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W3205936239 abstract "Article Figures and data Abstract Introduction Results Discussion Appendix 1 Appendix 2 Appendix 3 Appendix 4 Appendix 5 Appendix 6 Appendix 7 Data availability References Decision letter Author response Article and author information Metrics Abstract A key innovation emerging in complex animals is irreversible somatic differentiation: daughters of a vegetative cell perform a vegetative function as well, thus, forming a somatic lineage that can no longer be directly involved in reproduction. Primitive species use a different strategy: vegetative and reproductive tasks are separated in time rather than in space. Starting from such a strategy, how is it possible to evolve life forms which use some of their cells exclusively for vegetative functions? Here, we develop an evolutionary model of development of a simple multicellular organism and find that three components are necessary for the evolution of irreversible somatic differentiation: (i) costly cell differentiation, (ii) vegetative cells that significantly improve the organism’s performance even if present in small numbers, and (iii) large enough organism size. Our findings demonstrate how an egalitarian development typical for loose cell colonies can evolve into germ-soma differentiation dominating metazoans. Introduction In complex multicellular organisms, different cells specialise to execute different functions. These functions can be generally classified into two kinds: reproductive and vegetative. Cells performing reproductive functions contribute to the next generation of organisms, while cells performing vegetative function contribute to sustaining the organism itself. In unicellular species and simple multicellular colonies, these two kinds of functions are performed at different times by the same cells – specialization is temporal. In more complex multicellular organisms, specialization transforms from temporal to spatial (Mikhailov et al., 2009), where groups of cells focused on different tasks emerge in the course of organism development. Typically, cell functions are changed via differentiation, such that a daughter cell performs a different function than the maternal cell. The vast majority of metazoans feature a very specific and extreme pattern of cell differentiation: any cell performing vegetative functions forms a somatic lineage, that is, producing cells performing the same vegetative function – somatic differentiation is irreversible. Since such somatic cells cannot give rise to reproductive cells, somatic cells do not have a chance to pass their offspring to the next generation of organisms. Such a mode of organism development opened a way for deeper specialization of somatic cells and consequently to the astonishing complexity of multicellular animals. Outside of the metazoans – in a group of green algae Volvocales serving as a model species for evolution of multicellularity – the emergence of irreversibly differentiated somatic cells is the hallmark innovation marking the transition from colonial life forms to multicellular species (Kirk, 2005). While the production of individual cells specialized in vegetative functions comes with a number of benefits (Grosberg and Strathmann, 2007), the development of a dedicated vegetative cell lineage that is lost for organism reproduction is not obviously a beneficial adaptation. From the perspective of a cell in an organism, the guaranteed termination of its lineage seems the worst possible evolutionary outcome for itself. From the perspective of an entire organism, the death of somatic cells at the end of the life cycle is a waste of resources, as these cells could in principle become parts of the next generation of organisms. For example, exceptions from irreversible somatic differentiation are widespread in plants (Lanfear, 2018) and are even known in simpler metazoans among cnidarians (DuBuc et al., 2020) for which differentiation from vegetative to reproductive functions has been reported. Therefore, the irreversibility of somatic differentiation cannot be taken for granted in the course of the evolution of complex multicellularity. Terminal differentiation is a type of cell differentiation different from irreversible cell differentiation. Unlike irreversibly differentiated cells who are capable of cell division, terminally differentiated cells lose the ability to divide. Terminally differentiated cells often perform tasks too demanding to be compatible with cell division. For example heterocysts of cyanobacteria perform nitrogen fixation, which requires anaerobic conditions, therefore these cells are very limited in resources and do not divide. In the scope of this study, we do not consider terminal differentiation but focus on somatic cells that are able to divide while being part of an organism (or cell colony) but not able to grow into a new organism, that is, irreversible somatic differentiation. The majority of the theoretical models addressing the evolution of somatic cells focuses on the evolution of cell specialization, abstracting from the developmental process how germ (reproductive specialists) and soma are produced in the course of the organism growth. For example, a large amount of work focuses on the optimal distribution of reproductive and vegetative functions in the adult organism (Michod, 2007; Willensdorfer, 2009; Rossetti et al., 2010; Rueffler et al., 2012; Ispolatov et al., 2012; Goldsby et al., 2012; Solari et al., 2013; Goldsby et al., 2014; Amado et al., 2018; Tverskoi et al., 2018). However, these models do not consider the process of organism development. Other work takes the development of an organism into account to some extent: In Gavrilets, 2010, the organism development is considered, but the fraction of cells capable of becoming somatic is fixed and does not evolve. In Erten and Kokko, 2020, the strategy of germ-to-soma differentiation is an evolvable trait, but the irreversibility of somatic differentiation is taken for granted. In Rodrigues et al., 2012, irreversible differentiation was found, but both considered cell types pass to the next generation of organisms, such that the irreversible specialists are not truly somatic cells in the sense of evolutionary dead ends. Finally, in Cooper and West, 2018 a broad scope of cell differentiation patterns has been investigated in the context of evolution of cooperation. However, irreversible somatic differentiation was not considered in the study. Hence, the theoretical understanding of the evolution of irreversibly differentiated somatic cell lines is limited so far. In the present work, we developed a theoretical model to investigate conditions for the evolution of the irreversible somatic differentiation. In the model, we suppose there are two cell types: germ-role and soma-role, where only germ-role cells pass to the next generation of organisms while soma-role cells are responsible for vegetative functions. Both germ-role cells and soma-role cells can divide and they may switch to each other during growth. In our model, we incorporate factors including (i) costs of cell differentiation, (ii) benefits provided by presence of soma-role cells, (iii) maturity size of the organism. We ask under which circumstances irreversible somatic differentiation is a strategy that can maximize the population growth rate compared to strategies in which differentiation does not occur or somatic differentiation is reversible. Model We consider a large population of clonally developing organisms composed of two types of cells: germ-role and soma-role. The roles differ in the ability to survive beyond the end of the organism life cycle: soma-role cells die at the end, while germ-role cells continue to live. Each organism is initiated as a single germ-role cell. In the course of the organism growth, germ-role cells may differentiate to give rise to soma-role cells and vice versa, see Figure 1A,B. After n rounds of synchronous cell divisions, the organism reaches its maturity size of 2n cells. Immediately upon reaching maturity, the organism reproduces: germ-role cells disperse and each becomes a newborn organism, while all soma-role cells die and are thus lost, see Figure 1A. We assume that soma-role cells are capable to accelerate growth: an organism containing more somatic cells grows faster, so having soma-role cells during the life cycle is beneficial for the organism. Figure 1 Download asset Open asset Model overview. (A) The life cycle of an organism starts with a single germ-role cell. In each round, all cells divide and daughter cells can differentiate into a role different from the maternal cell’s role. When the organism reaches maturity, it reproduces: each germ-role cell becomes a newborn organism and each soma-role cell dies. (B) Change of cell roles is controlled by a stochastic developmental strategy defined by probabilities of each possible outcomes of a cell division. (C) Differentiation of cells requires an investment of resources and, thus, slows down the organism growth. Each cell differentiation event incurs a cost (cs→g or cg→s). (D) The growth contribution of somatic cells is controlled by a function that decreases the doubling time with the fraction of somatic cells. The form of this function is controlled by four parameters, x0, x1, α, and b. To investigate the evolution of irreversible somatic differentiation, we consider organisms in which the functional role of the cell (germ-role or soma-role) is not necessarily inherited. When a cell divides, the two daughter cells can change their role, leading to three possible combinations: two germ-role cells, one germ-role cell plus one soma-role cell, or two soma-role cells. We allow all these outcomes to occur with different probabilities, which also depend on the parental type, see Figure 1B. If the parental cell had the germ-role, the probabilities of each outcome are denoted by gg⁢g, gg⁢s, and gs⁢s respectively. If the parental cell had the soma-role, these probabilities are sg⁢g, sg⁢s, and ss⁢s. Altogether, six probabilities define a stochastic developmental strategy D=(gg⁢g,gg⁢s,gs⁢s;sg⁢g,sg⁢s,ss⁢s). In our model, it is the stochastic developmental strategy that is inherited by offspring cells rather than the functional role of the parental cell. To feature irreversible somatic differentiation, the developmental strategy must allow germ-role cells to give rise to soma-role cells (gg⁢g<1) and must forbid soma-role cells to give rise to germ-role cells (ss⁢s=1). All other developmental strategies can be broadly classified into two classes. Reversible somatic differentiation describes strategies where cells of both roles can give rise to each other: gg⁢g<1 and ss⁢s<1. In the strategy with no somatic differentiation, soma-role cells are not produced in the first place: gg⁢g=1, see Table 1. Table 1 Classification of developmental strategies. Classgg⁢gss⁢sIrreversible somatic differentiation<1= 1Reversible somatic differentiation<1<1No somatic differentiation= 1irrelevant In our model, evolution of the developmental strategy is driven by the growth competition between populations executing different strategies – these populations able to produce more offspring and/or complete their life cycle faster gain a selective advantage. Specifically, we measure the fitness in the growth competition by the population growth rate in a stationary regime of exponential growth (Pichugin et al., 2017; Gao et al., 2019). The rate of population growth is determined by the number of offspring produced by an organism (equal to the number of germ-role cells at the end of life cycle) and the time needed for an organism to develop from a single cell to maturity (improved with the number of soma-role cells during the life cycle). To obtain these growth rates, we simulate the process of the organism growth. Here, we assume that resource distribution among cells is coordinated at the level of the organism: Cells which need more resources will get more, such that cell division is synchronous. In our model, we consider synchronous cell division of organisms and our main results are dependent on this assumption. However, we shortly explore the effects of asynchronous cell division in Appendix G. Any organism is born as a single germ-role cell and passes through n rounds of simultaneous cell divisions. Each round starts with every cell independently choosing the outcome of its division with probability of each outcome given by the developmental strategy (D). This step determines what composition will the organism have at the next round of cell division. Then, the length of the cell doubling round (t) is computed as a product of two independent effects: the differentiation effect Fdiff representing costs of changing cell roles (Gallon, 1992) and the organism composition effect Fcomp representing benefits from having soma-role cells (Grosberg and Strathmann, 1998; Shelton et al., 2012; Matt and Umen, 2016), (1) t=Fdiff×Fcomp. Both Fdiff and Fcomp are re-calculated at every round of cell division. The cell differentiation effect Fdiff represents the costs of cell differentiation. The differentiation of a cell requires efforts to modify epigenetic marks in the genome, recalibration of regulatory networks, synthesis of additional and utilization of no longer necessary proteins. This requires an investment of resources and therefore an additional time to perform cell division. Hence, any cell, which is about to give rise to a cell of a different role, incurs a differentiation cost cg→s for germ-to-soma and cs→g for soma-to-germ transitions (and double of these if both offspring take a role different from the parent), see Figure 1C. The differentiation cost is the averaged differentiation cost among all cells in an organism (2) Fdiff=1+⟨c⟩=1+cs→g⁢(Ns→g⁢s+2⁢Ns→g⁢g)+cg→s⁢(Ng→g⁢s+2⁢Ng→s⁢s)N, where Ns→g⁢s is the number of soma-roll cells that produce a germ-role cell and a soma-role cell in a cell division step. Ns→g⁢g, Ng→g⁢s and Ng→s⁢s are defined in the analogous way. N is the number of total cells. As organisms undergo synchronous cell division, we have N=2n cells after the n th cell division. The composition effect profile Fcomp⁢(x) captures how the cell division time depends on the proportion of soma-role cells x=s/(s+g) present in an organism (s and g are the numbers of soma-role and germ-role cells). In this study, we use a functional form illustrated in Figure 1D and given by (3) Fcomp(x)={1for0≤x≤x01−b+b(x1−xx1−x0)forx0<x<x11−bforx1≤x≤1 With the functional form (3), soma-role cells can benefit to the organism growth, only if their proportion in the organism exceeds the contribution threshold x0. Interactions between soma-role cells may lead to the synergistic (increase in the number of soma-role cells improves their efficiency), or discounting benefits (increase in the number of soma-role cells reduces their efficiency) to the organism growth, controlled by the contribution synergy parameter α. The maximal achievable reduction in the cell division time is given by the maximal benefit b, realized beyond the saturation threshold x1 of the soma-role cell proportion. A further increase in the proportion of soma-role cells does not provide any additional benefits. With the right combination of parameters, (3) is able to recover various characters of soma-role cells contribution to the organism growth: linear (x0=0,x1=1,α=1), power-law (x0=0,x1=1,α≠1), step-functions (x0=x1), and a huge range of other scenarios. Previous works have shown that convex (accelerating) performance functions favour cell differentiation (Michod, 2006; Rueffler et al., 2012; Cooper and West, 2018). The performance functions measure the performance of organisms with respect to different traits, such as fertility and viability. Lately, the form of functions favoring cell differentiation has been extended to be concave (decelerating) by including topological constraints in organisms (Yanni et al., 2020). Our model extends the form of performance functions by allowing it has a contribution threshold and saturation threshold. Once the outcome of all cell divisions is known and the time needed to complete the current cell doubling round is computed, the current round ends and the next starts. The development completes after n rounds. At this stage, the number of germ-role cells (organism offspring number) and the cumulative length of the life cycle are obtained. In Gao et al., 2019, we have shown that the growth rate (λ) of a population, in which organisms undergo a stochastic development and fragmentation, is given by the solution of (4) ∑iGi⁢Pi⁢e-λ⁢Ti=1. Here, i is the developmental trajectory – in our case, the specific combination of all cell division outcomes; Gi is the number of offspring organisms produced at the end of developmental trajectory i, equal to the number of germ-role cells at the moment of maturity; Pi is the probability that an organism development will follow the trajectory i; Ti is the time necessary to complete the trajectory i – from a single cell to the maturity size of 2n cells. For a given combination of differentiation costs (cg→s, cs→g) and a composition effect profile (determined by four parameters: x0, x1, b, and α), we screen through a number of stochastic developmental strategies D and identify the one providing the largest growth rate (λ) to the population. In this study, we searched for those parameters under which irreversible strategies lead to the fastest growth and are thus evolutionary optimal, see model details in Appendix A. Results For irreversible somatic differentiation to evolve, cell differentiation must be costly We found that irreversible somatic differentiation does not evolve when cell differentiation is not associated with any costs (cs→g=cg→s=0), see Figure 2A. Only reversible differentiation evolves there, see Figure 2B. This finding comes from the fact that when somatic differentiation is irreversible, the fraction of germ-role cells can only decrease in the course of life cycle. As a result, irreversible strategies deal with the tradeoff between producing more soma-role cells at the beginning of the life cycle, and having more germ-role cells by the end of it. On the one hand, irreversible strategies which produce a lot of soma-role cells early on, complete the life cycle quickly but preserve only a few germ-role cells by the time of reproduction. On the other hand, irreversible strategies which generate a lot of offspring, can deploy only a few soma-role cells at the beginning of it and thus their developmental time is inevitably longer. By contrast, reversible somatic differentiation strategies do not experience a similar tradeoff, as germ-role cells can be generated from soma-role cells. As a result, reversible strategy allows higher differentiation rates and can develop a high soma-role cell fraction in the course of the organism growth and at the same time have a large number of germ-role cells by the moment of reproduction. Under costless cell differentiation, for any irreversible strategy, we can find a reversible differentiation counterpart, which leads to faster growth: the development proceeds faster, while the expected number of produced offspring is the same, see Appendix 2 for details. As a result, costless cell differentiation cannot lead to irreversible somatic differentiation. Figure 2 Download asset Open asset Impact of cell differentiation costs on the evolution of development strategies. The fractions of 200 random composition effect profiles promoting irreversible (A), reversible (B), and no differentiation (C) strategies at various cell differentiation costs (cs→g, cg→s). In the absence of costs (cg→s=cs→g=0), only reversible strategies were observed. Reversible strategies are prevalent at smaller cell differentiation costs. No differentiation strategies are the most abundant at large costs for germ-role cells (cg→s). Irreversible strategies are the most abundant at large costs for soma-role cells (cs→g). (D) Cumulative cell differentiation rate (gs⁢s+12⁢gg⁢s+sg⁢g+12⁢sg⁢s) in developmental strategies evolutionarily optimal at various differentiation costs (cs→g=cg→s), separated by class (irreversible somatic differentiation, reversible somatic differentiation, or no somatic differentiation). Thick lines represent median values within each class, shaded areas show 90% confidence intervals. For each cost value, 3000 random profiles are used in this panel. Evolutionary optimal reversible strategies (orange) have much higher rates of cell differentiation than irreversible strategies (green). Consequently, reversible strategies are penalized more under costly differentiation. (E–H) Shapes of composition effect profiles (compare Figure 1D) promoting irreversible (green lines), reversible (orange lines), and no differentiation (black lines) strategies at four parameter sets indicated in panel A. The maturity size used in the calculation is 210 cells. To confirm the reasoning that reversible strategies gain an edge over irreversible strategies by having larger differentiation rates, we asked which reversible and irreversible strategies become optimal at various cell differentiation costs (c=cs→g=cg→s). At each value of costs, we found evolutionarily optimal developmental strategy for 3000 different randomly sampled composition effect profiles Fcomp⁢(x). We found that evolutionarily optimal reversible strategies feature much larger rates of cell differentiation than evolutionarily optimal irreversible strategies, see Figure 2D. Even at large costs, where frequent differentiation is heavily penalized, the distinction between differentiation rates of reversible and irreversible strategies remains apparent. We screened through a spectrum of germ-to-soma (cg→s) and soma-to-germ (cs→g) differentiation costs, see Figure 2A–C. Irreversible somatic differentiation is most likely to evolve when it is cheap to differentiate from germ-role to soma-role (low cg→s) but it is expensive to differentiate back (high cs→g), see Figure 2A. Irreversible strategies are insensitive to high soma-to-germ costs, since soma-role cells never differentiate. At the same time, reversible strategies are heavily punished by high costs of soma-role differentiation. It is not very surprising to find irreversible differentiation where the differentiation costs are highly asymmetric. However, irreversible strategies are consistently observed in other regions of the costs space, even including these, where the asymmetry is opposite (it is hard to go from germ to soma but easy to return back), see Figure 2A,H. To identify what other factors, beyond asymmetric costs, can lead to evolution of irreversible somatic differentiation, below we focus on the scenario of equal differentiation costs cs→g=cg→s=c. Evolution of irreversible somatic differentiation is promoted when even a small number of somatic cells provides benefits to the organism The composition effect profiles Fcomp⁢(x) that promote the evolution of irreversible somatic differentiation have certain characteristic shapes, see Figure 2E–H. We investigated what kind of composition effect profiles can make irreversible somatic differentiation become an evolutionary optimum. We sampled a number of random composition effect profiles with independently drawn parameter values and found optimal developmental strategies for each profile for a number of differentiation costs (c) and maturity size (2n) values. We took a closer look at the instances of Fcomp⁢(x) which resulted in irreversible somatic differentiation being evolutionarily optimal. We found that irreversible strategies are only able to evolve when the soma-role cells contribute to the organism cell doubling time even if present in small proportions, see Figure 3A,B. Analysing parameters of the composition factors promoting irreversible differentiation, we found that this effect manifests in two patterns. First, the contribution threshold value (x0) has to be small, see Figure 3D – irreversible differentiation is promoted when soma-role cells begin to contribute to the organism growth even in low numbers. Second, the contribution synergy was found to be large (α>1) or, alternatively, the saturation threshold (x1) was small, see Figure 3C. Figure 3 Download asset Open asset Irreversible soma evolves when substantial benefits arise at small concentrations of soma-role cells. In all panels, the data representing the entire set of composition effect profiles Fcomp⁢(x) is presented in grey, while the subset promoting irreversible strategies is coloured. (A, B) Median and 90% confidence intervals of composition effect profiles at different differentiation costs (A, number of cell division n=10) and maturity sizes (B, differentiation costs c=5). (C, D) The set of composition effect profiles in the parameter space. Each point represents a single profile (c=5 and n=10). (C) The co-distribution of the saturation threshold (x1) and the contribution synergy (α) reveals that either x1 must be small or α must be large. (D) Co-distribution of the contribution threshold (x0) and the maximal benefit (b) shows that x0 must be small, while b must be intermediate to promote irreversible differentiation. A total of 3000 profiles are used for panels A, C, D and 1000 profiles for panel B. Both the contribution threshold x0 and the contribution synergy α control the shape of the composition effect profile at intermediary abundances of soma-role cells. If the contribution synergy α exceeds 1, the profile is convex, so the contribution of soma-role cells quickly becomes close to maximum benefit (b). A small saturation threshold (x1) means that the maximal benefit of soma is achieved already at low concentrations of soma-role cells (and then the shape of composition effect profile between two close thresholds has no significance). Together, these patterns give an evidence that the most crucial factor promoting irreversible somatic differentiation is the effectiveness of soma-role cells at small numbers, see Appendix 4 for more detailed data presentation. These patterns are driven by the static character of differentiation strategies we use: the chances for a cell to differentiate are the same at the first and the last round of cell division. Therefore, the optimal germ-to-soma differentiation rate is found as a balance between the needs to deploy soma-role cells early on and to keep the high number of germ-role by the end of the life cycle. This implies that irreversible somatic differentiation strategies produce soma-role cells at lower rate than reversible strategies, see Figure 2D. With irreversible differentiation, an organism spends a significant amount of time having only a few soma-role cells. Hence, the irreversible strategy can only be evolutionarily successful, if the few soma-role cells have a notable contribution to the organism growth time. We also found that profiles featuring irreversible differentiation do not possess neither extremely large, nor extremely small maximal benefit values b, see Figure 3D. When the maximal benefit is too small, the cell differentiation just does not provide enough benefits to be selected for and the evolutionarily optimal strategy is no differentiation. In the opposite case, when the maximal benefit is very close to one, the cell doubling time approaches zero, see Equation (3). Then, the benefits of having many soma-role cells outweighs the costs of differentiation and the optimal strategy is reversible, see Appendix 4. For irreversible somatic differentiation to evolve, the organism size must be large enough By screening through the maturity size (2n) and differentiation costs (c), we found that the evolution of irreversible somatic differentiation is heavily suppressed at small maturity sizes, Figure 4A. We found that either reversible strategies or the no differentiation strategy evolve in small organisms. Since reversible strategies can quickly reach a fixed fraction of soma-role cells, thus they can obtain maximised benefits from soma-role cells with small maturity sizes (Appendix 2—figure 1). Since the no differentiation strategy does not involve cell differentiation, they do not have cell differentiation costs. In contrast, irreversible strategies increase the fraction of soma-roles and increase the benefits of soma-role cells gradually as maturity size increases. Meanwhile, the cell differentiation costs for irreversible strategies decrease as maturity size increases as the fraction of germ-role cells decreases. Thus compared with other strategies, the irreversible strategies have advantages in large organisms. We found that under cs→g=cg→s, the minimal maturity size allowing irreversible somatic differentiation to evolve is 2n=64 cells. At the same time, organisms performing just a few more rounds of cell divisions are able to evolve irreversible differentiation at a wide range of cell differentiation costs, see also Appendix 5. This indicates that the evolution of irreversible somatic differentiation is strongly tied to the size of the organism. Figure 4 Download asset Open asset Irreversible differentiation can evolve if organism grows to a large enough size in the course of its life cycle. (A) The fraction of composition effect profiles promoting irreversible strategies at various cell differentiation costs (c=cs→g=cg→s) and maturity sizes (2n). Irreversible strategies were only found for maturity size 26 = 64 cells and larger. (B) The fraction of composition effect profiles promoting irreversible strategies at unequal differentiation costs cs→g=2⁢cg→s. A rare occurrences of irreversible strategies (∼1%) was detected at the maturity size 25=32 cells in a narrow range of cell differentiatio" @default.
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W3205936239 title "Author response: Evolution of irreversible somatic differentiation" @default.
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