Conceived and designed the experiments: CDN KRF JBX. Performed the experiments: CDN JBX. Analyzed the data: CDN JBX. Wrote the paper: CDN KRF JBX.
The authors have declared that no competing interests exist.
On its own, a single cell cannot exert more than a microscopic influence on its immediate surroundings. However, via strength in numbers and the expression of cooperative phenotypes, such cells can enormously impact their environments. Simple cooperative phenotypes appear to abound in the microbial world, but explaining their evolution is challenging because they are often subject to exploitation by rapidly growing, non-cooperative cell lines. Population spatial structure may be critical for this problem because it influences the extent of interaction between cooperative and non-cooperative individuals. It is difficult for cooperative cells to succeed in competition if they become mixed with non-cooperative cells, which can exploit the public good without themselves paying a cost. However, if cooperative cells are segregated in space and preferentially interact with each other, they may prevail. Here we use a multi-agent computational model to study the origin of spatial structure within growing cell groups. Our simulations reveal that the spatial distribution of genetic lineages within these groups is linked to a small number of physical and biological parameters, including cell growth rate, nutrient availability, and nutrient diffusivity. Realistic changes in these parameters qualitatively alter the emergent structure of cell groups, and thereby determine whether cells with cooperative phenotypes can locally and globally outcompete exploitative cells. We argue that cooperative and exploitative cell lineages will spontaneously segregate in space under a wide range of conditions and, therefore, that cellular cooperation may evolve more readily than naively expected.
Cooperation is a fundamental and widespread phenomenon in nature, yet explaining the evolution of cooperation is difficult. Natural selection typically favors individuals that maximize their own reproduction, so how is it that many diverse organisms, from bacteria to humans, have evolved to help others at a cost to themselves? Research has shown that cooperation can most readily evolve when cooperative individuals preferentially help each other, but this leaves open another critical question: How do cooperators achieve selective interaction with one another? We focus on this question in the context of unicellular organisms, such as bacteria, which exhibit simple forms of cooperation that play roles in nutrient acquisition and pathogenesis. We use a realistic simulation framework to model large cell groups, and observe that cell lines can spontaneously segregate from each other in space as the group expands. Finally, we demonstrate that lineage segregation allows cooperative cell types to preferentially benefit each other, thereby favoring the evolution of cooperation.
Many cell phenotypes alter the growth and division of nearby cells by changing local resource availability
How cooperative cell phenotypes evolve therefore presents an important question, one that is particularly challenging because any genetic variants that exploit others' cooperation – without themselves paying a cost – can potentially invade and increase in frequency. In light of this problem, social evolution theory has been developed to understand the evolutionary trajectories of cooperative traits
Variation among individual cells is a common feature of many cell groups: microbial biofilms are often composed of multiple strains or species
Local populations of bacterial and cancer cells are often established by groups of progenitors that proliferate into larger clusters. Experiments with bacterial colonies on agar have revealed that expanding cell groups can segregate into sectors that are each dominated by a single genetic lineage
By promoting interaction between individuals of the same genotype, the spontaneous segregation of different genetic lineages in space may also influence social evolution within cell groups
To study how the collective structure of cell groups arises from the activity of many individual cells, we used a computational model that employs mechanistic descriptions of solute diffusion and cell growth
Briefly, each cell is implemented as a circular agent in explicit two-dimensional space, and each simulation is set on one of two possible conditions. The first consists of cells growing on a flat surface with growth substrate (nutrients) diffusing from above. The second condition represents a cell cluster immersed in a resource pool, such that substrate diffuses into the cluster from all directions. The transport of all solutes occurs exclusively through diffusion. Each cell grows according to a Michaelis-Menten function of substrate concentration in its local environment and divides once it reaches a maximum radius (
We began with simulations in which the environment surrounding cell groups was altered by increasing or decreasing growth substrate concentration. These
When growth substrate was supplied to cell groups at saturating concentration, the red and blue cell lines appeared to remain well mixed relative to their random initial distributions. The advancing fronts of cell groups were smooth (
Simulations began with a 1∶1 mixture of red and blue cells, where cell color served a neutral marker for lineage segregation. As bulk substrate concentration was decreased, we observed an increased propensity for cell lineages to segregate in space. This pattern held true under (A–C) surface growth and (D–F) radial growth conditions.
When substrate availability was decreased to a moderate concentration, the surfaces of cell groups remained smooth, but their internal structures were substantially altered. Cell lineages segregated as group fronts advanced, creating adjacent red and blue cell sectors (
When substrate availability was sparse, we noted another qualitative shift in cell group structure. Red and blue cell lineages separated into adjacent sectors, just as described above. Additionally, the advancing fronts of cell groups became sensitive to small irregularities, which grew into tower clusters separated by open space (
Further exploration with the simulation framework suggested that these three structure regimes represent qualitatively different regions within a continuum of possibilities. When we altered substrate availability by small increments over a sufficiently large range, we observed cell group structures that were intermediate between those shown in
We quantified lineage segregation in cell groups by performing replicate simulations under the three substrate availability conditions shown in
We ran 50 simulations under each of the three substrate availability conditions shown in
Our next goal was to describe why environmental substrate concentration affects lineage assortment in expanding cell groups. Under limited growth substrate availability, the majority of cell growth and division occurs along a group's advancing front in an active layer whose depth depends on substrate penetration (
Cells are colored according to their growth rate: green cells are growing and make up the cell group's active layer. Black cells have become inactive due to lack of available growth substrate. The left-hand panel illustrates the vertical profile of growth substrate concentration along the dashed blue line.
Active layer depth is not solely a function of bulk growth substrate concentration. For example, higher substrate diffusivity increases active layer depth by allowing substrate to enter further into the cell group before being depleted. Faster cell growth rates, on the other hand, decrease active layer depth by raising the rate of substrate consumption at the cell group's outer surface. If we are correct that active layer depth is the underlying determinant of lineage segregation, all of the physical and biological factors that control active layer depth should also influence lineage segregation in cell groups.
Using an analytical technique from chemical engineering (
Here,
We performed three new sets of simulations to test the hypothesis that active layer depth controls cell lineage segregation. Within each set, we varied active layer depth (
The results are shown in
The factors influencing cell group active layer depth were combined into a single dimensionless number,
How does active layer depth influence cell lineage segregation? When growth substrate penetrates through most of a cell group before being depleted, all cells grow and divide, pushing each other into a homogeneous mixture. As active layer depth decreases below the total thickness of a cell group, however, cells that happen to fall below a critical distance from the group's front can no longer contribute to population expansion. Decreasing active layer depth thus reduces the cell group's effective population size, rendering it more susceptible to genetic drift along its advancing front. Because the cells are constrained in space, reductions in genetic diversity along the group's leading edge lead to localized clusters of individuals that all descend from a common progenitor
Reducing active layer depth even further yields an additional qualitative shift in cell group structure: the expanding population becomes sensitive to small irregularities along its leading edge. Cells in the peaks of surface irregularities retain access to substrate and grow into tower projections, while cells in the troughs of surface irregularities lose access to substrate and cease growing. This process is related to viscous fingering at the interface of two fluids
The spatial assortment of cell lineages is potentially critical for traits that affect the reproduction of other individuals in the population. It is increasingly recognized that cells express many such social phenotypes
In many cases the evolution of simple cooperative phenotypes depends on three factors: 1)
The segregation index depicted in
We tested our prediction by implementing a cooperative phenotype in our model framework and competing cooperative cells against exploitative cells that devote all resources to growth. Cooperative individuals secrete a diffusible compound that benefits all other cells in the local area (we will refer to the compound as an extracellular enzyme). Local availability of the secreted enzyme increases cell growth rate by a fold factor
We asked whether a cooperative cell line, which pays a cost to produce a diffusible, publicly beneficial compound, could outcompete an exploitative cell line that invests all of its resources into growth. Each competition simulation began with a randomly distributed 1∶1 mixed monolayer of the two cell types, and cell groups were grown to a maximum height of 100 µm. We then calculated the evolutionary fitness of the cooperative cell line, relative to that of the exploitative cell line (
We examined competition between enzyme-secreting cells (cooperative, labeled blue) and non-secreting cells (exploitative, labeled red) under three different active layer conditions:
When active layer depth is decreased (
Further decreasing active layer depth (
Our results show that thin active layer conditions allow cells expressing cooperative phenotypes to outcompete exploitative cells within a single cell group. To better account for the long-term evolution of a metapopulation comprising many cell groups, we performed an invasion analysis to determine whether a novel cooperative mutant can spread through a metapopulation otherwise containing only exploitative cells (Supporting Information,
The results of both our local competition and invasion analyses are robust to the cost/benefit ratio of cooperation, with one partial exception when cells invest very heavily into an expensive cooperative phenotype (Supporting Information,
Our study indicates that an order of magnitude change in nutrient availability, nutrient diffusivity, cell metabolic efficiency, cell growth rate, or biomass density can shift cell groups from a regime of lineage mixing to a regime of pronounced lineage segregation. The number
Previous work performed with bacteria in liquid planktonic culture has concluded that cooperative cell phenotypes cannot be selectively favored within a single population also containing exploitative cells
Like all models, ours uses simplifying assumptions. We deliberately omit some physical processes, such as shear stress, that may be applied to cell groups in the real world
In summary, our model suggests that clusters of genetically related cells can emerge quite easily in spatially constrained cell groups, even when cells possess no mechanism for actively gathering with clonemates. Lineage segregation allows cooperative cells to outcompete exploitative cells, and accordingly we predict that localized cooperation will evolve more readily in cell groups than suggested by models and experiments that only consider liquid environments.
We simulate cell groups using an individual-based model described in detail previously
Following the common assumption that reaction-diffusion is much faster than cell growth and division
Cell growth and division
1) Every cellular agent grows according to local substrate concentration and (for competition simulations) extracellular enzyme availability. Agents that exceed a critical radius are divided into two new agents.
2) Agents that now overlap due to their growth and/or division in the previous step are moved so as to eliminate overlap throughout the cell group. This process causes the cell group's front to advance in space.
Update solute concentration fields
3) Bulk concentrations of all solutes (growth substrate or extracellular enzyme) are held constant throughout the simulation. Thus, the bulk liquid (the region outside the boundary layer) acts as an infinite source, in the case of substrate, or a perfect sink, in the case of extracellular enzyme.
4) The new spatial concentration fields of all solutes are determined by solving Equation 2 (and an analogous equation for extracellular enzyme concentration) to steady state at each iteration.
The individual-based simulation framework was written in the Java programming language, and its related numerical methods are detailed elsewhere
To obtain the segregation index for a cell group at a single point in time, we first identify every actively growing cell. These
We define a genetic identity function,
Segregation with respect to a focal cell,
Finally, we define the segregation index for the entire cell group as the mean value of
Our segregation index measures the degree to which co-localized, metabolically active cells are clonally related to each other. The index is equal to a form of the relatedness coefficient from social evolution theory under the following assumptions: 1) A cell expressing the cooperative phenotype equally benefits all other individuals within a 10 cell-length radius; 2) Each cell within range of receiving cooperative benefits makes a contribution to mean relatedness proportional to its growth rate; 3) Cell groups are seeded randomly from a large population pool.
The dimensionless number,
Note that the factor multiplying the Laplacian of
We calculate the competitive fitness of each cell line as the mean number of rounds of cell division per unit time that each achieves over the course of a simulation:
Evolutionary invasion analysis for cooperative extracellular enzyme secretion.
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3-D simulations replicate the results of 2-D simulations examining cell lineage segregation. Cell lineage segregation increases as environmental growth substrate concentration decreases. This result is valid for both (A) surface growth and (B) radial growth conditions.
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A rare cooperative cell line can often invade a metapopulation of exploitative cells. Mean invasiveness (filled circles, with bars denoting SD) from 40 replicate simulations was calculated for a cooperative cell line invading a metapopulation of exploitative cells, and for an exploitative cell line invading a metapopulation of cooperative cells. (A) Under thick active layer conditions that promote lineage mixing, a rare cooperative cell line can invade from rarity (blue trace), despite losing in local competition with exploitative cells (see Main Text,
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The local competition and global invasion analyses were repeated with a higher cost/benefit ratio for cooperative enzyme secretion. Here, B = 0.5 and C = 0.3. Panels A–C summarize the local competition simulations. As for
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List of parameters used in our simulation models and subsequent analyses.
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Stoichiometry of cell metabolism used in our simulation models.
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We are grateful to Jim Adelman, Bonnie Bassler, Iain Couzin, Adrian de Froment, Nathan Gregory, Simon Levin, David Nelson, Katharina Ribbeck, Dan Rubenstein, and Ned Wingreen for discussions and comments on previous versions of this manuscript.