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Darcy that the scale at magnitude scopic of orders by ments supplies dispersal. that facilitates flow and fluid nutrients the with attenuate cells to tends limited, growth more biofilm much and is space environments, porous In constraints. 1073/pnas.1525228113/-/DCSupplemental at online information supporting contains article This Submission. 1 Direct PNAS a is article This interest. of conflict no declare authors The paper. the and wrote W.M.D. models; and mathematical K.R.F., the E.A.G., developed K.Z.C., W.M.D. and K.R.F., E.A.G., K.Z.C., experiments; uhrcnrbtos ... .. n ...dsge n efre h microfluidic the performed and designed W.M.D. and H.T., K.Z.C., contributions: Author b owo orsodnemyb drse.Eal ei.otrzoo.cu or [email protected] Email: addressed. be may correspondence whom To w.m.durham@sheffield.ac.uk. ei .Foster R. Kevin , r,orrslssgetta el ihnabol a obtain can slowly. the- more biofilm growing classical a by within with advantage cells competitive contrast a that In suggest results competitors. our to ory, instead divert- supply, it nutrient growing own ing fast its A off flow. choke to therefore, can, access strain their cells reduce as dilemma: however, to bac- dispersal; tend fundamental and that they grow, nutrients a for show flow face on We rely environments they habitats. porous these on in of light in teria bodies shed evolve diverse theory—to bacteria two that game how combine communities and we dynamics microbial Here, theory—fluid the them. of within live composition environments importance, the complex their these shape how Despite about little processes. understand we important facil- envi- they porous many where sediments, in itate and live aquifers, soil, bacteria like of ronments, majority overwhelming The Significance b ifim yial eueteflwtruhpru environ- porous through flow the reduce typically Biofilms ofo etefrMteaia ilg,Uiest fOfr,Oxford Oxford, of University Biology, Mathematical for Centre Wolfson PNAS a,c,1 atrawti ifim edt ompatches form to tend biofilms within Bacteria | n ila .Durham M. 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PHYSICS EVOLUTION PNAS PLUS are founded are initially mixed. This genotypic patchiness occurs genotypes were inoculated separately in either arm of the device, because in situ growth, combined with the low mobility of cells each of which represents a pore (Fig. 2 A and B). One of the within biofilms, means that clone mates tend to remain in close pores was irrigated with media mixed with dye, whereas the other proximity to one another (32, 33). Moreover, genotypic patch- was irrigated with clear media, which allowed us to measure the iness in biofilms is enhanced by population bottlenecks, which relative proportion of flow passing through each pore by tracking occur more frequently in nutrient-limited conditions, and when the dye interface downstream of their juncture (SI Text and Fig. biofilms are initiated from a sparse distribution of attached cells S1). Control experiments showed that neither the dye nor the (34–36). Based on these observations, we focus here on the com- fluorescent proteins used to differentially label the strains had petition between localized biofilm “patches” that each comprise an appreciable effect on biofilm formation (Fig. S2). a single genotype and assume that competing patches occupy dif- In porous environments biofilm growth is opposed by flow- ferent pore spaces. induced detachment, which reduces the thickness of biofilms by To investigate how biofilm growth influences the flow through shearing away cells from its surface (40–42). To simulate differ- a porous environment, we calculated the Stokes flow through a ent ambient flow conditions in our experiment, and thus the rela- representative network of pore spaces that is driven by a differ- tive amount of detachment, we applied a total flow rate of either −1 −1 ence in pressure at the boundaries (Fig. 1A and Materials and QT = 0.1 mL h or QT = 2 mL h . In the low-flow treat- Methods). The addition of a small impermeable biofilm patch ment, the rapidly expanding wild-type biofilm increased its pore’s sharply reduces the flow through the pore in which the biofilm hydrodynamic resistance and diverted flow to the neighboring resides, while concurrently increasing the flow through neigh- pore space containing the ∆rpoS biofilm. The reduction in flow boring pores (Fig. 1 B and C). Although the magnitude of this experienced by the wild-type biofilm further reduces its detach- flow diversion depends on the specific geometry of the pore ment, driving a positive-feedback loop that ultimately ends with space, this simulation shows that as a biofilm patch proliferates, the ∆rpoS biofilm capturing nearly all of the flow (Fig. 2 A, C, it tends to decrease its access to flow, while increasing the flow to and D; see SI Text for details). In contrast, under the high-flow patches of biofilm that reside along other flow paths. This diver- treatment, the flow-induced detachment is increased so that both sion of flow introduces a way in which biofilms can interact: geno- genotypes form much thinner biofilms (Fig. 2E), which allows types inhabiting a porous environment can affect one another both genotypes to maintain access to flow for the entire duration via modulating their respective access to flow. This “hydrody- of the experiment (Fig. 2 B and C). Each treatment was repeated namic interaction” differs from interactions observed in classi- three times, and each yielded the same results at steady state cal biofilm assays, where different genotypes growing together (Fig. S3). Access to flow is essential for biofilms to acquire nutri- on flat surfaces typically have to be in close proximity to inter- ents and disperse progeny downstream: these results suggest that act, for example, through capturing one another’s nutrients or the strength of the ambient flow places a key limitation on how via cell secretions. Rather, here we see that in porous environ- rapidly a biofilm can expand without diverting its flow supply to ments, biofilms can influence one another over much larger dis- genotypes that form thinner biofilms. tances, by either curtailing or increasing one another’s ability to capture flow. A Mathematical Model of Flow–Biofilm Interaction Reveals a Diver- Although porous substrates harbor many biofilm patches that sity of Competitive Regimes and Enables Prediction of How Cell Dis- can simultaneously perturb one another’s flow environment, we persal Varies in Experiments. Our microfluidic competition exper- idealize this network of interactions as a collection of its con- iments suggest that hydrodynamic interactions between biofilms stituent pairwise interactions. We then resolve the dynamics can profoundly affect genotypic competition. To understand this of competition between a single pair of biofilm patches, each process better, we next developed a model that couple two com- of which is composed of a different genotype. In this pairwise peting biofilms with a model of flow, enabling us to explore a approximation, the proportion of the total volumetric flow rate, much wider range of competitive scenarios. Whereas the two Q T , that passes each biofilm is a function of the hydrodynamic pores in our experiment are strongly coupled, such that flow resistance of both its pore space and that of its competitor, each diverted from one pore is fully absorbed by the other pore, of which, in turn, is a function of the thicknesses of the biofilms, in a network of pores, the strength of the hydrodynamic cou- k k D E 1 and 2 (Fig. 1 and ). In this model, the growth of a biofilm pling between two competing biofilms will vary depending on tends to decrease its access to flow and increase the flow past the geometry of the pore space and their relative proximity to F its competitor (Fig. 1 ). Importantly, our pairwise model cap- one another (Fig. 1 A–C). To account for this variability, we tures the dynamics observed in our Stokes flow simulation but consider two identical fluid pathways of width 2L colonized by is much more tractable and easily parameterized. Flow through biofilms of thickness k1 and k2, which are connected in par- a network of pore spaces can be modeled by fixing either the allel to a channel of width 2M that does not contain biofilm pressure gradient or the flow rate at the boundaries (37), with (Fig. 1 E). The dimensionless parameter M ∗ = M /L then mea- the former better characterizing flow through natural systems. sures the ability for the two biofilms to influence one another However, localized biofilm growth in either of these scenarios via flow: M ∗ = 0 corresponds to the strong coupling observed will produce a flow diversion at the pore scale, as observed in our in our experiments (which lack a third channel without biofilm), conceptual model. whereas for increasing M ∗, flow is more likely to be diverted around the focal biofilms as they proliferate. Importantly, for ∗ Microfluidic Experiments Show That Rapidly Expanding Biofilms Tend M > 0, both biofilms are capable of clogging. This model then to Divert Flow to Biofilms That Increase in Thickness More Slowly. provides a tractable way to resolve how changing the strength We next developed a microfluidic version of our pairwise flow of the hydrodynamic interaction between two biofilms affects model to experimentally test how pore-scale hydrodynamics their dynamics, without requiring an explicit representation of affects the competition between genotypes that form biofilms the pore structure. at different rates (Fig. 2 and Fig. S1). Our experiments used a A wide range of physical and biological processes can affect well-studied Escherichia coli experimental system. Specifically, biofilm development (43); however, the thickness of biofilms in we competed wild-type E. coli cells with ∆rpoS cells. The lat- flowing environments is chiefly governed by the balance between ter cells lack the ability to produce the sigma factor RpoS and, cell division and flow induced detachment (44, 45). Cell divi- as a result, form biofilms at a much slower rate than the parental sion in biofilms is often confined to a layer at the exterior of genotype (Fig. 2G and Fig. S2, and refs. 38 and 39). The two the biofilm, where substrates are exposed to nutrients from the

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PHYSICS EVOLUTION PNAS PLUS Fig. 2. Microfluidic competition experiments show biofilms that rapidly increase in thickness tend to divert flow to biofilms that expand more slowly. (A and B) The left pore of each device was seeded with wild-type cells (green), whereas the right pore was inoculated with ∆rpoS cells (red). Dyed media flows through the left pore, whereas clear media flows through the right pore. The dye interface downstream of the two pores (yellow line) allows us to dynamically track the proportion of the total flow, QT , moving through each pore space (Materials and Methods). (C) Following the movement of the dye interface (hD/HD, yellow circles in A and B) shows that in the weak-flow treatment (A) the wild-type biofilm diverted nearly all its flow supply after 38 h, such that, subsequently, the dye interface was not detectable at the measurement location (SI Text). However, in the strong-flow treatment (B) both biofilms are able to maintain access to flow for more than 70 h. (D and E) In the weak-flow treatment the wild-type biofilm (green line) increased in thickness, k, faster than the ∆rpoS-null biofilm (red line), which was responsible for the diversion of flow. In strong flow, both biofilms were thinner, such that the difference in biofilm thickness between the two strains was smaller. Shaded regions show the standard deviation about the mean (Materials and Methods). (F) A magnified view of the biofilms shown within the dashed black rectangles in A and B. (G) The observation that wild-type biofilms expand at a faster rate than ∆rpoS biofilms was confirmed in separate microfluidic experiments that exposed attached cells to much smaller shear stresses than in the competition experiment, which minimized the effect of flow induced detachment (SI Text). The upstream arms of the microfluidic devices used in the competition experiments (A–F) have a width of 2L = 65 µm and depth of 2B = 75 µm (Fig. S1).

to cell division is then given by the product of the growth rate, detachment of cells due to mechanical forces exerted at the sur- α, and min(δ, k), such that dk/dt = α min(δ, k), which takes into face of the biofilm by fluid motion (40). Although the literature account that the entire thickness of a biofilm is actively growing contains a diversity of parameterizations to model flow-induced when k < δ. Increases in biofilm thickness are countered by the biofilm detachment (see ref. 49 for a comprehensive review), a

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PHYSICS EVOLUTION PNAS PLUS by flow-induced detachment and that bacteria do not actively indicates that flow diversion can dramatically affect a biofilm’s regulate their propensity to detach. capacity to shed cells downstream. The results from the model are in broad agreement with the two distinct flow regimes observed in our microfluidic exper- The Impact of Flow on the Evolution of Bacterial Growth Rate. Our iments, which show that the wild-type biofilm growth tends model shows that a biofilm’s fate depends not only on its growth to reduce its access to flow at smaller flow rates (equivalent to rate but also on the behavior of other biofilms elsewhere within smaller β∗; regime f in Fig. 3) but is able to maintain access the porous network. However, how do hydrodynamic interac- to flow at larger flow rates (equivalent to larger β∗; regime tions between genotypes impact bacterial evolution? Over evolu- b in Fig. 3). Although we could not directly measure rates tionary timescales, it is expected that biofilm patches will repeat- of cell dispersal in our experiments, we combined our exper- edly form and dissipate as a result of both natural processes and imental data with a mechanistic model to predict how dis- human intervention [e.g., predation (56, 57), enzymatic decay persal rate of each genotype changes over the course of our (58), and the periodic flushing of a porous filtration systems microfluidic experiments. First, we developed a model to trans- (59)]. This continual turnover of biofilm patches means that if late the position of the dye interface hD into the volumet- new genotypes are introduced into a network of pore spaces— ric flow rates qi that pass through either arm of the device. whether through in situ mutation or immigration—then they will This information was then combined with measurements of the be able to form new patches and potentially compete with the biofilm thicknesses, ki , to estimate the shear stress, τi , acting resident genotype over many iterated rounds of competition. on the surface of either biofilm. Finally, both τi and ki Our model can then be used as a tool to measure the compet- were used as inputs in the model of flow-induced biofilm itive ability of a newly introduced genotype, allowing us to infer detachment explained above (see SI Text for details). This how its frequency will change in the population over time. analysis shows that in the high-flow-rate treatment (QT = To resolve how the bacterial growth rate would evolve over 2 mL h−1), both biofilms gradually increase their dispersal rate many successive rounds of competition, we embedded our until beginning to plateau after approximately 40 h (Fig. S5). In mechanistic model of flow–biofilm interaction within a game −1 contrast, in the low-flow treatment (QT = 0.1 mL h ), the wild- theoretical framework known as adaptive dynamics (60). Specif- type biofilm rapidly increases its dispersal rate until it begins to ically, this invasion analysis tests whether a novel genotype that divert its flow supply, which then causes a precipitous decrease grows at rate αM will be able to increase in frequency and ulti- in dispersal (Fig. S5). Although the dye interface cannot be mea- mately supplant a population of biofilms that grow at rate αR sured once the ∆rpoS flow path has captured ≈95% of the flow based on their relative fitness (Materials and Methods). Because (owing to the diffusion of the dye) (SI Text), by this point, our the ability of a biofilm to seed new patches is expected to increase analysis predicts that dispersal rate of the wild-type biofilm has with its rate of dispersal, we again use dispersal as a metric to already dropped nearly threefold from its peak value. During quantify evolutionary fitness. A matrix of different αR and αM the same time period, the ∆rpoS biofilm is predicted to sharply values is used to construct a so-called pairwise invasibility plot increase its rate of dispersal as it takes on the extra flow from (Fig. 4 and ref. 60), which systematically delineates the growth the wild-type biofilm. Although we cannot predict how the two rates for which a novel mutant can invade and displace the res- genotypes differ in their rate of dispersal (SI Text), this analysis ident population. This representation then allows a generalized

A 1.6 B 2 αESS ESS - α 1 0.75 β* 1.25 C 2 ESS + α 1 0.25 0.35 αM + δ* D 3 ESS - α 1 0.75 M* 1.25 E 4 ESS 0.6 α 2 0.6 1.6 0.3 αR 0 Φ*

Fig. 4. A game-theoretical analysis of the coupled biofilm model predicts an evolutionary stable growth rate. (A) We used adaptive dynamics to construct a pairwise invasion plot, which maps the region of parameter space where a mutant that grows at rate αM can invade a resident population of biofilms that grows at rate αR. The mutant can invade in the dark blue regions (+) and cannot invade in the light blue regions (−). In the white regions, the mutant and the resident biofilms both have a fitness of zero (Wi = 0) because they have either been fully detached by flow or have blocked their pore space. Arrows show an example evolutionary trajectory where mutant genotypes successively replace the resident population, driving the growth rate toward the ∗ −1/2 ∗ −1 ∗ ∗ ∗ evolutionary stable growth rate, αESS (red circle). Here, we set δ = 0.3αR and β = 1.1αR , M = 1, and Φ = 0. (B–E) To determine the effect of β , ∗ ∗ ∗ δ , M , and Φ on αESS, we held three of these parameters constant and varied the fourth (red circles show fixed values).

E166 | www.pnas.org/cgi/doi/10.1073/pnas.1525228113 Coyte et al. Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 ifim,last euto in reduction a to increas- process: leads this biofilms, influences also structure ing porous the of smaller ity a to plentiful—leads thickness edge ing larger a to 4 (Fig. how conditions ing environmental resolve the We of state. function steady cells fewer at disperse will downstream at latter the grows strain, that slower-growing a pore biofilm against its a at block when will grows latter Conversely, the that space. strain, biofilm faster-growing a a against when petes Intuitively, stable 4A). evolutionary rate a (Fig. reaches growth it the until geno- value, increase population new resident systematically of the to arrows) of predicted 4A, are (Fig. However, invasions types 4A). successive (Fig. population time, resident over the than larger slightly evo- over rate growth (60). population’s timescales a lutionary of trajectory the infer to way eut niaeta h ocuin foriiilmdlstill model initial al. et Coyte our of conclusions could the these interdependencies evolution, that and phenotypic indicate competition results other microbial that affect blocking Although qualitatively possible 4E). for (Fig. is potential rate the growth it stable increasing evolutionary that the idea reduces smaller predicted the a the with in that sistent reduction reveals additional a model this addi- to game-theoretical this leads of our to inclusion robust in the are term weak, Moreover, is dependency. flow but tional when rapid against is flow selected when are favored (Φ are S6 model genotypes faster-growing original (Fig. that our from same conclusions the the Thus, remain qualitatively regimes depen- competitive another various new the this the of of in locations inclusion the the Intu- changes Whereas dency space. processes. pore two its these block larger between a coupling itively, stronger assume a 3) cates (Fig. nondi- simulations the initial with our detachment and parameter growth mensional of between strength radiolabeled coupling the using measures the quan- parameterization environments This empirically porous sources. who in carbon parame- (62), coupling the DiGiano this using and tified model Speitel our of extended terization we bac- competition, influences model detachment terial To and 66). growth ren- (55, between morphologies, covariance detachment how to fragile susceptible growing more more rapidly them with because dering biofilms or (63) form together genotypes sub- cells exopolymeric glue of that secretions fast- stances in because flow-induced less occur invest to may genotypes growing dependency susceptible This more (62–65). detachment phenotypic are other that biofilms shown its have faster-growing from experiments previous independently However, vary characteristics. can rate Bacterial growth of Affect Predictions. Rates Qualitatively Not Our Does Between Detachment Flow-Induced Covariance and Growth Potential for Accounting liq- within the as for 61). selects such (16, evolution with genotype where assays, fastest-growing chemostats, contrast or laboratory stark cultures batch typical in uid in stand and observed environments that porous growth bacterial in of rates evolution fun- the a on places limitation blocking physical pore damental that slower-growing suggest com- of results around evolution These divert the genotypes. to promote layer flow would for growing biofilms, ability peting increased increased block- rates, an for flow or potential thickness, lower the through increasing whether that ing, idea the with consistent efidta uat a naeol hntergot aeis rate growth their when only invade can mutants that find We M β ∗ α ∗ freape yicesn h oa o rate—leads flow total the increasing by example, —for [ α hc nrae h blt fflwt yastefocal the bypass to flow of ability the increases which , ESS ∗ β , fe hc,n e eoye ilb bet invade to able be will genotypes new no which, after , α ∗ ] ESS hs ln,terpstoswt epc oone to respect with positions their plane, phase Φ u nlssaoeasm htabiofilm’s a that assume above analyses Our hl nraigtenniesoa grow- nondimensional the increasing while , ∗ δ eue h oeta htagntp will genotype a that potential the reduces ∗ Φ a a cu hnntinsaemore are nutrients when occur can —as ∗ IText (SI α ESS α n es 5ad6) although 62): and 55 refs. and ESS oevr h connectiv- the Moreover, . α l fteeted are trends these of All . Φ ESS ∗ 0 = hc saancon- again is which , larger a , α ESS α .Increas- B–D). ∗ ESS and 0 = α aisa a as varies ESS competes ,namely ), IText). SI Φ ∗ com- indi- Φ ∗ ye ihnte fetmcoilcmeiin hl u work our While competition. microbial geno- affect different them of distribution within the types and space pore the of structure to needed pro- the be impact will traits here. microbial described work of cesses diversity Further wide 83). the how (82, resolve (81), motility metabolism (80), cell sensing (78), and quorum polysaccharides condi- 79), extracellular nutrient (30, formation of or streamer hydrodynamic production the 77), of which (21, function biofilm adhesion, tions a cell influence be initial exten- can itself of traits for may strength microbial potential the Many including considerable work. formation, is our complexity there to the so sions simplify systems, greatly these assumptions of most Our where live. environments porous bacteria complex compete the bacteria within how evolve assays. understand and to biofilm fluid theory, including simple game theory, and of in focuses dynamics bodies or bacteria diverse combined cultures on have liquid we work Here, in of behavior majority their vast on the However, study. depriva- nutrient 76). to (75, sensing response quorum in detachment flow. and tion empirically to increased observed access hypothesis, been regain this has to with masse consistent favor en Broadly may detaching selection natural periodically occur, cells does distribu- In blocking exclusion. uniform where competitive more promote systems may a which and spaces, bioreactors pore flow of packed-bed of tion rates and constant nearly aquifers How- have (74). groundwater sizes some particle different and ever, rainfall mix of that patterns episodic processes to variablity geological due This common be diversity. to promote expected and will is flow size in pore fluctuations in temporal heterogeneity that expect We environments. blocking objective. where main sti- the contaminants, to is groundwater biobarriers of of movement where design the systems, the fle in treatment or water efficiency, effective reduces of implica- blocking design has the information for Such tions blocking. con- promote laboratory would homogeneous biofilms ditions in from of evolved cells growth inoculating have whereas that the space, communities pore favor their would block not system do that porous the from a cells of of that community effluent suggest a findings with our substrates Moreover, porous inoculating (73). that rates bacteria different of species at multiple grow maintaining by reactors reme- enhanced porous the the be favor in can contrast, to wastewater In way mercury-contaminated latter. a of the be diation over may bacteria rate of flow species larger former a using pre- often that work then inhibit into Our dicts (72). products to contaminant environmental these desirable potent oxidize a is nitrate, porous further it that in but species bacteria example, nitrite, slower-growing of to For species ammonia scales. fast-growing convert time relatively reactors, longer wastewater over growth different active with species rates multiple par- keep a or with rate species growth bacterial ticular a favor to systems microbial engineer to rates 3). growth (Fig. different flow with to conditions access biofilms flow maintain allow weak rates and flow inter- whereas mediate strong respectively, biofilms, relatively slow-growing and fast- that com- favor genotypes find different We how pete. affect dramatically hydro- can the media dynamics porous that and proliferation show biofilm analyses mathe- between feedback game-theoretical experiments, and proof-of-principle modeling, industry Our matical and 67–71). environment 24–26, natural the (8, range in wide processes a important facilitate of environments porous in growing Biofilms is detachment Discussion and growth between dependency included. a when hold uueefrswl lob eurdt eov o h specific the how resolve to required be also will efforts Future theoretical and empirical intense of subject the are Bacteria natural in compete cells how on light shed also may results Our to exploited be could principles these settings, industrial In PNAS | ulse nieDcme 2 2016 22, December online Published | E167

PHYSICS EVOLUTION PNAS PLUS predicts that bacteria can benefit from making less biofilm when the same result at steady state (Fig. S3). The time points shown in Fig. 2 and growing in a clonal patch, this may change in mixed-genotype Figs. S3 and S5 are measured from the end of the inoculation phase. biofilms, where the priority may shift to locally outgrowing com- petitors (84). It is interesting, then, that bacteria are known to Mechanistic Model of Biofilm Competition. Our mathematical model of respond to competing strains by increasing their investment into biofilm competition simulates the two processes that are predicted to dom- biofilm (85). inate biofilm development in flowing environments: bacterial growth and In sum, our approaches indicate that porous habitats, and the the flow induced detachment (45, 52). The differential equations that gov- flows within them, can have a profound impact on bacterial evo- ern the thicknesses of the two biofilms ki (Eq. 1) are hydrodynamically cou- lution. Although rapid division gives a microbe an evolutionary pled using an approach that is widely used for low Reynolds number flows advantage in typical laboratory environments, our results suggest (92). Specifically, we consider three flow paths of equal length connected in parallel, so the total volumetric flow rate, Q , divides among the three that this paradigm does not extend to many bacterial habitats. T pathways as a function of their hydrodynamic resistances, Ri. Poiseuille’s law states that qi = dP/Ri, where qi is the flow rate along each path, −dP is the Materials and Methods 3 drop in pressure across the system, and Ri = 3µ/4B(L − ki) is the hydrody- Modeling Stokes Flow Through a Representative Network of Pore Spaces. namic resistance per unit length of each flow path, where µ is the dynamic The geometry of the pore space (Fig. 1 A–C) was obtained using Parti- velocity of the fluid, 2B is the span wise dimension of the pore space, 2L is cle Flow Code in Two Dimensions (Itasca), which models the mechanical the pore width and L  B. processes that form many porous substrates. The particle locations were All three flow paths experience the same difference in pressure, dP = then imported into COMSOL Multiphysics to model incompressible Stokes QT RT , which is determined by the effective resistance of the entire system, flow within the pore spaces between the particles using the finite element RT , where (92) method. Zero-flux, no-slip boundary conditions were used at the left and 1 1 1 1 right boundaries of the computational domain as well as on the surfaces of = + + . [2] all of the particles. At the top and bottom boundaries of the computational RT R1 R2 R3 domain, the pressure was fixed at two different values, such that the result- ing pressure gradient was responsible for driving flow. The Stokes equations Solving for dP and substituting into the equation for qi yields were solved with and without the presence of a biofilm patch in one of the QT 1 pore spaces. Results were then exported into Matlab 2015a (MathWorks) for qi = , [3] R 1/R + 1/R + 1/R further analysis and plotting. i 1 2 3 which, can then be written in terms of the biofilm thicknesses, Bacterial Strains and Culturing. Our experiments used E. coli strain K12- 3 W3110 and a mutant with a rpoS819 allele insertion (86, 87). Each strain (L − ki) q = QT . [4] i 3 3 3 was labeled with either green fluorescent protein (GFP) or red fluorescent (L − k1) + (L − k2) + M protein (RFP). Cell cultures were grown overnight in tryptone broth (1× TB) ◦ (10 g of Bacto Tryptone per 1 L of water) at 37 C, diluted to an optical den- This expression conserves flow, so that QT = q1 + q2 + q3. We note that sity of 0.1 (at 600 nm), and then grown for a further hour at 37◦C so that the approach used here is analogous to that routinely used in the analysis cells were in exponential phase when they were first introduced into the of electric circuits (92). microfluidic devices. Our equation for hydrodynamic resistance assumes pressure-driven, pla- nar flow between two parallel plates separated by a distance 2(L−ki), where dP 2 2 Competition Experiments. Microfluidic device masters were fabricated from the velocity profile in the ith channel is given by u(y) = 2µ (y − (L − ki) ) SU-8 on silicon wafers using standard soft lithography techniques (88) and and y is the distance from the centerline of the channel. Thus, the hydrody- were cast with polydimethylsiloxane (PDMS) (Sylgard 184; Dow Corning). namic shear stress acting on the biofilm is given by The depth of these devices was 2B = 75 µm (Fig. S1). Cured PDMS was du 3µq bonded to glass coverslips (50 mm × 75 mm; no. 1.5 thickness; Agar Sci- τ = µ = i , 2 [5] entific) with a corona discharge system (BD-20AC; Electro-Technic Prod- dy 4B(L − ki) ucts) using previously described techniques (89). Tygon tubing (0.51-mm where du/dy has been evaluated at the biofilm’s surface, y = L − k . inner radius; Microbore) was used to plumb the inlets and outlets of the i Combining Eqs. 1, 4, and 5 yields the coupled differential equations that device. −1 govern k1 and k2, the thicknesses of the two biofilms: For the high-flow-rate treatments (QT = 2 mL h ), the outlet was con- nected to a 140 mL syringe (Harvard Apparatus), which was mounted on s 2 s dk1 3µQT χ (L − k1) a Harvard Apparatus PhD 2000 syringe pump. In the low-flow treatments = α1 min(δ1, k1) − k1 , [6] −1 dt 4B (L − k )3 + (L − k )3 + M3 (QT = 0.1 mL h ), the outlet was connected to a 20-mL syringe (Becton 1 2 Dickinson) mounted on a Harvard Apparatus PhD Ultra syringe pump. After the microfluidic device and tubing were primed with 1× TB to s 2 s dk2 3µQT χ (L − k2) remove air from the system, cells were introduced into the device by pulling = α2 min(δ2, k2) − k2 . [7] 3 3 3 cultures of the wild-type and ∆rpoS mutant cells through the device at dt 4B (L − k1) + (L − k2) + M Q = 0.1 mL h−1. Unlike many biofilm experiments, where cells are allowed T We nondimensionalized the governing equations above using the pore half- to attach to surfaces in the absence of flow (e.g., refs. 17, 90, 91), we width L as our characteristic length scale and the reciprocal growth rate of inoculated cells under flow to help keep the two strains confined to their strain 1, 1/α , as our characteristic time scale, such that k = Lk∗, k = respective pore spaces. Cultures of the wild-type and ∆rpoS mutant were 1 1 1 2 Lk∗, M = LM∗, and t = t∗/α . We obtain the dimensionless equations simultaneously drawn through the device for 20 h to allow cells to attach 2 1 and then we switched over to withdrawing tryptone broth (0.5× TB) (5 g s dk1 ∗ ∗ (1 − k1) of tryptone per liter of water) through the device for a further 48 h so that = min(k1, δ ) − β k1 , [8] dt θ a thin biofilm was established in each of the pore spaces. We initiated the biofilms in the high- and low-flow treatments in the same way in the first s  ∗  3 d of the experiment to ensure that the cell attachment was similar dk2 ∗ δ ∗ (1 − k2) = α min k2, √ − β k2 , [9] between the two treatments. After this initial inoculation phase, we con- dt α∗ θ nected one of the inlets of the device to a reservoir containing tryptone broth (0.5× TB) mixed with dye (Chicago Blue; Sigma Aldrich) that enabled where θ = (1 − k )3 + (1 − k )3 + (M∗)3, [10] us to dynamically track the relative proportion of flow passing through each 1 2

side of the device. where we have omitted the asterisks from ki and t for clarity. These equa- After the initial inoculation phase, we applied a flow rate of QT = tions were solved numerically using Matlab. Specifically, we initialized two −1 2 mL h in the high-flow-rate treatment, whereas in the low-flow-rate pore spaces with a thin layer of biofilm, k1 = k2 = 0.01, similar to the −1 treatment, we used a flow rate of QT = 0.1 mL h . We imaged the devices initially sparse seeding of cells in our experiments (Fig. 2 and Materials and every 30 min for the next 70 h, which allowed both treatments to reach a Methods, Competition Experiments) and then integrated the dimensionless steady state. Each treatment was repeated three times, and each yielded equations until each biofilm had converged to a steady state thickness.

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A and Aertsen decay CW, the Michiels P, for Moons model Physical 12. (2007) DC Forney DH, Rothman 11. 2 hlnrM(00 oprsno icogn fet nstrtdpru media porous saturated in effects bioclogging of Comparison (2010) M Thullner 22. Øvre V, Torsvik 10. 8 hfh ,VfiK(09 ifimafce hrceitc fpru structures. of porous of Influence characteristics affected (1991) Biofilm (2009) D K Vafai Crawford M, Shafahi F, 28. Abedeen W, porous the Characklis to related AB, as morphology Cunningham Biofilm 27. (2010) YA Pachepsky H, Choi partic- and JW, with Kim treatment plugging Wastewater 26. (2000) selective JJ Heijnen Microbial MC, Loosdrecht (1989) van C, MJ. Nicolella McInerney 25. RM, Knapp barriers RA, biofilm Subsurface Raiders (2003) 24. G James R, Hiebert RR, Sharp AB, Cunningham 23. reult hto h eietcmeigaantitself, against competing resident the of that to equal or ospln h eietgntp.Frt h teso h uatwhen mutant the “mutant” of a fitness denoted for the resident, hold First, the then genotype. against must competing conditions resident Two the 3). supplant properties (Fig. biofilm the to space and of rate, pore rate growth the competitor’s the its of to rate, equal growth its is of which function (Eq. state, state steady steady at at growth dispersal cell of rate a osdrtepiws neato fanvlgntp htgosat at grows growing that we population genotype resident that novel monomorphic means a a of assumption with interaction This pairwise genotype (94). the new mutation consider population a can which situ resident at the in rate displace through the introduced can with spaces—either are compared pore small genotypes interacting immigration—is novel or of which group at a adaptive rate envi- Specifically, into the porous genotype. a that displace “resident” assumes and by dynamics invade to colonized able already exam- is analysis ronment genotype This new 93). a (60, presented whether framework ines model dynamics mechanistic adaptive an the within embedded above we evolution, biofilm impact Analysis. Theoretical Game ot tal. et Coyte .GireW,Wlo T(98 irba clg ftetretilsubsurface. terrestrial the of ecology Microbial (1988) JT Wilson WC, majority. Ghiorse unseen The 9. Prokaryotes: (1998) WJ Wiebe DC, Coleman micro- WB, of Whitman frontiers the expanding 8. Microfluidics (2014) R Stocker M, Garren R, evolution. Rusconi and ecology 7. microbial in genomics Community (2005) JF for Banfield ‘omics’ EE, molecular Allen Integrating beyond: 6. and Sequencing (2015) al. on et perspective EA, ecological Franzosa An (2004) 5. BJM Bohannan KM, Carney MC, Horner-Devine allo- 4. 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R nio c Technol Sci Environ ,ms elre than larger be must ), itcnlBioeng Biotechnol α R . plEvrnMicro- Environ Appl W (α a e Micro- Rev Nat irmda J Bioremediat R , α idtype, wild rcNatl Proc R rtRev Crit W .This ). 97(6): 25(7): sa is , n J Int Proc Adv α M 4 ir ,Fse R(03 eoyi iwo oilitrcin nmcoilcommu- microbial in interactions social of view genotypic A (2013) KR Foster S, Mitri 34. groups cell into Insights in (2014) structure al. spatial et YA, of Millet Emergence 33. (2010) JB Xavier KR, clog- Foster biological CD, of Nadell modeling 32. Pore-scale (2001) PL McCarty PK, Kitanidis HJ, Dupin catastrophic 31. cause streamers Biofilm (2013) HA Stone BL, Bassler MCM, Y, Shen Loosdrecht K, Van Drescher C, 30. Picioreanu TRR, Pintelon DA, Schulenburg der von Graf 29. 3 anrO ue 18)Amlipce ifimmodel. biofilm multispecies A (1986) W Gujer biofilm one-dimensional O, of Wanner behavior Longtime 53. (2012) HJ Eberl modeling. 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Kov OP, Kuipers FJ, Weissing J, Gestel van 36. nfeunywti h ouain eod h teso h eietwhen resident the mutant, of the fitness increase against the gradually competing Second, to population. able the is within mutant frequency rare in initially an whether tests condition uatcmeigaantitself against competing mutant w rtrams odframtn oivd eietpopulation: resident a invade following to system the mutant formally, the a More for reinvade frequency. hold to must in criteria able increased two be has will mutant the strategy once growth resident original the a uddb uoenRsac oni rn 460 n ...was W.M.D. LT001181/2011L. and Fellowship Program 242670, Science Grant Frontier Council Human by Research funded European K.R.F. Council, by Research Sciences funded Physical was and Engineering the by funded was the ACKNOWLEDGMENTS. of trajectory evolutionary the 4 infer (Fig. to plot used invasibility rate. be pairwise growth can population’s a which construct 60), to ref. used and then are criteria These nities. bacteria. labeled fluorescently itoring cooperation. of evolution the and approach. mechanics material A 37(12):2965–2979. expansion: aggregate to due ging systems. medical and environmental USA Sci for Acad consequences Natl with flow of disruption media. porous in growth biofilm of Journal simulations AIChE Three-dimensional (2009) ML Johns oeswt ha eedn eahetrates. detachment dependent shear with models Canada). Guelph, Guelph, of (University thesis PhD 24(2):501–506. 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