A Three-Dimensional Computer Model of Four Hypothetical Mechanisms Protecting Biofilms from Antimicrobials

Four hypothetical mechanisms for protection of biofilms againstantimicrobials were incorporated into a three-dimensional modelof biofilm growth and development. The model integrated processesof substrate utilization, diffusion, growth, cell migration,death, and detachment in a cellular automaton framework. Comparedto simulations of unprotected biofilms, each of the protectivemechanisms provided some tolerance to antimicrobial action.When the mechanisms were compared to each other, the behaviorsof the four protective mechanisms produced distinct shapes ofkilling curves, nonuniform spatial patterns of survival andcell type distribution, and anticipated susceptibility patternsfor dispersed biofilm cells. The differences between the protectivemechanisms predicted in these simulations could guide the designof experiments to discriminate antimicrobial tolerance mechanismsin biofilms. Each of the mechanisms could be a plausible avenueof biofilm protection.

INTRODUCTION

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Introduction

Microorganisms within biofilms have a remarkable tolerance tokilling by antimicrobial agents (26, 39). The reduced susceptibilityof bacteria and yeast in biofilms is recognized as an importantfactor in the persistence of some chronic infections and thetroublesome recurrence of fouling in industrial systems. Whilethe reduced antimicrobial and biocide susceptibility in biofilmsis well documented, the mechanisms of resistance are incompletelyunderstood (26, 39, 41). Four leading hypotheses explainingthe reduced susceptibility of biofilms, diagrammed in Fig. 1,are poor antimicrobial penetration, deployment of adaptive stressresponses, physiological heterogeneity in the biofilm population,and the presence of phenotypic variants or persister cells (6,12, 25, 38). It seems likely that a combination of these factorsdetermines the overall protection in the biofilm (38, 39).

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FIG. 1. Four possible mechanisms of biofilm antibiotic resistance. The image is a cross section of a biofilm with the attachment surface (gray) at the bottom and the aqueous phase containing the antibiotic (yellow) at the top. In zones where there is nutrient depletion (red), antibiotic action may be antagonized. Some bacteria may activate stress responses (green), while others may differentiate into a protected phenotype (purple).

There have been a handful of papers describing neutralizationof an antimicrobial agent by a reaction as it diffuses intoa biofilm (1, 42). The biofilm is said to consume the antimicrobialagent in the same manner that it would consume a substrate.This consumption could allow biofilms to decrease the concentrationof an antimicrobial to a level that would be ineffective inthe deeper regions of the biofilm. However, such a protectivemechanism would be expected to be present only in thicker biofilms.Also, antimicrobial agents that do not react with or bind toa biofilm can be expected to penetrate in a matter of secondsor minutes (37). Examples of several antimicrobial agents thatpenetrate biofilms but fail to kill the sessile microorganismsat the rate observed for their planktonic counterparts are plentiful(1, 7, 10, 17, 33, 43, 49).

Bacteria are equipped with a host of stress responses that allowthem to cope with environmental adversity. It is possible thatthe same protective mechanisms are utilized by biofilms. Themost compelling version of this second mechanism of biofilmprotection is that stress response defenses are induced in biofilmbacteria when they face an environmental challenge, just asthey are in bacteria in aqueous suspension. The difference betweenfree-floating cells and biofilm-embedded cells is that the biofilmbacteria are sufficiently protected by other defenses, suchas retarded antimicrobial penetration or slow growth, whichallows the biofilm cells to respond to an antimicrobial challengethat overwhelms planktonic cells. An example of a stress responsethat is of obvious interest in the context of antimicrobialsis the expression of drug efflux pumps.

The possibility that substrate limitation within a biofilm createsregions of inactive and less susceptible cells remains an attractiveexplanation for the recalcitrance of biofilms to antimicrobialagents (3, 6, 19, 20). It is clear that there are substrateconcentration gradients within biofilms (13, 48). These concentrationgradients give rise to corresponding gradients in the microbialgrowth rate and activity, as observed by researchers using fluorescentprobes and reporter genes (35, 45, 46). Since antimicrobialsare thought to be more effective in killing actively growingcells, it seems reasonable that in substrate-limited regionsof a biofilm the microorganisms could better tolerate the presenceof an antimicrobial agent by virtue of their inactivity. However,one would expect that as growing cells within the biofilm arekilled, substrate would penetrate into regions that were previouslysubstrate depleted. Thus, dormant microorganisms might losetheir tolerance for the antimicrobial agent as substrate becomesavailable.

A fourth mechanism of antimicrobial resistance in biofilms invokesthe possibility of a unique and highly protected phenotypicstate that is adopted by a subpopulation of microorganisms ina biofilm (26, 41). This is conceptualized as true differentiationof the cells akin to spore formation that requires the expressionof specific sets of genes. Cells in this special state havebeen termed persisters. Such a phenotypic state is suggestedby experiments with young biofilms that display resistance eventhough they are too thin to pose a barrier to the penetrationof either an antimicrobial agent or metabolic substrates (7,11). Another indication that biofilms may harbor a subpopulationof resistant cells comes from experiments in which most, butnot all, of the biofilm is rapidly killed by an antimicrobial(2, 5, 21). The survivors, which may be 1% or less of the originalpopulation, persist despite continued exposure to the antimicrobial(2, 34).

Computer models of biofilm dynamics complement experimentalinvestigations and thus are valuable tools in the explorationof biofilm phenomena. Models can be used to test conjecturesor make predictions about how specific processes affect biofilmstructure or function. Theoretical explorations are particularlyattractive because often there are multiple mechanisms thatare difficult to separate experimentally. We have been interestedin using biofilm models to explore the degrees of protectionfrom killing by antimicrobials that can be conferred by specifictolerance mechanisms. Several previous studies have describedbiofilm models that incorporate antimicrobial action (8, 14,15, 23, 28, 36, 40, 44). Using a three-dimensional computermodel of biofilm dynamics, we investigated the levels of protectionagainst antimicrobials provided by each of four hypothesizedprotective mechanisms. The purpose of this study was to characterizethe predicted features of four different protective mechanismswhen they were incorporated into a multidimensional computermodel of biofilm dynamics. In particular, we sought to examinepopulation survival versus antimicrobial exposure time and thespatial patterns of chemical species and cell types within biofilmsduring or after antimicrobial treatment.

MATERIALS AND METHODS

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Materials and Methods

BacLAB, the computer model used in this study, has been describedin detail elsewhere (22). This model uses a hybrid modelingapproach in which all soluble components are modeled using discretizeddifferential equations while the individual microorganisms thatcompose the biofilm are modeled discretely using a cellularautomaton algorithm. A cellular automaton is an independentunit, here equated to a bacterial cell, that follows certainbehavioral rules. The resulting aggregate behavior of the biofilmtherefore emerges from the local interactions between the individualbacteria. The cellular automaton model produces realistic, structurallyheterogeneous biofilms (4, 9, 18, 24, 28, 29, 30, 47). Furthermore,it allows the artificial biofilm structure to evolve as a self-organizingprocess, emulating how bacterial cells organize themselves intobiofilms. Two advantages of the hybrid approach are the abilityto separate different biofilm processes according to the naturaltime scale and the fact that the aggregate behavior of the biofilmemerges from the local interactions between individual microorganisms.Some of the processes simulated by the computer model includediffusion of soluble components into the biofilm, substrateand antimicrobial consumption, microbial growth, and biofilmdetachment resulting from nutrient starvation. Parameter valuesare summarized in Table 1, and a representation of a typicalBacLAB biofilm simulation is shown in Fig. 2.

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TABLE 1. Summary of parameters used in the BacLAB model

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FIG. 2. Three-dimensional representation of the BacLAB model, showing a biofilm with live (green), dead (red), and persister (blue) cells at hour 300 (150 h after completion of a 50-h antimicrobial treatment) (A) and during a 300-h simulation in which the persister protection mechanism is active (B). Biofilm formation begins with the development of independent cell clusters that merge over time. Antimicrobial treatment initiated at 100 h rapidly kills most of the live cells, but persister cells survive. When persister cells eventually resuscitate, they give rise to new growth that begins in clonal pockets but rapidly extends throughout the biofilm. A video of this simulation can be viewed at www.erc.montana.edu/Res-Lib99-SW/Movies/Database/MD_DisplayScript.asp.

The following two sets of simulations were performed for eachof the four protective mechanisms: (i) protected with a continuousantimicrobial treatment initiated at hour 100 and lasting 50h and (ii) unprotected with a continuous antimicrobial treatmentinitiated at hour 100 and lasting 50 h.

For all unprotected studies the probability of killing due tothe presence of the antimicrobial agent was 0.6838 for a 1-hinterval. This value was calculated to provide a 6-log reductionin nongrowing suspended cell cultures in a 12-h treatment periodby solving the following equality: (1 – P)¹² = 10^–6,where P is the probability of killing. Therefore, the probabilitythat a cell will survive a 12-h treatment is 1 in 10⁶. At eachtime that the antimicrobial agent is present, every cell inthe simulation generates a random number from a uniform distributionon the interval [0, 1]. If the random number is less than orequal to the probability of killing (0.6838), the cell diesand remains metabolically inactive for the remainder of thesimulation or until it detaches from the biofilm. If the randomnumber is greater than 0.6838, the cell continues to functionnormally.

The slow penetration, stress response, and persister mechanismsuse the same probability for killing of live cells that is foundin the unprotected simulations. In order to provide a form ofprotection, the slow penetration and stress response mechanismsinclude restrictions on when this probability equation is activeas a result of the barrier to antimicrobial diffusion. For thepersister mechanism, no restrictions are placed on this probabilitysince the protection stems from the inclusion of the spore-likepersister cells. The substrate limitation mechanism is differentfrom each of these mechanisms and the unprotected simulationsin that the probability of killing is altered so that it isdirectly proportional to the local substrate concentration.

In the simulations in which the slow penetration mechanism isactive, both live and dead biofilm cells consume the antimicrobialas it diffuses into the biofilm. The parameters for antimicrobialdiffusion and consumption are shown in Table 2.

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TABLE 2. BacLAB parameters for use in antimicrobial diffusion and consumption

In the aqueous environment modeled here, the bulk liquid iswell mixed but imposes no shear stress on the biofilm. The antimicrobialis transported solely by diffusion in the biofilm. The localconcentrations are a result of molecular diffusion and reaction(consumption or production) with the bacteria. The diffusionaltime constant is approximately 100 orders of magnitude smallerthan that for bacterial cell division (28). Thus, moleculardiffusion can be assumed to be at a steady state with respectto the bacterial growth.

Since the antimicrobial is steadily depleted, there is an antimicrobialconcentration at which it is no longer effective against thebiofilm cells. This concentration, otherwise known as the MIC,is set at 1.0 g m^–3. It follows that as the thicknessof a biofilm increases, so too does the chance of thwartingan antimicrobial challenge.

The stress response mechanism includes the same rules that areused for slow penetration protection, diffusion and consumptionof the antimicrobial based on the parameters shown in Table2, and no killing below an MIC of 1.0 g m^–3, but withone variation: if the antimicrobial concentration is greaterthan or equal to one-tenth the MIC and the cell has not beenkilled by the antimicrobial, then the cell has some probabilityof switching to an adapted state. This probability is 0.06838,10% of the probability of death. In the adapted state the cellacquires absolute resistance to the effects of the antimicrobialand continues its cellular functions uninhibited by the antimicrobial.

For the substrate limitation mechanism, the antimicrobial efficacywas simulated to be proportional to the amount of substrateavailable to the microorganism; that is, P = (P_MAX/C_S₀) ·C_S, where P_MAX is the maximum probability of killing and isequal to the probability of killing used in the base case simulations,C_S₀ is the substrate concentration in the bulk fluid, and C_Sis the local substrate concentration at a particular cell. Thus,cells in substrate-rich regions of the biofilm have the lowestantimicrobial tolerance, whereas cells in substrate-depletedregions are expected to be tolerant to antimicrobial killing.

When the persister mechanism is simulated, the protection stemsfrom the random conversion of live cells to persister cells.Persister cells are nongrowing, spore-like cells that are nearlyimpervious to antimicrobial effects. Persisters are constantlybeing formed, with no regard to the presence of an antimicrobial.The probability of a live cell converting to a persister cellis 0.0015, and the probability of a persister cell convertingback to a live cell is 0.15. These values were chosen to yielda persister population that is approximately 1% of the totalpopulation. The probability that a persister cell will be killedby an antimicrobial is 0.0034, which makes such a cell 200-foldmore resistant to the antimicrobial than a normal live cell.

We did not conduct a full analysis of the sensitivity of themodel to the values of key parameters. Rather, it was our intentto illustrate the qualitative behaviors predicted when certainbiological and physical phenomena were simulated.

All simulations progressed through a 300-h experiment, including100 h of initial attachment and unchallenged growth, 50 h ofantimicrobial treatment, and 150 h of recovery.

RESULTS AND DISCUSSION

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Results and Discussion

The computer model used in this investigation simulated biofilmdevelopment over 300 h, along with the response to a 50-h continuousantimicrobial treatment for both unprotected and protected biofilms.Because there are stochastic components of the model, the simulationresults varied slightly from run to run even when the same parametersettings and initial conditions were used. We therefore raneach simulation case six times.

We selected a value for the antimicrobial killing rate thatcorresponded to a 6-log reduction in the number of viable cellsafter 12 h of exposure of planktonic cells to the antimicrobialagent in the absence of cell growth. Even with the inclusionof biofilm growth during an antimicrobial treatment, we anticipatedthat each of the unprotected biofilms would be eradicated bya 50-h treatment. In all cases, this was indeed the result.All of the unprotected biofilms were killed completely by hour15 of the antimicrobial treatment.

For the protected biofilms, Table 3 summarizes the log reductionsproduced by the 50-h antimicrobial treatment.

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TABLE 3. Log reductions for live cells for each protective mechanism after a 50-h antimicrobial treatment

Slow penetration.
The killing curve for the slow penetration investigations andthe corresponding base case simulations are shown in Fig. 3.The survival curve is highly nonlinear. Retarded antimicrobialpenetration provided good protection to the biofilm up untilaround 15 h after the onset of treatment. If the treatment hadbeen a 12-h treatment, the biofilm would have easily surviveddue to the protection of slow penetration. After this time,however, viability decreased sharply as the diffusion of theantimicrobial outpaced the neutralization by the bacteria. Thisimbalance led to complete disinfection of the biofilm colony15 to 20 h before the end of the 50-h treatment.

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FIG. 3. Log reduction in biofilm live cells during a 50-h antimicrobial treatment for unprotected biofilms and biofilms protected by the slow penetration mechanism. The biofilms without protection are completely eradicated after 13 h, while the protected biofilms are able to withstand the antimicrobial for 30 to 35 h.

When the slow penetration mechanism is active, both live anddead biofilm cells consume the antimicrobial. The effects ofthis consumption are evident in the profile of the antimicrobialconcentration in the biofilm 10 h after the treatment began,as shown in Fig. 4. The concentration of antimicrobial agentis reduced in and around the biofilm clusters, even in the fluid,where there is no consumption of the antimicrobial. This isbecause the stagnant fluid outside the biofilm provides resistanceto diffusive mass transfer. There are bands of live cells atthe bottoms of the larger biofilm clusters, where the antimicrobialconcentration is less than 10% of the bulk concentration. Theseparation between live and dead cells is distinct as thereare few live cells at concentrations above 1.0 g m^–3 andalmost no dead cells at concentrations below this concentration.

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FIG. 4. Concentration profile for the antimicrobial in a slow penetration simulation after hour 110, 10 h after introduction of the antimicrobial. The image is a two-dimensional cross section of the biofilm with the substratum at the bottom and the bulk fluid at the top. The isoline indicates antimicrobial concentrations (in g m^–3). The figure shows that there is a clear separation of live (green) and dead (red) cells at an antimicrobial concentration of 1.0 g m^–3. The antimicrobial concentration used was 10 g m^–3; this concentration occurs above the domain plotted.

The results of these simulations are most likely highly dependenton the choice of parameter values (Table 2). If the antibioticconsumption rate were increased, the biofilm would stand a greaterchance of surviving the treatment. There seems to be a criticalconsumption rate that, once passed, allows the biofilm to consumethe antimicrobial quickly enough that no investigation wouldreveal eradication of the biofilm. This assumption was not testedin this study. This concept has been discussed in previous studiesof beta-lactam penetration (14, 27).

It is interesting to consider the fate of a biofilm that isdisaggregated and then exposed to an antimicrobial agent. Inthe case of the slow penetration mechanism, the inherent susceptibilityof all the cells in a biofilm is identical to that of theirplanktonic counterparts. The only difference is that the antimicrobialconcentrations experienced by the biofilm population are heterogeneousand lower than those experienced by a planktonic population.If slow penetration is the sole basis for biofilm tolerance,we would anticipate that dispersal of a biofilm would immediatelyand completely restore its full planktonic susceptibility. Thisbehavior has been reported in some studies (2, 16, 42, 45).

Stress response.
When slow penetration is combined with an adaptive stress response,greater protection is predicted by the model (compare Fig. 5to Fig. 3). In this case, the antimicrobial fails to eradicatethe biofilm. This is due to the transformation of live cellsinto adapted cells, which are immune to the antimicrobial agent.The adapted cells continue to grow and outcompete other celltypes in the antimicrobial-treated biofilm community. By theend of the simulation, there are no nonadapted live cells remaining.

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FIG. 5. Log reduction in biofilm live cells during a 50-h antimicrobial treatment for unprotected biofilms and biofilms protected by the stress response and slow penetration mechanisms. The biofilms without protection are completely eradicated after 15 h, while the protected biofilms are able to withstand the antimicrobial throughout the treatment time with an average log reduction of 1.53 ± 0.06.

It is evident from the representative antimicrobial concentrationprofile shown in Fig. 6 that incomplete penetration of the antimicrobiallimits killing to the uppermost layers of the biofilm. Thereis a sharp delineation between live and dead cells correspondingto the isoline of antimicrobial concentration equal to 1.0 gm^–3. The antimicrobial concentration gradient allows cellsin the lower regions of the biofilm to adapt and convert fromthe live cell state to the adapted cell state (Fig. 6). Thistransformation occurs with a fixed probability wherever theantimicrobial concentration is greater than 0.1 g m^–3.

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FIG. 6. Concentration profile for the antimicrobial in a stress response simulation after hour 110, 10 h after introduction of the antimicrobial. The image is a two-dimensional cross section of the biofilm with the substratum at the bottom and the bulk fluid at the top. The isoline indicates antimicrobial concentrations (in g m^–3). The antimicrobial concentration used was 10 g m^–3; this concentration occurs above the domain plotted. A small band containing only live cells is also evident near the bottom of the biofilm. In this area the antimicrobial concentration is less than 0.1 g m^–3. Above this band, adaptive cells (yellow) are formed.

The outcome simulated here is dependent on the choice of parametervalues (Table 2). The threshold concentration for implementationof the stress response (0.1 g m^–3 in this study) is critical.When this value is less than the concentration required forkilling, then there is a window of antimicrobial concentrations(0.1 to 1.0 g m^–3 in this study) at which adaptation isrelatively favorable. Note that adaptation can still occur atconcentrations above the killing threshold concentration, butin this situation there is a race between the transformationof live cells to dead cells (killing) and the transformationof live cells to adapted cells (adaptation). The essential propertyof the adapted cell state is its invulnerability to killing,which allows such cells, even if only small numbers are generated,to eventually dominate the biofilm population.

One of the predictions implicit in the simulation of the stressresponse mechanism is that the adapted cells in an antimicrobial-treatedbiofilm should retain their antimicrobial tolerance for sometime even if they are dispersed from the biofilm. Adapted cellsmay revert to the unadapted state if they are grown in the absenceof the antimicrobial agent, but this process presumably requiressome time. A biofilm population that is disaggregated and immediatelychallenged with an antimicrobial agent would be expected tocontain some adapted cells and therefore exhibit susceptibilityintermediate between that of a normal (unadapted) planktonicpopulation and that of an intact biofilm. This has been observedin some experimental studies (3, 19, 20, 31). While in thisinvestigation we did not incorporate the process of adaptedcells returning to an unadapted state, this would be a straightforwardmodification.

Substrate limitation.
When substrate-limited killing is simulated, the biofilm iswell protected (Fig. 7). Since cells in the outer layers ofthe biofilm are killed (Fig. 8) and these dead cells no longerconsume substrate, substrate should permeate into the biofilm,feeding the inner layers and making them vulnerable to the actionof the antimicrobial. This process is not particularly rapid,as Fig. 7 shows. This result of prolonged tolerance affordedby the substrate limitation mechanism is in agreement with thepredictions of a previous study conducted with a one-dimensionalbiofilm model (32). Note that the simulations and results describedhere and below do not incorporate the slow penetration protectiondiscussed above.

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FIG. 7. Log reduction in biofilm live cells during a 50-h antimicrobial treatment for unprotected biofilms and biofilms protected by the substrate limitation mechanism. The biofilms without protection are completely eradicated after 15 h, while the protected biofilms are able to withstand the antimicrobial throughout the treatment time with an average log reduction of 0.61 ± 0.09.

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FIG. 8. Concentration profile for the substrate in a substrate limitation simulation after hour 110, 10 h after introduction of the antimicrobial. The image is a two-dimensional cross section of the biofilm with the substratum at the bottom and the bulk fluid at the top. The isoline indicates substrate concentrations (in g m^–3). The majority of dead cells (red) are concentrated at the top of the biofilm, where the local maximum substrate concentration occurs. Few dead cells are found deep within the biofilm, where the local substrate concentration can fall below 0.1 g m^–3. The substrate concentration used was 10 g m^–3; this concentration occurs above the domain plotted.

According to the substrate limitation mechanism, cells in substrate-richregions of the biofilm have the greatest antimicrobial susceptibility,whereas cells in substrate-depleted regions are expected tobe relatively tolerant to antimicrobial killing. This behavioris evident in the substrate concentration profile shown in Fig.8, which shows the domination of live cells in the innermost,and nutrient-limited, layers of the biofilm. Dead cells arelocalized preferentially in the surface layers of the biofilm,where substrate concentrations are highest. The stratificationof live and dead cells is not as sharp as that predicted bythe slow penetration and stress response mechanisms. Survivingcells can be found at the outermost reaches of the biofilm,and dead cells can be found deep in the biofilm interior.

If cells were dispersed from a biofilm protected by substratelimitation, how susceptible would they be to antimicrobial challenge?If the biofilm were dispersed in a substrate-replete medium,the susceptibility should approach that of the typical planktonicstate. Awakening from a nongrowing, starved state to a stateof rapid growth may require some time, so susceptibility maynot be restored instantly. This could explain the occasionalobservation of intermediate susceptibility of dispersed biofilmcells (3, 19, 20, 31). An interesting experiment would be todisperse biofilm cells in a substrate-limited medium (or mediumlacking substrate altogether) and then apply an antimicrobialchallenge. If substrate limitation is the sole protective mechanism,then these cells should retain the full level of tolerance exhibitedby the intact biofilm. There are very few examples of this kindof experiment, and the data are inconclusive.

Persisters.
The time course of killing of cells in a biofilm protected bypersister formation is distinct from the patterns exhibitedby the other three protective mechanisms (Fig. 9). Most of abiofilm consists of cells whose intrinsic susceptibility isthe same as that of a planktonic cell. Thus, the majority ofthe biofilm population is rapidly killed. The persister subpopulation,which constitutes approximately 1% of the biofilm initially,is very slowly killed. The rate of killing of the persistercells is controlled by the slow, random reversion of these cellsto the live cell state. As persisters convert to live cells,they become vulnerable to the antimicrobial. This mechanismleads to a bilinear killing curve in which rapid killing ofmost of the biofilm is followed by very slow killing of theremainder of the population. The noise at the bottom of thecurve comes from the stochastic conversion and resuscitationof live and persister cells, respectively.

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FIG. 9. Log reduction in biofilm live cells during a 50-h antimicrobial treatment for unprotected biofilms and biofilms protected by the persister mechanism. The biofilms without protection are completely eradicated after 11 to 19 h, while the protected biofilms are able to withstand the antimicrobial for 40 to 50 h with an average log reduction of 5.80 ± 0.25.

The pattern of survival and regrowth inside a biofilm protectedby persister formation is also distinct from the patterns predictedfor the other three protective mechanisms (Fig. 10). Regrowthof the biofilm from isolated persister cells occurs in randomlylocated clonal pockets. The lone persister in the second panelof Fig. 10 resuscitated to the live cell state and began togrow, effectively reseeding the biofilm. This spatial patternis qualitatively different from the stratified patterns of killingobserved with the other protective mechanisms. It is worth reiteratingthat this result occurs in an environment free of convectivemixing of biomass.

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FIG. 10. Cross section of a persister-protected biofilm. The same cross section is shown at 95, 145, 250, and 300 h. The results show that a single persister cell (yellow circle at hour 145) can reseed the colony with new growth after an antimicrobial treatment has ended.

Dispersing cells from a biofilm protected by persister formationshould not change the overall susceptibility, unless, of course,there is a period between the dispersal of the biofilm and theapplication of the antimicrobial that is sufficient to allowreversion of the persister cells to live cells. If the antimicrobialchallenge is applied quickly, however, the live cells remainvulnerable and persister cells should remain mostly invulnerable.Thus, the dispersed cells would be expected to exhibit susceptibilitysimilar to that of the intact biofilm. While experimenters rarelyanalyze the susceptibility of dispersed biofilm cells, whenthey do, they find that the dispersed cells are usually moresusceptible than the intact biofilm.

Conclusions.
A three-dimensional computer model of biofilm dynamics has beendeveloped as a tool for investigating mechanisms of protectionfrom antimicrobial agents in biofilms. All four of the hypotheticalmechanisms explored in this study provided protection accordingto model simulations. It is not appropriate to compare the relativedegrees of protection afforded by these mechanisms because theresults depend on the choice of key parameters whose true valuesare unknown. What can be compared are the qualitative featuresof the behaviors predicted by the simulations since these featuresare relatively insensitive to the choice of specific parametervalues. Features that were different in the four protectivemechanisms were the shape of the survival-versus-time curveand the spatial patterns of survival and cell type distribution(Table 4).

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TABLE 4. Characteristics of alternative protective mechanisms

These results may be helpful in designing laboratory experimentsto elucidate protective mechanisms in biofilms. We suggest thatthe most powerful approach to this problem would be to measure,in the same experimental system, all three of the aspects describedin Table 4 (i.e., the shape of killing curves, the spatial patternof antimicrobial action within the biofilm, and the relativesusceptibility of resuspended biofilm cells). Although thereare methods for measuring each of these features, we are awareof no single study in which all three have been measured concurrently.

One of the ways in which the work described in this paper differsfrom previous modeling studies of antimicrobial action againstbiofilms is in the incorporation of stochastic elements in themodel. Processes that have been simulated with random or probabilisticcomponents in the current study include the initial seedingof the substratum, the direction in which biomass is displacedwhen growth occurs, and the transformation of live cells todead cells in the presence of an antimicrobial. The result isthat no two simulations produce exactly the same quantitativeresult. The variability between simulations with identical inputparameter values captures some of the variation that is measuredby experimenters working with real biofilms. The stochasticelements of the model provide the ability to repeat experimentsand statistically analyze the results just as an experimenterwould in a real-world lab investigation.

ACKNOWLEDGMENTS

This work was made possible by grant 5R01GM067245-02 from theNational Institutes of Health.

FOOTNOTES

* Corresponding author. Mailing address: Center for Biofilm Engineering and Department of Chemical and Biological Engineering, Montana State University—Bozeman, Bozeman, MT 59717-3980. Phone: (406) 994-1960. Fax: (406) 994-6098. E-mail: phil_s{at}erc.montana.edu.

REFERENCES

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