Evolution of asymmetric gamete signaling and suppressed recombination at the mating type locus

The two partners required for sexual reproduction are rarely the same. This pattern extends to species which lack sexual dimorphism yet possess self-incompatible gametes determined at mating-type regions of suppressed recombination, likely precursors of sex chromosomes. Here we investigate the role of cellular signaling in the evolution of mating-types. We develop a model of ligand-receptor dynamics, and identify factors that determine the capacity of cells to send and receive signals. The model specifies conditions favoring the evolution of gametes producing ligand and receptor asymmetrically and shows how these are affected by recombination. When the recombination rate evolves, the conditions favoring asymmetric signaling also favor tight linkage of ligand and receptor loci in distinct linkage groups. These results suggest that selection for asymmetric gamete signaling could be the first step in the evolution of non-recombinant mating-type loci, paving the road for the evolution of anisogamy and sexes.

: Gametes communicate through ligand and receptor molecules. The ligand can be either membrane bound or released in the local environment. (a) When the interacting cells produce ligand and receptor symmetrically, the ligand will bind to receptors on its own membrane as well as those on the other cell. This may impair intercellular signaling. (b) Producing the ligand and receptor in an asymmetric manner resolves this issue.
⌫ L and ⌫ R describe the rate of production of the ligand and receptor respectively. L , R , and LR , Where is given by, We assume that the timescale of encounters and interactions between cells is longer than the 71 timescale of ligand and receptor production and degradation. Hence the concentrations of [L],

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[R] and [LR] in individual cells will be at steady state when two cells meet. The likelihood of a 73 successful mating between two cells depends not just on partner signaling levels but also on how 74 accurately the cells can compute the signal produced by their partner. Binding of ligand and re-75 ceptor originating from the same cell can obstruct this interaction. To capture this, we define the 76 strength of the incoming signal for cell 1 when it interacts with cell 2 as,  (1, 1, 0, 0) for both cells) rather than in an asymmetric manner (e.g. (⌫ L 1 , ⌫ R 1 , ⌫ l 1 , ⌫ r 1 ) = (1, 0, 0, 1) 139 and (⌫ L 2 , ⌫ R 2 , ⌫ l 2 , ⌫ r 2 ) = (0, 1, 1, 0)). The fold-increase in W 12 is large even when self-binding confers 140 no cost (n = 0), while larger values for n ramp up the costs (Fig. 2c). If cells produce the ligand and 141 receptor asymmetrically, self-binding ceases to be a problem in receiving incoming signals. 142 Although the strength of the signaling interaction between two cells (W 12 W 21 ) may improve 143 when the interacting cells produce the ligand and receptor asymmetrically, this need not be the case. Figure 3: Fitness advantage of rare mutations conferring signaling asymmetry. The fitness of a rare mutant is plotted relative to the resident [W 12 W 21 ] res+mut -[W 12 W 21 ] res+res . The production rate of the mutant cell is (⌫ L , ⌫ R , ⌫ l , ⌫ r ) mut = (1dx, 1dy, dx, dy), where dx and dy are plotted on the x and y axes respectively. The resident production rate (⌫ L , ⌫ R , ⌫ l , ⌫ r ) res is shown as a red dot and varies (a) ( Consider the interaction of a resident cell with production rates (⌫ L , ⌫ R , ⌫ l , ⌫ r ) res = (1, 1, 0, 0) with 145 itself and a mutant cell with production rates given by (  . 3a). It follows that (⌫ L , ⌫ R , ⌫ l , ⌫ r ) =

Evolution of mating types with asymmetric signaling roles
To explore the evolution of signaling asymmetry, we follow mutations that alter the relative pro-160 duction of two mutually incompatible types of ligand and receptor (L, R) and (l, r). To ease under-161 standing, the population symmetry s in the production of ligand and receptor is measured, The population is symmetric (s = 1) if cells produce ligand and receptor equally, for both types (i.e.

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with intermediate values of s ⇤ are not found. The exact production rates at E 1 and E 2 exhibit some 171 degree of noise due to mutation and finite population size (Fig. 4b, c). At E 2 , individual cells with 172 high ⌫ R (and low ⌫ r ) have low ⌫ L (and high ⌫ l ), confirming that s ⇤ ⇡ 0 captures a fully asymmetric 173 steady state.

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Whether E 2 is reached from E 1 depends on key parameters that determine the strength of self-175 binding and signaling interactions between cells. E 1 persists and no asymmetry evolves when k +

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(the intracellular ligand-receptor binding coefficient) is small (Fig. 4d). In this case, the concentra-177 tion of self-bound ligand-receptor complex is small (Eq. (6)) and there is little cost of self-signaling 178 (Eq. (8)), so there is weak selection in favor of asymmetry. The opposite is true for larger values 179 of k + , as self-binding now dominates and restricts between cell signaling, promoting the evolution 180 of asymmetry (Fig. 4d). The transition from E 1 to E 2 occurs at a smaller value of k + when the 181 degradation rate ( ) is decreased (Fig. 4d), as the effective removal of free ligand and receptor depends more strongly on intercellular binding (Fig. 2a, b).
Another important consideration is the relative strength of signaling within and between cells, 184 given by k + /kand k b respectively. For example, the threshold value of the within cell binding rate 185 beyond which symmetric signaling (E 1 ) evolves to asymmetric signaling (E 2 , Fig. 4a) increases 186 when k b becomes much larger than k + /k - (Fig. 4e). Furthermore, this threshold value is smaller 187 for larger values of n indicating that asymmetric signaling is more likely to evolve when the cost for 188 self-signaling is higher (larger n, Fig. 4e). However, asymmetric signaling can evolve even when when k + and µ a are high and is small (Fig. 5a-d), as predicted analytically (Fig. 2, 3) and in 203 accordance with our findings when mutations were continuous (Fig. 4). Note that the magnitude 204 of the mutation rates matters in our system. Single mutations can be slightly deleterious (as pre-205 dicted analytically, Fig. 3a), but the presence of mutants that are asymmetric in opposite directions 206 gives rise to positive epistatic effects ( Fig. 3b-d). This explains why smaller values of µ a result in 207 narrower basins of attraction for E 2 (Fig. 5). 208 We next investigated how mutations invade when the resident already signals asymmetrically  and (1, 1dy, 0, dy) at rate µ a and their fate is followed until they reach a stable frequency. Orange contours outside the dotted line show the region where both mutants are eliminated and the resident persists (s ⇤ = 1). All other colors indicate that the two mutants spread to equal frequency 0.5 displacing the resident (s ⇤ < 1). The degree of signaling symmetry at equilibrium is dictated by the magnitude of the mutations given by dx and dy. The different panels show (a) between cell signaling k + = 10, mutation rate µ a = 0.01 and degradation rate = 0.1, (b) higher mutation rate µ a = 0.001, (c) high degradation rate = 0.5 and (d) weaker between cell signaling k + = 5. The resident type is marked by a black dot at the origin. The dashed line marks the regions above which the two mutants spread to displace the resident and reach a polymorphic equilibrium at equal frequencies. Other parameters used and simulation details are given in the Supplementary Material.
. The mutant is introduced at a frequency µ a = 0.01. Other parameters used and simulations details are given in the Supplemental Material.
(i.e. produces both ligands). The resident was set to (⌫ L , ⌫ R , ⌫ l , ⌫ r ) res = (1dx, 1, dx, 0) and a mu-210 tant able to produce both receptors (⌫ L , ⌫ R , ⌫ l , ⌫ r ) mut = (1, 1dy, 0, dy) was introduced. If dx 6 = 0, a 211 mutant conveying a small asymmetry in receptor production increases in frequency until the pop-212 ulation reaches a polymorphic state with the resident and mutant at 50% (Fig. 6a). If on the other 213 hand the resident exhibits an asymmetry but the mutant does not (i.e. dy = 0 and dx > 0), the mu-214 tant replaces the resident. It follows that an asymmetry in both ligand and receptor production is 215 necessary for the evolution of a signaling asymmetry as predicted analytically (Fig. 3). We also 216 consider a resident type that produces both ligands and both receptors with some degree of asym-217 metry in ligand production (i.e. (⌫ L , ⌫ R , ⌫ l , ⌫ r ) res = (0.5dx, 0.5, 0.5 + dx, 0.5)) and map the spread 218 of a mutant with asymmetry is receptor production (⌫ L , ⌫ R , ⌫ l , ⌫ r ) mut = (0.5, 0.5dy, 0.5, 0.5 + dy).

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The pairwise invasability plots for values of dx and dy show that signaling asymmetries in oppo-220 site directions are favored. These evolve to a polymorphic state with equal frequencies of cells at 221 dx = dy = -0.5 and dx = dy = 0.5 (Fig. 6b). These findings together illustrate how the asymmetric 222 state E 2 evolves from the symmetric state E 1 .

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Finally, we wondered how synergy or competition between the two ligands (or receptors) could affect our results. When the two ligands (or receptors) exhibit synergy so that ⌫ L + ⌫ l < ↵ and 225 ⌫ R +⌫ r < ↵ for ↵ > 1, a signaling asymmetry evolves more easily (for smaller values of k + , Fig. S3).

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Now the second ligand (or receptor) begins to evolve without imposing a cost on the preexisting 227 ligand (or receptor) and can therefore remain present in the population longer until an asymmetry 228 in the opposite direction evolves in other cells. The reverse dynamics are observed when the two 229 ligands (or receptors) compete with one another (⌫ L + ⌫ l < ↵ and ⌫ R + ⌫ r < ↵ for ↵ < 1 ) (Fig. S3). The results above assume that the loci controlling ligand and receptor production are tightly linked 232 which prevents the production of deleterious combinations following meiosis. Recombination is 233 a minor problem at the E 1 equilibrium which is monomorphic (except for mutational variation).

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But it is likely to be a problem at the polymorphic E 2 equilibrium. At E 2 , mating between  Consider the effect of recombination on a population at E 1 . As before, the population either 240 stays at E 1 or evolves to E 2 dependent on parameter values (Fig. 7a). When the population evolves 241 to E 2 , s ⇤ becomes larger as the recombination rate (⇢), increases (Fig. 7 b). For low recombination 242 rates (⇢  0.1), the population largely consists of equal frequencies of (1, 0, 0, 1) and (0, 1, 1, b.
d. Figure 8: Equilibrium recombination rate ⇢ ⇤ . (a) Averaged across the population, ⇢ ⇤ varies with k + (within cell binding rate) and n = 0, 1, 2 (cost of self-binding). (b-d) Evolution of the recombination rate ⇢ (blue) and signaling symmetry levels s (orange) for different within cell binding rates: (b) k + = 10, (c) k + = 3 and (d) k + = 1. The recombination rate evolves under drift for the first 1000 generations, following which mutation at the ligand and receptor loci were introduced. When no asymmetry evolves the recombination rate fluctuates randomly between 0 and 0.5 (i.e. between its minimum and maximum value like a neutral allele). Other parameters used in simulations are given in the Supplemental Material. 8a). Furthermore, asymmetric signaling roles coevolve together with the recombination rate. The evolved trajectories of s and ⇢ depend on the strength of selection for asymmetric signaling. For 277 example, when k + is large (k + = 10), signal asymmetry rapidly evolves; s moves away from 1 and 278 this is followed by a sharp drop in the recombination rate (Fig. 8b). Eventually the population 279 evolves asymmetric signaling roles (s in orange, Fig. 8b) and tight linkage (⇢ in blue, Fig. 8b).

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These dynamics are similar when k + is smaller (k + = 3, Fig. 8c) and selection for asymmetry is 281 weaker. However, it now takes longer for the asymmetric types to co-evolve (Fig. 8c). When se-282 lection for asymmetric signaling is even weaker (k + = 1, fig. 8d), no asymmetry evolves (s remains 283 at 1) and the recombination rate fluctuates randomly between its minimum and maximum value as 284 one would expect in the case of a neutral allele. 285

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Explaining the evolution of mating types in isogamous organisms constitutes a major milestone 287 in understanding the evolution of anisogamy and sexes [1,3]. Mating type identity is determined 288 by a number of genes that reside in regions of suppressed recombination and code for ligands 289 and receptors that guide partner attraction and recognition, as well as genes that orchestrate cell 290 fusion and postzygotic events [27,8,13,12]. In this work we show that an asymmetry in ligand 291 and receptor production evolves as a response to selection for robust gamete communication and  signal. This framework also allowed us to quantitatively follow the evolution of ligand and receptor 306 production in mating cells for the first time. 307 We found that the ligand-receptor binding rate within a cell (k + ) is key in the evolution of 308 asymmetric signaling roles (Fig. 3, 4). k + holds an important role because it dictates the rate at discriminating between species) take longer to mate [43]. It would be interesting to further study 322 these trade-offs experimentally. 323 We never observed the co-existence of a symmetric "pansexual" type with asymmetric self-324 incompatible types. The two steady states consist of either a pansexual type or two mating types 325 with asymmetric signaling roles. This follows from the requirement for strong selection to initiate 326 evolution towards asymmetric signaling roles, and could explain why the co-existence of mating 327 types with pansexuals is rare in natural populations [11,12]. This is in contrast to previous models where pansexual types were very hard to eliminate due to negative frequency dependent selec-  The spread of asymmetric signalers generates stronger selection for further asymmetry (Fig. 3, 4).

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This also occurs when there is recombination (Fig. 7, 8). Even though recombination between the 337 two asymmetric types generates symmetric recombinant offspring, these are disfavored and elim-

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Mating type identity in unicellular eukaryotes is determined by mating type loci that typically 344 carry a number of genes [27,11]. Suppressed recombination at the mating type locus is a common 345 feature across the evolutionary tree [8]. Our work predicts the co-evolution of mating type specific 346 signaling roles and suppressed recombination with selection favoring linkage between loci respon-347 sible for signaling and an asymmetry in signaling roles. This finding suggests that selection for 348 asymmetric signaling could be the very first step in the evolution of tight linkage between genes 349 that control mating type identity. In yeasts, the only genes in the mating type locus code for the 350 production of ligand and receptor molecules [29]. These then trigger a cascade of other signals 351 downstream that also operate asymmetrically. Evidence across species suggests that mating type 352 loci with suppressed recombination are precursors to sex chromosomes [46,47]. In this way our ber to only two in many species [27]. It would be interesting to use the framework developed here We model N cells so that each cell is individually characterized by a ligand locus L and a receptor 374 locus R. Two ligand genes at the locus L determine the production rates for two ligand types l 375 and L given by ⌫ l and ⌫ L . Similarly, two receptor genes at the locus R determine the production 376 rates for the two receptor types r and R given by ⌫ r and ⌫ L . The two ligand and receptor genes in 377 our model could could arise from duplication followed by mutation that leaves two closely linked 378 genes that code for different molecules. In our computational set-up each cell is associated with 379 production rates ⌫ l , ⌫ L , ⌫ r and ⌫ R where we assume a normalized upper bound so that ⌫ l + ⌫ L < 1 380 and ⌫ r + ⌫ R < 1. renormalized so their sum is capped at 1. If a mutation leads to a production rate below 0 or above 391 1 it is ignored and the production rate does not change. 392 We implement mating by randomly sampling individual cells. The probability that two cells 393 mate is determined by their ligand and receptor production rates as defined in Eq. (9) in the main 394 text. We assume that K takes a large value relative to W 12 W 21 so that P is linear in W 12 W 21 . Because where ⇢ M 1,2 = 1 2 (⇢ M 1 + ⇢ M 2 ) is the joint recombination rate when cell 1 and cell 2 with recombination 432 rates ⇢ M 1 and ⇢ M 2 respectively mate. 433 We allow mutation at the recombination locus at rate µ ⇢ independently of the ligand and recep-434 tor loci. A mutation event leads to a new recombination rate so that ⇢ 0 . 435 We assume that the mutation-selection balance has been reached when the absolute change in s,          The role of mutation rates. The threshold value of k + , beyond which E 2 becomes stable against 698 E 1 , plotted versus n which dictates the cost of self-binding for µ = 0.1and µ = 0.001 to show that 699 lower mutation rates require more stringent conditions for the evolution of signaling asymmetry.  Synergy and competition between the production rates of the two ligands (and receptors).

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Steady state signaling asymmetry s ⇤ against the intracellular binding rate k + for ⌫ R + ⌫ r < ↵ and ⌫ L +