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(11, the film (13, gradients temperature to thin by similar a induced gradi- ents of is surface-tension spreading spreading generates mechanism forced gradient-driven essential pellicle The surface-tension spreading. liquid of cooperative drive a that in ents cells by biofilms of spreading the unknown. the remains on of surfactin consequences physical of the behavior the However, surfactant-like 10). for (9, necessary flows fluid be nal to of known colonies of is spreading surfactin species biosurfactant bacterial the different antago- (8) of in colonies (7), between structures interactions aerial nistic of of development being the to advection addition in propagative In implicated the flows. such fluid as but dispersive on (6), such depend biofilms mechanisms processes propagating in passive individual aggregates of cell of and role the motility highlighted cell have physical studies nutrient the between Previous about or sources. over known spread is colonies these little which very ini- by processes that 5), pathways (4, signaling growth the biofilm and on tiate other and each (1–3) to substrates abiotic bind to that adhesins studies the recent on many focused Although have . to resistance and viru- enhanced lence with bacteria pathogenic endow Biofilms charides. B hydrodynamics thin-film | biofilms bacterium The Angelini E. Thomas surfactant of subtilis w.nsog/ci/di/1.03/pnas.0905890106 / 10.1073 / doi / cgi / www.pnas.org o otoln h pedo biofilms. of spread methods nutri- the dispersal nonintuitive of controlling to enhanced for range points of and broader evidence motility, cooperative provides a through study of This digestion sources. chem- enable tive or and heat, populations stresses, predation, bacterial as ical protect such challenges to environmental known from waves. are surfactant to associations Com- viscosity. rise munity biofilm increasing give with film increases that flux bacterial spreading by model The the induced of mathematical rates structures. geometry accumulation a aerial the differential of and the formation how experiments the demonstrate present in we sur- aid the to Here of tension and surface fluid, the rounding lowering colonies by multicellular substrates of spreading nutrient the on enhance to known is which dtdb .PtrGeneg nvriyo ahntnSho fMdcn,Sate A n prvdAgs 8 09(eevdfrrve a 8 2009) 28, May review for (received 2009 18, August approved and WA, Seattle, Medicine, of School Washington of University Greenberg, Peter E. by Edited aoaoy nvriyo aiona ekly A970 and 94720; CA Berkeley, California, of University Laboratory, colo niern n ple cecs avr nvriy abig,M 02138; MA Cambridge, University, Harvard Sciences, Applied and Engineering of School odmntaetemcaimo olciesraig efirst we spreading, collective of mechanism the demonstrate To develops gradient surface-tension a context, present the In surfactin of concentration the in gradients that show we Here cei idt ufcsadt iudaritrae oform exopolysac- to by interfaces together cemented liquid–air cells of to mats thick and biofilms, surfaces to bind acteria ailssubtilis Bacillus a,1 acsRoper Marcus , ailssubtilis Bacillus rdcstemlcl surfactin, the produces b,1 nteasneo exter- of absence the in ped ysrn nwaves on surfing by spreads oet Kolter Roberto , c eateto irbooyadMlclrGntc,HradMdclSho,Bso,M 02115 MA Boston, School, Medical Harvard Genetics, Molecular and Microbiology of Department c ai .Weitz A. David , implying where uatsrfAA mutant n.Ters egto udwti h ue(h tube the within fluid of height enter- from rise dial- bacteria The a prevents surfactin but ing. with and capillary medium sealed the enter film nutrient is to the climbing capillary allows the the which of of membrane, end base plac- ysis bottom the by The near surfactant 2B). tube of (Fig. capillary levels 0.87-mm the a monitor ing directly we spreading, ftehih ftebol si lmstewl ssoni i.2 Fig. in shown is wall the climbs dependence it time as biofilm The the (15). of height motility the swarming of to due spreading rapid colonies the of with comparable vessel. mm/hr, exceeds conical conditions typically environmental the but to sensitive of of is climbing walls film wall thin the of speed a up The cells, dragged of is pellicle 12 a fluid Approximately of bacteria-laden appearance cells. sur- first packed free the tightly the the after of to hours in biofilm diffuse oxygen a or the forming swim bacteria face, After the freely. depleted, planktonic swim is a medium and in in multiply culture shown liquid initially is the medium state into liquid introduced with Bacteria filled 1. partially Fig. vessel conical young a a of in thin periphery a the of at move development film The bacteria climbing boundary. we which nonnutritive in inclined spreading, an scenario, cooperative up spreading of primitive physics a consider underlying the expose To Results hsatcecnan uprigifrainoln twww.pnas.org/cgi/content/full/ at online information supporting 0905890106/DCSupplemental. contains article This [email protected]. or [email protected], rsue eo h interface: the below (γ pressures tension surface the to pedn,tehih rp tterate the at drops height the spreading, hsatcei NSDrc Submission. 1 Direct PNAS a is article This interest. of conflict paper. no the declare wrote authors and The data, analyzed tools, performed reagents/analytic research, new designed M.P.B. contributed and research, D.A.W., R.K., M.R., T.E.A., contributions: Author ount al evn hnfimo h nieo h tube the of inside the on film thin a that leaving surfac- so of fall, Adsorption decreases to (16). interface column tube liquid–air the the in to tant liquid for angle contact ifim ial,w ueotidvda elmtlt stecause the the hag as whereas mutant that motility gella the demonstrating cell by of individual spreading motion the out of collective rule the we Finally, control (surfactin-production biofilm. rheology) cells biofilm individual and of rate, control quan- the how predicts under model tities The velocity. its of and shape front spreading the the spreading–both that observed model mathematical the a explains the present quantitatively below then We tension pellicle. surface the in of center decrease the of measurement direct subtilis B. owo orsodnemyb drse.Emi:[email protected], E-mail: addressed. be may correspondence whom To odmntaeta oriae ufci xrsindrives expression surfactin coordinated that demonstrate To ρg θ γ b a steweight/m the is ≈ elce,icuigbt h aeo pedn n a and spreading of rate the both including pellicles, eateto ahmtc n arneBree National Berkeley Lawrence and Mathematics of Department n ihe .Brenner P. Michael and , PNAS = .W esr h trigheight starting the measure We 0. − osnot. does γ − 0 osehbtcletv pedn,tesurfactin the spreading, collective exhibit does coe 7 2009 27, October ≡ 3m/.Drn h usqetinitial subsequent the During mN/m. 53 γ yblnigcplayadhydrostatic and capillary balancing by ) cos 3 ftelqi eimand medium liquid the of θ = ρgdh o.106 vol. 4 a,1 r h ˙ , r .subtilis B. = γ 0.87 n asstefluid the causes and o 43 no. r a erelated be can ) /r implying μm/hr, h elcegrown pellicle .subtilis B. r .4 cm, 2.445 = 18109–18113 θ sthe is fla- [1] A.

MICROBIOLOGY APPLIED MATHEMATICS the film is rapidly adsorbed to the interface, we assume that the rate of interfacial surfactant accumulation C˙ depends only on the thickness. Our direct measurements show that the accumulation rate asymptotes to a constant value within the colony. This cut- off is suggestive of regulation of surfactant production, either by a quorum-sensing mechanism that down-regulates surfactant expression within very dense colonies (21) or in colonies that exceed a critical thickness (22), or by localization of surfactant expression to cells that are close to the interface (23). In order to ˙ ˙ emulate this behavior, we set C = C0 for sufficiently thick regions h > hmax. There is no production of surfactant within regions of film that are too thin to contain bacteria. We therefore introduce ˙ a cut-off C = 0ifh < hmin. We smoothly interpolate between the two limits by using a half cosine. The observed spreading behavior is quite insensitive to the values of these bounds; in what follows, Fig. 1. Wall climbing at the edges of B. subtilis pellicles. Sequence of images: we take hmax = 0.32 mm and hmin = 2 μm. (A) Development of biofilm pellicle at an air–liquid interface. (B) The biofilm Toquantitatively compare with experiments, we must determine after the onset of wall-climbing. (C) The advancing film reaches a plateau the viscosity of the climbing biofilm. Although many viscometric length of approximately 8 mm in this example. measurements have been made for biofilms grown on solid sub- strates (6, 24, 25), the mechanical properties of biofilms formed γ˙ =−0.18 mN/m·hr. Because much of the surfactant expressed by at air–liquid interfaces are comparatively less well characterized. the bacteria is adsorbed onto bacterial surfaces, or into the extra- We expect the two types of biofilm to have very different viscosi- cellular matrix (17), actual rates of expression of surfactin may ties. The viscosity of biofilms on solid surfaces is dominated by the greatly exceed the rate of adsorption to the interface. The time excretion of the extracellular matrix, but we imaged expression of dependence of the is compared with the height EPS by using fluorescent reporter strains from ref. 23 and found of the meniscus in Fig. 2C. The surface tension drops linearly in that there is, initially, no EPS expression in the climbing biofilm time over the first 20 hours of the experiment. After a 12-hour (see Fig. S1). This finding means that the viscosity in the climb- delay, wall climbing of the bacterial film commences, at a speed ing film is determined entirely by steric interactions between the 1.39 ± 0.05 mm/hr. tightly packed bacteria and by the cell density (16). We imaged Mathematical Model. The experiments demonstrate that the bac- the climbing biofilm and found the cells arranged in a mono- ≈ terial spreading occurs simultaneously with a drop in the surface layer, with a volumetric cell density of 0.6 (Fig. S1). This finding η = · tension. We now proceed to understand how the speed U and the implies a fluid viscosity of 0.2 Pa s (26), which is consistent thickness of the film h∞ of the climbing bacterial film are set by with a previous measurement for a biofilm grown at an air–liquid the individual bacteria. Individual bacteria can control the rate of interface (27). surfactin production as well as effective parameters, such as the We solve Eq. 2 on a one-dimensional mesh by using second- viscosity η of the film, by modulating cell density or excreting the order centered finite differences to approximate the surface ten- extracellular matrix. sion and Marangoni stress terms and upwinding for the gravita- We model the mixture of and bacteria in the climbing film tional term, and integrating forward in time by using the Matlab as a viscous Newtonian fluid with density ρ, viscosity η, and surface (Mathworks) implicit solver ode15s. We include the full expres- sion for the capillary pressure in order to match the thin climbing tension γ0. This is an accurate description as long as exopolysac- charide (EPS) are low enough or spreading time scales are long enough that elastic stresses within the biofilm do not hinder its expansion (18). We assume that bacteria are uni- formly dispersed through the film, so that the rate of surfactin accumulation at the film surface, C˙ , is controlled entirely by the local thickness. Surfactin production modifies the surface ten- sion according to the equation of state γ = γ0(1 − c), where c(x, t) is the local interfacial surfactin concentration, measured in activity units; this equation of state is valid because the sur- factin concentrations in experiments during the stages of wall climbing considered here remain well below the critical concentration. Because the thickness of the climbing film, h(x, t), is much Fig. 2. Dynamics of climbing film and surfactin excretion. (A) Height versus smaller than the characteristic scale over which it varies, time of the wall-climbing biofilm. To create this intensity map, raw transmis- the dynamical Navier–Stokes equations reduce to the Reynolds’ sion images were inverted to make the edge of the film look bright, and the evolution equations for the film thickness h(x, t) and c(x, t) (19, 20): difference of successive inverted images were taken to reduce static back- ground and accentuating moving edges. At each time point, a region of 20   pixels was averaged horizontally, creating a map of the vertical height versus ∂h ∂ γ h3 ∂κ ρg cos αh3 h2 ∂γ + 0 − + = 0 time. The arrows point to the beginning and end of the “linear” climbing ∂t ∂x 3η ∂x 3η 2η ∂x region. (B) Height versus time of the meniscus in the capillary. The strip of   pixels across the center of the capillary was averaged to create the time- ∂c ∂ γ ch2 ∂κ ρg cos αch2 ch ∂γ + 0 − + = C˙ . [2] lapse image. The meniscus is seen as the dark trace in the figure. The drop in ∂t ∂x 2η ∂x 2η η ∂x meniscus height during wall climbing signals a decrease in the surface tension, consistent with surfactant production. (C) Plot comparing the decrease in sur- κ = + 2 3/2 ≡ ∂h face tension with time (black symbols) with the increase in the wall-climbing Here the interfacial curvature hxx/(1 hx ) , where hx ∂x 2 height with time (blue symbols). Surface-tension values are extracted from and h ≡ ∂ h , g is the gravitational acceleration, and α is the xx ∂x2 the meniscus height as described in the text. The linear fit shows that the inclination angle of the wall. Because any surfactant produced in biofilm climbs at a rate 1.39 ± 0.05 mm/hr.

18110 www.pnas.org / cgi / doi / 10.1073 / pnas.0905890106 Angelini et al. 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(arbitrary reference profiles dashed Thickness the region by magnified axes. indicated the with rise-height front, spreading and of scalings thickness The different film the the Note interface. x concentration. surfactant of the coding gives Color interface climbing. wall of red) onset (right-most, after hours 6 0 to from blue), intervals, (left-most, min 40 film at Simulated profiles thickness (A) film. bacterial the spreading of dynamics the reproduces pellicle the in 3. Fig. h imtikesand thickness Film the (D) with film. precursor advancing other the and film, terial rage) n 20 and triangles), h eghscale length shear U U h ntrso h ufci production surfactin the of terms in ecnslefor solve can we 4, ∞ 2 min ∞  = =  / ∼ Inset c steeulbimhih fteflat the of height equilibrium the is 0 a = c c τ γ τ η = γ η γ ∞ τ 0 0.25 C γ 0 0 ˙ C oe o ufcatproduction surfactant for model A ∞ 2 ˙ 3.57 0 2 0 aif optblt condition compatibility a satisfy 0 hw h nieitraeand interface entire the shows 1 c   rdsurs,2 squares), (red μm c 3 1/2 3/4 , . h c 2 τ min τ ∞ ∞ 2 o.106 vol. h bu circles). (blue μm γ dacn ihtebac- the with advancing , c eso olpefor collapse show We : η /γ max h 0 ∞ 0 2 h l thickness film the , / neednl fthe of independently t 2 a h = ∼ τ ∞ o 43 no. 0 i (dark min 900 = and c −1 .7 The 3.57. (green μm where , h U h min ∞ A.( 18111 ;we and [7] [6] [4] [5] = C) 5

MICROBIOLOGY APPLIED MATHEMATICS where the constants ah = 1.63 and aU = 0.46 can be determined from a similarity of the governing equations (see Materi- als and Methods). Eqs. 6 and 7 demonstrate that the thickness and speed of the climbing film depend in a nonlinear fashion on quan- tities that individual cells can control, the surfactin production rate and the biofilm viscosity.

Comparisons with Experiments. The simulations (Fig. 3A) predict that the shape of the climbing bacterial film has a characteristic bump in thickness at its edge, similar to that previously observed in thin film fluid flows driven by uniform surface tension gradients (14, 32). Strikingly, this characteristic bump is also observed in our measurements of the thickness profile of the climbing bacter- ial film (Fig. 3B), obtained by relative transmission intensities. The predicted thickness of the climbing film is h∞ ≈ 1 μm. Although we cannot directly measure the thickness, the fact that the climb- ing film is a monolayer (Fig. S1) is quite consistent with this prediction. The speed of advance and the film shape agree quite well with experimental observations. Inputting the directly measured value ˙ of C0, the predicted speed of advance is U ≈ 0.4 mm/hr, compared with the experimental measurement of 1.4 mm/hr (Fig. 2C). The model’s underprediction of the climbing rate likely results either from uncertainty in the true viscosity of the biofilm or from unmod- eled effects of spatial variations in biofilm viscosity: We expect the bacteria to spread more rapidly if the viscosity at the edges is less

than the viscosity at the center. The predicted scaling of biofilm − ∼ η1/2 Fig. 4. Bacterial spreading rate in WT (black squares), srfAA (surfactin thickness with viscosity h∞ , naturally explains the observed − 12-hour delay between the onset of surfactant expression and the knockout, green triangles) and hag (flagellum knockout, red circles) bac- teria. Both WT and mobility mutant bacteria exhibit wall climbing. Knocking beginning of wall climbing. For the climbing film to transport bac- out surfactin destroys the ability of the bacterial pellicle to collectively climb teria, the film thickness must exceed the thickness of a monolayer the wall, confirming that Marangoni stresses drive pellicle expansion, and of bacteria (≈0.5 μm), requiring that η  0.1 Pa·s. The viscosity of that surfactin gradients are responsible for these stresses. the bacterial pellicle increases with cell density and with the con- centration of extracellular polymers expressed by the cells, and and so can not swim, but retain the surfactin-expression pathway. we identify the delay with the waiting time for this critical vis- Strikingly, these mutants climb the wall as readily as swimming cosity to be be reached. This mechanical thresholding intimately strains (Fig. 4). ties Marangoni motility to cell density, both directly, and indi- rectly through the quorum-sensing pathways that mediate EPS Discussion expression (22, 33). We have presented evidence for cooperative spreading of bacterial ∼ 9/4 ˙ 5/4 Finally, we note that the flux of bacteria Uh∞ c C0 pellicles. In contrast to previously described dispersal mecha- 1/4 (η/γ0) , so that the flux actually increases with the viscosity of the nisms, dispersal by Marangoni waves increases as the viscosity bacteria-laden film. This behavior is in contrast to the swimming of of the bacterial pellicle is increased. This discovery suggests non- individual cells, which typically slows as viscosity is increased (34). intuitive strategies for controlling the spreading of biofilms. Bio- The one gross contradiction between the mathematical model surfactant coatings are already known to limit biofilm growth in and the experiments is that experimentally the colony stops some circumstances, but the effect has previously been attributed spreading several hours before surfactant stops being supplied to their inferred action (35). Inhibition of Marangoni to the interface. We attribute this stoppage to a change of phase waves provides an alternative physical explanation for the retar- at the colony edges: Simultaneous with their expression of sur- dation of spreading. Coating the wall with surfactant increases its factin, cells also produce a matrix of EPS which binds cells together wettability but may nonetheless make it harder to climb by saturat- (17). Once all cells in the colony periphery are tightly bound by ing the interface of the rising film or even imposing a Marangoni this matrix, spreading is arrested. Note, however, that secondary stress that opposes the surfactant wave generated by the bacteria. traveling bands propagate up the wall for as long as surfactant is The cooperative basis of this form of dispersal also merits fur- produced within the colony (Fig. 2A). Evidently, surfactant gradi- ther scrutiny—our simulations show that the cells that surf the ents continue to drive a thinner layer of fluid, which may or may Marangoni wave do not themselves need to produce surfactant, not contain cells, from under the pellicle of tightly bound cells. so that cells in the center may find themselves paying the entire When surfactant expression ceases, spreading of these secondary fitness cost of expressing surfactant without enjoying access to new bands stops. Our measurements show that the surface tension then substrates. Marangoni motility may therefore provide a new par- starts to increase, signalling either desorption of surfactant from adigm for studying the evolutionary stability of a costly form of the interface or that the entire colony has gelled (Fig. 2C). cell-to-cell cooperation with nontargeted benefits.

Surfactin Mutants Do Not Exhibit Collective Spreading. The collec- Materials and Methods tive spreading of the bacterial pellicles that we have described here Bacterial Strains and Growth. To grow the biofilm pellicles, we adapt the cannot be attributed to conventional motility, such as individual protocols in ref. 7. Strain 3610 B. subtilis cells are streaked from a −80◦C swarming or swimming (15). To confirm that the motility mech- freezer stock onto an LB medium plate, 1.5% agar. The plates are incubated ◦ anism described here is independent of mechanisms previously at 37 C for twelve hours. Three milliliters of LB liquid medium is inoculated with cells from an isolated colony on the plate. The inoculated LB medium is described, we repeated the experiment with two mutant strains. ◦ − incubated on a shaker at 37 C for three hours, when the optical density of srfAA bacteria do not express surfactin and do not exhibit wall the bacteria solution is approximately 0.6. Forty microliters of the bacteria − climbing (Fig. 4). In contrast, hag bacteria do not have flagella, solution is added to 4 mL of minimal salts glycerol glutamate medium (7) in a

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Swarming (2003) R Losick D, Kearns 15. 4 etziA üc ,Fno ,CzbtA(98 otc iesaiiyad“under- and stability line Contact film: (1998) A viscous Cazabat thin X, a Fanton A, on Münch spreading A, surfactant Bertozzi Insoluble (1992) 14. J fingering Grotberg of O, growth Jensen Exponential 13. (1992) F spreading Rondelez thin F, of Brochard–Wyart instability Fingering J, (1990) Brzoska P potassium Carles for 12. S, requirements Troian F, Genetic Heslot (2005) A, R Cazabat Fall M, 11. Hale DB, Kearns RF, Kinsinger 10. asa rm aeo neprfiemntsadpspoesdwt custom with also postprocessed mutations. are and hag::tet minutes strains five knockout per once The of software. rate frame a at days ( c ˙ .Wn ,PetnJ oe 20)The biofilms. (2004) of T description Romeo material J, the Preston biofilm- X, in Wang cohesion the of in Role 3. adhesion (2006) intercellular J Dockery of I, basis Klapper Molecular (1996) 2. al. et C, Heilmann 1. .KnigrR hr C alR(03 ai ufc oiiyin motility surface Rapid (2003) R Fall MC, Shirk R, Kinsinger between Interactions 9. (2006) R Kolter J, body Willey Fruiting (2001) P, R Straight Kolter R, Losick 8. S, Ben-Yahudar JE, González-Pastor S, Branda 7. .Hl-tolyL otro W tolyP(04 atra ifim:Fo h natural the From biofilms: Bacterial (2004) P Stoodley JW, Costerton L, Hall-Stoodley 6. regulation Quorum-sensing (2006) S Bodman von T, Minogue D, Tsaltas M, Koutsoudis 5. in formation biofilm of Initiation (1998) R Kolter G, O’Toole 4. ∞ = ξ /U hsRvE Rev Phys forming environment. UK). Microbiol opesv hcs ndie hnfimflow. film thin driven in shocks” compressive rupture. film and evolution Shock gradients. thermal horizontal under films 19:97–102. spreading of instabilities gradients. temperature by driven films subtilis. bacillus in spreading colony -dependent 5627–5631. tilis 188:4918–4925. and subtilis. bacillus by formation niomn oifciu diseases. infectious to environment in colonization host and development, stewartii biofilm adhesion, bacterial governs analysis. genetic A Microbiol pathways: signalling convergent multiple, via proceeds wcs365 formation. biofilm for required adhesin polysaccharide 186:2724–2734. a of synthesis the (x = )TC − sdpneto xrclua ufci n oasu ion. potassium and surfactin extracellular on dependent is .Afia osritaie rmterqieeto compatibility of requirement the from arises constraint final A 0. oeo ufcat nriigara structures. aerial raising in surfactants of Role subtilis: Bacillus √ (ξ, tpyoocseiemds o Microbiol Mol epidermidis. Staphylococcus 2 subspecies 49:581–590. 28:449–461. 74:031902. T c where ), )/ rnsMicrobiol Trends r h iesols oneprsto counterparts dimensionless the are nrdcint li Dynamics Fluid to Introduction twri.Po alAa c USA Sci Acad Natl Proc stewartii. ofidtedmninescefiinsi Eqs. in coefficients dimensionless the find To ξ = X rcNt cdSiUSA Sci Acad Natl Proc /T 9:222–227. sorsmlrt aibe and variable, similarity our is li Mech Fluid J a e Microbiol Rev Nat Nature C pgaABCD ◦ .subtilis B. = .Iae r olce o several for collected are Images C. hsRvLett Rev Phys 0, 346:824–826. 240:259–288. H CmrdeUi rs,Cambridge, Press, Univ (Cambridge ou of locus h(x Bacteriol J 20:1083–1091. = 98:11621–11626. 103:5983–5988. 2:95–108. 60wt rA:msand srfAA::mls with 3610 b , t ) as suooa fluorescens Pseudomonas shrci coli Escherichia 81:5169–5172. = tetmcscoelicolor Streptomyces ξ h 187:8462–8469. t →∞ ∞ ailssbii.Mol subtilis. Bacillus and H (ξ, T Bacteriol J and , uohsLett Europhys x = T ailssub- Bacillus ), 2) Both (20). Ut Bacteriol J Bacteriol J promotes c 6 (x Pantoea and /, C and , t = 185: Mol ) 7, = 1 fsersrs n l hcns hr h l et h ttcmeniscus: static the meets film the where thickness film H and stress shear of 8 rs ,TuosyS etrigW lneyB(2007) B Flannery W, Vetterling S, Teukolsky W, Press 28. 6 cwrzL(01 nteaypoi nlsso ufc-tesdie hnlyrflow. thin-layer surface-stress-driven of analysis asymptotic the On (2001) L Schwartz from Biosurfactant 36. (2004) R Oliveira motility. J, Teixeira bacterial H, Mei on der viscosity van L, of Rodrigues a Effect by (1974) 35. a driven R of development films Doetsch the W, of in signals Schneider shape cell-to-cell of and 34. involvement The Thickness (1998) al. (1996) et D, D Davies Quéré 33. A, plate. moving Cazabat a by X, liquid Fanton a lines. of contact 32. Dragging driven (1942) B of of Levich growth L, instability and Landau instability fingering Linear the 31. (1997) for A Model Bertozzi M, (1990) Brenner S Safran 30. E, Herbolzheimer S, Troian 29. biofilm air-liquid novel a of Characterization (2009) A Spiers suspensions. C, Moon P, colloidal Hallett of A, Koza Viscosity (1997) E 27. Cohen I, Schepper de R, Verberg 26. 5 iSeao ta.(09 iceatcpoete of properties Viscoelastic (2009) al. biofilm et bacterial of Stefano, quantitation di Absolute (2009) 25. J Lam T, Beveridge J, Dutcher P, Lau 24. 3 lmksH gia ,Lsc ,Kle 20)Cnrlo elft yteformation the by fate cell of Control (2008) R Kolter R, Losick C, Aguilar H, Vlamakis 23. omsraesrse 3) eeov h qain olt ie yusing by times late to equations the Eq. uni- to evolve imposed routines We than numerical (36). similar thinner stresses 25% surface films form produce therefore waves Marangoni nvriyfrfnigti eerh ..i upre yaflosi from fellowship Sciences. a in by Research Basic supported for is Institute M.R. Miller Harvard research. the at dis- this initiative useful funding research for for BASF Bertozzi exper-University the Andrea early acknowledge and gratefully for We Dechadilok Levy cussions. Panadda Rachel and and Branda investigations, Steve imental strains, for and help ACKNOWLEDGMENTS. respectively. ridge capillary the of and 8 lpe ,Rp ,CroR uvdr ,Sode 20)Vsolsi uddescription fluid Viscoelastic (2002) P Stoodley B, Purvedorj R, Cargo C, Rupp I, Klapper 18. 2 hp ,Krst ,MrnB askM(03 h eedneo urmsensing quorum of dependence The (2003) M Parsek B, Moran M, Kirisits and D, surfactant Chopp by driven production. 22. biosurfactant film of liquid genetics thin Molecular (1998) a ER of Sullivan motion down The 21. films (2006) thin M surfactant-laden Shearer of R, Flow Levy (2004) R 20. Craster O, Matar B, Edmonstone 19. ∞ eobtain We = n Math Eng J 66:306–311. lactis cus 117:696–701. biofilm. bacterial flow. marangoni USSR Fluids Phys drops. surfactant spreading Computing Scientific of E 7915.2009.00120.x. epidermidis lococcus deinadvsolsiiyb irba oc spectroscopy. force microbead by viscoelasticity and adhesion of fbceilbol aeilproperties. material biofilm bacterial of ndpho rwn biofilm. growing a of depth on 9:263–269. gravity. plane. inclined an a 55:3143–3158. U a suooa urses Microbiology fluorescens. Pseudomonas nacietrlycmlxbceilcommunity. bacterial complex architecturally an τ = (∂ 17:42–54. .6fo h hcns ftecibn l at film climbing the of thickness the from 0.46 C IMJAp Math Appl J SIAM /∂ 3ihbt irba deino iioerubber. silicone on adhesion microbial inhibits 53 9:530–539. ξ) 39:171–188. a 2 τ . Langmuir = Science n Math Eng J PNAS ;self-generated 3C); (Fig. simulations our from 3.57 CmrdeUi rs,Cmrde K,3dEd. 3rd UK), Cambridge, Press, Univ (Cambridge oomcoilbiofilms. mono-microbial etakHr lmks(avr nvriy for University) (Harvard Vlamakis Hera thank We 280:295–298. 66:1588. 12:5875–5880. hsRvLett Rev Phys coe 7 2009 27, October 50:141–156. ulMt Biol Math Bull n banfrtecoefficients the for obtain and 2, itcnlBioeng Biotechnol 65:333–336. 155:1397–1406. 65:1053–1079. 10.1111/j.1751- Biotechnol, Microb tpyoocsaureus Staphylococcus eeDev Gene o.106 vol. ueia eie:TeAtof Art The Recipes: Numerical plMcoilBiotechnol Microbiol Appl 80:289–296. ipy J Biophys 22:945–953. ξ = o 43 no. urOi Biotech Opin Curr caPhysicochim Acta n location and 0 96:2935–2948. and a Bacteriol J h Lactococ- hsRev Phys = Staphy- 18113 1.63

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