A population-based temporal logic gate for timing and recording chemical events

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1 Pulished online: My 7, Article A popultion-sed temporl logic gte for timing nd recording chemicl events Victori Hsio,*, Yutk Hori, Pul WK Rothemund & Richrd M Murry Astrct Engineered cteril sensors hve potentil pplictions in humn helth monitoring, environmentl chemicl detection, nd mterils iosynthesis. While such cteril devices hve long een engineered to differentite etween comintions of inputs, their potentil to process signl timing nd durtion hs een overlooked. In this work, we present two-input temporl logic gte tht cn sense nd record the order of the inputs, the timing etween inputs, nd the durtion of input pulses. Our temporl logic gte design relies on unidirectionl DNA recomintion medited y cteriophge integrses to detect nd encode sequences of input events. For n E. coli strin engineered to contin our temporl logic gte, we compre predictions of Mrkov model simultions with lortory mesurements of finl popultion distriutions for oth step nd pulse inputs. Although single cells were engineered to hve digitl outputs, stochstic noise creted heterogeneous single-cell responses tht trnslted into nlog popultion responses. Furthermore, when single-cell genetic sttes were ggregted into popultion-level distriutions, these distriutions contined unique informtion not encoded in individul cells. Thus, finl differentited su-popultions could e used to deduce order, timing, nd durtion of trnsient chemicl events. Keywords DNA memory; event detectors; integrses; popultion nlysis; stochstic iomoleculr models Suject Ctegories Quntittive Biology & Dynmicl Systems; Synthetic Biology & Biotechnology DOI.55/ms.5 Received 7 Octoer 5 Revised April Accepted April Mol Syst Biol. () : 89 Introduction Engineered cteri could one dy e powerful self-replicting iosensors with environmentl, helth, nd industril pplictions. Synthetic iology hs mde importnt strides in identifying nd optimizing genetic components for uilding such devices. In prticulr, much work hs focused on Boolen logic gtes tht detect the presence or sence of sttic chemicl signls (Grdner et l, ; Anderson et l, 7; Wng et l, ; Moon et l, ; Shis et l, 4) nd compute digitl response. Temporl logic gtes, which process time-vrying chemicl signls, hve een much less explored. Pioneering work y Friedlnd et l (9) used serine integrse-sed recomintion for the counting nd detection of sequentil pulses of inducers. But thus fr, no work hs studied the potentil for temporl logic gtes to provide informtion out the durtion of signl, or the time etween two chemicl events. Here, we present temporl logic gte tht llows us to infer nlog signl timing nd durtion informtion out the sequentil ppliction of two inducer molecules to popultion of cteril cells. Similr to previous temporl logic gtes, our design tkes dvntge of the irreversiility of serine integrse recomintion. While istle switches hve een successfully deployed s memory modules in genetic circuits (Kotul et l, 4), such switches require constnt protein production to mintin stte nd re sensitive to cell division rtes nd growth phse. The lrge serine integrses, on the other hnd, relily nd irreversily flip or excise unique frgments of DNA (Yun et l, 8). Thus, logic circuits uilt from integrses intrinsiclly include DNA-level memory tht requires virtully no cellulr resources to mintin stte, thus enling permnent nd low-cost genetic differentition of individul cteril cells sed on trnsient integrse induction. Further dvntges of the serine integrses include the short length (4 5 p) nd directionlity of their ttchment sites. Serine integrses recognize flnking DNA inding domins (ttb, ttp) nd susequently digest, flip or excise, nd re-ligte the DNA etween the ttchment sites. Flipping or excision ctivity is determined y the reltive orienttion of the sites, which llows complex orienttiondependent ehvior to e progrmmed into integrse circuits. Wellknown serine integrses include Bx, TP9-, nd ΦC, ll of which hve een used to demonstrte sttic-input logic gtes (Bonnet et l, ; Siuti et l, ), nd some hve cofctors tht cn reverse directionlity (Khleel et l, ; Bonnet et l, ). Recently, n entirely new set of orthogonl integrses ws chrcterized, gretly expnding the set of circuits tht cn e uilt (Yng et l, 4). In contrst to previous studies of temporl logic gtes, our work leverges the stochstic nture of single-cell switching to crete Biology nd Biologicl Engineering, Cliforni Institute of Technology, Psden, CA, USA Applied Physics nd Physico-Informtics, Keio University, Yokohm, Kngw, Jpn Computtion & Neurl Systems, Cliforni Institute of Technology, Psden, CA, USA *Corresponding uthor. Tel: ; E-mil: vhsio@cltech.edu ª The Authors. Pulished under the terms of the CC BY 4. license Moleculr Systems Biology : 89

2 Pulished online: My 7, Moleculr Systems Biology Popultion-sed integrse event detector Victori Hsio et l roust popultion-level response to time-vrying chemicl signl. The fundmentl nture of living cells tht mkes them so ttrctive for engineering their extremely low energy opertion in the limit of using smll numers of molecules to represent informtion is lso inextricly linked to stochsticity nd noise. By trditionl engineering stndrds, synthetic circuits would idelly perform identiclly within every cell of popultion. When this idel is pplied to iology, the stochstic nture of moleculr processes, prticulrly t low-copy numers, presents significnt rrier to relile outputs from engineered cells. Thus, while nturl cellulr dynmics nd differentition tke dvntge of noisy gene expression (Elowitz et l, ; Süel et l, 7), synthetic circuits often require noise reduction for proper function (Dunlop et l, 8). Recent work hs tken different direction, towrd understnding of popultion-level dynmics. This includes nlysis of oth stochstic cellulr responses to inputs (Uhlendorf et l, ; Ruess et l, 5) nd chnges in collective popultion-level memory in response to stress (Mthis & Ackermnn, ). Such efforts suggest tht deeper understnding of the inherent heterogeneity in iologicl systems might eventully led to circuit designs tht operte on distriutions of cellulr responses, rther thn depending on homogeneous responses from ll cells. It is with this vision in mind tht we designed two-input temporl logic gte using strtegiclly interleved nd oriented integrse (Bx, TP9-) DNA recomintion sites nd used this gte to engineer n E. coli strin with four possile geneticlly differentited end sttes. This strin contins single genomic copies of the temporl logic gte, ensuring digitl-yet-stochstic responses from individul cells. We then utilized the heterogeneity of individul cellulr responses to encode sequences of chemicl inputs into the overll popultion response nd used stochstic model of singlecell trjectories to predict the popultion response. By nlyzing the distriutions of finl cell sttes, we cn deduce the timing nd pulse durtion of trnsient chemicl pulses nd show tht cumultive popultion-level distriutions contin dditionl event informtion not encoded in ny single cell. Furthermore, ecuse the sttes re geneticlly encoded, we cn recover detils of chemicl event long fter its occurrence. Results Design of two-integrse temporl logic gte We hve designed two-input temporl logic gte tht differentites etween the strt times of two chemicl inputs nd produces unique outputs ccordingly (Fig A). The design relies on system of two integrses with nested DNA ttchment sites (Fig B). The use of integrses irreversily inverts segments of DNA, resulting in memory feture tht cn e mintined for multiple genertions (Bonnet et l, ). The design of the integrse temporl logic gte hinges on interleving the ttb ttchment site of integrse B (intb) with the ttp site of integrse A (inta), thus ensuring tht the possile DNA flipping outcomes re mutully exclusive (Fig B). The serine integrses used in this design re TP9- (inta) nd Bx (intb). The fluorescent proteins mkte-rfp (RFP) nd superfolder-gfp (GFP) re used oth s plceholders for future downstrem gene ctivtion nd s rel-time redouts of the logic gte. The design lso fetures termintor (B-B5) nd strong constitutive promoter (P7). In the cse where there re no inputs, the termintor prevents expression of RFP from the constitutive promoter. There re five possile sic events tht could occur in twoinput system (Fig C): no input, inducer only (E ), inducer only (E ), inducer followed y t lter time (E ), nd inducer followed y t lter time (E ). Consequently, in perfectly resolved temporl logic gte, there should e five unique DNA sttes corresponding to the five types of events: (the initil stte), S, S, S, nd S. This design is limited to only four DNA sttes due to excision when E occurs (S = S ). The two fluorescent outputs correspond to the two sttes tht occur when inducer is detected first RFP is produced when the cell is in stte S, nd GFP is produced when the cell is in stte S. Fig D illustrtes the sequence of recomintion tht occurs during n event E tht results in DNA stte S nd the production of GFP. Upon ddition of inducer t time t, TP9- flips the DNA etween its ttchment sites, reversing the directionlity of the termintor nd the Bx ttb recognition site (stte S ). Then, when inducer is dded t some time t tht is greter thn t, the directionlity of the Bx sites is such tht the DNA is flipped to reverse the directionlity of the P7 constitutive promoter (stte S ). If inducer is dded first (Fig E), the Bx ttchment sites re unidirectionl configurtion tht results not in recomintion, ut in excision of the DNA etween the sites (stte S ). Once DNA recomintion hs occurred, it is irreversile. The unique ttb nd ttp ttchment sites re recomined into ttl nd ttr sites, respectively, with which the integrses cnnot ind to without dditionl cofctors (Ghosh et l, 5). The nesting of the integrse ttchment sites is the key design feture tht produces the temporl then logic, nd the irreversiility of the recomintion records the event in DNA memory. The result is genetic record tht cn oth e sequenced lter nd immeditely red vi constitutive production of fluorescent outputs. A Mrkov model for integrse recomintion The most compelling dvntge of engineered iologicl systems over mn-mde sensors lies in their inherent cpilities for repliction nd prllel sensing with miniml energy nd resource requirements. Thus, deployment of synthetic cteril devices would lmost certinly involve popultions of cells, never just single cell. It is therefore importnt to understnd how stochstic single-cell responses ffect overll popultion-level distriutions nd outcomes. We creted Mrkov model of integrse-medited DNA flipping nd then used stochstic simultion lgorithm (Gillespie, 977) to simulte individul cell trjectories (Fig A). All of the four possile DNA sttes re represented in the model: the originl stte ( ), the intb excision stte (S ), the inta single flip stte (S ), nd the then doule flip stte (S ). We hve implemented the system experimentlly y chromosomlly integrting the trget DNA into the genome of the E. coli cell. This llows us to ssume tht ech cell only hs one copy of the temporl logic gte (Hldimnn & Wnner, ) nd tht ech cell cn e chrcterized Moleculr Systems Biology : 89 ª The Authors

3 Pulished online: My 7, Victori Hsio et l Popultion-sed integrse event detector Moleculr Systems Biology A B temporl logic gte output temporl logic gte inta intb time RFP ttb ttb ttp ttp GFP t t Termintor P_constitutive C Event only(e ) DNA stte S Output RFP D t time E then (E ) then (E ) time S t o only(e ) S t S t S then (E ) then (E ) S S GFP t S t Excision No response Figure. Design overview of temporl logic gte. A A temporl logic gte distinguishes etween two chemicl inputs (, ) with different strt times. B Implementtion of the temporl logic gte using set of two integrses with overlpping ttchment sites. Chemicl inputs nd ctivte production of integrses inta nd intb, which ct upon chromosoml DNA cssette. C Tle with ll possile inputs nd outcomes to the event detector. D Sequence of DNA flipping following inputs with inducer efore inducer (event E ). E Sequence of DNA flipping following inducer inputs with first (event E ). In ny events in which precedes, the unidirectionlity of the intb ttchment sites results in excision. y the tuple (DNA; IntA; IntB) (Fig B). The DNA terms re, S, S,orS, nd IntA nd IntB re non-negtive integers representing the moleculr copy numer of ech integrse. Once DNA cssette hs flipped into ny of the sttes other thn the originl stte, there is no reverse process. The logic gte is designed such tht if integrse B is expressed prior to integrse A, the DNA cssette is excised nd the chin reches the ded-end S stte. In order for cell to successfully detect E, it first needs to switch into stte S then trnsition into stte S upon ddition of inducer. Since ech cell contins only single copy of the temporl logic gte DNA, we cn expect ech cell to ehve differently nd to e highly susceptile to internl nd externl noise. This stochstic ehvior will crete heterogeneous popultion response tht cn e nlyzed for more complex profile of event thn if ll the cells ehved uniformly. In order to cpture the heterogeneity of cell popultion, we model the temporl logic gte using stochstic model. Specificlly, the stochstic trnsitions etween the DNA sttes nd the production/degrdtion of integrses re mthemticlly modeled y continuous-time Mrkov chin over the stte spce (DNA; IntA; IntB) s illustrted in Fig B. Definitions of trnsition rtes cn e found in Appendix Tle S. In silico, the dynmics of single cell trnsltes to ech stochstic simultion of the Mrkov model strting with (DNA = So; IntA = ; IntB = ) stte. We define P t ð Þ;P t ðs Þ;P t ðs Þ; nd P t ðs Þs the proility tht the DNA stte of single cell is ; S ; S ; nd S t time t, respectively. The temporl dynmics of the proility cn e modeled y the following ordinry differentil eqution (ODE) (see eqution ). Where the nottion E t ½jŠ stnds for the conditionl expected vlue t time t (Full derivtion, Appendix Section.). Serine integrses re produced s monomers tht form dimers, serch for specific ttb nd ttp sequences, nd, once oth ttb nd ttp sites re occupied, form tetrmer (dimer of dimers) tht digests, flips, nd re-ligtes the DNA (Yun et l, 8; Rutherford et l, ). Though some coopertivity in ΦC inding to ttb hs d dt 4 P t ð Þ P t ðs Þ P t ðs Þ P t ðs Þ 7 5 ¼ E t ½ ðintbþj Š E t ½ ðintaþj Š E t ½ ðintaþj Š E t ½ ðintbþjs Š 7 4 E t ½ ðintbþj Š 54 E t ½ ðintbþjs Š P t ð Þ P t ðs Þ P t ðs Þ P t ðs Þ 7 5 () ª The Authors Moleculr Systems Biology : 89

4 Pulished online: My 7, Moleculr Systems Biology Popultion-sed integrse event detector Victori Hsio et l A Initil stte B DNA sttes Protein sttes C Excision first S t t t only S then S S S t D Numer of cells (x ) S t = h Time (h) S S S Ø Ø inta inta intb intb inta intb t = 5 h Time (h) S S S Figure. A B C D A Mrkov model of integrse-medited DNA flipping. The four possile DNA sttes, illustrted with DNA stte digrms. All DNA egins in the initil stte, nd there re no reverse processes. The propensity functions,, nd re dependent on the concentrtion of the two integrses nd correspond to the events first (E ), only (E ), nd then (E ), respectively. Representtion of the sme model s Mrkov chin. Integrses re represented simply s protein sttes with production (c A ; c B ) nd degrdtion (d A ; d B ) rtes. Grphicl representtion of inducer step functions. Δt is defined s difference etween the strt time of the first inducer nd strt time of the second. Simultion results for inducer seprtion times of nd 5 h. There re four possile DNA sttes, ut ll cells end up in either the S or S finl sttes. Individul trjectories re simulted for 5, cells nd the numer of cells in ech DNA stte is summed for ech time point (Appendix Fig S). een found (McEwn et l, 9), coopertivity in Bx or TP9- integrse inding to ttb nd ttp not een oserved (Ghosh et l, 5; Singh et l, 4). Rther thn ccount for ll individul DNA-integrse interctions, we hve creted miniml model of stochstic trnsitions where only the finl DNA sttes (, S, S, S ) nd the numer of integrse monomer molecules (inta, intb) re trcked nd ll integrse ctivity is encompssed in the k flip term. Since no coopertivity hs een oserved in Bx or TP9- DNA inding (i.e., occuption of ttb does not increse the proility of ttp inding), we represent the required tetrmeriztion s frction where flipping efficiency is zero unless t lest four molecules re present. Thus, the propensity functions for stte trnsitions s function of integrse concentrtion, i ðint Þ, re defined in eqution () where Int is integrse concentrtion; K d is the dissocition constnt; k flip is the rte of flipping if the tetrmer is formed; i = ; ; ; nd *= A;B (See Appendix Fig S for visuliztion of i ðint Þ nd Appendix Section. for full derivtion). We lso define the time etween the introduction of the first inducer (t ) nd the rrivl of the second inducer (t ) s the inducer seprtion time (Dt), such tht Dt ¼ t t ; () s shown in Fig C. In the following set of simultions nd experiments, we will consider cses with step inputs (Fig C), where the inducers re either present or not present. Concentrtions of the inducers when they re on will e held constnt. Also, it is importnt to note tht inducer is still present during nd fter time Dt when inducer is introduced. Simultions of the Mrkov model were done with iologiclly plusile prmeters in order to predict qulittive circuit ehvior (Appendix Tle S). We limited the prmeters to only the sic processes (integrse production, degrdtion, nd DNA flipping), nd prmeter vlues were chosen to e within iologicl orders of mgnitude. The single production rte constnts, k proda nd k prodb, comine the trnscription nd trnsltion rtes of ech integrse. Int ðint ÞðInt ÞðInt Þ i ðint Þ :¼ k flip Kd 4 þ K d Int þ Kd Int ðint ÞþK d Int ðint ÞðInt ÞþInt ðint ÞðInt ÞðInt Þ () 4 Moleculr Systems Biology : 89 ª The Authors

5 Pulished online: My 7, Victori Hsio et l Popultion-sed integrse event detector Moleculr Systems Biology When n integrse in the model is induced, its production rte, c, is the sum of k prod nd ny leky trnscriptionl expression, k lek (*= inta or intb). The integrse monomer disssocition constnt, K d, ws estimted from mesured Bx inding constnts (Singh et l, ). Prmeter vlues for preliminry simultions were k proda ¼ k prodb ¼ 5ðlm hþ, k deg ¼ : h (. h hlf-life), k flipa ¼k flipb ¼:4h, k leka ¼k lekb ¼ðlm hþ, nd K da ¼K db ¼ molecules. Our nlysis of initil numericl simultion results highlights the significnt role tht the inducer seprtion time, Δt, plys in setting the finl popultion distriutions (Fig D). For ech Δt, individul cell trjectories were generted with the ssumption tht ech cell only hs one copy of the trget DNA (N = 5, trjectories). Then, t every time point, the totl numer of cells in ech DNA stte is counted (Appendix Fig S). Fig D shows the contrst etween dding oth inducers simultneously (Δt = h) nd dding inducer fter 5-h dely (Δt = 5 h). Since oth inducers re present y the end of simultion, ll of the cells must hve finl stte tht is either the S stte or the S stte. No cells remin in the originl configurtion. S is trnsient stte tht uilds up prior to the ddition of inducer nd egins to convert to S immeditely fter the introduction of. These initil simultion results suggest tht Δt my e wy to relily tune the finl popultion frctions of S versus S stte cells. Popultion distriutions reflect inducer order nd seprtion time We used the model to further investigte the effects of vrying oth inducer order nd seprtion time on popultion distriutions in our experimentl system nd to understnd the possile outcomes. In Fig, we simulte in silico cell popultions tht hve een exposed to sequence of overlpping step functions (N = 5, trjectories). In the cse of n E event, the proportion of cells tht successfully detect then nd switch to stte S is function of the inducer seprtion time, Δt (Fig A). High Δt mens incresing the time tht cells spend in only inducer, llowing for most of the popultion to trnsition from? S efore the ddition of ny inducer. Exposing cells to the inverse sequence of events, E, results in decrese of S cells proportionl to incresing Δt (Fig B). High Δt in n E event mens tht? S is the dominnt rection nd cells tht re prtitioned into S will not respond to inducer. If we plot the finl numer of S cells from oth E nd E s function of Δt (Fig C), we see tht the two curves do not overlp. S frctions exposed to E increse monotoniclly with Δt, while those exposed to E decrese monotoniclly with Δt. Thus, mesuring the frction of S cells y itself is sufficient to determine oth the order of events nd the timing, Δt, etween them. Additionlly, we cn define detection limit, Δt 9, for which the inducer seprtion time results in 9% of the popultion switching into the S stte (Fig C). This Δt 9 limit provides wy to cpture the two response regimes of the popultion. If the inducer seprtion time is less thn the detection limit (Δt < Δt 9 ), then the rte of popultion switching is fst enough such tht the numer of S cells will correspond uniquely to some Δt vlue. If Δt > Δt 9, then most cells hve lredy switched to finl stte, nd the differences in S cell count re too smll to uniquely determine Δt. The single-cell limittions of the temporl logic gte circuit cn e overcome y mesuring the numer of S cells s frction of totl cells. Though the logic gte itself does not hve unique genetic S stte nd cnnot distinguish etween only event versus then event, these simultion results suggest tht popultion-level frctionl phenotypes cn provide this dditionl informtion (Fig D). In the cse of E, frctions of S will lwys e ove 5%, while S frctions less thn 5% indicte E. Additionl figures showing how popultions of S, S, nd cells chnge with Δt cn e found in Appendix Figure S. In vivo step induction dt supported model predictions nd showed tht popultion frctions of S cells could e tuned using Δt (Fig 4). DH5-Z cells were chromosomlly integrted with one copy of the integrse trget DNA nd then trnsformed with highcopy plsmid contining Ptet-Bx nd PBAD-TP9-. When Δt ws vried from to 8 h, we oserved results qulittively similr to model predictions. In Fig 4A, the cells hve een exposed to n E event, where inducer is present from time t = htot end, nd is present from t = Δt htot end. GFP expression during time course mesurements is used s proxy for S stte cells, nd flow cytometry ws used to mesure finl popultions. Comprisons of ulk fluorescence versus cytometry cell counts suggest tht in single-copy integrnts, overll GFP fluorescence is good pproximtion of popultion S levels (Appendix Fig S). In Fig 4A, the numer of cells in the GFP-expressing S stte increses proportionlly with incresing Δt nd continues to e responsive even when the two inducers re seprted y 8 h. There is some expression of GFP in the presence of only inducer (E ), indicting some sl levels of intb. RFP expression, proxy for the numer of cells in stte S, egins to increse t t = h nd drops t time t = Δt when inducer is dded (Appendix Fig S4A). Aligning ll of the GFP expression curves y Δt (Appendix Fig S5) shows tht lower vlues of Δt not only hve lower finl GFP expression vlues, ut lso hve slower rtes of GFP production. This is consistent with modeling results ecuse if we ssume inducer hs n equl proility of entering ny one cell, then in cse of smll Δt (Δt 9 4 h), there re much lrger numer of cells nd so the rte of S? S stte conversion will e lower. In the cse of Δt > 4 h, the mjority of cells in the popultion re lredy in the S stte configurtion, nd so the rte of cell stte conversion to S will e much higher. When cells re exposed to E, the numer of S cells decreses monotoniclly with incresing Δt (Fig 4B), nd there is no RFP expression ove ckground (Appendix Fig S4B). In oth types of events, the cells mintined their stte for up to h in liquid culture nd when re-streked s single colonies. (Additionl dt with more distinct color scheme nd OD curves for this set of experiments cn e found in Appendix Figs S nd S7. Single-colony nlysis in Appendix Fig S.) Finl S (GFP) popultion frctions re sufficient to differentite etween popultions tht hve een exposed to E versus E within h of seprtion time etween inducers (Fig 4C). Finl popultions fter h of growth were mesured vi flow cytometry nd plotted ginst Δt. As Δt increses, so does the S supopultion. The cells tht encountered E hve lower S frctions with high Δt, nd t Δt = h, the finl S su-popultion is equl ª The Authors Moleculr Systems Biology : 89 5

6 Pulished online: My 7, Moleculr Systems Biology Popultion-sed integrse event detector Victori Hsio et l A B C Cells in stte S (frc/totl).8..4 t E. only 4 Time (h) t: -h Cells in stte S (frc/totl) t E 4 Time (h) only t: -h Cells in stte S (frc/totl) t 9 E event E event 5 Inducer seprtion time, t D Event only only then then Single-cell level DNA stte S S S S Color RFP GFP Popultion level Popultion frction (%) S S S >5 <5 Figure. Simultion results for inducer seprtion time for Δt = h. A The popultion frction (N/5, cells) tht switches into stte S following n E event is dependent on the inducer seprtion time, Δt. The gry to drk green color grdient represents incresing Δt vlues. Squre mrkers indicte finl popultion frctions for specific vlues of Δt. B In the cse of the inverse E event, the frction of cells in stte S decreses monotoniclly with incresing Δt. Circulr mrkers indicte finl popultion frctions for specific vlues of Δt. C Finl S cell frctions from (A, B) re plotted s function of Δt. Blue line with squre mrkers shows end point popultion frctions from n E event. Yellow line with circulr mrkers shows finl end point popultion frctions from n E event. The grdient inside the mrkers corresponds to incresing Δt vlue. The dotted gry line corresponds to the Δt 9, the vlue of Δt t which 9% of the cells re in stte S. All simultions were done with popultion of N = 5, cells. D Chrt showing differences in informtion tht cn e recorded t the single-cell versus the popultion level. In prticulr, E does not hve unique single-cell genetic stte, ut hs cler distinct popultion-level phenotype. to the seline expression of the only popultion, indicting tht the ddition of inducer fter -h exposure to only inducer hs no effect t ll. Bsed on where the GFP frction exceeds 9% of the mximum S popultion frction, the Δt 9 detection limit for the experimentl system is ~4 h. These experimentl results show tht the S popultion frction clerly diverges for E nd E when Δt ¼ h, indicting tht S frctions lone cn e used to determine oth event order nd seprtion time. Further nlysis of popultion-level dt for ll of the mesurle fluorescent cell sttes cn provide dditionl insights into differences in su-popultion growth rtes nd leky integrse expression (Fig EV, Appendix Figs S8 S). In Fig EV, experimentl popultions from the step input experiments hve een gted into qudrnts such tht S, S, nd + S popultions cn e counted. Even with mximum induction t highest Δt, the mximum popultion frction tht cn e switched ppers to e pproximtely % of the totl popultion. We elieve this is due to the non-fluorescent cells (, S ) hving slight growth dvntge over differentited cells. Studies hve shown tht unnecessry protein production hs inverse effects on cell growth (Tn et l, 9; Scott et l, ), nd even with single-copy integrnts, this would result in some overrepresenttion of non-fluorescent su-popultions within the popultion. Single-colony nlysis of the finl popultions shows tht cells persist in the popultion even with 4 h of inducer exposure (Appendix Fig SE). Leky expression of inta nd intb cn lso e inferred from the no inducer, only, nd only popultions (Fig EVA nd B), nd we cn conclude tht leky expression is quite low, not exceeding ~.5 %. Even ccounting for the overrepresenttion of nonfluorescent cells, the seline popultion split when oth nd re dded simultneously (Δt = h) is just under 5% of the totl GFP popultion frction. This suggests tht the integrse flipping Moleculr Systems Biology : 89 ª The Authors

7 Pulished online: My 7, Victori Hsio et l Popultion-sed integrse event detector Moleculr Systems Biology A B C t t GFP/OD (x ) No inducer only t = h t = h t = h t = h t = 4h t = 5h t = h t = 7h t = 8h Time (h) t: - 8h GFP/OD (x ) No inducer only t = h t = h t = h t = h t = 4h t = 5h t = h t = 7h t = 8h Time (h) t: - 8h GFP popultion (%) only only t 9 E E 4 8 Inducer seprtion time, t (h) Figure 4. In vivo results for vrying inducer seprtion time from Δt = 8 h. A Popultions of cells exposed to n E event sequence. Cell switching to stte S (indicted y GFP fluorescence) egins when inducer (Tc) is dded. Mximum normlized GFP fluorescence increses s function of the inducer seprtion time Δt. Gry to drk green grdient represents incresing Δt vlues. Squre mrkers re finl end point mesurements. Error rs represent stndrd error of the men. B Cells exposed to the inverse E sequence of events. GFP fluorescence decreses monotoniclly with incresing inducer seprtion time etween nd. Circulr mrkers re finl end point mesurements. C Finl popultion distriutions from (A, B) t h re plotted s function of Δt. Cells were gted y GFP fluorescence to identify percentge of S cells. Dotted line mrks Δt 9 detection limit. Source dt re ville online for this figure. rtes, k flipa nd k flipb, my not e equl nd tht the sl expression rtes, k leka;b should e nonzero. Vrying model prmeters for integrse ctivity nd sl expression Prior to proceeding with dditionl model-driven experimentl designs, model prmeters were modified to etter represent symmetricl integrse ctivity. The prmeters for integrse flipping nd leky sl expression were tuned to ccount for the symmetricl popultion responses to E versus E events (Fig 4C). We hypothesized tht this symmetry rises from comintion of unequl integrse ctivity when serching for nd flipping the DNA, s well s leky ckground expression of the integrses (Fig 5). To understnd overll trends in model ehvior, we vried k flipa nd k lekb while holding the other prmeters constnt. When the reltive flipping efficiency of inta (k flipa ) ws vried from. to.5 h (k flipb =. h ), we oserved is in the seline popultion split when oth inducers re introduced simultneously, Δt = h (Fig 5A, N =,). Previously in the preliminry model (Fig C), the two integrses were ssigned equl flipping rtes, nd the popultion split ws expected to e 5/5 for S /S. As the flipping rte of inta decreses reltive to tht of intb, tht seline shifts downwrds to fvor the more ctive integrse, intb. Vrying the sl expression of intb (k lekb ) from % to % of the intb production rte (k prodb ) monotoniclly decreses the mximum S popultion frction tht cn e reched in n E event (Fig 5B, N =,). If there is constnt level of un-induced intb, then there will lwys e minimum popultion of S cells inhiiting the mximum frction of S cells. These simultion results showed tht y vrying k flipa nd k lekb, we could tune the seline shift t Δt = nd the mximum S ceiling t high Δt to etter pproximte our experimentl system. However, experimentl mesurements of leky integrse expression showed tht ckground expression ws ctully quite low (% for inta, % for intb) (Figs 4C nd EV, only, only). Given ctul mesurements for k leka;b, we constrined those prmeters nd fit the model y vrying k flipa;b. In order to find the est pir of vlues for k flipa nd k flipb, the flipping efficiency prmeters for oth integrses were vried from. to. h in silico (N = 5 cell trjectories), creting mtrix of simulted S popultion frctions for ech comintion (Appendix Fig S). Leky sl expression of the integrses ws held constnt sed on experimentlly mesured vlues (k leka = % of k proda, k lekb = % of k prodb ), nd experimentl dt were normlized to 7% popultion mximum for fitting purposes. Men squred error ws found y compring model fits with experimentl dt (Appendix Fig SA), nd the comintion with the minimum MSE ws chosen (Appendix Fig SB). Fig 5C shows Δt versus S popultion simultion results for finl revised prmeters. The finl prmeters were set to e k flipa ¼ :h, k flipb ¼ :h, k leka ¼ : k proda ðlm hþ, nd k leka ¼ : k prodb ðlm hþ (Appendix Tle S). The introduction of leky integrse expression into the model suggests tht due to leky expression of intb, round % of the popultion will detect E nd e in stte S even when no inducer hs een introduced. Additionlly, preliminry simultion results suggest tht the Δt 9 detection limit cn e tuned y incresing or decresing the overll production rte k prod (*= A or B) (Appendix Fig S4), though this remins to e experimentlly verified in future work. ª The Authors Moleculr Systems Biology : 89 7

8 Pulished online: My 7, Moleculr Systems Biology Popultion-sed integrse event detector Victori Hsio et l A B C Frction of S cells E *k flipb =. k flipa =.5 k flipa =.4 k flipa =. k flipa =.. E. 4 8 Seprtion time, t (h) Frction of S cells E *k leka = % k lekb = % k lekb = % k lekb = % E 4 8 Seprtion time, t (h) Frction of S cells E Exp. dt Initil model Revised model * k leka = %, k lekb = % * k flipa =., k flipb =. E 4 8 Seprtion time, t (h) Figure 5. Vrying model prmeters for integrse flipping nd leky expression. A As DNA flipping rtes of inta (k flipa ) re decresed reltive to k flipb, the popultion of S cells t Δt = h hs downwrd shift. Simultions re done with N =, trjectories/mrker. B Incresing the leky expression of intb (k lekb ) chnges the mximum threshold of cells tht correctly identify S even t high Δt. Lekiness is defined s percentge of the induced integrse production rte (k prod ). C The model ws revised to more closely mtch the experimentl dt y constrining prmeters for leky expression nd vrying integrse flipping (N = 5,). Men squred error ws clculted etween the experimentl dt nd the initil nd revised models to find n optimized pir of k flipa;b vlues (Appendix Fig S). The revised prmeters re k flipa =. h, k flipb =. h, k leka = % ofk proda (lm h), nd k lekb = % ofk prodb (lm h). In silico prmeter spce explortion shows tht vrying k flip nd k lek prmeters enles tuning of seline Δt = h split for E /E nd the mximum ceiling for S popultion frction. Foldchnge vritions in reltive rtes llowed us to understnd overll trends in the finl popultions, nd we djusted the model to ccount for inequlities in integrse flipping nd leky sl expression. Since leky expression ws mesured to e smll, we primrily tuned flipping rtes. This process led us to more relevnt modelinformed predictions of experimentl outcomes. With the refined model, we were interested to see whether distriutions of the RFPexpressing S stte could provide informtion tht mesuring S frctions lone could not. Deducing pulse width from S popultion frctions Using the frction of S (GFP) cells lone, we cn determine Δt vlues up to Δt 9 limit for ny given sequence of two step inputs. Now consider pulse type of event, in which inducer egins t time t = h, remins constnt throughout, nd inducer is introduced s finite pulse t time t = Δt h (Fig A). The strt time of inducer then ecomes reference for when the entire system is ctivted nd redy to detect inducer. Cell sttes re mesured vi flow cytometry t time t end, where t end > 4 h. Modeling results presented in this section re using the refined set of prmeters defined in Fig 5C nd Appendix Tle S. If either of the two inducers is present in the medi to some limit t end, we would expect ll of the cells to end up in one of two popultions (Fig B). Cells tht encounter inducer first will e in the S stte, while cells tht encounter first will either e in the S or S sttes. In the previous sections, once n inducer ws dded to the popultion, it ws not removed, nd the ssumption ws mde tht t times > 4 h, only negligile numer of cells remined. This type of step function induction lso ment tht only the finl numer of S cells (GFP) ws needed to uniquely determine the seprtion time Δt ecuse ny nd ll cells tht hd switched to S would eventully ecome S. However, in the cse of trnsient pulse, some cells tht re in the S stte (RFP) will not ever encounter inducer. Assuming tht k lekb is smll, these cells will remin in the S stte. Therefore, the popultion of first cells equls S + S. We simulted mtrix of popultions exposed to vrying inducer seprtion times (Δt) nd inducer pulse widths (PW ) to mesure the resolution of detectle events (Fig C). In simultion (Fig D), we cn see tht the two popultions mirror ech other to dd up to % of the totl cells (N =, cells, dditionl simultions in Appendix Fig S). Given tht the step induction of is equivlent to pulse of infinite length (PW = ) nd our prior experimentl evidence showed tht virtully no cells remin in stte S when PW =, we resoned tht the finl numer of S cells could e used to deduce informtion out the pulse width of. This hypothesis ws tested in silico y running mtrix of simultions with vrying Δt nd PW. In Fig E, we see tht the frction of S cells over the totl numer of cells decreses monotoniclly with incresing PW, nd the curves overlp regrdless of Δt. The overlp occurs despite nonzero leky expression of inta nd intb. The mximum numer of S cells does not go to t PW = h ecuse of leky intb expression (k lekb =. k prodb ). Anlyticlly, we solved eqution () for P t ðs Þ to ensure tht the S popultion frction is only dependent on PW. If inducer is used s constnt reference signl, ll cells trnsition into one of S ; S ;or S sttes, thus P ðs Þ¼ ðp ðs ÞþP ðs ÞÞ. If we ssume tht the sl leky expression of intb is zero (k lekb = ), P t ðs ÞþP t ðs Þ¼ holds for t Dt, since there is no intb to switch the DNA stte into S or S. Thus, we cn show tht P t ðs ÞþP t ðs Þ is dependent only on PW, the durtion of the pulse width of inducer B, for t > Δt. This conclusion holds s long s k lekb is negligily smll compred to other kinetic constnts (k flipa, k flipb, k deg, c A, nd k prodb ) (See Appendix Section. for full derivtion). 8 Moleculr Systems Biology : 89 ª The Authors

9 Pulished online: My 7, Victori Hsio et l Popultion-sed integrse event detector Moleculr Systems Biology A B C S t PW D (S +S ) / S totl S / S totl t end Time (hours) S S S S S S 4 5 Pulse width, PW (h) t = h t = h t = h t = h t = 4h t = 5h t = h S first popultion E S / S totl S first popultion S PW = Cells in only stte t = h t = h t = h t = h t = 4h t = 5h t = h 4 Pulse width, PW (h) PW = PW = 4 PW = F S / S totl S t = t = t = Cells in then stte 4 Pulse width, PW (h) t = h t = 5h 4h t = h t = h t = h t = h Figure. Simultion results for pulse width modultion. Simultions were done with revised prmeters found in Fig 5C. A Inducer cn e used s reference signl ginst which to mesure the time nd durtion of the inducer pulse. B The popultion eventully divides into one of two su-popultions: those tht see inducer first nd those tht see inducer first. Only if cell hs entered the first pthwy does it hve the possiility to express RFP or GFP. Furthermore, S cn e thought of s necessry precursor to S. C A mtrix illustrting suset of the Δt nd PW vlues to e tested. D Simultion results show tht for ny given Δt, the numer of cells in S = (totl numer of cells (S + S )) E The frction of the popultion in the S stte is totlly independent of Δt nd depends only on the pulse durtion of inducer. F Once PW is known, then the frction of the popultion in S stte cn e used to find the time t which the pulse of inducer egn. N =, cell trjectories for ech vlue of Δt, PW. If S popultion frctions cn e modulted y chnging PW, then conversely, we should e le to use mesured experimentl RFP popultion frctions s wy to determine PW. Once PW is known, then the S frction cn e used to uniquely determine the time etween inducers, Δt (Fig F). Furthermore, the geneticlly encoded stte mens tht these popultion frctions should e mintined nd mesurle t time, t end, tht is much lter thn the time of the events. These conclusions cn e extended in simultion to crete sctterplot of S cells versus S cells in popultion (Fig 7A) over n prmeter mtrix vrying Δt nd PW from to h in increments of.5 h (Additionl plots in Appendix Fig S7). Ech point on the chrt in Fig 7A represents simulted popultion (N =,) exposed to unique comintion of Δt nd PW vlues. Verticl lines represent the sme PW vlue, nd points with the sme shpe nd color hve the sme Δt vlue. The simultion results suggest sufficient resolution of events s long s PW nd Δt vlues re etween nd 4 h. For ny single vlue of PW, we cn follow the incresing Δt vlues verticlly nd see tht the popultion response sturtes fter 4.5 h resulting in overlpping etween popultions with 4.5 < Δt < h. We cn trce ny individul Δt vlue horizontlly from right to left nd oserve tht the points egin to cluster nd overlp when 4.5 < PW < h. These simultion dt suggest tht there should e some defined detection rnge of Δt nd PW where every possile comintion of the two is uniquely identifile. Experimentlly, we tested 7 7 mtrix of vrying Δt nd PW ( h, h increments) on independent popultions of the temporl logic gte E. coli strin (Fig 7B). All popultions, except for the control, were exposed to inducer (L-r.%/vol) t time t to t end. Pulses of inducer (Tc, ng/ml) were chieved y smpling 5 ll of the popultion nd diluting : into fresh medi with only inducer (M9CA +.%/vol L-r). Popultions were collected nd mesured vi flow cytometry fter 4 dditionl hours of growth in inducer (~ h fter strt of experiment) (Fig EV). For ll vlues of Δt, the numer of S cells (RFP) is highest when there is no exposure to inducer (PW = h) nd decreses monotoniclly s function of PW (Fig 7B, top). We see more pronounced seprtion of the Δt curves when we look t S (GFP) cell frctions (Fig 7B, ottom). The numer of S cells is dependent on oth Δt nd PW nd increses proportionlly with oth incresing pulse durtion nd inducer seprtion time. By counting popultion frctions of RFP versus GFP-expressing cells, we cn resolve the different popultions tht result from vrying Δt nd PW vlues (Fig 7C). As with Fig 7A, ech point on the grph represents n independent popultion of cells (OD~.7, ~ ª The Authors Moleculr Systems Biology : 89 9

10 Pulished online: My 7, Moleculr Systems Biology Popultion-sed integrse event detector Victori Hsio et l A 4 PW (h) B 7 C S / S totl S / S totl t = h t = 5h t = 4h t = h t = h t = h t = h RFP popultion (%) GFP popultion (%) Ctrl t = t = t = t = t = 4 t = 5 t = 4 5 Pulse width (h) GFP popultion frction (%) PW (h) t = h t = 5h t = 4h t = h t = h t = h t = h RFP popultion frction (%) Figure 7. Determining rrivl time nd pulse durtion of inducer with popultion frctions. A Simultion results from testing n mtrix of prmeters with Δt nd PW vrying from to h in increments of.5 h. Ech point represents popultion of, cells. Incresing PW goes from right to left, nd incresing Δt goes from ottom to top. B Experimentl results showing RFP nd GFP popultion frctions s function of incresing Δt nd PW. Experimentl results were otined y exposing temporl logic gte E. coli popultions to vrying PW nd Δt vlues ( h,.%/vol L-r, ng/ml Tc, mesurements tken t 48 h). C A sctterplot of ech popultion using their RFP nd GFP frctions s coordintes (~ cells per popultion). The non-induced control smples re indicted with dotted circle on the ottom left, nd the smples with PW = h re on the ottom right. Smples with the sme PW re connected with solid line, nd line drkness represents incresing PW durtion. Smples with the sme Δt re shown with the sme colored shpe mrker nd incresing Δt goes from ottom to top. Source dt re ville online for this figure. cells counted per popultion). All of the popultions exposed to either or oth of the inducers occupy frctionl coordintes tht re unique from tht of the no inducer controls (indicted y dotted circle). We see tht if Δt is constnt nd PW increses (Fig 7C, right to left), then the S frction decreses s S frctions increse. For constnt PW with incresing Δt (Fig 7C, ottom to top), the S cell frction remins mostly constnt reltive to incresing S. In the cse where there is no pulse (PW = h), we see mximum S (RFP) cell frctions of out % with miniml S popultions tht re out the sme s no inducer S levels. Overll, popultions with different PW exposures re well seprted y S (RFP) frction up to 4 h. Even for PW t 5 nd h, the popultions hve unique S /S coordintes, just not unique S frctionl vlues. This method of profiling is only vlid if the frction of S stte cells cn e used s mesure of PW tht is independent of Δt. In previous experiments with step inputs (Fig EV), there would e significnt popultion of cells with oth GFP nd RFP fluorescence, since they hd trnsitioned to S ut hd not yet fully diluted out uilt up RFP protein levels from eing in S for extended periods. If significnt percentge of the popultion remined in this trnsition stte (Q), tht would mke RFP n unrelile mesure of S stte cells. However, flow cytometry nlysis of the pulsemodulted popultions (Fig EV) showed tht lthough there were some cells expressing oth RFP nd GFP (Q), these cells were lwys < % of the totl popultion. (Additionl flow cytometry nlysis cn e found in Appendix Figs S8 S.) Thus, RFP ws mesured to e relile determinnt of S stte cells, nd susequently, of PW. For ny given PW, we oserved higher experimentl S (RFP) popultion frctions with lower Δt (Fig 7A top), resulting in digonl slnt for ech vlue of PW (Fig 7C). Upon further investigtion, we elieve this is due to slower! S trnsition thn we nticipted. In our model, we ssume! S is equl to S! S, since oth trnsitions re medited y intb. However, the grdul decrese in S frctions with incresing Δt for ech vlue of PW suggests tht the trnsition rte my e ctully e slower thn or. Simultion results with djusted trnsition rtes ( < = ) recpitulted the slnting S popultion frctions (Appendix Fig S5). This inequlity in trnsition rtes could hve risen from differences in DNA sequence length or from differences in the DNA excision required for trnsition to S insted of the recomintion tht occurs in the other trnsitions. Differences in DNA excision or recomintion for single integrse re importnt experimentl prmeters, ut do not ultimtely ffect our conclusions out the overll system. Despite unequl intb trnsition rtes, experimentl implementtion of the temporl logic gte still produces unique (S, S ) frctionl coordintes for ech comintion of Δt, PW, even though S vlues re not unique for higher PW. Model-informed predictions on popultion frctions in response to pulses of inducer led to experiments tht could produce unique S nd S coordintes for different comintions of Δt nd PW. However, experimentl dt lso reveled res in which the model hd een oversimplified. While it is importnt to hve model to understnd overll properties nd limittions of the experimentl system, it is lso imprcticl to design simultions tht cn ccount for ll possile vritions tht might occur in the implementtion of Moleculr Systems Biology : 89 ª The Authors

11 Pulished online: My 7, Victori Hsio et l Popultion-sed integrse event detector Moleculr Systems Biology iologicl devices. Therefore, we elieve tht future workflows should lso involve clirtion protocols for specific pplictions of engineered iologicl popultions. Prcticl use nd clirtion of popultions for event detection Curve-fitting methods were used to utomticlly convert experimentlly mesured RFP nd GFP popultion frctions into PW nd Δt vlues nd to evlute the resolution with which popultion rtios cn e used to determine inducer seprtion time nd pulse durtion. Using the experimentl dt from Fig 7B nd C, we generted fitting curves for PW s function of RFP popultion percentge (R) nd for Δt s function of oth GFP popultion percentge (G) nd PW (Appendix Figs S nd S7, Appendix Tle S). We will denote these functions with PW (R) nd Δt(G, PW ), respectively. The functions PW (R) nd Δt(G, PW ) cn then e used to generte mesh of estimted PW nd Δt vlues for ny given normlized fluorescence vlues (Fig 8A, Appendix equtions 8 ). The estimted vlues were compred ginst the ctul vlues to determine the pproximte time window with which specific PW or Δt vlue cn e resolved. For ech ctul vlue of PW nd Δt, we clculted the verge nd stndrd devition for the set of estimted vlues. The stndrd devition llows us to visulize the rnge for which the mjority of predictions will fll for ny given ctul vlue. For instnce, PW of h cn e detected.5 h, ut s PW increses, this prediction window widens nd for PW h, the resolution of detection is closer to h (Fig 8B). Similrly, predicted vlues of Δt fll within.5 h for < Δt < h nd increse to h when Δt h (Fig 8C). Using these fitting functions, we cn lso pre-generte reference tle tht converts RFP nd GFP popultion frctions into predicted PW nd Δt vlues (Appendix Tle S4). Discussion Engineered iologicl systems hve inherent cpilities for repliction, prllel processing, nd energy efficiency. These dvntges rely on the existence of cteri not s single cells, ut s popultions. As the field moves forwrd with synthetic gene circuits, it is importnt to understnd outcomes not just s single-cell outputs ut s overll popultion-level distriutions. We hve designed nd implemented temporl logic gte tht tkes dvntge of the popultion dynmics to collectively sense nd record sequences of trnsient chemicl inputs. We show oth tht single cells independently sense nd record events nd tht ggregte popultion frctions crete unique outcomes tht provide informtion not encoded in single cells. As with ll engineered systems, proper clirtion of these temporl logic gte popultions will e required prior to deployment in the field. We envision process similr to the one descried in this report. First, experimentl popultions re exposed to mtrix of PW nd Δt vlues. This will set the mximum nd minimum RFP nd GFP popultion frctions nd provide necessry dt for determining the Δt 9 limit nd producing the fitting functions PW (R) nd Δt(G, PW ). Once the fitting functions hve een determined, vlues for PW nd Δt for experimentl smples cn e estimted within.5 to h of the ctul vlues. A clirted tle could lso e generted nd used for s reference for smples tht hve een exposed to unknown conditions. The stochstic nture of moleculr processes often presents significnt rrier to homogenous outputs from n engineered popultion of cells. This implementtion of event detection vi popultion frctions tkes dvntge of stochstic nd heterogeneous individul responses to environmentl conditions in order to mp finl popultion frctions ck to unique sequences nd durtions of chemicl events. The sensitivity of the system nd the Δt 9 A 7 B 7 C 7 GFP popultion (%) 5 4 Estimted PW (h) 5 4 Estimted t (h) RFP popultion (%) Actul PW (h) Actul t (h) Figure 8. Determining prediction resolution for PW nd Δt from popultion dt. A A mesh generted from fitted curves for PW s function of RFP popultion percentge(r) nd Δt s function of pulse width nd GFP popultion percentge(g). Experimentl dt re overlid. B Comprison of ctul versus estimted PW vlues generted y fitted function PW (R). For ech ctul PW vlue, the verge of the estimted PW vlues with stndrd devition (slightly offset on the x-xis for etter comprison). C Comprison of ctul versus estimted Δt generted y the fitted function Δt(G; PW ). For ech ctul Δt vlue, the verge of the estimted Δt with stndrd devition (slightly offset on the x-xis for etter comprison). Source dt re ville online for this figure. ª The Authors Moleculr Systems Biology : 89