Bacterial growth control & control by bacterial growth. PICB, Shanghai July 18, 2008

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1 Bacterial growth control & control by bacterial growth PICB, Shanghai July 18, 2008

2 Systems biology: from molecules to physiology Physiology: the working of a living organism; reproduction & adaptation to the environment Bacterial physiology (E. coli): bacteria can sense the environment and rapidly adjust their life style growth Carbon + Nitrogen biomass doubling time: 20 min to > 500 min depending on nutrient survival coping with stressful conditions heat shock, acid shock, osmotic response, oxidative stress, non-growth conditions: stationary phase, dormancy, sporulation, This talk: Bacterial growth physiology review of bacterial growth laws their impact on gene expression and genetic circuits phenomenological model of bacterial growth

3 Mass/cell (µ doubling/hour) 200 min 20 min

4 2 µ Mass/cell (µ doubling/hour) 200 min 20 min phenomenological law! dependence on the medium through growth rate µ only -- universal! cell mass (~size) increases exponentially with growth rate µ natural unit of growth rate ~ 1 doubling/hr (universal speed limit)

5 2 1.5µ RNA/cell (µ doubling/hour) RNA content increases more rapidly than cell mass (mostly protein) macromolecular composition (e.g., RNA:protein) strongly µ dependent similar growth laws seen in E. coli and other bacteria

6 Growth rate dependence of macromolecular composition for E. coli B/r [ Bremer & Dennis, 1996] doubling time minutes Protein/mass 10 aa/od RNA/mass 10 nuc/od DNA/mass 10 8 gen/od Cells/mass 10 8 cells/od protein cell mass strong increase in RNA/cell weak increase in DNA/cell

7 Growth-rate dependence of the cellular RNA content cellular RNA ribosomal RNA ribosome level from stoichiometry ribosome content growth rate dependent a significant fraction of cellular proteins are ribosomal proteins at fast growth doubling time minutes RNA/cell 10 7 nuc Ribosome/cell r-protein/protein % Alternative form of Schaecter et al s 2nd growth law

8 What do the growth laws have to do with modern biology? Consider constitutive gene expression: p m p m m mean-field description (rate eqn) m = # functional mrna/cell p = # of protein product/cell [p] = protein concentration d dt m = g m m m steady-state d p * dt p = p m p p = g m p m p V Q: growth rate dependence of [p*]? -- many factors depend passively on growth rate: g, V, p, p (and others) -- more complex for actively regulated genes -- gene regulation mostly accompanied by changes in growth rate growth rate dependence affects the robustness of genetic circuits must consider growth dependence in physiological studies of gene reg

9 Growth rate dependent expression of unregulated genes DNA replication C 40 min required to replicate chromosome fixed time of D 20 min between completion of one round of replication and cell division multiple replication forks for doubling time < C+D x oric terc gene copy # at position x on chromosome (different for plasmids) g x = 2 µ C (1 x)+ D [Cooper & Helmstetter, JMB 1968]

10 Transcription: determined by the abundance of free RNAP in exponential growth, RNAPs fall into one of 5 classes N tot = N ns + N r + N m + N free + N immat non-specifically bound to DNA N ns transcribing mrna. N m free N free immature N immat transcribing rrna, N r N tot directly measured N m,n r estimated from measured transcription rates partition inactive RNAPs into N ns,n free, N immat using microscopic model all needed parameters known except two (non-specific binding constant and RNAP maturation time) determine by fit of (N free +N immat )/N (fraction of cytoplasmic RNAP) to data from DNA-free minicells at different growth rates

11 Resulting partitioning of RNAP free RNAP rrn P2 predicted growth-rate dependence of free RNAP agree well with measured tsx rates for several constitutive promoters rrn P2 not a constitutive promoter in agreement with in vitro results (Gourse) P spc,p bla [Liang et al, JMB 1999]

12 mrna stability: lifetime lacz mrna (Liang et al. 1999) dbl/hr, dbl/hr genome-wide study (Bernstein et al. 2002): small growth-rate dependence in mrna lifetime

13 growth rate dependence of mrna levels

14 Growth-rate dependence of translation efficiency ( burstiness ) [Bremer & Dennis, 1996] [Liang et al, J. Bact 2000] avg burstiness = (total protein/cell ln2/dt)/(measured total mrna syn rate/cell) burstiness of r-protein mrna (r-protein/cell ln2/dt)/(tsx rate of Spc prom/cell) burstiness of lacz mrna ( -gal activity/total protein ln2/dt) (total protein/total RNA) / (lacz mrna/total RNA) independence of burstiness on growth rate despite strong growth-rate dependence of ribosome/mass global feedback mechanism (via mrna cleavage?)

15 growth rate dependence of protein levels

16 Compare to experiments: -- generally good agreement for different promoters and genes in different strains and grown in different media

17 Expression from plasmids -- gene dosage = plasmid copy number -- pbr322: increases weakly with growth rate expect stronger growth-rate dependence on plasmids [Lin-Chao & Bremer, MGG 1986]

18 Growth-rate dependence of regulated genes consider tsx init control only (for simplicity), with = c G 1 ln G A 1 ln G R slope n slope n f -1 f -1 ( ) n G R = 1 + f ( ) n G A = f 1 + [A]/K A 1 + [A]/K A K A ln([a]) K R 1 ([R]/K R ) n ( ) n 1 + [R]/K R ln([r]) -- growth-rate independent: fold-change (f) Hill coeff (n), dissoc const (K) -- growth-rate dependent: transcription rate (c), cell volume,

19 Negative control by constitutively expressed repressor R E constitutive cooperative repression non-cooperative repression Negative control by an autorepressor R E wide occurrence in bacteria cooperative negative autoregulation can provide stable protein pools

20 Autoactivator A toggle switch A B region of bistability growth-rate dependent overlap of bistable region at slow and fast growth requires large fold-change and/or large cooperativity more complex behaviors for -- circuits involving srna -- circuits affecting growth

21 Back to the 2nd growth law cellular RNA ribosomal RNA ribosome level from stoichiometry ribosome content growth rate dependent a significant fraction of cellular proteins are ribosomal proteins at fast growth doubling time minutes RNA/cell 10 7 nuc Ribosome/cell r-protein/protein % Rb synthesis/cell per minute # rrn gene/cell Rb synthesis limited by rrna initiation max rrna transcription rate (100/min) x no. rrn genes/cell

22 Quantitative understanding of the 2nd growth law Ribosome availability determines the growth rate let = fraction of Rb synthesizing Rb and suppose ribosomes efficiently used in protein synthesis 1 d ln 2 dt M Rb = M Rb µm Rb 1 d Rb P 1- ln 2 dt M = (1 ) M µm P Rb P 1 : time for one Rb to synthesize a Rb µ = ln a.a./rb 5 min : master growth control 20 a.a./sec i is not observable, but can be deduced from Rb content: = M Rb M Rb + M P predicted growth rate dependence of Rb content: r M Rb M Rb + M P = µ /

23 Compare to data: r = µ / r = + µ / M RNA M Rb = r M tot (µ + ) 2 µ 5% 16 dbl/hr 22 a.a./sec no adjustable parameter! discrepancy suggests a fraction of inactive ribosomes model: a fraction of Rb inactivated then, µ = ( - ) Rb Rb 1- P or, r M Rb + M Rb M Rb + M Rb + M P = = µ +

24 Details more complicated:

25 Growth rate dependence may have several components: Divide proteome into 3 components: slow growth total protein ribosome related Q R P fast growth catabolic? Q R core (Q) P

26 Three component model of growth R: ribosomal proteins + affiliates; regulated by R (via ppgpp) Q: core proteins; regulated by Q (fixed, via autorepression?) Q R P: others; P = 1 - R - Q (not showing inactive ribosomes for clarity) 1 d ln 2 dt M = R R R M R µm R R 1 d P R P ln 2 dt M = P P R M R µm P Q Q 1 d ln 2 dt M Q = Q R M R µm Q P let M R = M Rb, then R = / µ = R / and R = M R M R + M P + M Q M Rb i relation between observables unchanged: r = µ / M R + M P + M Q i new constraint: r r max (1 Q )/ or µ µ max = r max i growth-rate dependent expression: P = 1 Q R µ max µ

27 include nutrient input (e.g., aa-limited growth) a.a. n flux balance at steady-state: a.a. consumption = a.a. supply R R P P E N Rb k E N E n n + K n = k E E N P n n + K n Q Q assume E P E: rate-limiting catabolic enzyme M R = (n, E,...) M P or R = P R + P + Q = 1 ( ) ( ) r = R / = r max + µ = r = r max + growth rate (µ) determined jointly by nutrient source/level ( ) and the speed of the ribosome ( ) simple Michaelis form if independent of µ (!) can be tested by eliminating : ( ) µ = r max r

28 Expt #1: Test the predicted form µ(, ) = r max Alter Rb elongation rate using antibiotic (Cm) (1 ) + K D [ Cm] KD [Harvey & Koch, 1980] test µ(, ) by measuring µ for different growth media ( ) at various Cm concentrations ( ) µ µ µ 0 = 0.3 dbl/h µ 0 = 0.5 dbl/h µ 0 = 1dbl/h µ 0 = 2 dbl/h predicts stronger growth inhibition on faster growing cells [ Cm]( µ M )

29 vary growth rate via N-source in M9 glycerol medium µ / µ Alanine (µ 0 =0.35 dbl/hr) NH 4 + (µ 0 =0.51 dbl/hr) Cytidine (µ 0 =0.59 dbl/hr) NH 4 + (µ 0 =1.03 dbl/hr) + CAA ( ) IC 50 µ M [Cm] (in µm) Doubling time (min) single parameter fit (K D ) to all data sets semi-quantitative agreement with prediction IC 50 strongly growth rate dependent K D

30 Expt #2: Test the predicted relation between µ and r i in the absence of drug, expect r = + µ / R % P P dbl/h = 20 a.a./s NH 4 + +caa NH 4 + Cytidine Alanine Glucose 40 min (1.53 dbl/h) 70 min (.90 dbl/h) 81 min (0.74 dbl/h) 125 min (0.48 dbl/h) 58 min (1.04 dbl/h) 104 min (0.67 dbl/h) 130 min (0.46 dbl/h) Growth Rate µ (dbl/h)

31 Expt #2: Test the predicted relation between µ and r i in the absence of drug, expect r = + µ / i with drug altering, expect µ = ( r max r) R % P P dbl/h = 20 a.a./s NH 4 + +caa NH 4 + Cytidine Alanine Glucose 40 min (1.53 dbl/h) 70 min (.90 dbl/h) 81 min (0.74 dbl/h) 125 min (0.48 dbl/h) 58 min (1.04 dbl/h) 104 min (0.67 dbl/h) 130 min (0.46 dbl/h) Growth Rate µ (dbl/h)

32 Expt #2: Test the predicted relation between µ and r i in the absence of drug, expect r = + µ / i with drug altering, expect µ = ( r max r) R % P P linearity of µ and r supports µ-independent suggests bottleneck of nutrient uptake reside in catabolic pathways (positive autoregulation) dbl/h = 20 a.a./s R R Q NH 4 + +caa NH 4 + Cytidine Alanine a.a. P simple model of nutrient influx: n M P = k E E N P n + K n P Q Glucose 40 min (1.53 dbl/h) 70 min (.90 dbl/h) 81 min (0.74 dbl/h) 125 min (0.48 dbl/h) E n 58 min (1.04 dbl/h) 104 min (0.67 dbl/h) 130 min (0.46 dbl/h) Growth Rate µ (dbl/h)

33 Expt #2: Test the predicted relation between µ and r i in the absence of drug, expect r = + µ / i with drug altering, expect µ = ( r max r) R % P P linearity of µ and r supports µ-independent suggests bottleneck of nutrient uptake reside in catabolic pathways (positive autoregulation) all minimal media exhibited similar r max ~ 25% composition of the metabolic core (Q)? dbl/h = 20 a.a./s NH 4 + +caa NH 4 + Cytidine Alanine Glucose 40 min (1.53 dbl/h) 70 min (.90 dbl/h) 81 min (0.74 dbl/h) 125 min (0.48 dbl/h) 58 min (1.04 dbl/h) 104 min (0.67 dbl/h) 130 min (0.46 dbl/h) Growth Rate µ (dbl/h)

34 Expt #2: Test the predicted relation between µ and r i in the absence of drug, expect r = + µ / i with drug altering, expect µ = ( r max r) linearity of µ and r supports µ-independent suggests bottleneck of nutrient uptake reside in catabolic pathways (positive autoregulation) all minimal media exhibited similar r max ~ 25% composition of the metabolic core (Q)? 40 Note: r max 40% for rich medium % r- Protein/Total Protein xYT 14.6 dbl/h = 20 a.a./s NH 4 + +caa NH 4 + Cytidine Alanine Glucose 40 min (1.53 dbl/h) 70 min (.90 dbl/h) 81 min (0.74 dbl/h) 125 min (0.48 dbl/h) 58 min (1.04 dbl/h) 104 min (0.67 dbl/h) 130 min (0.46 dbl/h) Growth Rate µ (dbl/h)

35 Summary bacterial growth in different media growth rate as a critical variable growth-rate dependent effects on gene expression complex dependence even for constitutive promoters growth-rate dependence can be minimized by negative autoregulation taming growth-rate dependent effects essential for robust genetic circuits phenomenological model of growth rate control three components: R (ribosome+affiliates), Q (core), P (catabolic) experiment supports the simplest (coarse-grained) description of metabolic control: trade-off between P and R core fraction similar for all minimal media tested

36 Stefan Klumpp Matt Scott Funding: NIH, NSF, HFSP