The Evolution of Bacteriocin Production in Bacterial Biofilms

vol. 178, no. 6 the american naturalist december 2011

E-Article

The Evolution of Bacteriocin Production in Bacterial Biofilms

Vanni Bucci,1 Carey D. Nadell,2 and Joao B. Xavier1,*

1. Program in Computational Biology, Memorial Sloan-Kettering Cancer Center, New York, New York 10065; 2. Department ofEcology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544; and Department of Molecular Biology, PrincetonUniversity, Princeton, New Jersey 08544

Submitted February 24, 2011; Accepted July 25, 2011; Electronically published October 26, 2011

Online enhancements: appendix, videos.

abstract: Bacteriocin production is a spiteful behavior of bacteriathat is central to the competitive dynamics of many human path-ogens. Social evolution predicts that bacteriocin production is favoredwhen bacteriocin-producing cells are mixed at intermediate fre-quency with their competitors and when competitive neighborhoodsare localized. Both predictions are supported by biofilm experiments.However, the means by which physical and biological processes in-teract to produce conditions that favor the evolution of bacteriocinproduction remain to be investigated. Here we fill this gap usinganalytical and computational approaches. We identify and collapsekey parameters into a single number, the critical bacteriocin range,that measures the threshold distance from a focal bacteriocin-pro-ducing cell within which its fitness is higher than that of a sensitivecell. We develop an agent-based model to test our predictions andconfirm that bacteriocin production is most favored when relatednessis intermediate and competition is local. We then use invasion anal-ysis to determine evolutionarily stable strategies for bacteriocin pro-duction. Finally, we perform long-term evolutionary simulations toanalyze how the critical bacteriocin range and genetic lineage seg-regation affect biodiversity in multistrain biofilms. We find that bio-diversity is maintained in highly segregated biofilms for a wide arrayof critical bacteriocin ranges. However, under conditions of highnutrient penetration leading to well-mixed biofilms, biodiversity rap-idly decreases and becomes sensitive to the critical bacteriocin range.

Keywords: social evolution, spite, agent-based modeling, bacteriocins,microbiome, biodiversity.

Introduction

Bacteriocin production, a trait by which bacteria secretetoxic substances to suppress the growth of competitors,has long fascinated the scientific community. Though met-abolically expensive, bacteriocin secretion is a very com-mon behavior among known bacteria and is thus likely tobe a signature of environmental factors and selective forcesthat are common to many bacterial species (Kerr 2006).

* Corresponding author; e-mail: [email protected].

Am. Nat. 2011. Vol. 178, pp. E162–E173. � 2011 by The University of Chicago.

0003-0147/2011/17806-52848$15.00. All rights reserved.

DOI: 10.1086/662668

From the perspective of social evolution theory, bacteri-ocin secretion also represents a rare example of spitefulbehavior that is expensive for the producer and harmfulto others (Hurst 1991; Gardner et al. 2004; Foster 2005;West et al. 2006, 2007; West and Gardner 2010). Whatconditions lead bacterial strains to evolve highly costlybehaviors that are harmful to others? This question hasmotivated a diverse series of experimental (Adams et al.1979; Chao and Levin 1981; Levin 1988; Tait and Suth-erland 2002; Inglis et al. 2009; Be’er et al. 2010; Majeedet al. 2010) and theoretical studies (Frank 1994; Durrettand Levin 1997; Iwasa et al. 1998; Riley and Gordon 1999;Nakamaru and Iwasa 2000; Kerr et al. 2002; Czaran andHoekstra 2003; Gardner et al. 2004; Szabo et al. 2007;Prado and Kerr 2008).

Social evolution theory has traditionally focused on co-operative behaviors, which are costly to the actor and ben-eficial to the recipient. Such traits are predicted to evolveunder a condition known as Hamilton’s Rule, ,rb 1 cwhere c is the fitness cost of performing cooperative be-havior, b is the fitness benefit conferred to the recipient,and r is relatedness, or the coefficient of correlation ofrecipient genotype on actor genotype (Hamilton 1964a,1964b, 1970). Fixing b and c, cooperation is more likelyto evolve when r is high, namely, when cooperative benefitsare preferentially distributed to other cooperative individ-uals relative to the total frequency of cooperative individ-uals in the competitive neighborhood. Hamilton imme-diately recognized that his rule might also apply to spitefulbehaviors, which are in some ways the inverse of coop-eration. For spiteful traits, recipients are harmed; that is,b is negative. Spite is therefore predicted to evolve whenr is also negative, which is satisfied when the harmfuleffects of the spiteful behavior are preferentially directedtoward competitors that do not share the same genotype.

Gardner and colleagues refined the theoretical foun-dation describing the evolution of spite in general and ofbacteriocin production in particular (Gardner and West2004; Gardner et al. 2004). Without assuming any partic-

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Evolution of Bacteriocin in Biofilms E163

ular toxin production cost function, they demonstratedthat bacteriocin production is most strongly favored atintermediate relatedness. Their conclusion, which wasconfirmed in a recent experimental study (Inglis et al.2009), rests on the fact that the net benefit for a lineageof bacteriocin producers is largest when lineages are spa-tially mixed and competition for resources is localized,such that suppressing the growth of nearby competitorsbecomes an effective strategy. The analysis of Gardner etal. (2004) was also supported by experiments in whichbacteriocin-secreting cells were competed against non-producing cells in surface-bound bacterial communities,or biofilms (Tait and Sutherland 2002). One major dif-ference between theory and experiment arose here, how-ever: spatially structured biofilm environments allowed thecoexistence of both bacteriocin-producing and bacterio-cin-sensitive strains, which was not observed under plank-tonic or well-mixed conditions.

Understanding the evolution of bacteriocin productionin biofilms is important, as biofilm formation plays a ma-jor part in bacterial life. For example, it is estimated thatthe vast majority of human bacterial infections involvebiofilms (Costerton et al. 1999). The spatial structuringinherent to these closely packed communities can dra-matically influence the evolution of bacterial social inter-actions (Nadell et al. 2009). While the predictions of socialevolution theory (Gardner et al. 2004) agree qualitativelywith experimental biofilm observations (Tait and Suth-erland 2002), we do not understand the mechanistic bridgebetween abstract theory and lab experiment. How do thephysical and biological processes involved in biofilm for-mation influence relatedness and the size of competitiveneighborhoods, such that bacteriocin production isadvantageous?

Here, we analyze the evolution of bacteriocin productionin biofilms using several modeling approaches. We applymathematical analysis to identify the threshold length-scalewithin which a focal bacteriocin-producing cell achievesgreater fitness than a sensitive cell. The concept of length-scale is widely used in the physical sciences to describe theorder of magnitude of a system. In this study, our derivedlength-scale groups together the physical (e.g., bacteriocindiffusivity) and biochemical (e.g., rate of bacteriocin syn-thesis) properties of the system that ultimately set the spatialscale at which bacteriocin secretion confers a competitiveadvantage. By determining the critical bacteriocin range inthis way, we simplify the total evolutionary analysis of bac-teriocin production by collecting important parameters intoone compound parameter.

We then use individual-based simulations to test thehypothesis that the critical bacteriocin range controls theevolution of bacteriocin production in bacterial biofilms.Individual-based modeling, which uses multiple agents gov-

erned by a set of rules that mimic the behavior of realmicrobes, is a powerful approach for studying the evolutionof microbial communities in the environment (Hellwegerand Bucci 2009). The spatial and evolutionary dynamics ofthe population emerge from the interactions among indi-viduals. Using these simulations we carry out in silico com-petition between bacteriocin-producing and -sensitivestrains. By initiating biofilm growth with different ratios ofthe two strains or by changing environmental conditionsthat lead to variation in lineage segregation, we confirm thatin dual-strain biofilms, bacteriocin production is moststrongly favored when relatedness is intermediate and com-petition is predominantly local. Finally, we carry out long-term evolutionary simulations to analyze the influence ofbacteriocin-mediated competition and genetic lineage seg-regation in the maintenance of bacteriocin diversity in dual-and multistrain biofilms.

Results and Discussion

Gardner et al. (Gardner and West 2004; Gardner et al.2004) find two critical factors influencing the evolution ofbacteriocin production: (1) relatedness, which measuresthe association between genotypes of cells affected by bac-teriocins and cells producing bacteriocins, and (2) the scaleof competition, that is, the length-scale on which cellscompete with each other for limited growth substrate.Here, we develop a mechanistic model of bacteriocin evo-lution in biofilms to provide an explanation for their find-ings in relation to the spatially structured environmentsthat bacteria often occupy.

In addition to relatedness and the scale of competitionfor nutrients, we hypothesized that the length-scale atwhich bacteriocins exert an influence on competitorswould be important for the evolution of bacteriocin pro-duction. To determine the physical and biological param-eters that set the critical bacteriocin range in biofilms, weuse the model of bacteriocin kinetics introduced by Wil-kinson (2002). Bacteriocin producers secrete toxin at arate proportional to their growth. Bacteriocin-sensitivecells, in turn, are killed at a rate proportional to bacteriocinconcentration (T, for “toxin”). As previously described(Nadell et al. 2010), the growth of both bacteriocin-pro-ducing and bacteriocin-sensitive bacteria is also a functionof a growth-limiting nutrient (N):

dP Np (1 � f )m P, (1)maxdt N � KN

dS Np m � k T S, (2)max T( )dt N � KN

where mmax (1/h) is the maximum specific growth rate, N

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(g N/L) is the nutrient concentration, KN (g N/L) is thehalf saturation constant for nutrient, P and S (g X/L) are,respectively, the concentrations of bacteriocin-producingand bacteriocin-sensitive cells, f is the fraction of substrateinvested in bacteriocin production rather than biomassproduction, and kT (L/g T/h) is the killing rate per unitmass of bacteriocin.

The solute species, toxin and nutrient, are governed byreaction-diffusion:

dT N2p afm P � D ∇ T, (3)max Tdt N � KN

dN 1 N2p � m (P � S) � D ∇ N, (4)max Ndt Y N � KN

where a (g T/g X) is the stoichiometric coefficient of bac-teriocin production, T (g T/L) is the bacteriocin concen-tration, Y (g X/g N) is the yield of biomass production,and DT and DN are respectively the diffusivities of toxinand nutrient (mm2 h�1). The stoichiometric table for thismodel (table A1) and a table explaining our choices forparameter values (table A2) are available online.

We carried out a dimensional analysis of this model(app. A, available online) and derived the critical bacte-riocin range (Lbac):

ak ! m 1TL p , (5)bac 2pDT

where !m1 (g X/L) is the average biomass of a bacteriocin-producing cell. The critical bacteriocin range, Lbac, com-bines physical and biological parameters to represent thethreshold distance within which the cost of bacteriocinproduction is offset by the killing of sensitive cells in thesurrounding area. Smaller values of Lbac indicate more lo-calized bacteriocin-mediated killing, and vice versa. Belowwe demonstrate that bacteriocin-mediated killing is a func-tion of Lbac but largely independent of the specific valuesof the parameters that define it.

In Silico Competitions Using Agent-Based Modeling

We performed in silico competitions between bacteriocin-producing and bacteriocin-sensitive strains to analyze howthe critical bacteriocin range (Lbac) influences the evolutionof bacteriocin production in biofilms (fig. A1, availableonline). We used a well-established individual-based sim-ulation framework, which mechanistically describes dif-fusion of solutes and cell growth (Xavier and Foster 2007;Nadell et al. 2008, 2010). Bacterial cells are modeled ascircular agents growing on a flat surface. Cell growth is afunction of local microenvironment conditions experi-enced by individual cells, as described in equations (1)

and (2). Each cell grows until it reaches a maximum radius,at which point it divides to produce two daughter cells.Cells also move passively when pushed by neighboring cellsas they grow and divide. The spatial concentrations ofsolutes—bacteriocin and nutrient—are updated at eachiteration by solving reaction-diffusion equations. We ini-tiated our simulations by inoculating the bacteriocin-pro-ducing and -sensitive strains on the solid substratum atvarying initial ratios, depending on the aim of the partic-ular simulation. For this first set of simulations, we allowthe biofilm to grow until a predefined height of 150 mm,which is a typical size for bacterial biofilms and within arange (50–250 mm) often used in biofilm modeling (Pi-cioreanu et al. 2000).

Bacteriocin Production Is Favored as the CriticalBacteriocin Range Increases

We first evaluated the effect of Lbac on competition betweena bacteriocin producer and a sensitive strain. In order tofocus on the effect of Lbac, we assumed high nutrient pen-etration (N), which leads to well-mixed biofilms with rel-atively smooth advancing fronts (Nadell et al. 2010). Wecarried out competitions in which the two strains wereinoculated at a 1 : 1 ratio, and we measured the outcomecompetition by calculating the change in frequency of theproducer strain (DP/P0), defined as

DP P � Pf 0p , (6)P P0 0

where P0 and Pf are, respectively, the initial and final pro-portions of bacteriocin producers in the biofilm. Nor-malizing by P0 effectively measures the fold change in pro-ducer frequency and allows for clearer comparison amongexperiments with different initial sensitive-to-producer ra-tios (see next section). We performed competitions forseveral values of Lbac, which we varied by changing eitherDT, kT, a, or !m1 (fig. 1). As one might expect, thesesimulations showed that the advantage of bacteriocin pro-duction increases with the critical bacteriocin range (fig.1; video 1, video 2, and video 3, available online). As before(Xavier and Foster 2007; Nadell et al. 2008, 2010), wecarried out replicate runs by altering the seed for the sim-ulation framework’s random number generator. The re-sults were robust, with very little variation among repli-cates (fig. 1).

Next, we evaluated the effect of Lbac on the competitiveadvantage or disadvantage of different levels of investmentinto bacteriocin production. We carried out a range ofsimulations varying Lbac and f, calculating the fold changein bacteriocin-producer frequency at the end of each rep-licate (fig. 2). For values of Lbac lower than 0.002 mm, we


Figure 1: Effect of the critical bacteriocin range (Lbac) on selection for bacteriocin production. The fold change in bacteriocin-producerfrequency (DP/P0) is plotted as a function of Lbac for competition between bacteriocin producers and bacteriocin-sensitive strains in biofilmswith high nutrient penetration. Results are for simulations with a bacteriocin production investment value (f) of 0.3. Simulations were runvarying one parameter defining Lbac at a time and keeping the others constant: kT (blue circles), DT (yellow triangles), a (green diamonds),and !m1 (red squares). For each parameter, the simulations were repeated 11 times with different initialization of the random numbergenerator in order to estimate the robustness of our system’s analysis. Also, for ease of visualization, the data are randomly positionedaround their respective Lbac values, and a sigmoid expression (black line) was fitted to the data. Images are model snapshots for Lbac valuesof (1) 0.000, (2) 0.002, and (3) 0.005 mm. In inset panels, blue circles represent bacteriocin-sensitive cells, green circles represent bacteriocin-sensitive cells experiencing local bacteriocin concentrations such that their growth rate is lower that the one of the neighboring bacteriocinproducers, and red circles represent bacteriocin-producing cells.

observed no increase in bacteriocin-producer frequencyfor any level of investment in production. On the otherhand, as Lbac increases above 0.002 mm, bacteriocin pro-duction becomes favorable, but only up to a point. Al-locating more than 70%–80% of resources to bacteriocinproduction becomes too costly and results in a decreasein bacteriocin producers’ frequency for all Lbac values.

Bacteriocin Production Is Favored atIntermediate Relatedness

After confirming the central role of the critical bacteriocinrange, we analyzed the effect of relatedness on selectionfor or against bacteriocin production. As was done in ex-isting experiments (Inglis et al. 2009), we changed relat-edness in our individual-based simulations by inoculatingthe biofilm with different initial ratios of the two com-peting strains (fig. 3A). We conducted the simulations at

mm, which we found to be the minimumL p 0.002bac

value at which bacteriocin production can be advantageous(fig. 2). Our simulations showed that bacteriocin produc-tion is most advantageous at intermediate initial frequen-cies of the bacteriocin-producing strain. This result sup-ports existing theoretical and experimental studies(Gardner and West 2004; Gardner et al. 2004; Inglis et al.2009). Interestingly, our simulations show that the advan-tage of bacteriocin production vanishes for extreme valuesof investment (f less than 0.1 or more than 0.7), suggestingthat both intermediate relatedness and intermediate in-vestment are important for the competitive advantage af-forded to bacteriocin producers. Also consistent with pre-vious experimental and theoretical results (Inglis et al.2009), selection for bacteriocin production is not sym-metric with respect to relatedness but rather biased towardhigher relatedness values. Starting at higher frequency al-lows producers to flood the biofilm with bacteriocin earlyduring biofilm growth, a highly effective strategy (see video4, available online).


Figure 2: Selection for bacteriocin production as a function of investment in bacteriocin production (f). Results are from simulatedcompetitions between a bacteriocin-producing and a bacteriocin-sensitive strain inoculated at a 1 : 1 ratio in a smooth biofilm characterizedby high nutrient penetration. Different colors correspond to simulations performed for different Lbac values (0.0002–0.005 mm). The thickorange line corresponds to the Lbac value chosen for the subsequent analysis.

Bacteriocin Production Is Favored When Genetic LineagesAre Mixed and Competition Is Localized

After confirming selection for bacteriocin production isstrongest at intermediate frequencies of producing cells,we analyzed the effects of nutrient penetration and geneticlineage segregation on competition between bacteriocin-producing and -sensitive strains. Previous work has shownthat the penetration of a growth-limiting nutrient stronglyinfluences segregation between genotypes in biofilms and,consequently, the evolution of cooperation (Nadell et al.2010). The same work defined a dimensionless compoundparameter d to quantify nutrient penetration:

N D Ybulk N�d p , (7)2m rhmax

where Nbulk (g N/L) is the nutrient concentration in theliquid bulk, DN (mm2/h) is the nutrient diffusivity, r (g X/L) is the bacterial density, and h (mm) is the thickness ofthe diffusion boundary layer. High values of d translate todeep nutrient penetration into the biofilm, producingsmooth biofilms with thorough cell lineage mixing. Con-versely, low values of d translate to decreased nutrientpenetration and lead to genetic segregation as well as highly

structured biofilms with towerlike surface projections(Nadell et al. 2010). Notably, d also dictates the scale ofcompetition for growth substrate in biofilms. When d ishigh, biofilms are largely saturated with nutrients, andsubstrate consumption by a focal cell only reduces nutrientavailability to its immediate neighbors. When d is low, onthe other hand, nutrient access is more limited withinbiofilms, and substrate consumption by a focal cell reducesnutrient availability for other cells well beyond its im-mediate vicinity. In other words, d is inversely proportionalto the scale of competition for nutrients.

In agreement with the social evolution literature, selec-tion for bacteriocin producers was maximized at high d

values (small scale of nutrient competition) and for anintermediate investment value (f) equal to 0.4 (figs. 3B,4A; video 5, available online). For low d values (large scaleof nutrient competition), the bacteriocin-sensitive cellsoutgrow producers in the initial instants of biofilm for-mation and build fingerlike protrusions that limit theircompetitors’ access to growth substrate (fig. 4B; video 6,available online). Similar to our earlier observations (fig.3A), as the system is tuned away from an intermediatebacteriocin investment value of 0.4, bacteriocin produc-tion is less favored.


Figure 3: Effects of relatedness and cell lineage segregation on selection for bacteriocin production in dual-strain biofilms. A, Selection forbacteriocin production as a function of producer initial frequency for different investments in toxin production (f). Simulations were runby inoculating the producer and sensitive strains at different initial proportions. B, Selection for bacteriocin production as a function of dfor different investment in bacteriocin production. In this particular case, high d values (16) correspond to intermediate relatedness (localmixing ratio of 1 : 1 ratio) and more localized competition, while lowering d corresponds to increasing relatedness and more globalizedcompetition. Results shown are for an Lbac value of 0.002 mm (see text). Simulations were run until a maximum biofilm height (150 mm)was achieved.

Evolutionarily Stable Strategies

So far, our results illustrate how physical and biologicalprocesses affect the scale of bacteriocin-mediated com-petition within biofilms and, consequently, the competitiveadvantage gained by bacteriocin producers. Next, we con-ducted simulations to determine the optimal level of bac-teriocin investment that prevents rare mutants from in-vading, that is, the evolutionarily stable strategy (ESS;Maynard Smith and Price 1973; Otto and Day 2007). TheESS was investigated by competing two producer popu-lations (each sensitive to the other’s toxin) that differedin bacteriocin investment by a small quantity Df (Xavierand Foster 2007; Nadell et al. 2008, 2010). The simulationswere seeded with the two producer strains at a 1 : 1 ratio,

and simulations were stopped again when biofilms reached150 mm. For consistency with the simulations shownabove, we used mm.L p 0.002bac

The results from the ESS calculation are presented infigure A2, available online. Consistent with our earlier con-clusions (fig. 3B), bacteriocin production is favored fordecreasing genetic segregation and more localized com-petition for nutrients (increasing d) and maximized whencells are locally assorted at a 1 : 1 ratio. The predictedoptimal investment in bacteriocin production was lowerthan that observed in previous sections (0.2 rather than0.4), suggesting that the benefit of investing into bacte-riocin production is lower when competing with otherproducers than with bacteriocin-sensitive cells.


Figure 4: Effect of genetic segregation on bacteriocin-mediated com-petition. A, High segregation (high relatedness, large scale of com-petition) and formation of single-strain towerlike protrusions. Bac-teriocin-sensitive cells (blue) outgrow bacteriocin-producing cells(red) in the early stages of competition and prevent bacteriocin pro-ducers from accessing nutrients. B, Low segregation (intermediaterelatedness, small scale of competition) and formation of smoothbiofilm. Due to higher nutrient penetration, bacteriocin-producingcells are able to flood the biofilm with the secreted toxin and dom-inate the population. The isocontour lines represent gradients ofnutrient concentration in the biofilms.

We expect that interesting dynamics could arise if abacteriocin-resistant (but nonproducing) strain wereadded to the system. This could conceivably occur viamutation in a bacteriocin-sensitive strain that confers re-sistance or through mutation in a bacteriocin-producingstrain that disrupts bacteriocin production while leavingits resistance intact. The presence of a sensitive strain couldlead to complex “rock-paper-scissor” dynamics. Such sys-tems have already been successfully studied (Durrett andLevin 1997; Kerr et al. 2002; Kirkup and Riley 2004) andare beyond the context of this work.

Coexistence in Dual-Strain Biofilms

In well-mixed environments, competition between bac-teriocin-sensitive and bacteriocin-producing cells alwaysleads to the extinction of one of the two competing strains,depending on initial conditions (Riley and Gordon 1999).However, competition in spatially structured environ-ments such as agar plates (Frank 1994; Durrett and Levin1997) and biofilms (Tait and Sutherland 2002) can leadto coexistence of producers and nonproducers. In orderto investigate the coexistence of multiple strains producingdifferent bacteriocins, we extended our model to performlong-term simulations of mixed biofilms. We included twonew processes essential for the realistic modeling of biofilmdynamics over longer periods: (1) endogenous biomassdecay and (2) biofilm detachment (Xavier et al. 2005b).Our extended model assumed a first order biomass decayrate, and that biofilm detachment increases with the squareof the distance from the solid substratum (Xavier et al.2004, 2005a). For each simulation we quantified biodi-versity in the biofilm using Shannon’s index (SH):

N

S p � p log p . (8)�H i 2 iip1

Shannon’s index has been used previously to quantifybiodiversity in microbial consortia (Turnbaugh et al.2009). Term pi is the proportion of the ith population inthe system. In our first set of simulations, . Below,N p 2we will use the same index to quantify biodiversity inmultistrain biofilms ( ).N p 10

The results of our long-term, dual-strain biofilm com-petition simulations (sensitive vs. producer) are presentedin figure 5. Biodiversity is strongly influenced by nutrientpenetration (parameter d; fig. 5A). For d lower than 0.1,the biofilm forms thin fingerlike protrusions that aremostly monoclonal (fig. 5C1). As d increases, protrusionsbecome less defined and local mixing among the twostrains increases (fig. 5C2, 5C3). This leads to a reductionin biodiversity, which is ultimately lost when nutrients fullypenetrate and the biofilm is completely mixed (fig. 5C3).

Under this latter condition, one strain or the other goesto fixation, and the outcome of competition appears tobe strongly dependent on Lbac (fig. 5B). The model, there-fore, predicts that biodiversity is strongly related to en-vironmental factors influencing biofilm morphology, suchas nutrient penetration. In agreement with laboratory ob-servations (Tait and Sutherland 2002), our simulationsshow that biofilm heterogeneity with respect to lineagesegregation and surface structure tends to favor the co-existence of bacteriocin producers and sensitive strains.

It is interesting to note that introducing biomass decayand biofilm erosion changes the evolutionary dynamics ofbacteriocin production, which is evident from a compar-ison between the results of this section and those reported

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Figure 5: Results from long-term simulations in dual (bacteriocin-producer vs. bacteriocin-sensitive) strain biofilms. The d-Lbac parameterspace was analyzed for regions of high bacteriocin-producer and bacteriocin-sensitive strain coexistence. Biodiversity was calculated usingthe Shannon (SH) index (see main text). Biodiversity (coexistence) is predicted to be strongly dependent on genetic segregation and biofilmmorphology. A, Biodiversity as a function of d and Lbac. B, Mean change in producer frequency as a function of d and Lbac. C, Representativeframes depicting different biofilm structures, which are largely a function of d: (C1) single-strain towerlike protrusions, (C2) a large dual-strain protrusion (at left), and (C3) a completely smooth biofilm. Bacteriocin-producing cells are red, bacteriocin-sensitive cells are blue,and dead/inert biomass is gray. The isocontour lines represent the gradients of nutrient concentration in the biofilms.


in the sections above. In simulations that do not imple-ment biomass decay or erosion, bacteriocin production isnegatively selected when nutrient penetration is low andpositively selected when nutrient penetration is high. Weexpect this pattern to apply most strongly when biofilmsare relatively short-lived. On longer timescales, however,when biomass decay and biofilm erosion must be explicitlyconsidered, bacteriocin production may persist when nu-trient penetration is low, and its evolutionary dynamicsare sensitive to initial conditions when nutrient penetra-tion is high.

Biodiversity in Multistrain Biofilms

We extended our simulations to include multiple strainsof bacteriocin producers and investigated the conditionsgoverning biodiversity with respect to bacteriocin pro-duction. We considered two slightly different scenarios.First, nine bacteriocin producers and one bacteriocin-sen-sitive strain were inoculated at equal initial frequencies.Each producer strain allocated the same amount of re-sources ( ) to bacteriocin production and was im-f p 0.1mune to its own toxin but sensitive to all eight of the otherproducers’ bacteriocins. In the second scenario, we omit-ted the sensitive strain, and 10 bacteriocin producer pop-ulations were competed with each other. As before, eachstrain allocated an equal amount of resources to bacteri-ocin production ( ), and was immune only to itsf p 0.1own toxin. Since all strains had the same competitive fea-tures, this second scenario served to evaluate the effect ofstochasticity (genetic drift) on the decay of bacteriocinbiodiversity.

Our simulations were run until their global strain com-positions appeared to reach a steady state. We then assessedthe population composition by determining each strain’sfrequency with time (fig. A3A, available online) and mea-suring Shannon’s index (SH; fig. A3B). In all simulations,biodiversity decreased from its initial value, albeit at dif-ferent rates. In order to compare simulations carried outwith different values of d and Lbac, we quantified the rateof biodiversity loss by calculating the biodiversity half-life(t1/2), which estimates the time it takes for biodiversity todecay down to half of its initial value. This was done byfitting the rate of exponential decay from a biodiversitytime series (fig. A3C) using a least-square fitting method(Michel et al. 2011).

We obtained curves to determine biodiversity half-lifeversus d for different values of Lbac and for both compe-tition scenarios. In accordance with simulations in whichonly one bacteriocin producer and one sensitive straincompeted (fig. 5), the multistrain competitions illustratetwo important results (fig. 6A, ). First, biodiversity remainshigher in spatially structured, genetically segregated bio-

films (i.e., low d for low nutrient penetration; fig. 6C1,6C3, 6C5). Biodiversity is rapidly lost in simulations car-ried out at higher nutrient penetration (high d; fig. 6C2,6C4). Second, if d is fixed, biodiversity remains higher forsmaller critical bacteriocin ranges (lower Lbac; fig. 6C3 cf.6C5). Higher Lbac produces longer-range interactionsamong competing strains, increasing the probability ofdriving some more quickly to extinction. This is evidentfrom the concentrations of toxin accumulated in the bio-film (higher in fig. 6C5 cf. fig. 6C3. Higher Lbac produceslonger-range interactions among competing strains, in-creasing the probability of strain extinction).

It is, however, important to note that the mechanismresponsible for decreasing biodiversity is different in thetwo scenarios analyzed. When a sensitive, nonproducingstrain is included with bacteriocin producers, the modelpredicts that the sensitive strain goes to fixation. The in-crease in “warfare” among bacteriocin-producing strainsresulting from increased cell lineage mixing (high d) andincreased bacteriocin killing efficacy (higher Lbac) decreasesthe average fitness of all producing strains. They are thusmore easily outcompeted by a sensitive strain investing allof its resources into growth than a single bacteriocin pro-ducer with greater strength in numbers (fig. 6C2). Whenonly bacteriocin-producing strains are present, on theother hand, the loss of biodiversity is purely stochastic. Atthe beginning of biofilm growth, chance effects lead a fewstrains to increase in frequency. These strains have an in-herent advantage, as their secreted toxins accumulate tohigher concentrations, and ultimately one strain can driveout all the others (fig. 6C5). The dynamics of this systemmay thus be described as genetic drift with positive feed-back. The rate at which this stochastic loss of biodiversityoccurs is an increasing function of both the scale of bac-teriocin-mediated killing (Lbac) and nutrient penetration(fig. 6B).

Conclusions

Bacteriocin production is an important feature of bacteriallife and a key process in the ecology of multistrain biofilms(Tait and Sutherland 2002). Our study aims to bridge gen-eral social evolution theory and specific experimental find-ings in biofilms by analyzing how physical and biologicalprocesses combine to drive the evolution of bacteriocinproduction in spatially structured biofilms. With generalityin mind, we chose to implement a simple kinetic modelof bacteriocin production and its action (Wilkinson 2002).The model omits processes that can regulate bacteriocinproduction but may be restricted to specific bacterial spe-cies, such as bacteriocin signaling (Gillor et al. 2008b),cross-induction mechanisms (Majeed et al. 2010), or quo-rum-sensing regulation (Nadell et al. 2008).

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Figure 6: Bacteriocin biodiversity is maintained longer in structured biofilms. A, Bacteriocin biodiversity half-life for biofilms with onesensitive strain and nine bacteriocin-producing strains. B, Bacteriocin biodiversity half-life for biofilms with 10 bacteriocin-producing strains;95% confidence intervals were smaller than the point markers and were therefore omitted. C, Representative frames from biofilm simulationscontaining (C1) nine bacteriocin producers and one bacteriocin-sensitive strain, with and , and (C2) nine bacteriocind p 0.1 L p 0.0005bac

producers and one bacteriocin-sensitive strain, with and . C3, Ten bacteriocin-producing strains, with andd p 10.5 L p 0.0005 d p 0.1bac

. C4, Ten bacteriocin-producing strains, with and . C5, Ten bacteriocin-producing strains, withL p 0.0005 d p 0.5 L p 0.0005 d pbac bac

and .0.1 L p 0.1bac


By analyzing a simple model we derive a length-scaleof bacteriocin-mediated killing, Lbac, a single compoundparameter that describes the combined effects of bacte-riocin production, transport, and toxicity to a recipient.Parameter Lbac sets the critical spatial range around a focalbacteriocin-producing cell within which its fitness is higherthan that of a recipient sensitive cell. Similarly, by mech-anistically modeling biofilm nutrient penetration, set byanother compound parameter d, we describe how the scaleof competition for limited nutrients is affected by otherphysical and biological properties. Building upon previoussocial evolution models (Frank 1998; Gardner and West2004; Gardner et al. 2004), we decouple the effects of thesetwo processes and show that both the critical bacteriocinrange and the scale of competition are important driversgoverning the evolution of bacteriocin production in bio-films. The critical bacteriocin range is particularly impor-tant under conditions of high nutrient penetration andlocalized competition for limited growth substrates. Wealso show, in agreement with previous laboratory findings(Tait and Sutherland 2002), that conditions of nutrientlimitation that lead to the formation of monoclonal tow-erlike protrusions are essential to the maintenance of bio-diversity with respect to bacteriocin production (fig. 6C).

Scientists are increasingly interested in social interactionsamong microbes in biofilm communities and their impli-cations for human health (Nadell et al. 2009). For example,bacteriocin-mediated competition between commensal andpathogenic Streptococci species in the oral cavity has beenintensively studied and recognized to affect the developmentof oral disease (Kreth et al. 2008). Spatially explicit theo-retical models such as those discussed in this article areimportant for developing new conceptual approaches totuning such competitive bacterial environments, and en-hancing the success of beneficial species could become animportant strategy to treat biofilm-related pathogenic in-fections (Nadell et al. 2009; Xavier 2011).

The human gut microbiota is an especially promisingtarget for study, as it is a spatially structured multispeciesconsortium that plays an important role in resisting in-fection by enteropathogenic bacteria (Stecher and Hardt2008; Neish 2009; Ubeda et al. 2010). Many examples showthat bacteriocins play a major role in gut microbial ecology(Gillor et al. 2008a). Ruminococcus gnavus, a commoncommensal, produces the antibacterial rumococcin, whichis effective against several pathogenic Clostridia (Dabardet al. 2001). The probiotic Lactobacillus salivarius UC118protects against the pathogen Listeria monocytogenesthrough bacteriocin secretion (Corr et al. 2007). Recentadvances in metagenomics are leading a generation of newstudies into gut microbiota and its implications for humanhealth and disease (Marchesi and Shanahan 2007). Theseadvances must be accompanied by mechanistic knowledge

of the processes governing species composition dynamicsand function. Our study sheds new light onto the ecologyof microbiomes by unveiling the mechanisms driving theevolution of bacteriocin-mediated competition.

Acknowledgments

This work was supported by a National Institute ofCancer Center for Integrated Cancer Biology grant(1U54CA148967–01) and a seed grant from the LucilleCastori Center for Microbes, Inflammation, and Cancer.C.D.N. is supported by a Princeton University CentennialFellowship and a National Science Foundation GraduateResearch Fellowship.

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The Evolution of Bacteriocin Production in Bacterial Biofilms