion and function of the exoproducts themselves (Figure 18). Figure 18: Schematic of bacterial cooperation machinery. Schematic represents QS module (orange) and exoproduct machinery (green), each with different possible targets for inhibition strategies 3.3 Modeling a population of QS cooperators and cheaters Here we extend our previous mathematical modeling framework (chapter 2, eqs ) to account for a heterogeneous population of cooperators and cheaters. In our system, cooperator (N) and cheater (C) growth is reduced by the presence of a stress- causing agent such as an antibiotic. Cooperators produce a costly exoenzyme that provides a benefit to the entire population by degrading this stress- causing agent (as seen in Figure 8). However, cooperator growth is additionally reduced by the cost of 66

83 exoenzyme synthesis. Cheaters, that do not produce exoenzyme, avail of its benefit (the global reduction in stress) without incurring any cost. As before, we model benefit available to both cooperators and cheaters as the increase in growth rate due to degradation of the antibiotic: Benefit = b 0 b m b m + Ab, (3.1) b 0 is the maximum growth rate in the absence of any antibiotic and with no enzyme production, b m the antibiotic concentration at which growth rate is half maximal, and Ab the antibiotic concentration. For cooperators, we assume cost increases directly with activation E (where 0 E 1 is the fraction of maximal activation) of exoenzyme production: Cost = c p E. (3.2) Here, growth rate is reduced by both, antibiotic presence and production cost and we assume an additive relationship between them. Overall cooperator growth rate (hr - 1 ) can be written as g N = Benefit Cost (3.3) and cheater growth rate (hr - 1 ) can be written as g c = Benefit (3.4) We model cooperator and cheater growth using the logistic equation. 67

84 dn dt ( ) " N + C % = gn $ 1 ', (3.5) # & N M dc dt ( ) " N + C % = gc$ 1 ' # & N M (3.6) where N and C are the cell densities (cells/ml) of cooperators and cheaters respectively and NM is carrying capacity of the medium (cells/ml). Figure 19 shows the results obtained from simulating the above set of equations and eqs Consider the growth of mixed population of cooperators and cheaters (1:1) at low initial density (Figure 19A). During the initial period of growth until QS- mediated activation, cooperators grow the same as cheaters as they do not activate production of exoproducts (green and red curves are indistinguishable). Following QS- mediated activation at sufficiently high density, cooperators (green curve) produce exoenzyme which, in turn, degrades antibiotic and results in faster growth. However, this same benefit is also available to cheaters in the population (red), which do not undertake the cost of production and hence outgrow cooperators at any stage. Thus, cooperator frequency decreases in a density- dependent manner after QS- mediated activation (Figure 19B). Growth for both species flattens out as carrying capacity is reached. 68

85 Figure 19: Simulations of population growth and cheater invasion (A) Growth of a 50:50 mix of cooperators (green) and cheaters (red) in the absence of any inhibition. (B) Cooperator frequency in the mixed population (blue curve in A) decreases with increasing density (as well as time) in the absence of any inhibition. Using the above model, we simulated growth of bacterial populations comprising of various ratios of cooperators to cheaters. For each such population we examined how inhibition affects cheater invasion and overall population growth. 3.4 Effect of inhibition on total population growth In the absence of inhibition, the total population growth has a non- monotonic dependence on the initial cooperator fraction (Figure 20 A, black curve). When compared to a pure cheater population, increasing cooperator fraction increases total population growth up to a point. The decrease in total growth following further increase in cooperator fraction is a result of interplay between the total cost accrued by cooperators during growth and the amount of benefit in the form of exoproducts 69

86 provided for maximal population growth. We use this dependence as the baseline to compare the effects of inhibition. We consider QS inhibition as from an agent that degrades the QS signal in the environment, decreases the signal production rate, or inhibits binding of signal to receptors (59, 75, 85-87). Consider the scenario where signal inhibition targets signal production: increasing signal inhibition in the form of slower signal production results in a lower signal concentration at any given cell density. This in turn leads to an increase in the critical cell density at which the threshold signal concentration for activation is reached. The same effect holds for other targets of QS inhibition as well. We thus modeled QS inhibition as an increase in the critical density at which exoproduct production is activated. At full QS inhibition (100 %), cooperators do not activate exoproduct production during the growth period. Simulations show that QS inhibition decreases total population growth, regardless of cooperator frequency (Figure 20A, orange curves). Increasing QS inhibition reduces the overall production of the beneficial exoproducts during the growth period. The lower benefit accrued leads to the lower total population growth. Notably, at the highest levels of inhibition, the effect on growth across different cooperator frequencies flattens out as no activation of cooperators takes place during the growth period. As a result, cooperators act no different from cheaters. 70

87 We next examined inhibition directed at the exoproduct machinery (88, 89). Under this category, we modeled treatments that decrease the benefit provided by the exoproducts without directly affecting the exoproduct production rate itself. A chemical agent that binds and degrades the exoproduct in the environment serves as a generic example. At full exoproduct inhibition (100%), no benefit is derived from the exoproducts. Simulations show that, as observed with QS inhibition, exoproduct inhibition monotonically reduces growth (Figure 20B, green curves). A key difference, however, is that the effect on growth across cooperator frequencies does not flatten at highest inhibition levels. Instead, at these high inhibition levels, overall growth reduces with increasing cooperator frequency. Here, exoproduct inhibition reduces benefit without directly affecting the timing of QS- mediated activation. Cooperators in the population under high exoproduct inhibition, while unable to derive any benefit from the exoproducts, still incur the cost of production under QS- mediated activation. As such, with increasing cooperator frequency, the total cost incurred in the absence of benefit increases. The absolute difference in growth between pure cheaters and pure cooperators (which is zero under maximum QS inhibition) indicates the maximum cost of production that could be incurred during growth. 71

88 Figure 20: Effect of inhibition strategies on cooperator growth and frequency. Growth of populations starting from the same initial density but with different ratios cooperators to cheaters was simulated. In each case, total population density and cheater invasion (measured as change in cheater frequency final- initial) at the end of growth period were calculated. The simulations were repeated under different levels of both QS (orange) and exoproduct (green) inhibition. (A- D) Black curve shows growth and cooperator frequency in the absence of inhibition across all mix ratios. (A) QS inhibition reduces total population growth. At full inhibition (100%), all mixed populations behave as pure cheaters wherein no QS- mediated activation takes place during growth. (B) Exoproduct inhibition monotonically reduces growth. At full inhibition (100%), cheaters grow the highest and population growth decreases with cooperator frequency as cooperators incur cost of exoproducts without benefit. (C) As in A, QS inhibition decreases cheater invasion and the no cheater invasion takes place at full QS inhibition where no QS- mediated activation takes place. (D) Exoproduct inhibition leaves cheater invasion largely unchanged. The small decrease is an indirect 72

89 effect of total population size and density- dependent activation (See text for more details). 3.5 Effect of inhibition on cheater invasion In the absence of any inhibition, simulations show that cheater frequency in any mixed population always increases during growth (Figure 20C, black curve is always above zero). This positive cheater invasion is a characteristic of a well- mixed system where any secreted exoproduct and its benefit is freely and equally available to both cheaters and cooperators. Thus, it is the cost of exoproduct synthesis that determines the growth advantage (and invasion) of cheaters over cooperators. Additionally, the change in cheater frequency is bimodal. Low cooperator frequency (close to zero) in the initial population limits population growth and cheater invasion; at the other end the population is essentially comprised purely of cooperators. Maximal increase in cheater frequency is seen at intermediate frequencies. Simulations show that increasing QS inhibition reduces cheater invasion in any mixed population (Figure 20C, orange curves). Increasing QS inhibition decreases exoproducts produced by cooperators during growth but this also reduces the total cost incurred by cooperators during growth (Figure 20A). Since it is this cost that determines the extent of growth advantage that cheaters have over cooperators, it results in lower cheater invasion. As expected then, at the highest levels of inhibition, the change in cheater frequency with initial cooperator frequencies flattens out as no activation of cooperators takes place during the growth period. Again, as cooperators here act no 73

90 different from cheaters, the initial frequency of the mixed population is maintained through growth. On the other hand, simulations show that inhibiting the exoproduct leaves cheater invasion largely unchanged (Figure 20D, green curves). Here, exoproduct inhibition reduces benefit without directly affecting QS- mediated activation. Cooperators under high exoproduct inhibition, incur production costs but without corresponding benefit (for themselves or the entire population), preserving the increase in cheater frequency. The small but finite decrease in cheater invasion in any mixed population is an indirect effect of effector inhibition. By reducing the benefit gained from the exoproducts, effector inhibition reduces the overall growth of a population containing cooperators at any frequency (Figure 20B). Under QS- control, exoproduct synthesis (and hence cost incurred) and cheater invasion increases with cell density. Thus the total population density reached at the end of the growth period limits the overall cheater invasion. 3.6 How is cooperation maintained as a trait despite the presence of cheaters? In a well- mixed population of cooperators and cheaters, secreted exoproducts and their benefits are equally available to all cells while only the cooperators incur the cost burden of their production. Thus, in any such well- mixed group, the proportion of 74

91 cheaters always increases at the expense of cooperators (Figure 20C and (51)). Despite this, mechanisms such as population structure can select for cooperation in nature. To examine the impact of inhibition strategies on the evolutionary selection for cooperation, we first set- up the population structure based scenario that selects for cooperative traits and then quantify how inhibition affects this selection (Figure 21). Figure 21: Population structuring provides evolutionary selection for cooperation despite cheater invasion. Initial total population consists of subpopulations of equal size but varying cooperator frequency (overall cooperators=cheaters). After growth, the cooperator frequency in the total population depends on both, the size of each subpopulation and the cooperator frequency within them. Higher growth of subpopulations with high cooperator frequency result in increase in cooperator frequency in the total population (pooling of all subpopulations) despite cooperator frequency having decreased within each subpopulation 75

92 Consider an initial global population that is the combined sum of multiple subpopulations all of equal population size but each with varying frequencies of cooperators (Figure 21). Under such population structuring, cooperator frequency in the global population can increase after growth even if cooperator frequency decreases within each subpopulation. This Simpson s paradox (51, 90) takes place since the overall growth of a subpopulation depends on cooperator frequency (Figure 20A). As a result, the cooperator frequency in the global population after growth is a population- weighted pooled sum of cooperator frequencies in the individual subpopulations (Figure 21). Such scenarios can select for cooperation as a trait, despite cheater invasion. 3.7 How is the evolutionary maintenance of cooperation affected by inhibition? We simulated an initial global population consisting of different subpopulations (simulation details discussed in section 3.8): subpopulations have the same initial population size but with cooperator frequencies at equally spaced intervals between zero and one (note that overall cooperator frequency is thus 0.5). Here, knowing the final population density (Figure 20A and B) and cooperator frequency (Figure 20C and D) in each subpopulation after growth is sufficient to calculate the pooled cooperator frequency in the global population (Figure 21). Simulations show that global cooperator frequency can be maintained at its initial value (Figure 22 at zero inhibition remains at 0.5) despite cooperator fraction decreasing in each subpopulation (Figure 20 C and D at 76

93 zero inhibition). We select this as the base case, where cooperation is maintained due to the population structure, and study the effect of inhibition. We find that the global cooperator frequency is a bimodal function of QS inhibition (Figure 22 orange curve). Cooperator frequency initially increases with QS inhibition before decreasing but does not decrease below its initial value of 0.5. The increase in cooperator frequency at low levels of inhibition is a result of the decrease in total population growth (Figure 20 A) and cheater invasion (Figure 20 C) with QS inhibition. At high levels of inhibition the result follows from that seen earlier; at the highest levels of QS inhibition, cooperators act no different from cheaters. As such, the initial global cooperator frequency (of 0.5) is maintained during growth. In contrast, global cooperator frequency decreases monotonically with increase in exoproduct inhibition to be always lower than the initial frequency (Figure 22 green curve). This effect follows from the monotonic decrease in population growth under exoproduct inhibition (Figure 20B) with little effect on cooperator frequency (Figure 20D). 77

94 Figure 22: Effect of inhibition on long- term evolutionary selection for cooperation. Initial subpopulation mix frequencies were at eight equal intervals between zero and one so that initial cooperator frequency (averaging across subpopulations) was 0.5. Pooled cooperator frequency was calculated from subpopulations as depicted in Figure 21. Panels A- D provide the necessary information for this calculation (weighted sums of all subpopulations after growth). Pooled cooperator frequency has a non- monotonic dependence on QS inhibition but is never reduced below its initial pooled frequency of 0.5. As such, QS inhibition does not select against long- term maintenance cooperation. Exoproduct inhibition monotonically reduces cooperator frequency and always selects against long- term maintenance of cooperation Overall, our results demonstrate that in inhibiting QS- mediated cooperation, targeting QS as the initiation of cooperation, has drastically different consequences in comparison to targeting the exoproduct machinery that is the effector for cooperation. While inhibiting QS- based signaling can reduce population growth, it reduces the potential for cheater invasion and as such, can increase or maintain the selection for 78

95 cooperative variants. On the other hand, exoproduct inhibition both reduces population growth and maintains cheater invasion potential. Thus, exoproduct inhibition selects against cooperative variants in the long- term. These results indicate that exoproduct inhibition is preferable over QS inhibition as potential antibacterial therapy and that the effects of inhibiting novel targets in bacterial machinery may often be counterintuitive. 3.8 Simulation methods for population growth and inhibition Population growth For each data point in Figure 20, the system of equations describing bacterial population growth in the presence of a stress- causing agent in the environment were simulated. In these simulations, the initial bacterial population was set at the same low initial density of 10 5 cells/ml but was composed of a desired ratio of cooperators to cheaters (indicated by initial cooperator frequency in Figure 20). Cheaters were modeled to be signal blind (34, 64), wherein they act the same as cooperators in signal production but do not activate exoproduct production in response to signal. Population density and cooperator frequency at the end of fixed growth period was recorded. Note that given enough time, all populations will reach carrying capacity Inhibition QS inhibition was modeled to increase the critical density at which production of exoproducts was activated by the QS system. In the absence of inhibition, QS system 79

96 half- maximally activates production at 10 7 cells/ml. Full QS inhibition was taken to increase activation density 10 4 fold. For intermediate values of inhibition (100 points), fold reduction values were linearly spaced over the four Log10 range. For exoproduct inhibition, increasing inhibition was modeled to reduce the reaction rate at which the exoproduct degrades the stress- causing agent in the environment. Full exoproduct inhibition was taken to decrease reaction rate 10 3 fold and for intermediate values of inhibition (100 points), fold reduction values were linearly spaced over the three Log10 range Evolutionary maintenance of cooperation by population structuring To examine the effect of inhibition on the maintenance of cooperative traits (Figure 22), the data of total population growth (Figure 20A and B) and cheater invasion (Figure 20 C and D) under inhibition was used as follows. The total initial population was taken to consist of eight subpopulations of equal initial size (10 5 cells/ml) but with cooperator fraction at seven linearly spaced intervals between zero (pure cheater) and one (pure cooperator) so that initial pooled cooperator fraction was 0.5. Following simulations of growth, final density and cooperator fraction of the eight sub- populations (simulations performed as described above) were used to calculate the cooperator fraction in the total population after growth. The base case QS system for examining cooperator maintenance was chosen as follows. Given a set of cost- benefit parameters and subpopulation structure, whether 80

97 population structuring results in maintenance of cooperative traits (pooled cooperator fraction >=0.5) also depends on the timing (critical density) at which a QS system activates exoproduct production. Indeed, as we have shown elsewhere (53), a QS system that activates production too early (or keeps production always ON) reduces growth incurring the cost of production at low density where dilution of exoproducts results in little benefit. Thus, pertinent to the evolution of cooperative traits, we assumed the base case QS system to be the one that activates production at an appropriately high density so as to maintain cooperation (final cooperator fraction =initial fraction 0.5) in the absence of inhibition. In Figure 22, the data point at zero inhibition represents this QS system. Simulations of the effect of inhibition and the resultant calculation of pooling were then performed with this QS system as described above. 3.9 Experimentally examining inhibition strategies The simulation results discussed in chapter 3 (Figure 20 and Figure 22), demonstrate critical differences in the outcomes of antibacterial therapies directed at QS or the exoproduct machinery. Here we describe the design, methods, and preliminary results for a synthetic system (based on work described in chapter 2) that will be used to experimentally compare the results of inhibition strategies Plasmids and strains for cheaters and cooperators A two- plasmid system similar to that used in chapter 2 is used for both cooperators and cheaters. As before, plasmid pexoi (p15a, Kan R ) is responsible for 81

98 IPTG- inducible production of LuxI and for BlaMs production (under PLuxI) induced by AHL- bound LuxR. This plasmid is common to both cooperators and cheaters. Cooperators carry prtrans (ColE1, Cm R ) which expresses LuxR, reporter GFPmut3/mCherry, and the transporter genes under an anhydrotetracycline (atc) inducible promoter PLTet0-1. Cheaters carry plasmid ptrans which is the same as prtrans but it lacks LuxR and expresses reporter GFPmut3/mCherry and the transporter genes under PLTet0-1. prtrans and ptrans constitutively expresses the tetr repressor for low, tightly controlled expression. As such, cheater cells are incapable of responding to AHL and producing exoenzyme, while simultaneously enabling us to identify cheater cells from cooperator cells using flow cytometry (Figure 16) Method for measuring cooperator or cheater frequency in a mixed population. For both cooperators and cheaters, 1 ml overnight culture was spun down, washed and suspended in 1 ml distilled water. 250µl of washed cooperator and cheater culture was mixed to create an initial mixture of cooperators and cheaters (at desired ratio). This mixture as well as pure cooperators and pure cheaters were then diluted in the same way in TBK media as mentioned earlier. All treatments of IPTG, 6- APA, and exoproduct inhibitor were applied similarly to these three cultures. At the start and the end of each experiment, cells from the mixed cultures were first diluted 100 fold in TBK media and cultured for 6 hours. The cultures were then activated with 100 ng/ml atc (for reporter expression) and regrown for 3 hours before being fixed in 1% 82

99 formaldehyde. Cooperators and cheaters were identified by their respective reporters using flow cytometry (see Figure 16) Preliminary data: effect of inhibition on population growth and cheater invasion To examine QS inhibition, we modulated QS- mediated activation using IPTG. We compared growth of a population of pure cooperators under different levels of IPTG (Figure 23A orange). Increasing IPTG leads to faster AHL production and shifts QS activation to lower density. Thus, decreasing IPTG is akin to increasing signal inhibition. Consistent with simulation results (see Figure 20A for pure cooperator population), QS modulation results in a biphasic landscape (Figure 23A orange). The biphasic landscape (highest level at 0.5 mm IPTG) represents a trade- off (as discussed in chapter 2, Figure 15) between the costliness of early activation and the loss of obtainable benefit in late activation. To test exoproduct inhibition we used clavulanic acid, a well- studied beta- lactamase inhibitor (91, 92), and monitored growth of pure cooperator population under different levels of the inhibitor. Consistent with simulations (Figure 20B for pure cooperator population), increasing inhibitor concentration lead to a monotonic decline in population growth (Figure 23A green). To experimentally examine the effect of inhibition strategies on the potential for cheater invasion, we examined the growth of a mixed population of cooperators and 83

100 cheaters (~ 50:50 mix). Consistent with simulations (Figure 20C and D), increasing QS inhibition decreased cheater invasion (Figure 23B orange) while increasing exoproduct inhibition maintained cheater invasion (Figure 23B green). Figure 23: Experimental results on inhibition strategies. (A) 1 mm IPTG was used as the base case for cooperator growth. For QS inhibition (orange), IPTG levels were decreased from 1 mm to zero corresponding to zero and 100% inhibition respectively. For exoproduct inhibition (green), increasing clavulanic acid concentration was used as indicated in the presence of 1 mm IPTG. Readings across the levels are shown normalized to the highest OD reading (which is 0.5 mm IPTG for QS inhibition and in the absence of clavulanic acid for exoproduct inhibition). For both curves, OD values were compared at the time when sufficiently high OD (~0.12) was reached by any inhibition level within the treatment (given sufficient time all cultures would reach carrying capacity). Exoproduct inhibition monotonically reduces cooperator growth while QS inhibition results in a biphasic landscape (see discussion in text). In both cases, higher levels of inhibition reduces cooperator growth. n=3 replicate wells for QS inhibition and n=4 replicate wells for exoproduct inhibition (B) Cooperator frequency after growth of a mixed (~1:1 initial mix 84

101 of cooperator to cheater) population. In the absence of inhibition, cooperator frequency decreases by ~10%. QS and exoproduct inhibition was carried out as discussed in A. QS inhibition reduces cheater invasion towards initial mix value while exoproduct inhibition leaves cheater invasion largely unchanged. n=3 replicate wells for estimating cooperator frequency under QS inhibition and n=4 replicate wells for exoproduct inhibition Overall, the results demonstrate that the described synthetic system faithfully captures the actions and interactions of QS cooperators and cheaters as seen in simulations. In future, this system will be used to test all aspects (Figure 20, Figure 22) of the effects of inhibition strategies on population growth and cheater invasion and to monitor the long- term effects of inhibition on the selection for cooperation. 85

102 Appendix A A.1 A general modeling framework for QS signaling across bacteria When deriving the equations for signal concentration, we assume that the signal is uniformly distributed within a cell and in its microenvironment. We also neglect the effect of a periplasm around the cell and assume that transport across the cell membrane is rate limiting. We justify these assumptions and their limitations below. A.1.1 Uniform concentration For simple diffusion of a particle in a liquid, the root- mean- square displacement in three dimensions with time t is given by ~ r = ( 6ηt ) 1/ 2, where η is the diffusion constant. The diffusion coefficient of AHLs (MW ~ 200 g/mole) is estimated to be ~ cm 2 /sec, by comparing with molecules of similar molecular weight(93). This corresponds to a diffused distance of ~ 5 10 cm in 1 second, which is greater than the size of a typical bacterium (a few microns). The same analysis applies to peptide 3 signals(94) such as CSP(95) in Streptococcus pneumoniae with molecular weight of about 2 kda (D = cm 2 /sec). Thus, we assume signal concentration to be well mixed and uniform within a cell (Eq. 1.1 for Type I sensing and Eq. 1.3 for Type II sensing). In the much larger microenvironment, however, the spatial and temporal distribution of signal Ae depends on the diffusion and mixing characteristics of the scenario. The general diffusion equation (22, 96) for signal concentration A is given by 86

103 A = η ΔA +ψ t (A.1) where ψ represents reaction or source terms and Δ is the Laplace operator. To study the signal distribution in the microenvironment, we solve Eq. S1.1 for signal diffusion from a single cell (as a point source) in a spherical enclosure of radius R. The signal concentration at the cell s surface is denoted by A0. Signal concentration Ae at 0<r<R and time t is: A A e 0 ( 1) 2 ( nπ ) n 2 = 1+ sin n n= 1 z 2 2 ( nπz) exp( π τ ) (A.2) respectively. tη r R where z = and τ = are the rescaled distance and time measures 2 R R The required time for Ae at the enclosure boundary ( z 0 ) to reach within 99% of A0 is: τ Even for the largest noted enclosures for activation ( R 10 2 cm for V V e c 6 = 10 η 6 ) this corresponds to < 1 minute (assuming = 10 cm 2 /sec) which is much faster than cell division. Virtually uniform concentration of a QS signal is thus established quickly in a liquid microenvironment. Also, the time scale for diffusion ( D 1 3 ( ) < 10 2 s) is much smaller than signal degradation ( >10 s) and does not change the assumption of uniform concentration in the microenvironment (Eq. 1.2 for Type I d a R 2 sensing and Eq. 1.4 for Type II sensing). We note that the above analysis is based on 87

104 diffusive processes only. The inclusion of convection in the microenvironment will increase mixing of the signal and will further reduce the time required to establish uniform concentration. Diffusion of signal in solid media, however, may be slower. In most cases, solid media such as agar(97) and biofilms(98, 99) appear to allow free diffusion of signal molecules. An assumption of uniform concentration distribution of signal in other cases is reasonable only if the microenvironment size is not too much greater than the diffusion length scale of the signals. A.1.2 Transport across the membrane is rate limiting When signal molecules are added to a culture, the intracellular signal concentration reaches equilibrium in seconds(6, 7) for small AHLs such as C4- HSL and 3OC6- HSL. For larger molecules, such as 3OC12- HSL in P. aeruginosa, the time to equilibrium is in minutes(7). This is much larger than the time estimated for free diffusion across a cell. Hence, passage across the bacterial membrane is far slower than that under free diffusion and is rate limiting (7). A.1.3 Effect of bacterial periplasm is negligible Gram- negative bacteria possess a phospholipid outer membrane with a periplasmic space in between(100). In this case, the signal first crosses the inner membrane and enters the periplasmic space and is then exchanged with the microenvironment. As the periplasm is only nm in width(100), we assume the 88

105 signal concentration is uniform across it. To investigate effects of periplasm on our modeling analysis, we rewrite the model equations considering first the transfer from the cell to the periplasm and then transfer from the periplasm to the microenvironment. Consider a Type II case (since most gram negative bacteria use Type II sensing) where the subscript pp denotes the periplasm (Figure 24). The intracellular concentration change is given by: dai dt = k D( A A ) d i pp a A i (A.3) We assume that degradation of signal in the periplasm happens at the same rate (rate constant da) as in the cytoplasm or microenvironment. Dpp is the transport rate constant for signal transport between the outer membrane and the microenvironment. The signal concentration change in the periplasm is given by: da dt pp Vc = D( A ) ( ), (A.4) i App d a App D pp App Ae V pp where the last term in Eq A.4 accounts for exchange across the outer membrane. The signal change in the microenvironment is; da dt e V = Dpp ( App Ae ) V pp e d a A pp (A.5) Solving these equtaions for Ai, we get: 89

106 90 (A.6) Figure 24: Signal diffusion across bacterial periplasm We note that Vpp <<Vc and Ve (bacterial periplasm is typically ~5-12 % of volume(100, 101)) and the outer membrane is far less diffusion resistant than the inner membrane due to the presence of porins (100, 102), so that Dpp >> D. With these observations, Eq. A.6 approximates to the Type II case (Eq. A.6). The same analysis holds true for Type I sensing. We hence neglect the effect of periplasm and consider the transport across the bacterial membranes as one step. A.1.4 Modeling positive feedback Many QS systems are regulated by positive feedback( ). We model positive feedback by assuming that signal synthesis rate increases linearly with its own = e pp pp c pp a e pp pp c pp a a e pp pp c a pp c pp a a i V V V V D D d V V V V D D D d d V V V V D d Dk V V D D d k d A 1 1 2

107 concentration with rate constant ka. This is an approximation of feedback behavior observed in QS and is valid for most bacterial systems where a graded increase in signal synthesis is observed with signal concentration(106, 107). With positive feedback, Eqs. 1.1 and 1.3 become: dai dt = k + k a A i DA i d a A i (A.7) dai dt = k + k a A i D ( Ai Ae ) d a Ai (A.8) For Type I sensing, using Eq. A.7 we get: A e = V V e c Dk 2 ( da + Dd a ) Dka (A.9) For Type II systems, we have: A i = 2 Dda + Dvda a ( D + vd a ) + vd k ( D + vd ) k a a (A.10) Solving these Eqs. A.9 and A.10 for steady state signal concentration and then explicitly for v at which A = K as done earlier, we get δα ( + β) Type I v =, (A.11) δ Type II v =, (A.12) α + β 1 δ 91

108 where k α = a d a is the dimensionless parameter for feedback scaled using da. From these equations we see that for both Type I and Type II, positive feedback (as α) acts to effectively increase β, which corresponds to increased signal synthesis. The effect of α on v can thus be studied equivalently as the effect of β on v. A.1.5 Type Ia and Type IIa sensing: Type Ia is a variation of Type I sensing where the signal is free to diffuse in both directions. This case is the same as Type II sensing, except that the extracellular concentration Ae is sensed. Solving Eqs. 1.3 and 1.4 at steady state for Ae, we have: A e v Dk ( da + Dda ) + Dda = 2 (A.13) Solving explicitly for v at Ae = K gives: δ ( β 1) v = 1 + δ (A.14) In Eq. A.14 the only effect of two way diffusion across membrane is a reduction in β. The net result of two way diffusion is a decrease in v over the basic Type I case. In the type IIa variation, bacteria appear to employ specialized pumps for export and import of large signaling molecules. An example is the PhrC- controlled competence development in B. subtilis(108). The export (D) and import (Dimp) rate constants may be different. In this case, the equations for Ai and Ae are: 92

109 dai dt = k DA i + D imp A d e a A i (A.15) da dt e = Vc ( DAi Dimp Ae ) da Ae V e (A.16) By solving Eqs. A.15 and A.16 at steady state and setting Ai = K, we have: ( β 1) δ imp v = δ + 1 β Dimp where δ (A.17) imp = d a Eq. A.17 indicates that v increases linearly with δimp. This result reflects the increased ability of a Type II sensing system to sample the microenvironment with increased signal import rate. A.2 Modeling the target (Effector) Effector activation E under QS control is given by E E max = a V V e c v a + v a (A.18) where Emax is the maximal synthesis rate and a is the hill coefficient depending on the co- cooperativity of signal induced activation (see section 1.6). For the exoenzyme case, E represents the enzyme synthesis rate. We model the exoenzyme dynamics using the following equations: dpi dt = E D P d P (A.19) p i p i 93

110 dpe dt D p Pi = d p Pe (A.20) Ve V c where i and e indicate concentrations inside the cell and in the microenvironment respectively. Dp and dp are the transport rate constant and the degradation rate constant of P, respectively. Enzyme- substrate kinetics and nutrient: Following a model of bacterial foraging(109) where the enzyme absorbed to the substrate catalyzes the production of nutrient (93), the rate of production of nutrient in the environment ( dn e ) is given by dt k n K m P e + P e where kn and Km are appropriate reaction rate and binding constants respectively. With nutrient transport and degradation rate constants of Dn and dn respectively, the mass balance equations for N are: dn dt dn dt e i P V e ( Ne Ni ) dnne e = kn Dn / (A.21) Km + Pe Vc n ( N e N i ) d n N i = D (A.22) Cost, benefit and fitness: For any enzyme synthesis rate E and enclosure size Ve, above equations are solved simultaneously for steady- state concentrations of enzyme b n N i and nutrient. The benefit provided by N is then calculated (35) as B =, where b + N 94 nm i

111 Ni is intracellular nutrient concentration. The cost of effector activation can be modeled (35, 110) as c pe C =. bn, bnm (nm), cp, cpm (nm - 1 hr), are benefit and cost function 1 c E pm parameters such that B and C unitless. Fitness Δ f = B C (A.23) Growth rate g (hr - 1 ) is modeled as a linear combination of the growth seen in the absence of an effector (g0 hr - 1 ) and in its presence. Without any loss of generality of our conclusions, we assume: g = g0 +Δ f. The collective fitness nt is given by n T = T dn dt, where cell growth during T is modeled by a logistic equation dt dn n = gn 1, with n m as carrying capacity. nt from a QS sensor of given potential dt n m v is obtained by numerical integration of the logistic growth equation where growth rate at each time point is calculated based on Δf. To obtain vopt the procedure is repeated for a range of v s and nt versus v is plotted to find the v at which nt is maximal. We use the following equation to represent the benefit function for a general QS- controlled effector: x bne B = (A.24) y x V e b + + nm E bnv Vc 95

112 This equation captures the characteristics of a wide range of beneficial effectors depending on choice of parameters (bn, bnm, bnv) and hill coefficients (x,y). Note that B increases with 1/Ve and E but saturates eventually. Calculation of nt for the general function is repeated as above with Eq. A.24 being used in Eq. A.23 to calculate Δf. A.3 Optimal regulation strategy For the effector model of exoenzyme secretion, we calculate the optimal enzyme synthesis rate Eopt that maximizes Δf for a bacterium in an enclosure of volume Ve (note that this is independent of QS). Observing how Eoptchanges with Ve provides the mathematically optimum regulation strategy. Comparing this with the QS strategy provides an insight into the advantage of QS control against constitutive induction at a fixed level. Eoptis obtained by solving: Δf E E= E opt = 0 (A.25) for non- negative E values. To maximize Δf during growth, enzyme synthesis should match this Eopt for varying Ve. As depicted in Figure 25, this optimal regulation strategy dictates that for maximum Δf during growth, synthesis of P should, (1) remain zero until Ve is small enough for benefit to exceed cost (low cell density); (2) increase with decreasing Ve when the latter is at intermediate values (intermediate cell density); 96

113 (3) decrease with further reduction in Ve. Comparing this theoretical optimal regulation level with QS regulation reveals the nature of QS benefit S R E max E nm hr Shutoff Induction E opt OFF Q P V e /V 4 5 c Figure 25: Optimal exoenzyme synthesis strategy ( E opt ) during growth. Arrows indicate the optimal effector induction path to be followed during bacterial growth. Typical regulation regions are labeled. Dotted (red) line shows an arbitrary Emax. No effector induction (Eopt = 0) is required for growth starting and ending between points P and Q. Constitutive enzyme synthesis (Eopt = Emax) provides the best fitness for growth starting and ending between points R and S. At very high cell densities (low Ve/Vc) cost compares to the benefit and the effector is best kept off. Following parameters were used for generating the figure: Cost- benefit: bn = 1000, bnm= 10 4 nm, cp= 0.4, cpm= 10-4 nm - 1 hr. Effector: Dp =100 hr - 1, dp=0.01 hr - 1. Nutrient: Dn =100 hr - 1, dn=0.01 hr - 1. Reaction: kn=10 3 nm hr - 1, km=100 nm Scenarios where QS regulation is unnecessary: The optimal strategy helps visualize the two scenarios (Figure 25) where effector regulation by QS is unnecessary. If the cell density is always insufficient for benefit to outweigh the cost of secretion ( Δ f <0) during T, the best strategy is to not to activate the effector (Eopt = 0). If the benefit overwhelms cost so that Eopt > Emax during T, constitutive enzyme synthesis at Emax is the best solution. 97

114 A.4 Generality of cost-benefit analysis results Here we examine in more detail the cost and benefit characteristics discussed in the section 1.7 and 1.8. Consider first the simpler scenario of a bacterium in an enclosure of unchanging volume Ve. Let Eopt be the optimal effector activation level for a host function of this bacterium. Eopt can be calculated by solving Eq. A.25 where Δ f = B C with B depending on the function and scenario (Cost relation but not its parameters assumed to be unchanged between functions). Regulation of this effector by QS is unnecessary when Eopt is calculated to be either zero (no induction) or larger than an Emax (constitutive induction) where Emax is the maximal effector activation determined by the physical or genetic characteristics on the function s effector. Thus, the cost- benefit condition for QS regulation of a function to be advantageous is: 0 < Eopt < Emax (Figure 26). 0 0 Cost or Benefit Benefit Δf max 0 Cost E opt E max Activation E Figure 26: Cost- benefit scenario for bacterium in enclosure of unchanging Ve. Typical plot of cost relation alongside benefit. Emax marks the maximum possible activation E. If Eopt is smaller than Emax, QS regulation is advantageous and the sensor v tuned to achieve activation of Eopt is optimal. On the other hand if Emax was smaller than 98

115 marked Eopt, constitutive activation of the effector would be the best strategy. Note that the benefit relation depends on Ve while the cost relation does not. For different Ve s the benefit curve would shift according to its relation with Ve and the Eopt would change accordingly. This condition can be understood as a tradeoff between cost and benefit with effector activation. If the function and scenario is such that cost dominates over benefit, the effector is best kept off with Eopt=0 (v=0). On the other hand, if the benefit of activating the function overwhelms its cost, the effector is best operated at full activation Eopt =Emax (v=infinity). In the intermediate range, operating the effector at Eopt provides maximal fitness. This Eopt level of activation can be achieved by QS with a corresponding potential vopt given by Eq. 1.8 in the enclosure of volume Ve. We next apply the above conditions to the general function discussed in section 1.8. This general function has the property that benefit increases with increase in E and with decrease in Ve but eventually saturates: x bne B =. (A.26) y x V e b + + nm E bnv Vc Solving Eq. A.26 using Eq. A.25 shows that Eopt has only one real positive solution irrespective of the parameters. For example, with x, y = 1 we get: E opt =!! V b n c p b nm + b e $ $!! V # nv # && 1+ b nm c pm + b nv c e $ $ # pm # && " " V c %%" " V c %%!! 2 c p b n c pm # b nm + b nv # " " 2 V e V c V ( )# b nm + b e nv # c p + b n c pm $ $ && %%! "! " V c $ $ && %% (A.27) 99

116 as the only real positive solution. As discussed earlier, the cost- benefit condition on a function for QS regulation to be useful is: 0 < Eopt < Emax. We see that applying this condition to Eq. A.27 along with Eq. A.1.8 for the corresponding v, always gives a unique vopt when the inequality is satisfied (vopt equation not shown). For the batch culture scenario with changing Ve an analytical solution of the equations for Eopt and vopt is not possible anymore since cell number n at any time is directly linked to Δf through growth rate which itself is indirectly linked to Ve and hence n. The same result is shown through simulation by calculating for a range of cost- benefit parameters (Figure 6C). 100

117 Appendix B B.1 Construction of plasmids for QS-mediated cooperation B.1.1 pexo Construction of BlaMs was based on work by Chervaux et al(54) and Tzschaschel et al(111). An intermediate plasmid, pblam was constructed by PCR- amplifying bla gene from psnd- 1 (gift from Dr. Ron Weiss) without the first 66 base pairs and inserting it under Plac/ara- 1 of pprolar.a122 (Clonetech). The first 66 base pairs code for periplasmic location peptide and its removal makes BlaM cytoplasmic in contrast to wild- type Bla(112). A start codon (atg) for the truncated bla was included during the PCR, resulting in blam. Effective N- terminal sequence of blam is - ATG*CACCCAGAAACG.., where * indicates the position of sequence that is removed. The inducible expression and β- lactamase activity of the cytoplasmic BlaM in plasmid pblam was first tested and confirmed. BlaMs, the secretion proficient protein, was designed from blam and hemolysin secretion signal tag hlyas from the hlya gene using fusion PCR(54, ). Plasmid pblam was used as template for the BlaM part (Primers 1 and 3). The hlya signal tag was PCR- amplified (primers 2 and 4) from the hlya containing plasmid plg612-1b (kind gift of Dr. Barbara Tzschaschel) (111). The two fragments were combined using primers 1 and 4 and the fusion gene was cloned in pprolar.a122 vector using KpnI and BamHI digestion to give pexo coding BlaMs under Plac/ara- 1. Primer 1: cgggtacccatgcacccagaaacgctggtgaaag 101

118 Primer 2: cctcactgattaagcattggcatcccgggggaaattctcttgcaaaaaatgtatt Primer 3: (reverse complement of Primer 2): aatacattttttgcaagagaatttcccccgggatgccaatgcttaatcagtgagg Primer 4: gcggatccttatgctgatgctgtcaaagt B.1.2 pexoi This plasmid consists of two parts coding for BlaMs under PLuxI, and LuxI under Plac/ara- 1. Fragment for PLuxI controlled BlaMs was constructed using fusion PCR with aatii sites at both ends. Plasmid pluxgfpuv(115) where GFPuv is under PLuxI control was used as template (Primers 1 and 3) for the lux box. pexo (primers 2 and 4) was used as the template for the BlaMs gene. Primer 1: cgaacgcgacgtcagtcctttgattctaataaattggatttttgtcac Primer 2: gtcgaataaacgcaagggaggttggtatgcacccagaaacgctggtgaaag Primer 3: ctttcaccagcgtttctgggtgcataccaacctcccttgcgtttattcgac Primer 4: ctctctgacgtcttatgctgatgctgtcaaagt The two fragments were combined using primers 1 and 4 and was cloned into the aatii site of pluxri (116) giving pexori. pexoi was then obtained by deleting the LuxR gene (digestion with EcoRI and BamHI, followed by blunting and ligation). B.1.3 prtransp This plasmid expresses LuxR and the transporter genes HlyB and HlyD under the control of PLtetO- 1 and was constructed using pprotete (Clontech). For tight, low 102

119 expression of these genes, the repressor tetr transcribed constitutively from a PlacIq promoter was included at the single aatii site (JM109 does not natively carry the repressor tetr). NotI digested fragment from pvdl9.3 (kind gift of Dr. Barbara Tzschaschel(111)) carrying the transporter genes and KpnI- BamHI digested LuxR from pluxri were inserted sequentially. Plasmid name Origin and selection marker Table 3: Plasmids used in our study Description pprolar.a122 p15a, Kan Base vector for cloning. IPTG controls expression of genes from hyrbid Plac/ara- 1 promoter(117) pblam pexo pexoi pluxri pluxr p15a, Kan p15a, Kan p15a, Kan p15a, Kan p15a, Kan Intermediate plasmid for cloning, expression of cytoplasmic BlaM IPTG controls expression of BlaMs from Plac/ara- 1 promoter AHL 3OC6HSL inducible expression of BlaMs in the presence of LuxR. IPTG controls expression of LuxI IPTG controls expression of LuxR and LuxI. QS controlled expression of GFPuv when paired with plasmid pluxgfpuv. IPTG controls expression of LuxR. Used as detector for inducer 3OC6HSL when paired with plasmid pluxgfpuv. 103

120 pvdl9.3 sc101,cm Expression of transporter genes under the Plac promoter(111) pprotete cole1,cm Base vector for atc inducible gene expression (Clontech) ptethlybd cole1,cm atc inducible promoter, PLtetO- 1 for expression of transporter genes. Repressor TetR constitutively expressed from PlacIq promoter. prtrans cole1,cm atc inducible promoter, PLtetO- 1 for expression of transporter genes and LuxR. Repressor TetR constitutively expressed from PlacIq promoter. pgfptrans cole1,cm atc inducible promoter, PLtetO- 1 for expression of transporter genes and GFPmut3. Repressor TetR constitutively expressed from PlacIq promoter. Complementary to prtrans as cheater plasmid. pluxgfpuv cole1,cm Reporter GFPuv under PLuxI promoter to observe QS activation(115) B.2 Testing enzyme secretion and function BlaMs is cytoplasmic but can be secreted into the extracellular medium by hemolysin transport proteins HlyB and HlyD (54). When cytoplasmic, the enzyme offers no protection to beta- lactam antibiotics such as 6- APA, which target penicillin binding proteins in the periplasm (112, 118). We verified this property using a GFP reporter under the control of PampC (119) which is induced as a result of bacterial cell wall damage caused by 6- APA action (Figure 27). We compared the protection against 6- APA 104

121 provided by BlaMs (Top) with that by wildtype Bla (Bottom). These experiments were performed as follows: JM109 cells carrying PampC reporter and either pexo or pbla were diluted fold in fresh TBK media with or without IPTG, after overnight growth. After raw OD reached ~0.06 (about 5 hours), 25 µμg/ml 6- APA was added. Samples were taken four hours after 6- APA treatment and subject to flow cytometry analysis. Figure 27: Cytoplasmic BlaMs (unlike wildtype periplasmic Bla) does not prevent cell wall damage from beta- lactam antibiotics. PampC is induced as a result of 6- APA action that causes cell wall damage. We compared the protection against 6- APA provided by BlaMs (Top) with that by wildtype Bla (Bottom). IPTG was used to induce expression of BlaMs and Bla from plasmids pexo and pbla, respectively. If cytoplasmic BlaMs prevents 6- APA caused cell wall damage, its expression should decrease the induction of PampC reported by GFP (relative fluorescence units R.F.U). GFP expression did not show significant difference between with (green) and without (blue) BlaMs induction, indicating that BlaMs expression did not prevent cell wall damage by 6- APA. Induction of wildtype Bla caused significant decrease in GFP expression to a level that matches basal- level GFP expression (in the absence of 6- APA). As a control, measurements without 6- APA treatment are shown for the cases with (pink) and without (red) 1mM IPTG. When secreted into the extracellular space by hemolysin transport proteins HlyB and HlyD, BlaMs can degrade beta- lactam antibiotics and permit bacterial growth (54, 105

122 112) (Figure 28A and B). To confirm this, we extracted the supernatant of cells carrying pexo in the presence or absence of transporter pvdl9.3 grown at 37ºC in LB in the presence of 1 mm IPTG. To extract supernatant, 1-2 ml of culture was centrifuged and supernatant was then filtered using sterile syringe filter with 0.2 µμm cellulose acetate membrane. The assay involved mixing a culture of sensitive MG1655 cells that carry no resistance against carbenicillin (but carrying control plasmids providing kanamycin and chloramphenicol resistance) with the supernatant. Growth of this mixture was monitored by OD measurement. When treated with carbenicillin, only the mixture with supernatant from transporter- expressing cells showed growth of sensitive cells (Figure 28A). The assay was also repeated on hard agar containing carbenicillin (Figure 28B) wherein sensitive cells plated onto the agar form clear growth zones around wells filled with supernatant from transporter- expressing cells. The hlyb and hlyd genes from pvdl9.3 were used in plasmid prtrans for atc inducible expression of the transporter genes (see Figure 28C for secretion test). We note here that the LuxR homolog SdiA in E. coli interacts strongly with the rhli promoter in the RhlR/RhlI system from P. aeruginosa but has no significant unintended interference with the LuxR/LuxI QS module in our system (120). As shown in Figure 28D, the circuit shows no detectable signal- based leaky activation of BlaMs in the absence of LuxR. Overall in our circuit, in the presence of AHL (produced through LuxI or added exogenously), AHL- bound LuxR within cells can activate synthesis of 106

123 BlaMs (at a cost), which when secreted through the transport complex provides benefit in the removal of beta- lactam 6- APA. Figure 28: Liquid phase test of BlaMs secretion by hlyb- hlyd transporter. (A) Sensitive cells supplemented with supernatant from cells grown with the transporter (filled circles) recovered from beta- lactam carbenicillin treatments of indicated concentration while no recovery was seen in the absence of transporters (unfilled circles). (B) Solid phase test of BlaMs secretion. Sensitive MG1655 cells from a high density culture were spread on agar plates containing 5 µμg/ml carbenicillin. Holes were made into the agar and filled with supernatant from indicated cell strains grown with pexo with or without transporter in the presence of IPTG. After overnight incubation at 37ºC, only the wells holding supernatant from cells with the transport machinery show clear growth zones corresponding to diffusing BlaMs. (C) Testing of atc inducible BlaMs secretion by hlyb- hlyd in the synthetic circuit. JM109 cells carried 107

124 plasmid ptethlybd (Table 4, hlyb and hlyd under PLtetO- 1) along with a compatible plasmid for constitutive (atc independent) BlaMs expression. Supernatant from overnight growth at 30ºC was tested for protection against beta- lactam antibiotic as in A. (D) Control test for luxr function in AHL binding and BlaMs production during growth. JM109 cells carrying pexoi and ptrans (all circuit genes except LuxR) were treated with 6- APA. Presence or absence of AHL made no difference to the growth in contrast with Figure 10 where cells (JM109 carrying pexoi and prtrans) at high initial density showed initial growth retardation followed by overtake of un- induced cells. B.3 Testing QS-mediated activation. LuxR and LuxI are QS components from V. fischeri (116, 121, 122). To measure QS activation, we used a fluorescent reporter GFPuv under the control of the PLuxI promoter (pluxgfpuv, ColE1, Cm R ) (115). QS was activated through IPTG. LuxR was expressed under the control of PLtetO- 1. atc induction was kept constant for all the experiments. To measure QS activation, overnight cultures were diluted at different levels ( to fold) in media with 1mM IPTG (to activate LuxI expression). 200 µμl replicates of these cultures were laid out in 96- well microplates (Corning). 50 µμl of mineral oil was added to prevent evaporation and the plate was incubated in plate reader (Victor3, Perkin- Elmer) at 30 C. Absorbance at 600 nm (OD) and GFP fluorescence (CW lamp filter 485 nm, emission filter 535 nm, counting time 0.1 s ) were measured every 10 minutes with periodic shaking (5 s fast orbital followed by 5 s pause). As shown in Figure 29A, GFP expression (normalized per cell) follows the same density- dependent path independent of the initial culture density, an important property of QS- mediated regulation. 108

125 To modulate QS activation through expression of LuxI, overnight grown cells were diluted fold in media with different levels of IPTG and cultured as before. Increasing IPTG increases signal synthesis leading to earlier activation visible as higher expression at any given density (Figure 29B). Figure 29: Density- dependent activation under QS control through AHL based signaling. (A) Density- dependent activation (of GFPuv) is independent of initial density. JM109 cells carrying the QS circuitry and the lux based GFPuv reporter were grown overnight and diluted (10 3 -, , and fold) to different initial densities (shown in different colors respectively) in the presence of 1 mm IPTG to activate the QS circuit for 109

126 LuxI production. Normalized GFP expression was calculated from subtracting GFP reading of blank TBK (~2900 counts) and dividing by corresponding OD600 subtracted for blank TBK (0.042). Dots indicate mean values and error bars indicate standard deviation from 4 replicate measurements. Demonstrating the density- dependent target gene activation under QS, GFP expression follows the same density- dependent path independent of the initial culture density. Inset: Growth curves of the corresponding three dilutions. (B) Increasing IPTG (LuxI production) shows shift in activation to lower density fold diluted culture was grown with indicated IPTG levels. Normalized GFP expression calculated as in A. (C) Estimation of AHL level in high- density culture. Blue points show reporter expression at indicated inducer concentration. Brown circle on the vertical axis marks the observed reporter expression from the JM109 cells (carrying pexoi and prtrans) that overlaps the calibration around 9 nm. Error bars for all points are from three replicates. (D) Benefit of exoenzyme production increases with increase in 6- APA. Adapted from Figure 15C, compares QS (1mM IPTG) to OFF at varying 6- APA levels. In each case, ratio was taken when either QS or OFF reach a high OD=0.13. Error bars are propagated values from 4 replicates B.4 Estimating 3OC 6 HSL concentration in QS population at high density As a reference for the ON strategy, we estimated the AHL concentration reached by the QS population at a high density (Figure 29 C). Cells carrying the full circuitry (pexoi and prtransp) produce the AHL inducer in the presence of IPTG. These cells, when grown in the absence of IPTG, do not produce the inducer and provide the appropriate base media for building an AHL calibration curve. As a reporter of inducer concentration, we used MG1655 cells with plasmids constitutively expressing LuxR and GFPuv under promoter PLuxI (carrying the same antibiotic resistance as the QS population)(115). Single clones were grown overnight (final OD~0.35 for both) in 2 ml TBK media. Next morning, the cells were diluted 100- fold in TBK media. 200 µμl cultures of cells with 50 µμl mineral oil were then grown in a 96 well plate and the OD was 110

127 monitored. 12 replicate wells were used for QS culture (with 1 mm IPTG) and 72 wells for the inducer free base media (without IPTG). At a sufficiently high OD (~0.15) where high QS activation is clearly observed, incubation was stopped and the cultures were extracted carefully (180 µμl from each well) to avoid mineral oil. Both cultures were centrifuged and sterile- filtered (using 0.2 µμm filters) to extract supernatant. Overnight culture (OD~0.5) of reporter cells was diluted 20- fold into both the supernatants. Supernatant from QS culture mixed with the reporter cells was laid out in triplicate 200 µμl in a 96 well plate. To build the calibration curve, the inducer free base media mixed with the reporter cells was first split into 12 aliquots in 1.5 ml microcentrifuge tubes (1 ml each). Inducer made in TBK media (see Methods) was added at 12 different concentrations indicated. 200 µμl cultures from each of these tubes were laid in triplicate with 50 µμl mineral oil and the plate was incubated with shaking for ~12 hours after which cultures ware analyzed by flow cytometry. For each well, mean reporter expression was estimated from the cytometry data. Values reported are the geometric mean and standard deviations from the triplicate wells. The plot of the reporter expression profile shows that QS population had an inducer level of ~ 9 nm at the cut- off density (Figure 29C). This inducer level was then used as the activation level for the ON state. 111

128 B.5 Stochastic variation in initial density We made use of the stochasticity generated during extreme dilution to examine its effects on QS benefit. In comparing QS versus OFF (Figure 14), overnight culture was first diluted fold into fresh medium without IPTG. This dilution level gives an appropriate frequency of unseeded wells - from 2 to 6 empty wells per 48 wells (f) giving a mean seeding density (λ=- ln(f)=2.57), corresponding to 2 to 3 cells per well. This culture was then split into two, to one half 1mM IPTG (QS) was added and the other half received an equivalent amount of water (OFF). These QS and OFF cultures were then laid out in a 96 well plate (48 wells each). After a 6 hour incubation 6- APA was added to all wells and the plate was then re- incubated as before with periodical monitoring of OD. To study the effect of stochastic spread on QS benefit, we simulated growth of two QS populations, each consisting of multiple subpopulations, with high and low spread in the initial densities of their subpopulations. Experimentally, we made use of the fact that higher dilution would result in higher spread when compared at any mean population density after growth. We first verified this effect by comparing the growth of two un- induced OFF cultures diluted and fold (10- fold lower dilution) in the absence of 6- APA. As expected, higher dilution showed higher spread in growth (Figure 14 B and Figure 30). 112

129 The same experiment also showed the time lag between the means of the two dilutions. To fairly compare two QS systems under stress, we needed to add 6- APA at the same mean density for the two populations. From three replicate growth experiments (un- induced, no 6- APA) we saw that the two dilutions had time lags of 2.3, 2.5 and 3 hours. Therefore, we adopted a 2- hour time delay in addition of 6- APA to the high dilution culture. With this lower (underestimated) time delay, the density at which 6- APA is added to the high dilution culture will likely be lower but not higher than the density at which 6- APA is added to the low dilution. This ensures that the effect of spread we observe (wherein high- spread outgrows low- spread) is not simply due to a difference in initial density at the time of 6- APA addition. The experiment was then carried out at follows: Overnight grown culture was first diluted in media (TBK with 1mM IPTG) in two 25 ml tubes and fold. The dilutions were then laid out in a 96 well plate (48 wells for each dilution). After about 6 hours of incubation, 6- APA was added first to low- dilution wells and the plate was re- incubated. After another 2 hours, the plate was removed and the same 6- APA concentration was added to the high- dilution wells. For both dilutions 6- APA used was from aliquots kept frozen prior to the experiment, and thawed for 15mins before addition. The plate was then re- incubated and OD was monitored for a period of 48 hours. 113

130 Figure 30: Growth dynamics under poisson dilution. Higher dilution generates higher spread. Growth of high ( fold) and low ( fold) diluted un- induced (OFF) populations in the absence of 6- APA. The higher spread (green) in the high dilution over the low dilution case (orange) case is visible. The two growth curves showed a time lag of 2.3 hours between them. Each dot is averaged 114

131 over 48 wells and shaded area captures the standard deviation.(b) Results from four additional replicate experiments comparing growth of QS populations under high and low dilution in the presence of 6- APA. B.6 The optimal control strategy for controlling exoproduct production Here we determine the optimal exoenzyme production rate E opt for bacteria starting growth from low population density in the presence of antibiotic. Consider the logistic growth equation for a population dn dt = gn ( 1 N), where N is cell density (C, cells/ml) normalized with respect to the carrying capacity (NM, cells/ml). The specific growth rate (g, 1/hr) depends on exoproduct production, secretion, and its effect on antibiotic concentration, and simply maximizing it throughout the growth period cannot be used to determine E opt. The reasoning can be elaborated as follows: since antibiotic is added at the start and is not continuously maintained (no steady state antibiotic concentration), the history of antibiotic concentration becomes a governing factor. Mathematically, the change in antibiotic concentration Ab can be written as Ab( τ ) Ab 0 = τ 0 " dab % $ ' dt, (B.1) # dt & where Ab 0 is the initial concentration of antibiotic in the environment and Ab( τ ) is the antibiotic concentration after time τ. 115

132 Consider the growth of OFF cells ( E = 0 ) at time t g E=0 = b 0 b m b m + Ab t ( ) (B.2) Assuming the antibiotic is stable by itself and degrades very slowly in the absence of the exoproduct, we write b m g E=0 = b 0 b m + Ab 0 (B.3) Now we consider the case where at time t, cells which were initially OFF begin to produce exoproduct ( E > 0 ) g E>0 = b 0 b m b m + Ab( t) c E p (B.4) Comparing Eqs. B.3 and B.4, for change in growth rate by exoproduct production # 1 Δg E = b 0 b m % $ b m + Ab t & b m + Ab ( c E p 0 ' ( ) 1 (B.5) From B.5 we note that the extent of reduction in antibiotic concentration ( Ab( t) versus Ab 0 ) determines Δg E. However, there is an inherent time lag between exoproduct production and its secretion followed by antibiotic degradation. Thus, given an exoproduct where coefficients and intermediate reaction rate are finite, Δg E < 0 immediately after production until benefit from antibiotic degradation is realized. The time window during which this occurs depends on the kinetics of enzyme synthesis, 116

133 secretion and degradation. The faster these steps are, the smaller the time during which OFF>ON. The above analysis shows that simply maximizing instantaneous growth rate could rule out scenarios (see Figure 10 D) where the initial drop in growth pays off with increased growth at a later time. Instead, the cumulative account of production determines the " optimal strategy - one that maximizes population size NT $ # T 0 " $ # N t % % ' dt' at the end of the & & growth period. The nature of the equations and history dependence makes it difficult to find an analytical solution for E opt that maximizes NT. However, a closer look at the equations provides some insight into the nature of E opt. Consider the quasi- steady state where exoproduct transport is fast in comparison to exoproduct production. For any given activation level E, the steady state exoproduct concentration in the environment can be dp derived by setting i and giving dt = 0 dp e = 0 dt P i,ss = k E p D p + d p P e,ss = CV cd p d p! k p E $ # " D p + d & p % (B.6) This dependence of P e on cell density C underlies the requirement for an optimal strategy to be density- dependent. As C 0 (for low population density), P e,ss 0, implying high dilution takes exoproduct concentration in the environment to 117

134 zero. At this low density, antibiotic concentration would remain relatively unaffected by ( ) C 0 exoproduct production Ab C 0 Ab 0. Since exoproduct production is costly, as, E opt 0 the best option. However, exoproduct secretion is beneficial at sufficiently high E opt density where is a positive finite value. Thus, to maximize NT, is a specific E opt density- dependent path in which the appropriate activation level during T depends on the cell density at any given time as well as the stress level and cost of exoproduct synthesis. Quorum sensing provides a physical realization of such a density- dependent path. For a QS system of potential v this path is given by E QS v a ( N) =! 1 $ # &+ v a " CV c %. Tuning the QS system to v = v opt provides the best possible QS controlled activation path. We note that this optimal QS controlled path may not be the same as E opt which, by itself, may not be physically realizable. If no density exists where activation is beneficial, E opt = 0 is the trivial solution where OFF always wins (such as the no antibiotic case). Similarly, if cost is negligible in comparison to benefit, the trivial solution is to produce exoproduct at the highest rate independent of density E opt =1. 118

135 B.7 QS advantage across different initial densities and lifecycle times To examine the specific scenarios where QS is not optimal, we simulated growth of QS, ON, and OFF populations across different values for three parameters: stress level, initial density, and sensing potential. The results shown in Figure 31 demonstrate two scenarios, each lasting over a very short time window, during which QS (over a specific potential range) is not optimal. The first (OFF>QS) occurs due to the inherent delay between the start of exoproduct production and the realization of its benefit (see Figure 31A). While cost is incurred immediately during production, the beneficial reduction in antibiotic requires the dynamical processes of transport and enzymatic reaction, which are not instantaneous. This leaves a small time window during which QS controlled activation results in slower growth in comparison to OFF that does not incur any cost. This time window shortens as v is decreased but, being inherent to the dynamics of the process, cannot be completely eliminated by tuning v. We discuss this in more detail below. The second, less frequent scenario (ON>QS), occurs when a high- density population is exposed to high stress (see Figure 31B and E). Under QS control, production is gradually activated with growth while for the ON case activation is immediate. To a population already at sufficiently high density at the onset of high stress, immediate activation of exoproduct production can be advantageous. In this scenario, a QS system with a low sensing potential (late activation) is not favorable 119

136 against ON. As expected, this region is eliminated when a QS system with high v is considered (Figure 31C and F). Barring the above two exceptions, in general QS emerges as the best control strategy. Further, the simulations demonstrate that QS may be tuned appropriately to maximize the region over which it is advantageous, depending on the stress level. In the system shown, the intermediate v represents the optimal QS characteristics, being advantageous or non- losing in most cases (Figure 31A and D). 120

137 Figure 31: Comparing different QS systems across stress levels. Simulations comparing ON, OFF and QS were carried out with QS systems that activate at an intermediate density (v=10 4 ), high density (v=10 2 ) or low density (v=10 6 ) for low (100) and high (200) antibiotic concentration. See experimental procedures for definition of sensing potential v as a metric for QS- mediated activation. The intensity of the color (red to green) indicates ratio of the density reached by QS and OFF at any given time. Colored lines are shown to help demarcate the scenarios where a particular strategy is best. To demarcate the regions a difference of 1% in cell- density at any point was considered significant. Moving along the diagonal from left to right (say in panel A), the red line indicates transition from QS=OFF to OFF> QS. The next transition following this occurs at the green line where QS>OFF. Blue area covers region where ON>QS. With low v=10 2 (B and E), production occurs later in growth and the time 121

138 window where OFF>QS is reduced (not visible at this scale) but correspondingly, the area where ON is the best strategy increases. With high v=10 6 (C and F), production occurs early during growth (at lower density) where higher dilution increases the time window in which OFF>QS. vopt would be an intermediate value (as seen with v=10 4 ) that maximizes the area. The interplay continues at higher antibiotic level but the relative areas occupied by QS, ON and OFF are now different, suggesting a different vopt B.8 Parameter values for modeling QS-mediated exoenzyme production The parameters used in the simulations are listed in Table 4. Typical values were chosen for bacterial cell volume V c, maximal growth rate b 0, and carrying capacity of medium N M. Antibiotic was assumed to be relatively stable in media until degraded by exoproduct and an inherent decay rate d Ab, 100- fold lower than that for exoproduct degradation rate d p was chosen. Remaining parameters were manually chosen to qualitatively capture the major growth characteristics observed experimentally. The density- dependence of benefit and, in- turn, the optimality of QS are intrinsic features of this exoenzyme secretion scenario that arise when cost and benefit parameters are significant and comparable (low 6- APA level in our study). These same features can be shown in other scenarios as well, such as with exoenzymes that generate nutrients from available substrates in the environment. As such, changes in parameter values change the quantitative aspects of the dynamics shown but do not change the conclusions drawn. 122

139 Vc Table 4: Modeling parameters for QS- mediated exoproduct activation 15 Intracellular volume of an average E. coli cell l 9 NM 10 cells/ml Carrying capacity of growth medium. E 0 to 1 Fractional activation of exoproduct production. k p 100 nm hr - 1 Maximum intracellular exoproduct production rate on full activation. D p 100 hr - 1 Transport rate constant of exoproduct from intracellular to extracellular space. d p 0.1 hr - 1 Inherent decay rate of beta- lactamase protein. Ab 0 d Ab, p units.5 unit - 1 µμm - 1 hr - 1 Initial antibiotic concentration. Active beta- lactamase catalyzed degradation of antibiotic. d Ab hr - 1 Inherent decay rate of antibiotic. Assumed to be relatively stable by itself. b m 100 units Antibiotic concentration at which growth rate is half maximal. b o.75 hr - 1 Benefit parameter representing the maximal growth rate. c p 0.25 hr - 1 Cost parameter for (fractional) reduction in growth rate at maximal activation. a 1-2 For the luxr, luxi system from V. fischeri, we a =1.6 take See reference (123). 123

140 Appendix C: Long-term monitoring of bacterial growth and plasmid segregation. Plasmids are circular, extrachromosomal, self- replicating units and are commonly used as vectors for genetic manipulations (in our case for the design of gene circuits). The total number of copies of a plasmid in a cell varies from one to hundreds depending in the type of plasmid. Specific dynamic mechanisms control the total copy number of plasmids with a cell. In an ongoing project (joint with Yu Tanouchi) we study the variations in plasmid number during bacterial growth. In our study, we monitored individual cells carrying two plasmids that express different fluorescent reporters (Venus (YFP) or mcherry expression from tet promoter (117)) but are identical in their replication mechanisms (Figure 32). Such plasmids are typically called incompatible as the cellular replication machinery does not identify them as different (same origin of replication) and hence cannot maintain a steady copy number of each (124). A heteroplasmid cell carrying these two plasmids will, after sufficient divisions, lead to homoplasmid cells where all plasmids are of the same type. We thus theorized that changes in the plasmid numbers during growth and division, such as increase in one plasmid compared to the other, should reflect in the ratio of YFP to mcherry expression. 124

141 Figure 32: Plasmid segregation during bacterial growth. Plasmids of the same origin of replication but expressing YFP and mcherry are shown. Consider a cell carrying equal number of both. Plasmid segregation during cell division will determine the ratios of plasmids inherited. Following division, each daughter cell will then replicate these plasmids up to the copy number determined by the plasmid type. Note that in our experiment, after division the bottom daughter cell becomes the new mother cell. We used a microfluidic device (a kind gift of Dr. Suckjoon Jun, UCSD) and fluorescence microscopy for long- term, high- frequency observations of bacterial growth and plasmid expression. This device ( mother machine ) allows the same mother cell to remain continuously trapped and observed in the channel while daughter cells are eventually pushed out following sufficient cell divisions (see Figure 33 and (125) for more details). 125

142 Figure 33: Trapping and imaging E. coli in microfluidic device. DIC (left) and CFP image (right) of cells growing in device. Orange arrow point direction in which cells are pushed due to growth and division after which they are flushed out in the main channel by flowing media (white arrow). The CFP image helps clearly identify and segment individual cells from background. C.1 Plasmids, strains and growth conditions. Both plasmids carry identical elements for cellular replication, governed by the identical cole1 origin (126). However, for selection purposes, we designed the plasmids with different antibiotic resistance markers; ptetmcherry carries kanamycin resistance gene while ptetvenus carries chloramphenicol resistance gene. To reiterate, the two plasmids were identical aside from the reporter and antibiotic resistance genes (Figure 32). MC4100 cells with constitutive chromosomal CFP expression (kind gift from Roy Kishony) were used for all observations. The CFP expression cassette carries ampicillin resistance. Thus cells were always cultured in LB media with ampicillin to prevent 126

143 contamination. (Note: ampicillin resistance does not provide any cross resistance for kanamycin or chloramphenicol). Electrotransformation was used to co- transform both plasmids into MC4100 cells. Transformed cells were selected on LB agar plates supplemented with kanamycin and chloramphenicol (~12 hr growth on plate at 37 C). Single colonies from these plates were grown in LB (with kanamycin and chloramphenicol) and an exponential phase culture was used to make a glycerol stock for storage. Individual cells within this stored population were observed to be mostly double, expressing both YFP and mcherry, as observed by microscopy. Before the experiment, cells from the glycerol stock were inoculated into LB with antibiotics (with kanamycin and chloramphenicol) and grown at 37 C for ~5 hours (OD~0.2). The use of antibiotics was to maintain the selection for heteroplasmid cells until the start of experiment. 4ml cell culture was spun down and concentrated by resuspending in 100 µl LB. These cells were then loaded into the microfluidic device using a syringe. After loading, the device was briefly spun (~3 minutes) in a microcentrifuge to make the cells enter into the microchannels. The device was imaged to confirm the presence of cells inside microchannels and then connected to a syringe pump to flow LB media (no antibiotics) at a rate of 100 µl/hr. Device connected with syringe pump was loaded into the imaging chamber of DeltaVision maintained at 37 C and imaged with a 100x oil immersion lens. 127

144 C.2 Long-term monitoring of bacterial growth and reporter expression. Note that the LB media now contains no antibiotics. As such, we expect all dynamics observed to be independent of selection and a resultant of plasmid number dynamics. This plasmid dynamics includes replication during growth and segregation during cell division (Figure 32). Thus heteroplasmid cells can display fluctuations in the ratios of two plasmids or even loose one plasmid entirely. Cell growth and fluorescent reporter expression (CFP, YFP, mcherry) was followed for ~ 16 hrs. Data from microscopy was analyzed using ImageJ and custom C code developed by Rumen Stomatov. The microscopy observations capture the long- term growth and fluorescence expression from cells (Figure 34). Cell growth showed regular divisions of the mother cell with occasional spikes (125) (Figure 35). Consistent with our expectations we observed heteroplasmid cells loose one plasmid type over time (plasmids once lost cannot be regained, both orange to red and orange to green were seen). In addition, as expected with the randomness of plasmid segregation in heteroplasmid cells, we observed long- term non- monotonic fluctuations in YFP to mcherry expression (Figure 35 bottom panel). 128

145 Figure 34: Long- term observation of plasmid expression dynamics in a microfluidic device. Overlaid (DIC, YFP, mcherry) images of E. coli growing in vertical microchannels (same frame, 12 hours apart). Cells carry different ratios of two plasmids that express YFP (green) and mcherry (red) reporter proteins - orange represents a mix of both. Change in color with time captures long- term changes in plasmid ratios. Note that mother cell 2 changes from orange to red while mother cell 4 changes from green to orange. Figure 35: Quantitative observations from microscopy. Panels show example data generated from long- term observations. Imgaes were taken 3 minutes apart and indicated by frame numbers. Observation points were joined by straight lines for clarity. Top panel tracks the growth of a single mother cell as per cell length (CFP channel). The peak of spikes indicate a cell division event. Bottom panel: 129