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Pleiotropic constraints promote the evolution of cooperation in cellular groups

['Michael A. Bentley', 'Department Of Zoology', 'University Of Oxford', 'Oxford', 'United Kingdom', 'Department Of Biochemistry', 'Christian A. Yates', 'Department Of Mathematical Sciences', 'University Of Bath', 'Bath']

Date: 2022-06

The evolution of cooperation in cellular groups is threatened by lineages of cheaters that proliferate at the expense of the group. These cell lineages occur within microbial communities, and multicellular organisms in the form of tumours and cancer. In contrast to an earlier study, here we show how the evolution of pleiotropic genetic architectures—which link the expression of cooperative and private traits—can protect against cheater lineages and allow cooperation to evolve. We develop an age-structured model of cellular groups and show that cooperation breaks down more slowly within groups that tie expression to a private trait than in groups that do not. We then show that this results in group selection for pleiotropy, which strongly promotes cooperation by limiting the emergence of cheater lineages. These results predict that pleiotropy will rapidly evolve, so long as groups persist long enough for cheater lineages to threaten cooperation. Our results hold when pleiotropic links can be undermined by mutations, when pleiotropy is itself costly, and in mixed-genotype groups such as those that occur in microbes. Finally, we consider features of multicellular organisms—a germ line and delayed reproductive maturity—and show that pleiotropy is again predicted to be important for maintaining cooperation. The study of cancer in multicellular organisms provides the best evidence for pleiotropic constraints, where abberant cell proliferation is linked to apoptosis, senescence, and terminal differentiation. Alongside development from a single cell, we propose that the evolution of pleiotropic constraints has been critical for cooperation in many cellular groups.

As we disuss in detail in the Supporting information ( S1 Text ), a limitation of this model is that it did not explicitly capture group-level birth and death events or allow groups to develop for long enough to see the importance of pleiotropy for stabilising the evolution of cooperation. The time allowed for groups to develop is important because the problems with cheater lineages only becomes apparent as groups age ( Fig 1 ). Pleiotropy only becomes subject to significant between-group selection, therefore, in longer-lived groups when cheater mutants have time to threaten the group. We show in the Supporting information that increasing the length of time that groups live for increases the levels of cooperation that evolve via pleiotropy in the model of [ 29 ]. However, problematic assumptions such as unbounded explonential growth prevented us from exploring this effect further ( S1 Text ). We, therefore, decided to develop a novel age-structured multilevel selection model for the evolution of cooperation in cellular groups, including both microbes and multicellular organisms. Our model predicts that pleiotropy is a powerful way to promote the evolution of cellular cooperation.

However, a recent theoretical paper argued broadly against the idea that pleiotropy is an explanation for the evolution of cooperation [ 29 ]. In particular, the authors argued that pleiotropy only evolves under conditions when kin selection is already operating to stabilise cooperation (Fig 2 in [ 29 ]), with, at best, a very minor impact on the evolved level of cooperation (i.e., seen in S14 and S16 Figs but not Fig 2 in [ 29 ]). As such, they concluded “Pleiotropy does not help stabilise cooperation over evolutionary time—cooperation is only favoured in the region where Hamilton’s rule is satisfied because of indirect fitness benefits.”

Given the potential for cheater lineages, it has been suggested that genetic architecture can evolve to help stabilise cooperation. When the expression of a cooperative trait is linked to a private trait that helps a cell to survive or divide, mutations that ablate cooperation can also ablate the private trait and, thereby, stop the evolution of cheater lineages. This pleiotropic linkage of cooperative traits and private (personally benefitial) traits has been identified experimentally to be a mechanism that helps to promote cooperation in multiple microbial species [ 21 – 25 ]. In addition, an agent-based model of microbes found that links between metabolic and secretion genes helped to stabilise cooperation [ 26 ], and a theoretical study suggested that pleiotropy can promote niche construction, which is related to cooperation [ 27 ]. These studies raise the possibility that the evolution of pleiotropy might be a general mechanism to promote cooperation in cellular groups [ 28 ].

(A) Mutation–selection dynamics can undermine clonal multicellular groups. Mutation of cooperative cells (blue) can generate noncooperative cells (dark grey) that do not pay the costs of cooperation but reap its rewards. These cheater lineages can spread within multicellular groups because they divide more rapidly than wild-type cells. Invasion of spontaneous mutant lineages can lead to a breakdown in group function (distorted shape). (B) Pleiotropy promotes cooperation in our model because it leads to between-group selection on the rate at which cooperation breaks down within groups as they age. Beginning with groups founded by 1 pleiotropic and 2 nonpleiotropic lineages, we see that groups founded by the nonpleiotropy lineages loose function and are eventually replaced by the pleiotropic lineage. Cells are coloured in 3 parts according to whether they display cooperation (blue), a privately beneficial trait (red), and pleiotropy (yellow), whereby the cooperative and private traits are linked. Mutations can make some traits inactive (grey). When cooperation is lost in a pleiotropic cell lineage (top row), the cells also lose their private trait, which stops them from proliferating. Group function is thereby preserved. When cooperation is lost in a nonpleiotropic lineage (second row), cheater lineages emerge that spread and group function is lost. As a result, pleiotropic groups thrive relative to nonpleiotropic ones and seed more groups, giving rise to between-group selection for pleiotropy.

The potential for cheater lineages is well documented in microbes. Mutants lacking a range of cooperative traits have been shown to outcompete wild-type cells [ 4 – 10 ] and occur in the field and clinic [ 11 – 13 ]. Such observations beg the question of how cooperation persists over evolutionary time. A key explanation is that many cellular groups, both in microbes and multicellular organsims, are recently derived from a single cell (clonal) [ 1 , 2 , 14 , 15 ]. In the terminology of sociobiology, this leads to high relatedness and kin selection, which is a major driver of cooperation across many systems [ 16 , 17 ]. The argument is that, when cell groups are clonal, interactions between cooperative and cheater genotypes are prevented, which allows cooperative genotypes to prosper as cheater genotypes lose the shared benefits of cooperation. While kin selection is undoubtedly important [ 1 , 2 , 14 , 15 ], this explanation neglects a key feature of the biology of cellular groups: Even in a group founded from a single cell, cooperation can still break down due to the emergence of mutant noncooperators from within [ 18 – 20 ] ( Fig 1 ). Indeed, with nonzero mutation rates, the question is when, not if, these lineages will emerge.

There is widespread cooperation in cellular groups where cells invest in costly traits that benefit all cells in the vicinity, such as bacteria that secrete an extracellular enzyme to digests nutrients or the more complex coordinated phenotypes of multicellular organisms. Cooperative traits can require that cells forego their own reproductive interests in favour of the reproductive interests of the group as a whole [ 1 , 2 ]. This effect, in turn, can lead to the evolution of noncooperative lineages—sometimes known as “cheaters”—that make use of collective benefits without investing in them and threaten cooperative function [ 3 ].

Results

We are interested in understanding how multicellular groups founded by cells with pleiotropic constraints function as compared to groups founded by otherwise similar cells that lack these constraints. We follow the effects of pleiotropic links between cooperative traits (that benefit the whole group) and private traits (that benefit the individual cell that carries them) on multilevel selection dynamics using an age-structured modelling approach (see Methods). A group in our model is intended to capture a group of microbes or a proto-multicellular organism, which lacks the division between germ and soma. Groups start from a single cell and display logistic growth up to a carrying capacity K, which defines the size of the group at maturity. A second parameter, λ, determines the expected life span of a group. This is important because it impacts on the amount of cell turnover that is expected after a group reaches reproductive maturity. Such cell turnover can be major contributor to the number of cell divisions within a multicellular group. For example, high rates of cell turnover occur in bacteria, which commonly live attached to surfaces in structures known as biofilms where dispersing cells are replaced by dividing cells below them [1]. It is also common In multicellular organisms: Members of the genus Hydra (Fig 1) can live for several years, while their epithelial cells are estimated to turnover every few days [30].

The fact that groups start from a single cell in our model ensures high relatedness and strong kin selection, which is consistent with microbes that grow in clonal patches [1] and the biology of multicellular organisms [20]. However, we later reduce this within-group relatedness to study its effects on pleiotropy and cooperation. To study the effects of pleiotropy on cooperation, our modelling has to capture the stochastic effects of mutations. For this reason, the heart of the model is a stochastic simulation that captures populations of cells as they grow, and potentially mutate to other genotypes, within a group. However, as we discuss later, we also need to capture the evolutionary effects of cooperation at the group level, which is done with partial differential equations (PDEs) that allow us to capture a large (infinite) number of competing groups. We hope that this novel approach—stochastic simulations embedded in PDEs—will prove useful to understand a wide range of traits under multilevel selection (Methods).

Pleiotropy slows the breakdown of cooperation within cellular groups Regulatory networks, and the maps from genotype to phenotype, are often complex [31]. Evolutionary models of cooperation typically overlook this complexity and instead study optimal trait values, an approach known as the phenotypic gambit [32]. Here, we treat genetic architecture as a trait, like any other, that can itself evolve in response to natural selection [26,29]. We do this with a simplified model of pleiotropy. The definition of pleiotropy can vary between disciplines and authors [29,33–35], and here we mean the commonly used definition: Pleiotropy is when a single locus affects 2 or more traits [24]. Specifically, our model captures how mutation at a given locus affects 1 cooperative and 1 private trait (Fig 2). While there are a vast range of possible regulatory networks that might influence any 2 traits of interest, the impacts of pleiotropy can be captured by a single value ϕ, which is the probability that a mutation in a network with an active, cooperative, and private trait will give rise to a pleiotropic effect (Fig 2A). PPT PowerPoint slide

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TIFF original image Download: Fig 2. Modelling pleiotropy. (A) One way to measure the strength of pleiotropy in real-world regulatory networks is to compute the ratio of those mutations in the network that simultaneously impact 2 terminal phenotypic traits to the number of genes. We call this measure ϕ. In principle, this value can be calculated for any network regulating 2 traits. We show illustrative networks that would generate varying levels of pleiotropy across the range of values of ϕ. (B) Genotype–phenotype map for our mathematical model of pleiotropy. To keep things simple, we model 3 traits: a terminal cooperative trait, (blue circles), a terminal private trait, (red circles), and a pleiotropic regulation trait, (yellow circles). All traits in our model can be either active (coloured as above) or inactive (grey circles). This means there are 8 possible genotypes, each labelled g i , where i∈{1,2,…,8}. Although pleiotropy can be active or inactive for a given genotype, we use a parameter ϕ∈[0,1] to tune the strength of its effect. This allows us to use our simple genotype–phenotype map to model biological scenarios when pleiotropy is expected to be weak as well as strong. Furthermore, we assume that pleiotropy only has a functional effect when both other traits are active. Thus, although active pleiotropy is present in genotypes g 2 , g 4 , g 6 , and g 8 , we assume it only affects genotype g 8 , where it influences the probability, ϕ, that a g 8 cell experiences a pleiotropic mutation given that a loss-of-function mutation has deactivated one of its other traits. https://doi.org/10.1371/journal.pbio.3001626.g002 There are, therefore, 3 traits in our model: a cooperative trait, a private trait, and a pleiotropy trait, which gives rise to 8 possible genotypes (Fig 2B). The goal of our model is to explore which of these 8 genotypes is favoured by natural selection in the long term due to competition among cells within and between groups. For a given cell, each of the traits is in either an active or inactive state. At the heart of the model is a tension between selection for cooperation within and between groups, i.e., the cooperative trait decreases a cell’s relative division rate within a group but brings benefits to the group function as a whole. This trait might, for example, represent a secreted enzyme that helps nutrient acquisition in a microbial group, or the suppression of cell proliferation in a simple multicellular organism to ensure proper functioning [18]. By contrast, the private trait simply increases a cell’s survival rate within its group. This trait might represent an enzyme involved in central metabolism, for example. With pleiotropy, mutations that ablate the cooperative trait increase the probability that the private trait is also lost and vice versa [29], where ϕ determines this probability (Fig 2A). A mutation matrix specifies the transition probabilities between all 8 genotypes in the model as a function of the strength of pleiotropy (see Methods). Under a null model in which pleiotropy does nothing, mutations affect each trait independently, where mutations that cause loss-of-function in a trait occur with rate μ, and gain-of-function trait mutations occur with rate νμ, where ν<1. This value reflects the fact that it is typically easier to break trait functionality than to restore or create it, and we typically take ν = 0.01 to capture the strength of this bias. We use μ = 0.0001 per generation for the base mutation rate in most analyses, which describes the probability that a trait is mutated—and function is lost—per cell division. This value is expected to vary widely between systems and traits and is intended only as an illustration. We later perform parameter sweeps of both μ and ν across several orders of magnitude. We begin by following the evolutionary dynamics within a group. In our first model, each group is founded by a single cell, which gives 8 possible group types corresponding to the 8 cell genotypes (Fig 2B). While groups all start their life with clonal expansion of their founder, mutation–selection processes mean that their genotypic composition may change through time as they age. We can describe this process for each of the 8 group types. The dynamics for groups founded by genotypes 1 to 7 are shown in the Supporting information (S1–S7 Figs), and we focus here on genotype 8 groups (Fig 2B), hereafter referred to as “pleiotropic cooperators,” because they capture the effects of pleiotropy on cooperation (Fig 3). Groups with these genotypes initially grow towards their carrying capacity by clonal expansion but, depending on the strength of pleiotropy, have the potential to be invaded by cheater lineages that lack the cooperative trait but express the private trait (genotype 4; see Fig 2A). Importantly, we see that the extent and rate of invasion of the cheater lineage is diminished as the strength of pleiotropy, ϕ, is increased. Cheater lineages make up 25% of the group by approximately day 25 in groups without pleiotropy, by day 40 in groups with intermediate pleiotropy, and never (not before 50 days) in groups with strong pleiotropy (Fig 3B). PPT PowerPoint slide

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TIFF original image Download: Fig 3. The evolution of cooperation within groups depends on the strength of pleiotropy ϕ. Within-group mutation selection dynamics are shown for a group founded by a cell with genotype g 8 , which actively expresses a cooperative trait, , a private trait, , and a pleiotropy trait, . Growth of the group as its age, y, increases, is logistic, with a carrying capacity K = 200 at which point cells continue to divide, die, and turnover (see Methods). Dynamics are shown from left to right for 3 different strengths of pleiotropy, ϕ, where pleiotropy is absent/has no effect in the left-hand side column (ϕ = 0). For comparison, the vertical dashed line in (A-C) shows the point at which noncooperative lineages shown in orange make up 25% of the group. Pleiotropy leads to this point being delayed (ϕ = 0.5) or prevented (ϕ = 1). (A) Changes in genotype abundances, nc(y). (B) Changes in genotype relative frequencies, xc(y). (C) Changes in the average levels of cooperation, private trait expression, and pleiotropy, . (D) Distribution of fitness effects: Shown is the effect on within-group fitness of the different types of loss-of-function mutations that occur, which are coloured by their phenotypic effect, where blue is loss of cooperative trait, red is loss of the private trait, yellow is loss of pleiotropy, and brown is loss of both cooperation and private trait (due to pleiotropy). When pleiotropy is weak or absent, loss-of-function mutations to cooperative traits increase the fitness of cells within the group, and loss-of-function mutations to private traits decrease the fitness of cells within the group. When the strength of pleiotropy is increased, mutations to either trait tend to have pleiotropic effects, which cancel one another out, meaning mutant cell lineages no longer gain an advantage within the group. Formally, the fitness effect is , where and are the within-group birth rates of the mutant descendant and ancestral wild type, respectively, and and are the death rates of the mutant descendant and ancestral wild type, respectively. Parameters: sc = sg = 0.95; K = 200; μ = 0.0001; ν = 0.01. The code required to generate this figure can be found at https://github.com/euler-mab/pleiotropy and https://zenodo.org/record/6367788#.YjSBVurP2Uk. https://doi.org/10.1371/journal.pbio.3001626.g003 The resistance to invasion by cheater lineages occurs because pleiotropy reduces the frequency with which mutations give rise to a cheater phenotype. As a result, pleiotropy is able to increase the level of cooperation in groups (Fig 3C). The distribution of fitness effects (DFE) of loss-of-function mutations helps to show why pleiotropy is an effective mechanism for limiting cheater cell lineages within a given group (Fig 3D), something also clear from the dos Santos study [29]. When the strength of pleiotropy is relatively weak, mutations to the cooperative trait frequently give rise to mutant descendants that have a competitive advantage over the cooperative cells within the group. By contrast, when the strength of pleiotropy is relatively strong, mutations tend to have have neutral or deleterious effects on cells because a loss of cooperation also comes with a loss of the private trait. In the model, we assume that the effects of expressing the cooperative and private trait on within-group fitness are equal and opposite in magnitude, which is what leads to neutrality when both are lost. Some examples suggest that the loss of a private trait may have a stronger negative effect, such as cell death via apoptosis [36–38]. Such examples may lead to a negative change in within-group fitness when both traits are lost. We do not consider this case explicitly here, but it is only expected to strengthen the ability of pleiotropy to remove potential cheater lineages and thereby improve group function.

Pleiotropy evolves to stabilise cooperation across a wide range of conditions We have so far assumed that groups are formed from a single cell. While this is realistic for the majority of multicellular organisms, other cellular groups, particularly microbial groups, commonly contain multiple genotypes that meet and mix. If large numbers of different genotypes meet and mix—and relatedness is close to 0—the evolution of pleiotropy and indeed cooperation does not occur in our model. Under these conditions, there is no between-group genetic variation and the outcome of competition is determined solely by within group dynamics (S10 Fig). Here, so long as genotypes that lack the cooperative phenotype can arise at some point, they will take over and pleiotropy serves no function. However, relatedness can often be relatively high in microbial groups due to spatial structure, where a patchwork of groups form, each dominated by a single genotype [1]. We can study the effects of an intermediate level of relatedness in our model by assuming groups are founded by 2 cells (chosen uniformly at random from their parent group), such that there are now up to 32 different group genotypes in the population. This case has an important difference to the single-cell bottleneck case where cheater cells always start a new group alone with little chance of survival. With 2 cells, cheater cells now have the chance of founding groups alongside cooperators that they can exploit, thus greatly improving their prospects. Despite the added complexity, we see again that the evolution of pleiotropy is often favoured and able to promote the evolution of cooperation as it evolves (S11 Fig). While the importance of pleiotropy in our model rests upon some relatedness between cells, therefore, it does not rest upon a single cell origin. Our conclusions are also robust to changing other assumptions and parameters. One key consideration is that there may be a cost to pleiotropy if, for example, the regulation of 1 trait is compromised by its linkage to another [41]. However, we find that pleiotropy still evolves if it carries such costs to a group’s functioning (S12 Fig), which is further testament to its ultimate importance for improving group function. Another important parameter is the benefit of cooperation (strength of group selection). Reducing the benefit of cooperation in our model reduces the scope for the evolution of cooperation but, importantly, where cooperation can evolve there are broad parameter ranges where pleiotropy evolves to increase cooperation (S13 Fig). Notably, the evolution of pleiotropy is even seen when natural selection for cooperation is very weak, as may have occurred at the inception of multicellular life. Varying the relative probability of gain-of-function mutations has little impact on outcomes (S14 Fig). However, as expected, the baseline mutation rate is important. Increasing this mutation rate causes the more rapid breakdown of cooperation, which requires stronger pleiotropic effects for cooperation to be maintained. However, so long as strong pleiotropic links are possible, we see that they rapidly evolve and again stabilise cooperation (S15 Fig). For reduced mutation rates, cheater lineages arise less often and so, even in the absence of pleiotropy, cooperation can be maintained more easily. All else being equal, therefore, pleiotropy will now only evolve in larger or longer-lived cellular groups. For example, halving the mutation rate (μ = 0.00005) roughly doubles the number cell divisions where pleiotropy becomes critical for cooperation (compare Fig 4 with S16 Fig). However, even if we lower the mutation rate an order of magnitude (μ = 0.00001), we still observe the widespread evolution of pleiotropy in groups of only 10,000 to 20,000 cell divisions (S16 and S17 Figs show this effect, with and without a cost to pleiotropy, respectively). In summary, we observe that the evolution of pleiotropy promotes cooperation for relatively small multicellular groups across a wide range of parameters.

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