Cheating on the Edge

Citation: Dugatkin LA, Dugatkin AD, Atlas RM, Perlin MH ( Lee Alan Dugatkin 0 Aaron D. Dugatkin 0 Ronald M. Atlas 0 Michael H. Perlin 0 Angus Buckling, Oxford University, United Kingdom 0 1 Department of Biology, University of Louisville, Louisville, Kentucky, United States of America, 2 Murray Hill Academy , Louisville, Louisville, Kentucky , United States of America We present the results of an individual agent-based model of antibiotic resistance in bacteria. Our model examines antibiotic resistance when two strategies exist: ''producers''-who secrete a substance that breaks down antibiotics-and nonproducers (''cheats'') who do not secrete, or carry the machinery associated with secretion. The model allows for populations of up to 10,000, in which bacteria are affected by their nearest neighbors, and we assume cheaters die when there are no producers in their neighborhood. Each of 10,000 slots on our grid (a torus) could be occupied by a producer or a nonproducer, or could (temporarily) be unoccupied. The most surprising and dramatic result we uncovered is that when producers and nonproducers coexist at equilibrium, nonproducers are almost always found on the edges of clusters of producers. - Funding: Partly funded by AREA grant 1 R15 AI060667-01A1 from the National Institutes of Health and by a grant from the Office of the Vice President for Research at the University of Louisville. Funding agencies had no role in the design and conduct of the study, in the collection, analysis, and interpretation of the data, and in the preparation, review, or approval of the manuscript. Competing Interests: The authors have declared that no competing interests exist. The evolution of traits that may benefit others, as well as self, has long been an interest of evolutionary biologists [18]. This issue has been brought to the forefront recently by experimental work on group-beneficial traits in model bacterial and yeast systems [6,920] including, but not limited to, work using Staphylococcus aureus, Pseudomonas fluorescens, Pseudomonas aeruginosa, Myxococcus xanthus, Saccharomyces cerevisiae and Escherichia coli. In addition, theoreticians have actively debated the role of individual, kin, group, and frequency-dependent selection in explaining the results of these experiments [6,17]. Using both theoretical and empirical tools, we have been examining the evolution of group-beneficial traits in the context of bacterial antibiotic resistance in E.coli. In two earlier papers, we examined the evolution of producers (who secrete a substance that breaks down antibiotics) and nonproducers (cheats) who do not secrete, or carry the machinery associated with secretion. Our prior models examined the evolution of these strategies in a single, very large population [21], as well as in metapopulations containing discrete trait groups [22]. Here, we examine the evolution of producers and nonproducers using an individual agent-based model. The model allows for populations of up to10,000, in which bacteria are affected by their nearest neighbors. Each of the 10,000 slots on our grid (a torus) could be occupied by a producer or a nonproducer, or could (temporarily) be unoccupied. Our empirical work suggests that this agent-based model may best mimic the dynamics of bacterial interactions in the context of shared antibiotic resistance. For example, our experimental work has found that when b-lactamase is produced to break down antibiotics, it is tethered to the producer cell, and hence primarily affects the producers nearest neighbors. Our agentbased model captures this dynamic in ways that prior models have not. The Model We consider two genotypes, labeled producers and nonproducers. Producers create a substance that provides them with a benefit and provides benefits to other group members as well, while nonproducers do not produce such a substance. In this model the substances we focus on are enzymes, such as b-lactamase, that break down blactam antibiotics (e.g.,ampicillin). In terms of bacterial antibiotic resistance, producers will possess a gene (often, but not exclusively, plasmid-borne) that codes for an antibiotic resistance mechanism that protects them from damage due to antibiotics. Plasmid possession carries a cost, in that cellular resources are required for plasmid replication and maintenance [13]. Nonproducers do not carry the plasmid with the gene for antibiotic resistance, but receive protection as a function of the number of producers in their neighborhood (it is in that sense that we consider producers as providing group- or neighborhood-level benefits to others). If nonproducers are surrounded by other nonproducers they die (details below), and hence the typical invasion problems associated with group-beneficial traits do not apply to our producer strategy, as pure populations of nonproducers are not viable. In our model, the benefit (B) associated with b-lactamase ranged from 0 to 1. Producers always received this benefit. Because blactamase may be tethered to the outside of a cell, we created a variable called help that measures the proportional benefit that cells near a producer receive, as a result of the b-lactamase tethered to that producer (that is; 0,help,B). Producers pay a cost (0,C,1) associated with b-lactamase production [13]. The fitness of the producers = B2C+(number of producers in neighborhood x B x help) The fitness of the nonproducers = 0; if no producers are in neighborhood or = number of producers in neighborhood x B x help; if one or more producers are in neighborhood. Figure 1. Two-dimensional snapshots of the 10,000 slot torus. B/C = 0.62, help = 0.14 (this help value was chosen, in part, as the result of unpublished experimental work on blactamase secretion in producer cells). a) Generation 1, b) Generation 10, c) Generation 20, d) Generation 40, e) Generation 300 and f) Generation 1000. Note that for generations 1999, any yellow (nonproducers) cells surrounded by only yellow or by only yellow and white cells would die and be replaced the next generation. doi:10.1371/journal.pone.0002763.g001 Figure 2. Two-dimensional snapshots of the 10,000 slot torus. B/C = 0.56, help = 0.19. a) Generation 1, b) Generation 10, c) Generation 20, d) Generation 40, e) Generation 300 and f) Generation 1000. Note that for generations 1999, any yellow (nonproducers) cells surrounded by only yellow or by only yellow and white cells would die and be replaced the next generation. doi:10.1371/journal.pone.0002763.g002 We used NetLogo simulation software [23] to build an agentbased model for the evolution of antibiotic resistance when producers and nonproducers interact. A 1006100 torus (no edges) with 10,000 slots was created, and we assumed that an antibiotic, such as ampicillin, was present at all times during our simulations. At the start of a simulation, each slot held either a producer or a nonproducer with probability 0.5 (qualitatively similar results were fo (...truncated)