Stochastic Turing patterns in a synthetic bacterial population

David Kariga,b,1, K. Michael Martinic,1, Ting Lud,1, Nicholas A. DeLateure, Nigel Goldenfeldc,2, and Ron Weissf,2

aResearch and Exploratory Development Department, Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723; bDepartment of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218; cDepartment of Physics, Center for the Physics of Living Cells and Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801; dDepartment of Bioengineering and Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801; eDepartment of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139; and fDepartment of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

Contributed by Nigel Goldenfeld, May 9, 2018 (sent for review November 29, 2017; reviewed by Raymond E. Goldstein, Eric Klavins, and Ehud Meron)

The origin of biological morphology and form is one of the stability operator about the spatially uniform steady state (8). deepest problems in science, underlying our understanding of This amplification means that the magnitude of spatial patterns development and the functioning of living systems. In 1952, Alan arising from intrinsic noise is not limited by the noise amplitude Turing showed that chemical morphogenesis could arise from a itself, as one might have thought naively. These developments linear instability of a spatially uniform state, giving rise to periodic imply that intrinsic noise can drive large-amplitude stochastic pattern formation in reaction–diffusion systems but only those Turing patterns for a much wider range of parameters than the with a rapidly diffusing inhibitor and a slowly diffusing activator. classical, deterministic Turing theory. In particular, it is often These conditions are disappointingly hard to achieve in nature, the case in nature that the activator and inhibitor molecules and the role of Turing instabilities in biological pattern formation do not have widely differing diffusion coefficients; neverthe- has been called into question. Recently, the theory was extended less, stochastic Turing theory predicts that, even in this case, to include noisy activator–inhibitor birth and death processes. pattern formation can occur at a characteristic wavelength that Surprisingly, this stochastic Turing theory predicts the existence has the same functional dependence on parameters as in the of patterns over a wide range of parameters, in particular with deterministic theory. no severe requirement on the ratio of activator–inhibitor diffu- To explore how global spatial patterns emerge from local sion coefficients. To explore whether this mechanism is viable interactions in isogenic cell populations, we present here a syn- in practice, we have genetically engineered a synthetic bacterial thetic bacterial population with collective interactions that can population in which the signaling molecules form a stochastic be controlled and well-characterized (an introduction to this activator–inhibitor system. The synthetic pattern-forming gene perspective is in ref. 9), where patterning is driven by activator– circuit destabilizes an initially homogenous lawn of genetically inhibitor diffusion across an initially homogeneous lawn of cells. engineered bacteria, producing disordered patterns with tun- Synthetic systems can be forward-engineered to include rela- able features on a spatial scale much larger than that of a tively simple circuits that are loosely coupled to the larger natural single cell. Spatial correlations of the experimental patterns agree quantitatively with the signature predicted by theory. These Significance results show that Turing-type pattern-forming mechanisms, if driven by stochasticity, can potentially underlie a broad range In 1952, Alan Turing proposed that biological morphogene- of biological patterns. These findings provide the groundwork sis could arise from a dynamical process in reaction systems for a unified picture of biological morphogenesis, arising from with a rapidly diffusing inhibitor and a slowly diffusing acti- a combination of stochastic gene expression and dynamical vator. Turing’s conditions are disappointingly hard to achieve instabilities. in nature, but recent stochastic extension of the theory pre- Turing patterns | biofilm | synthetic biology | signaling molecules | dicts pattern formation without such strong conditions. We stochastic gene expression have forward-engineered bacterial populations with signal- ing molecules that form a stochastic activator–inhibitor system that does not satisfy the classic Turing conditions but exhibits central question in biological systems, particularly in devel- Aopmental biology, is how patterns emerge from an initially disordered patterns with a defined length scale and spatial homogeneous state (1). In his seminal 1952 paper “The chemi- correlations that agree quantitatively with stochastic Tur- cal basis of morphogenesis,” Alan Turing showed, through linear ing theory. Our results suggest that Turing-type mechanisms, stability analysis, that stationary, periodic patterns can emerge driven by gene expression or other source of stochasticity, from an initially uniform state in reaction–diffusion systems may underlie a much broader range of patterns in nature than where an inhibitor morphogen diffuses sufficiently faster than an currently thought. activator morphogen (2). However, the requirements for realiz- ing robust pattern formation according to Turing’s mechanism Author contributions: D.K., K.M.M., T.L., N.G., and R.W. designed research; D.K., are prohibitively difficult to realize in nature. Although Turing K.M.M., T.L., N.G., and R.W. performed research; D.K., T.L., and R.W. contributed new reagents/analytic tools; D.K., K.M.M., T.L., N.A.D., N.G., and R.W. analyzed data; D.K., patterns were observed in a chemical system in 1990 (3), the gen- K.M.M., T.L., N.A.D., N.G., and R.W. wrote the paper. eral role of Turing instabilities in biological pattern formation Reviewers: R.E.G., University of Cambridge; E.K., University of Washington; and E.M., has been called into question, despite a few rare examples (ref. 4 Ben-Gurion University, Blaustein Institutes for Desert Research. and references therein). Recently, Turing’s theory was extended to include intrin- The authors declare no conflict of interest. sic noise arising from activator and inhibitor birth and death Published under the PNAS license. processes (5–8). According to the resulting stochastic Turing Data deposition: The DNA sequences of plasmids reported in this paper have been theory, demographic noise can induce persistent spatial pat- deposited in the GenBank database (accession nos. MH300673–MH300677). tern formation over a wide range of parameters, in particular, 1 D.K., K.M.M., and T.L. contributed equally to this work. removing the requirement for the ratio of inhibitor–activator 2 To whom correspondence may be addressed. Email: [email protected] or rweiss@mit. diffusion coefficients to be large. Moreover, stochastic Turing edu. theory shows that the extreme sensitivity of pattern-forming This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. systems to intrinsic noise stems from a giant amplification result- 1073/pnas.1720770115/-/DCSupplemental. ing from the nonorthogonality of eigenvectors of the linear Published online June 11, 2018.

6572–6577 | PNAS | June 26, 2018 | vol. 115 | no. 26 www.pnas.org/cgi/doi/10.1073/pnas.1720770115 Downloaded by guest on October 7, 2021 Downloaded by guest on October 7, 2021 n e ursetpoen(F)aeepesdfo the 2 section from Appendix, expressed (SI observation are of (RFP) repression protein and alleviates fluorescent and red and LacI binds that a emdltdb leigtecnetaino isopropyl of concentration system the our altering in by formation of β modulated Pattern transcription RhlR. be represses and can turn, LasR, of in RhlI, expression which LasI, activates the CI, with complex repressor complex This lambda a RhlR. forming by protein itself regulatory and of A3OC12HSL is copy of thesis LasR second To self-activation, a synthase. A3OC12HSL by IC4HSL regulated of an sensitivity RhlI, the and increase synthase, A3OC12HSL an ai tal. et Karig after emerge to S12). Fig. begin Time Appendix, (SI 2A). patterns h (Fig. that 16 fluorescence approximately reveals red intense precisely microscopy the positioned series of voids dark locations with the fluores- pattern in green than a Simultaneously, larger in (10–1,000×). develops much cell cence sizes single with a emerge over of However, that spots fluorescence. feed- fluorescent no red positive exhibits lawn time, synthase cell A3OC12HSL the 30 loop, the at back of Before h needed. 24 self-activation as for captured the incubated are is images Methods). fluorescence dish and microscope petri (Materials an the form cells plating, to of After dish petri “lawn” a homogeneous on and plated media, initially and liquid concentrated in are cultured they first then, are Controls. cells engineered and behavior, Patterns expres- Experimental GFP activating between RhlR, regions green bind spots. to domains. red lead fluorescent to processes red these free it Collectively, the sion. is allows of IC4HSL IC4HSL is outside of GFP regions Here, S8), rate into Fig. diffusion diffuse and faster to 4 The section (18). 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Bacterial network a of Biology Synthetic (14), Results cells Experimental of mechanism. an population Turing either a expanding show required an which or of or (12) neither (13) time template in biology oscillations initial synthetic on in focused efforts formation have phenom- pattern propagation to Previous front easier (11). even ena it and biological (10) makes the of phenomenon This underpinnings pattern molecular embedded. the are control and they design which into system - -butanoyl- D noreprmna eu,teAO1HLatvtrdiffuses activator A3OC12HSL the setup, experimental our In 1tiglcoyaoie(PG,asalmlcl inducer molecule small a (IPTG), -1-thiogalactopyranoside las B P and yrdpooes epciey oadi experimental in aid to respectively, promoters, hybrid Las−OR1 suooa euioalas aeruginosa Pseudomonas .AO1HLatvtsits activates A3OC12HSL 1). section Appendix, SI L hmsrn atn,dntdhr sIC4HSL, as here denoted lactone, -homoserine hspooe euae xrsino LasI, of expression regulates promoter This . .aeruginosa P. µm N P (-xddcny)homoserine -(3-oxododecanoyl) Las−OR1 2 s h xeietlydeter- experimentally The /s. ). osuypattern-forming study To 1) 3C2S serves A3OC12HSL (15). and eto 3 ). section Appendix, SI CHLihbt syn- inhibits IC4HSL . norsnhtcgene synthetic our In rhl P urmsensing quorum Rhl−lacO ◦ ,and C, µm GFP . 2 rhl /s, A hc sepce odces ciao ptszs hl causing while sizes, spot activator morphogens, decrease both to of expected increased to inhibition is The increases which reporter. used ultimately GFP CI and be of CI range of can from repression LacI cells IPTG expression relieves individual CI system, in IC4HSL affecting pattern- our of by our efficiency In inhibitory in the circuit. outcomes modulate global gene different forming to lead interactions of emergence no showing patterns. section uniform, are Appendix, experiments (SI control both plating after point 5 some at observable cell decisions whether made autonomously fate cells test individual if we emerge would switches, patterns independent differentially toggle harbor that of green/red cells clusters bistable with experiment of an growth performing by 2 outward (Fig. the cells of colored result a ply global a produce and above pattern. profiles multicellular the to according proteins with mir- fluorescence (C, roughly correlates expression. line) line) RFP (green (red expression rors expression GFP RFP while concentrations, proteins. A3OC12HSL reporter of profiles tial aigseiscnetain n1 pc.Tedse rneadblue and (C orange respectively. dashed IC4HSL, The and A3OC12HSL space. to 1D correspond in an lines is concentrations (C, IPTG species dynamics. boxes, boxes. naling system colored white by modulating by indicated inducer are indicated external sequences Genetic are coding with (B) protein regions synthesis, while binding. Promoter their competitive implementation. repressing via species inhibitor circuit A3OC12HSL signaling an by of is repression two synthesis IC4HSL additional catalyzing of while activator an species, consists is both system A3OC12HSL IC4HSL. the and A3OC12HSL Abstractly, (A) formation. 1. Fig. C B A .Tefloecnefilsatr2 ficbto t30 at incubation of h 24 after fields fluorescence The ). cellular lawn et eeaiehwcagsi h tegh flocalized of strengths the in changes how examine we Next, sim- not are patterns our that show we experiments, control In fluo markers diffusible signals p(Lacq) eino ytei utclua ytmfreegn pattern emergent for system multicellular synthetic a of Design p(Las)-OR1 atvtr (inhibitor) (activator) A 3OC12HSL LacI LasR λ PNAS P(R-O1) B etclsieo ellw.Clsexpress Cells lawn. cell of slice vertical A Bottom) IPTG and p(Las)-OR1 RhlR | C ue2,2018 26, June and p(Rhl)- A P 3OC12HSL LasI .Also, 5). section Appendix, SI Rhl−lacO LacO RhlI I | C4HSL CI o.115 vol. pcfial,IPTG Specifically, . lutaino sig- of Illustration Top) dsRed GFP | o 26 no. , Spa- Middle) I C4HSL Space A I GFP RFP C4HSL 3OC12HSL | ◦ in C 6573

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4 2 0 6 pta re parameter order Spatial Θ We model the hybrid promoters using the following Hill F A BC DE Pattern statistics over IPTGtrary modulation unit. for stochastic modeling. a.u., arbi- morphogens A3OC12HSL and IC4HSL, respectively; Fig. 3. ulation experiments andmodulation of simulations. pattern (A)to formation Experimental with specific results microscopy IPTGused images for concentrations for corresponding IPTG in allenced by images IPTG in modulation.experimental (C results. (D)tic Pattern reaction–diffusion obtained model fromIPTG with simulating modulation a for determinis- simulating deterministic our modeling. deterministic (F ral model model (Upper (Lower where are the concentrations of corresponding(AHL) acyl homoserine synthases, lactone respectively; and the system atfollows: the communication signals and protein levels as functions: ) GFI 4 3 2 1 0 µm.) (B) Engineered patterning cells ) cells expressing GFP, and (Right ) Fluorescence density plots com- Mix of red and green cells Green cells only C). In addition to offering further and We first developed a detailed deterministic Green cells only A ) Cells expressing RFP, (Center Red cells only Mix of red and green cells Experimental observations of emergent pattern formation mea- www.pnas.org/cgi/doi/10.1073/pnas.1720770115

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R θ θ and 2 4 v   Y , r the are f X corre- sthe is 2 [11] [10] [12] are [7] [6] [9] [8] K SI .Bt models Both 9B). section includes Appendix , explicitly also (SI and that examined morphogens systems model we the genetic stochastic tails, only the reduced with of these a tail model of developed law stochastic implications detailed power the our a observe understand also ter of we exponent channel, an RFP the For of exponent a exhibits of that behavior spectrum response asymptotic power an the with the noise, Lorentzian, for a white is additive variable random by the driven peri- but damped a deterministic motion executing has odic is that which system a walk, a for exhibits random because that a of spectrum and behavior power diffusing the simply is follows concentration) therefore, (i.e., variable random fol- the as simply interpreted The be lows. can and are respectively, with values noise, patterns additive the Turing exponent deterministic of and The patterns characteristic Turing 25). wavenumber, stochastic exponent of (7, function an source a with noise as wavenumbers, tail spec- law large power power for a the have that will predicts of trum both Theory for reporters. spectrum fluorescent power the our measured we patterns, Turing tic increased, is Turing regular concentration more honeycomb become 3G). IPTG patterns (Fig. deterministic simulated the and a experimental peaks as both in pronounced Moreover, present contain pattern. be 2DFT simulated would experimen- transform the the that Fourier Neither nor 2D 8). 2DFT in section tal and Appendix, space (SI space real (Fig. (2DFT) both model in deterministic simulations the tic dif- for and predicted experiments 3F our those in from observed patterns ferent which the intervals, to and similar intensity, shape, are with size, spot patterns in produce variability generically large model Simu- stochastic deterministic. the as of diffusion lations approximates in morphogens but effects and system proteins our stochastic (SI the in of captures model degradation model and deterministic production This our the in 8). used section stochastic constants Appendix, a rate dif- constructed and reactions, param- biochemical we fusion, of same model, the range using wider deterministic model spatiotemporal a a over can than patterns system eters of our emergence in diffusion the morphogen cause and expression gene ing Turing stochastic for 2.48 of threshold nor- (5–8). a for patterns to 27.8 of patterns threshold Turing a diffusion mal from of formation ratio pattern required for the random constants reduces discrete processes death plankton– with and associated pattern-forming birth noise a patterns the in Turing ecosystem, example, stochastic herbivore For form 10 stringent. to of less order requirements the are the on morphogens factor (1), large two 100 a require by or differ design that rates for- Turing diffusion pattern original with and the In breaking via 28) (7). symmetry mation formation (27, spatial pattern membranes Turing-like whereas exhibit biological particular, that on models in in molecules discovered and recently of been clustering 26). also (25, the populations has of stabilization are oscillations fluc- Noise-driven temporal that systems, drive predator–prey systems in can other example, tuations stabi- in For equilibrium. noise observed of Similar be the out fluctuations. can to the usual phenomena correspond of pat- lization the systems mode The Turing to decaying agent. stochastic destabilizing slowest contrast in a in observed as serves terns form, noise patterns that expectation which in (24). parameters system our fact in that the present suggesting be and numbers, could cells low patterns in of Turing present volume stochastic are small reactants the many to that due noisy stochastic microbes in inherently where expression is regime gene Indeed, the (5–8). within occur patterns still Turing but formed are patterns o h F hne,w bev oe a alwt an with tail law power a observe we channel, GFP the For stochas- observing are we that hypothesis the test further To underly- reactions chemical the in noise whether determine To of range the expands patterns Turing stochastic in Noise .W aecmae h xeietlpten ihstochas- with patterns experimental the compared have We ). rss eas tsalfeunyo wavenumber, or frequency small at because arises, −2 −2.3 −3. ± PNAS 9 0. ± 4 0.4 Fg 4B (Fig. | ue2,2018 26, June .T bet- To 9A ). section Appendix, (SI oe a.The law. power −2 and eto 9A). section Appendix, SI exponent. −4 | o.115 vol. and −2 | o 26 no. arises, −4 for −4 | 6575 k ,

SYSTEMS BIOLOGY BIOPHYSICS AND COMPUTATIONAL BIOLOGY ABCRadial Power Spectrum GFP Simulated Radial Power Spectrum Parameter Range 5 7 10 10 power spectrum trials 4 best fit −2.3±0.2 6 mean power spectrum 10 10 best fit −2.4±0.4

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Fig. 4. Spectral analysis and parameter analysis. (A) Pattern-forming regimes in parameter space and estimated parameters for our system. Parameters above the green surface of neutral stochastic stability can form stochastic patterns, and parameters above the blue surface of deterministic neutral stability can form deterministic Turing patterns. The ratio of the diffusion coefficients ν/µ, the ratio of degradation rate to production rate d/p, and the ratio of production rates are estimated for our system by the yellow ellipsoid. The parameters for our system are mostly in the regime where stochastic patterns form and outside the region where deterministic Turing patterns form. Example stochastic simulations are shown for parameters drawn from a deterministic parameter region with Dν /Dµ = 100 (Upper Right) and a stochastic region with Dν /Dµ = 21.6(Lower Right). (B) Radial power spectrum of green fluores- cence and best fit power law tail with an exponent of −2.3 ± 0.2. (C) Radial power spectrum for eight trials of our stochastic simulation, their mean, and the best fit power law tail.

predict that our experimental parameters will produce a stochas- parameters. Overall, varying the parameters one at a time, 68% tic pattern with a power law tail of −2 for both the activator of the values yield stochastic Turing patterns. and the inhibitor at asymptotically large wavenumbers (Fig 4C To quantify the way in which stochasticity enlarges the pattern- and SI Appendix, section 9C). However, in the range of param- forming regime of parameter space, we simultaneously varied all eters likely to correspond to the experiments (Fig. 4A and SI model parameters and performed the classification used above. Appendix, section 9C), the detailed stochastic model predicts that Specifically, we used Latin hypercube sampling to randomly gen- the exponent of the power law tail for the activator will be −4 erate 500 parameter sets, where all of the parameters were over a large range of intermediate wavenumbers before it even- allowed to vary between 0.5× and 1.5× their nominal value. For tually undergoes a cross-over to a power law with an exponent this analysis, we found that 24.8% of parameters produced unsta- −2 at high wavenumbers (SI Appendix, Fig. S24). This behavior ble fixed points, 43.2% produced stable homogeneous states, once again agrees with our experimental data and supports our 13.2% produced stochastic Turing patterns, and 18.8% produced identification of stochastic Turing patterns. In summary, spectral Turing patterns. Thus, over this arbitrarily large range of param- analysis of the patterns of activator and inhibitor is consistent eters, pattern formation occurs only 18.8% of the time in the with a model in which fluctuations in the amount of signaling absence of stochasticity but 32% of the time when stochasticity is morphogens drive stochastic Turing patterns. included. By including stochasticity, the range in which patterns Our analysis of the stochastic Turing model predicts that can form has been increased by 70%. stochastic patterns form over a wide range of parameters (SI Appendix, section 8). Indeed, our stochastic model predicts that Discussion stochastic Turing patterns are possible at the measured ratio Alternative Hypotheses. Now, we consider alternative hypothe- of diffusion rates for A3OC12HSL and IC4HSL (Figs. 3F and ses to our claim that the theory of stochastic Turing patterns 4A). In addition, to determine the sensitivity of the stochastic explains our experimental observations. We consider the dura- model to the parameters chosen, we individually varied parame- tion and dynamics of our pattern formation experiments. One ters from 0.5× their nominal value to 1.5× their nominal value may expect to observe early events in Turing pattern formation, while keeping all other parameters fixed at their best estimated such as splitting of clusters or increases in intercluster distances. value. For each set of parameters, we calculate the analytical These processes may be, in fact, be taking place but may be dif- power spectrum and the eigenvalues of the Jacobian (linear sta- ficult to observe due to weak reporter expression in the earlier bility matrix) of the stochastic model evaluated at a fixed point stages. In addition, we must consider the limited duration of our found numerically. Based on this analysis (SI Appendix, section experiments and the possibility that, theoretically, longer obser- 8), we classify each set of parameters as producing an unstable vations may result in different patterns if nonlinear processes homogeneous state at wavenumber k = 0, a stable homogeneous eventually began to dominate dynamics. Indeed, we do not feed state, a stochastic Turing pattern, or a deterministic Turing pat- fresh nutrients to sustain the system for extremely long dura- tern. Specifically, we classify a set of parameters as producing a tions. However, as confirmed by analysis of the dynamics in SI pattern if they produce a peak in the calculated power spectrum Appendix, Fig. S12, cluster size growth and spacing between clus- at a nonzero wavenumber. To distinguish between stochastic ters appear to be stabilizing toward the end of the experiment. In Turing patterns and deterministic Turing patterns, we examine addition, domains are neither created nor destroyed in the later the eigenvalues of the corresponding Jacobian. If the real part time periods. Essentially, it appears that the patterns are close to of all of the eigenvalues is negative for all wavenumbers, then stabilizing within the 32-h observation period. the pattern must be due to stochasticity. If there is any range Another alternative hypothesis is that cell growth dynamics of wavenumbers that have corresponding positive real parts of primarily drive the observed pattern formation. Our control their eigenvalues, then the pattern is produced by the tradi- experiments with mixtures of red and green cell populations (SI tional Turing mechanism. The results of this analysis are shown Appendix, Fig. S9) along with our bistable switch control (SI in SI Appendix, Fig. S22 and illustrate the significant ranges Appendix, Fig. S10) suggest that cell growth does not explain for each parameter that can lead to stochastic Turing patterns. our patterns. Moreover, our ability to tune pattern character- Indeed, the estimated parameter values yield stochastic Turing istics offers support for the fact that our patterns are not a patterns and variation of Du , Dv , and IPTG, and several other simple consequence of natural biofilm growth morphologies but parameters never produce deterministic patterns; therefore, our rather, are driven by our genetic circuit. However, growth may results are very insensitive to estimation error of these important indeed impact regularity and may likely explain the fact that our

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SI mixtures as noise with not random experiments and of patterns Turing amplification stochastic Patterns. showing showing for Turing evidence Stochastic our for rize Evidence of Summary our by driven patterns. observed mechanism our Turing explains a circuit strongly genetic that experiments hypothesis our our collectively, support but would support, patterns) further labyrinth in (e.g., offer patterns observed of classes those 3F different (Fig. than show models regular stochastic less our are patterns experimental ai tal. et Karig .ShlsN,Iaa 21)Atrese rmwr o rgamn pattern programming for framework in three-step noise A of (2017) amplification M Giant Isalan (2017) NS, N Scholes Goldenfeld patterns. 9. F, turing Jafarpour Fluctuation-driven T, (2011) Biancalani N 8. brusselator Goldenfeld the in T, by patterns turing induced Butler Stochastic (2010) formation 7. 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Bmp-Sox9-Wnt a by pattern. chemical nonequilibrium Turing-type 64:2953–2956. standing sustained a Sci Biol 12:30–39. hsRvE Rev Phys 237:37–72. urOi hmBiol Chem Opin Curr Science 5:132–134. 81:046215. 334:238–241. hsRvE Rev Phys u atrigsse a osrce sn two using constructed was system patterning Our and a hmBiol Chem Nat 80:030902. ,and S20), and S13 Figs. Appendix, SI 40:1–7. .I addition, In S13 ). Fig. Appendix, SI Bacteriol J .Ide,ftr xeiet to experiments future Indeed, ). hsRvLett Rev Phys .Teemdlpten resem- patterns model These ). 13:706–708. o ytBiol Syst Mol 185:1485–1491. 118:018101. hlsTasRScLn e B Ser Lond Soc R Trans Philos 2:0028. and a Phys Nat IAppendix , SI esumma- We n pFNK512 and 11:1037–1041. hsRvLett Rev Phys hsRvE Rev Phys ilCybern Biol Science Nature and 9 od ,MuaT(00 ecindfuinmdla rmwr o understanding for framework a as model sensing Reaction-diffusion quorum (2010) rhl T and Miura las S, of Kondo Regulation (1997) 19. 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(2006) NAM Monk EA, Gaffney 22. M J, reaction-diffusion Sharpe X, non-gradient Diego in L, formation Marcon Pattern 21. (1994) E Meron A, Hagberg 20. beat able Availability. Code rmteCne o h hsc fLvn el hog ainlScience National through Cells Living 1430124. of PHY Physics Program support Center the Frontiers partial Physics for acknowledges Foundation Center K.M.M. the Laboratory. from discus- Physics Uni- Hopkins for Johns Applied Li, the of Y. versity Program the and Development from Foundation Davidsohn, and support Wroblewska, Science Research acknowledges National Independent N. L. D.K. mutant. and CNS-1446474. NIH Grecu, especially RhlR and the CCF-1521925 C. the by R.W., Grants supported Chen, of of was M. work creation laboratory This in Gupta, sions. the help S. for Sun, of Ku J. members J. thank and We construction. Mehreja We plasmid R. in help thank for also Andriananto E. and modeling ematical ACKNOWLEDGMENTS. cyanobacteria the in of patterns colonies Turing stochastic of observation independent Proof. in Added Note environments. simulation hybrid the (30). a and models using soft- algorithm models C simulation spatiotemporal house-developed stochastic stochastic in developed also using We equations ware. differential integrating cally experimental Modeling. the Mathematical analyzing by software. computed Matlab custom all with collectivity data were spots, microscopy I time-lapse red Moran’s of area and total metric, fluorescence, green averaged rescence, the Analysis. and Data h) (0 experiment h). the (24 of experiment beginning the of the per- end at we cytometry populations, cell flow switch formed toggle of evolution fluorescence single-cell 30 con- of mL 0.5 (60 (29); (OD antibiotics 30 solutions appropriate cell 0.1 at with centrated media reached antibiotics M9 was corresponding in nm resuspended with 600 media at liquid OD LB in grown Procedure. Experimental lEDRFoch0sa?dl=0. techniques. in and recombination here 2 described DNA are and details construction cloning Plasmid standard using constructed . shrci coli Escherichia ilgclptenformation. pattern biological aeruginosa. Pseudomonas in signals. cell-to-cell aeruginosa Pseudomonas of transport n-iesoa ynbceilorganism. cyanobacterial one-dimensional systems. reaction–diffusion of simulations 451:136–140. spatial for methods consortium. biofilm microbial a 104:17300–17304. in consensus a mediates tion polarity. cell membranes. cell on clustering nanometer-scale proteins. of number copy low the to stochasticity. demographic phenotypes. to theories systems. formation pattern Gierer–Meinhardt on delays systems. signals. formation diffusing equally with patterning for networks 5:e14022. turing identifies ysis bifurcations. front of effects The systems: o × ,adfloecneiae eecpue eidcly oeaiethe examine To periodically. captured were images fluorescence and C, 5m er ih ofr ellrlw.Pae eeicbtdat incubated were Plates lawn. cellular a form to dish) petri 15-mm https://www.dropbox.com/sh/di3hbaaubx5qd0q/AADpSOMfJtm Anabaena Nature loecnedniypos oe pcrmo re fluo- green of spectrum power plots, density Fluorescence tanM15 a sdfralexperiments. all for used was MG1655 strain utmcd sdi hsmnsrp scretyavail- currently is manuscript this in used code Custom ulMt Biol Math Bull 454:886–889. fe h opeinadacpac fti ok an work, this of acceptance and completion the After p a eotd(31). reported was sp. etakD ofo n .Dnn o epi math- in help for Danino T. and Volfson D. thank We PNAS a e Genet Rev Nat el abrn prpit lsiswr initially were plasmids appropriate harboring Cells h atrigsse a iuae ynumeri- by simulated was system patterning The hsRvLett Rev Phys 600 Bacteriol J Science | = le 21)Hg-hogptmteaia anal- mathematical High-throughput (2016) P uller ¨ 68:99–130. ue2,2018 26, June )wr ordot %M grplate agar M9 2% a onto poured were 2.0) − hsRvLett Rev Phys 329:1616–1620. .Clswr hncnetae and concentrated then were Cells 0.3. 6:451–464. 179:3127–3132. 94:218102. Nonlinearity IAppendix SI LSBiol PLoS hmPhys Chem J 90:128102. | 16:e2004877. o.115 vol. 7:805–835. ulMt Biol Math Bull Bacteriol J a eal bu the about details has 141:205102. IAppendix SI rcNt cdSiUSA Sci Acad Natl Proc | o 26 no. hmPy Lett Phys Chem 181:1203–1210. 72:2139–2160. section , ◦ until C | 6577 eLife F

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