Non-Local Interaction via Diffusible Resource Prevents Coexistence of Cooperators and Cheaters in a Lattice Model

Wingreen NS (2013) Non-Local Interaction via Diffusible Resource Prevents Coexistence of Cooperators and Cheaters in a Lattice Model. PLoS ONE 8(5): e63304. doi:10.1371/journal.pone.0063304 Non-Local Interaction via Diffusible Resource Prevents Coexistence of Cooperators and Cheaters in a Lattice Model David Bruce Borenstein 0 Yigal Meir 0 Joshua W. Shaevitz 0 Ned S. Wingreen 0 Matjaz Perc, University of Maribor, Slovenia 0 1 Lewis-Sigler Institute for Integrative Genomics, Princeton University , Princeton , New Jersey, United States of America, 2 Department of Physics, Ben-Gurion University , Beer-Sheva , Israel , 3 Department of Physics, Princeton University , Princeton , New Jersey, United States of America, 4 Department of Molecular Biology, Princeton University , Princeton, New Jersey , United States of America Many cellular populations cooperate through the secretion of diffusible extracellular resources, such as digestive enzymes or virulence factors. Diffusion of these resources leads to long-range intercellular interactions, creating the possibility of cooperation but also the risk of exploitation by non-producing neighbors. In the past, considerable attention has been given to game-theoretic lattice models of intercellular cooperation. In these models, coexistence is commonly observed between cooperators (corresponding to resource producers) and cheaters (corresponding to nonproducers). However, these models consider only interactions between direct competitors. We find that when individuals are allowed to interact non-locally through the diffusion of a shared resource coexistence between cooperators and cheaters is lost. Instead, we find population dynamics similar to simple competition, either neutral or biased, with no balancing selection that would favor coexistence. Our results highlight the importance of an accurate treatment of diffusion of shared resources and argue against the generality of the conclusions of game-theoretic lattice models. - Funding: N.S.W. was supported by National Science Foundation Grant PHY-0957573. D.B.B. was supported in part by the National Science Foundation Physics of Living Systems program (PHY-0957573) and the National Institutes of Health National Human Genome Research Institute training grant T32 HG003284 (Botstein, PI). Y.M. was supported by the National Institutes of Health (www.nih.gov) grant R01 GM082938. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. A vast array of species employ diffusible extracellular factors to alter the local environment of their cells. Most multicellular organisms secrete digestive enzymes and acids in their digestive tracts. Both healthy and cancerous human cells secrete a host of signaling factors to regulate growth processes [1]. Microbes living in biofilms use diffusible molecules to degrade host tissues, digest nutrients, chelate metals, neutralize antibiotics, and sequester toxins [27] (Fig. 1a). In some cases, the processed substrate, rather than the extracellular factor itself is what diffuses [6]. In either case, diffusible resources help cells engineer their surroundings, providing the cells with a variety of benefits. However, in addition to conferring benefits on the producers, extracellular resources can confer a benefit on nearby, potentially unrelated cells (Fig. 1b). Diffusible extracellular resources can find and interact with substrates that are inaccessible to the producing cell. For this reason, they have the potential to perform functions that private resources, even surface-bound extracellular factors, cannot. For example, the opportunistic human pathogen Pseudomonas aeruginosa exports the diffusible phenazine pyocyanin, which can act as a rudimentary circulatory system [8], as well as attack both host tissue and competing species of bacteria [9]. Notably, cells coordinate their pyocyanin production in response to that of other cells [10]. Other examples include the iron scavenging pigment pyoverdine [11] and enzymes such as exoglycosidases, which digest high molecular weight polysaccharides into simpler sugars [12]. Clearly, if the diffusion length is long and the cost of production is significant, nearby nonproducing cells can enjoy a competitive advantage over producers. Hence, an invader or a nonproducing mutant in a group of resource-producing cells may outcompete the producers, eventually leading to the loss of extracellular resource production in the population. How is it then that production of diffusible resources is widely observed, even among microorganisms in multispecies consortia [1315]? In fact, the persistence of high genetic diversity in such consortia (e.g. dental biofilms) over long times suggests a mechanism for the coexistence of producers and nonproducers. Highly detailed, ad-hoc individual-based models (IBMs) have been developed to study population dynamics in competitive cellular populations. For example, Xavier and colleagues developed an IBM for growth of multispecies biofilms featuring cell-cell adhesion and detachment, fluid transport, nutrient depletion and the transport of extracellular particles [16]. Recently, Momeni and colleagues explored a mutualistic interaction in yeast involving diffusible extracellular resources using both computational and experimental methods. Their IBM, which incorporated nutrient uptake, diffusion, and release, as well as cell division, death, and Figure 1. Diffusible resources. Microbes in biofilms often secrete extracellular resources despite the close proximity of unrelated cells. (a) A multispecies biofilm isolated from an extracted human tooth. Streptococcus sp. are shown in yellow, other species in orange and red; cells of Streptococcus oralis produce enzymes that release nutrients to all nearby cells [12]. Scale bar = 5 mm. Figure from Vincent Zijnge [42]. (b) Cells (blue) release diffusible resources into the environment. These resources confer a growth benefit on all nearby cells, including non-kin nonproducer cells (red), potentially leading to the risk of exploitation of producers at domain boundaries. doi:10.1371/journal.pone.0063304.g001 rearrangement, predicted that strongly interdependent mutualists would form alternating layers, consistent with their experimental results [17]. These individual-based modeling approaches facilitate a mechanistic understanding of the interaction between cells in specific microbial environments. For broader claims about the fate of cooperating populations, theorists have generally turned to spatial extensions of game-theoretic models. The two most broadly used classes of game-theoretic models are the Prisoners Dilemma and the Snowdrift Game. The Prisoners Dilemma (PD) is a pairwise interaction, or game, nominally involving two accused criminal confederates. In this game, the highest payoff goes to (...truncated)