Abstract Defense against infection incurs costs as well as benefits that are expected to shape the evolution of optimal defense strategies. In particular, many theoretical studies have investigated contexts favoring constitutive versus inducible defenses. However, even when one immune strategy is theoretically optimal, it may be evolutionarily unachievable. This is because evolution proceeds via mutational changes to the protein interaction networks underlying immune responses, not by changes to an immune strategy directly. Here, we use a theoretical simulation model to examine how underlying network architectures constrain the evolution of immune strategies, and how these network architectures account for desirable immune properties such as inducibility and robustness. We focus on immune signaling because signaling molecules are common targets of parasitic interference but are rarely studied in this context. We find that in the presence of a coevolving parasite that disrupts immune signaling, hosts evolve constitutive defenses even when inducible defenses are theoretically optimal. This occurs for two reasons. First, there are relatively few network architectures that produce immunity that is both inducible and also robust against targeted disruption. Second, evolution toward these few robust inducible network architectures often requires intermediate steps that are vulnerable to targeted disruption. The few networks that are both robust and inducible consist of many parallel pathways of immune signaling with few connections among them. In the context of relevant empirical literature, we discuss whether this is indeed the most evolutionarily accessible robust inducible network architecture in nature, and when it can evolve. coevolution, evolutionary simulation, evolvability, optimal immunity, robustness, signaling networks Introduction Host immune defenses must balance costs of infection with costs of immunity (Sheldon and Verhulst 1996). On one hand, infection can drastically impair host reproduction and survival (Wilson et al. 2002; Mahanty and Bray 2004; McKerrow et al. 2006). On the other hand, immune defenses are metabolically expensive to maintain and deploy (Lochmiller and Deerenberg 2000), and they risk immunopathologies that also reduce host fitness (Graham et al. 2005). This poses a conundrum for hosts: To minimize costs of infection, hosts must clear parasites as rapidly as possible; yet to minimize costs of immunity, reduced rates of parasite clearance are optimal (Cressler et al. 2015). In theory, the best strategy to balance these opposing selective pressures is for immunity to be rapidly inducible—that is, inactive until an infection is detected, followed by rapid activation and high activity until the infection is cleared, followed by rapid deactivation (Frank 2002). Nevertheless, many immune defenses observed in nature are constitutive—that is, continuously active even when the host is uninfected—including systemic molecular as well as barrier defenses (Asano et al. 1994; Tzou et al. 2000; Lamberty et al. 2001; Moret and Schmid-Hempel 2001; Millet et al. 2007; Abbas et al. 2016; Riessberger-Gallé et al. 2016). To explain the evolution of constitutive defense despite its costs, several theoretical models have identified ecological and evolutionary circumstances in which some degree of constitutive immunity is optimal (Shudo and Iwasa 2001, 2002; Hamilton et al. 2008; Ito and Sakai 2009; Westra et al. 2015; Kamiya et al. 2016). A key gap in our evolutionary understanding of immunity arises, however, because these models only address what the optimal immune strategy is, not whether that strategy can evolve. They represent immune strategies phenomenologically, using single parameters or state variables to quantify the proportions of defense that are constitutive versus inducible. This implicitly assumes that any strategy is at least evolutionarily achievable. However, it may be the case that a given immune strategy is optimal in theory but unattainable in practice. To study the evolvability of immune strategies, we must recognize that properties such as inducibility are not directly genetically encoded. Instead, they are emergent observations produced by the proteins that participate in immunity, and their patterns and strengths of interaction. These immune proteins fall into three categories: 1) detectors, which directly sense parasites (e.g., Toll-like receptors in mammals, peptidoglycan receptor proteins in insects), 2) effectors, which directly damage or kill parasites (e.g., antibodies in mammals, antimicrobial peptides in insects), and 3) signalers, which relay information from the detectors to the effectors (e.g., cytokines in mammals, Spätzle and Imd in insects) (Buchon et al. 2014; Abbas et al. 2016). Together, these three types of proteins form a complex interaction network. The vertices of this network are proteins, or else modules of tightly coregulated proteins, and the edges are interactions among them. Network “architecture” refers to the collective arrangement of all vertices and edges in a network, and network “structures” refer to any organizational features of a network’s architecture, such as the density of edges per vertex. The architectures of innate immune networks are being elucidated in model organisms such as Drosophila melanogaster (Teixeira 2012), Arabidopsis thaliana (Kim et al. 2014), and Caenorhabditis elegans (Alper et al. 2008; De Arras et al. 2013). However, it is unknown which network structures underlie different properties of optimal immune strategies, or how selection acts on protein networks to build these structures. To study how network architecture underpins optimal immune strategies and governs their evolution, we used a theoretical model simulating the evolution of immune networks, inspired by invertebrate innate immune systems. Our model begins with a population of 1000 hosts. Each host is defined by its immune network, which includes a detector protein, an effector protein, and a variable number of signaling proteins (supplementary fig. S1, Supplementary Material online). Host fitness depends on its performance under infection (supplementary fig. S2, Supplementary Material online). Following the conclusions of Frank (2002), we select for hosts with strong inducible immunity. However, a host’s realized immune strategy is generated by the architecture of its underlying protein network. This architecture is subject to mutation between generations, including duplication or deletion of proteins, as well as addition, deletion, or altered strength of protein–protein interactions. By explicitly tracking individual hosts within an evolving population, our simulations include essential population genetic processes that are absent from many network evolution studies (Lynch 2007). We defined two scenarios, pure “evolution” and “coevolution.” In the evolution scenario, each host is infected by the same inert parasite strain every generation. In the coevolution scenario, infections come from a coevolving population of diverse parasite strains; each strain disrupts immune signaling by up- or downregulating a specific host signaling protein. Parasites in this coevolving population mutate their signaling disruption strategy with higher probability than that of host mutation (see supplementary table S1, Supplementary Material online, for parameter justification). Parasite disruption of immunity is extraordinarily common (Schmid-Hempel 2008), and therefore optimal immune systems ought to be robust against targeted disruptions (Bergstrom and Antia 2006). We focused on signaling disruption because examples abound in nature (Flynn and Chan 2003; Hartmann and Lucius 2003; Seet et al. 2003; Tenor et al. 2004; Li et al. 2005; Schlenke et al. 2007; Dunbar et al. 2012; de Jong et al. 2017), and moreover, signatures of positive selection in the Drosophila genome suggest that the signaling stage of immunity is most targeted by parasite disruption strategies (Lazzaro 2008). Even so, signaling disruption has been studied less frequently than detector and effector disruption (Kamiya et al. 2016). We find that the coevolution scenario produces Red Queen dynamics often observed in experimental and natural coevolution, including analogues of fluctuating selection (Decaestecker et al. 2007; Koskella and Lively 2009; Hall et al. 2011) and repeated selective sweeps (Paterson et al. 2010; Hall et al. 2011). Though we do not explicitly model coevolution of individual proteins at a molecular level, we do observe coevolution at the host–parasite organismal scale, in the form of reciprocal changes in hosts’ network architectures and counter-changes in parasite disruption strategy. Coevolution also selects for robustness—that is, the ability of a host’s immune signaling network to continue functioning as normal, despite the up- or downregulation of any given protein by an infecting parasite. However, the coevolution scenario surprisingly prevents the emergence of inducible immunity in the host population in most cases, despite direct selection for this property. We identify structural features of networks producing inducible immunity, and additional structural features that make several rare inducible networks also robust against targeted disruption. Finally, we suggest two reasons why protein interaction networks prevent the evolution of theoretically optimal immunity in the biologically common case of coevolution with a signal-disrupting parasite. Results Parasite Coevolution Produces Red Queen Dynamics Compared with pure evolution simulations, coevolution with a signal-disrupting parasite complicated the evolutionary dynamics of the host population. Under pure evolution, within the first 30 generations, the diverse pool of randomly generated hosts was narrowed down to several of the most fit host networks initially present. Typically, these hosts were still well below the theoretically maximal fitness produced by induced immunity. Average host fitness remained low, until one or a series of mutations swept through the population, driving average host fitness upward in a stepwise fashion until near-maximal fitness was attained (fig. 1A). The proportion of hosts surviving each generation was always nearly 100%. Fig. 1. View largeDownload slide Representative model simulations. (A) Under evolution, the host population achieves high fitness via discrete mutational steps that sweep through the host population. This is indicated by the near-vertical jumps in the black line. (B) Coevolution leads to Red Queen dynamics at the organismal level, indicated by the oscillations in the red and black lines. Here, parasites went extinct just after generation 200. (C) Parasite disruption strategies from the same sample coevolution simulation as in (B). For each generation, the height spanned by each color equals the proportion of the parasite population with the corresponding disruption strategy. “2 D” refers to the parasite strategy of downregulating host signaling protein 2, “2 U” refers to the parasite strategy of upregulating host signaling protein 2, and so on. Abrupt changes in the dominant parasite interference strategy coincide with major increases in average parasite fitness, indicating that the parasite population is adapting to changes to the most prevalent host network architectures. Series of new dominant colors (e.g., green, yellow, and red in Generations 20–35) is analogous to repeated selective sweeps of new mutations. Alternation of two different dominant colors (e.g., gray and green in Generations 90–140) is analogous to negative frequency dependent fluctuating selection. Fig. 1. View largeDownload slide Representative model simulations. (A) Under evolution, the host population achieves high fitness via discrete mutational steps that sweep through the host population. This is indicated by the near-vertical jumps in the black line. (B) Coevolution leads to Red Queen dynamics at the organismal level, indicated by the oscillations in the red and black lines. Here, parasites went extinct just after generation 200. (C) Parasite disruption strategies from the same sample coevolution simulation as in (B). For each generation, the height spanned by each color equals the proportion of the parasite population with the corresponding disruption strategy. “2 D” refers to the parasite strategy of downregulating host signaling protein 2, “2 U” refers to the parasite strategy of upregulating host signaling protein 2, and so on. Abrupt changes in the dominant parasite interference strategy coincide with major increases in average parasite fitness, indicating that the parasite population is adapting to changes to the most prevalent host network architectures. Series of new dominant colors (e.g., green, yellow, and red in Generations 20–35) is analogous to repeated selective sweeps of new mutations. Alternation of two different dominant colors (e.g., gray and green in Generations 90–140) is analogous to negative frequency dependent fluctuating selection. In contrast, under coevolution, the first 20–100 generations were spent in rapid fitness cycles, in which average host and parasite fitnesses rapidly alternated between high and low values. Fitness troughs for both organisms were often accompanied by temporary declines in the proportion of surviving individuals. Subsequent generations produced diverse dynamics, often including further rapid fitness cycles (fig. 1B). In these cycles, sharp increases in host fitness often cooccurred with decreases in parasite fitness, and vice versa, but not always, due to the asymmetry of the fitness functions for hosts and parasites. During these fitness cycles, swings in average host fitness were accompanied by changes in the dominant disruption strategy in the parasite population (fig. 1C). Thus, the cycling indicated a repeated pattern of: 1) low average host fitness, 2) emergence of a new or rare host network architecture that effectively cleared parasites, 3) selective spread of that network architecture through the host population, 4) selection for a different parasite disruption strategy that thwarted the newly dominant host network architecture, and 5) return to low average host fitness. Repeated alternation between two dominant parasite disruption strategies is analogous to negative frequency-dependent fluctuating selection. Sequential appearance of new dominant parasite disruption strategies is analogous to selective sweeps. Both types of organismal-scale Red Queen dynamics are marked in figure 1C. Parasite Coevolution Selects for Host Robustness During coevolution, hosts could evolve a network architecture robust to parasite disruption—that is, the host’s fitness score is nearly unchanged when any single signaling protein is disrupted. Because coevolving parasites disrupt signaling proteins, the coevolution scenario selected for robustness as well as inducibility, whereas the evolution scenario selected only for inducibility. Indeed, among hosts that achieved inducible immunity, the networks of coevolved hosts were significantly more robust than those of purely evolved hosts (Wilcoxon rank-sum test, P < 2.2×10−16, effect size = 0.373) (fig. 2). Fig. 2. View largeDownload slide Among hosts that achieved high fitness, coevolved hosts (N = 129) are significantly more robust than evolved hosts (N = 1687) (P < 2.2×10−16, effect size = 0.373, Wilcoxon rank-sum test). MCH: most common host, the host network structure best represented in the host population at the end of a simulation. The robustness score is the expected proportion of fitness retained by a host network when a signaling protein is disrupted. A robustness score of 1 indicates that the functioning of a host immune network is unaffected by the up- or downregulation of any single signaling protein. Outliers with robustness >1 represent rare cases in which the most common host’s immune network functions better with disruption than without. Fig. 2. View largeDownload slide Among hosts that achieved high fitness, coevolved hosts (N = 129) are significantly more robust than evolved hosts (N = 1687) (P < 2.2×10−16, effect size = 0.373, Wilcoxon rank-sum test). MCH: most common host, the host network structure best represented in the host population at the end of a simulation. The robustness score is the expected proportion of fitness retained by a host network when a signaling protein is disrupted. A robustness score of 1 indicates that the functioning of a host immune network is unaffected by the up- or downregulation of any single signaling protein. Outliers with robustness >1 represent rare cases in which the most common host’s immune network functions better with disruption than without. (Co)Evolution Leads to Four Distinct Host Immune Strategies Because our model’s fitness functions account for immune costs as well as infection costs, high absolute fitness required hosts to have inducible immunity that quickly cleared the parasite and then waned. Constitutive immunity also cleared the parasite, but resulted in lower absolute fitness. As expected, under pure evolution, hosts with strong induced immunity triumphed in most simulations (1687/1979 = 85.2%). The remainder of pure evolution simulations (292/1979 =14.8%) produced hosts with a mixed immune strategy, in which effector levels were low before infection and increased during infection, but remained high after the infection was cleared (fig. 3A and B). To the contrary, coevolution with a signal-disrupting parasite produced hosts with inducible immunity in very few simulations (129/1996 = 6.5%). Instead, most coevolution simulations (1866/1996 = 93.5%) resulted in hosts with constitutive immunity and low absolute fitness (fig. 3C and D). (The host population went extinct in one model run [<0.1%]). Thus, coevolution of a signal-disrupting parasite led to nonoptimal immunity. Fig. 3. View largeDownload slide Simulation outcomes cluster into four qualitatively different host immune strategies, as shown in the histograms. For each of these four outcomes, infection dynamics of a representative host infected with a nondisrupting parasite are shown. The four strategies are as follows: (A) Under evolution, hosts usually (1687/1979) evolve strong inducible immunity. (B) Occasionally (292/1979), however, hosts evolve a mixed immune strategy which does not fully clear the parasite or does not shut down after the parasite is cleared. (C) Under coevolution, hosts rarely (129/1996) evolve strong inducible immunity that rapidly clears the parasite and results in high fitness. (D) Instead, hosts usually (1866/1996) evolve strong constitutive immunity that rapidly clears the parasite but results in low fitness. (In one coevolution simulation, the host population went extinct). Fig. 3. View largeDownload slide Simulation outcomes cluster into four qualitatively different host immune strategies, as shown in the histograms. For each of these four outcomes, infection dynamics of a representative host infected with a nondisrupting parasite are shown. The four strategies are as follows: (A) Under evolution, hosts usually (1687/1979) evolve strong inducible immunity. (B) Occasionally (292/1979), however, hosts evolve a mixed immune strategy which does not fully clear the parasite or does not shut down after the parasite is cleared. (C) Under coevolution, hosts rarely (129/1996) evolve strong inducible immunity that rapidly clears the parasite and results in high fitness. (D) Instead, hosts usually (1866/1996) evolve strong constitutive immunity that rapidly clears the parasite but results in low fitness. (In one coevolution simulation, the host population went extinct). The inability of host populations to achieve optimal inducible immunity in the presence of a coevolving, signal-disrupting parasite population is not predetermined by the model framework or parameter choices (see supplementary table S1, Supplementary Material online, for default parameter values). In particular, this result was insensitive to the cost and frequency of infection. We initially assumed that the cost of infection was equal to the cost of immunity, but when the cost of infection exceeded the cost of immunity, host populations were even less likely to evolve inducible immunity (supplementary fig. S3, Supplementary Material online). Even assuming that the cost of infection was only half the cost of immunity, host populations still evolved inducible immunity <10% of the time (supplementary fig. S3, Supplementary Material online). We also conservatively assumed that the parasite species causes only one infection per host per generation. Increasing the number of infections per host lifetime further reduced the evolvability of inducible immunity (supplementary fig. S4, Supplementary Material online). Likewise, the model results are not sensitive to variation in parameters governing mutation and selection. The mutation probabilities for parasites and hosts affect the relative amounts of variation and thus the relative efficiency of selection in each population. And yet, across a 1000-fold range of parasite:host relative mutation probabilities, host populations remained unlikely to evolve optimal inducible immunity (supplementary fig. S5A, Supplementary Material online). Even favoring certain types of mutations to host signaling networks (e.g., addition of new protein–protein interactions, etc.) did not substantially improve the ability of host populations to evolve inducible immunity (supplementary fig. S6A, Supplementary Material online). Relatively Few Network Architectures Produce Robust Inducible Immunity Thus, despite the higher absolute fitness conferred by inducible immunity, most coevolution model runs surprisingly produced hosts with constitutive immunity (fig. 3). This likely reflected the difficulty of assembling an inducible signaling network which is also robust against disrupting parasites. Using terminology from figure 3, Coevolved Inducible hosts were more constrained in their network architecture than Coevolved Constitutive hosts, according to an analysis of three-motifs. Three-motifs are patterns of connection among subgroups of three vertices embedded in a larger network (see Materials and Methods). The prevalence of each of the 13 possible directed 3-motifs (supplementary fig. S7, Supplementary Material online) characterizes a network’s total architecture. Therefore, the variance in 3-motif prevalence across a set of networks describes the range of architectures present in the set. For all 13 3-motifs, networks of Coevolved Inducible hosts had lower variance in motif prevalence than networks of Coevolved Constitutive hosts. This reduced variance was statistically significant after Bonferroni correction for seven of those 13 3-motifs, and nearly significant for an eighth (Brown–Forsythe test, P < 0.0038, effect sizes ranged from 0.023 to 0.061) (fig. 4). Thus, Coevolved Inducible hosts had substantially less variable network architectures than Coevolved Constitutive hosts. Fig. 4. View largeDownload slide Coevolved Inducible hosts (N = 129) have more constrained network architectures than Coevolved Constitutive hosts (N = 1866) as revealed by 3-motif analysis. For 8 of 13 possible 3-motifs, Coevolved Inducible hosts had significantly or nearly significantly smaller variances in 3-motif prevalence than did Coevolved Constitutive hosts after Bonferroni correction (Brown–Forsythe test, P < 0.0038). + P < 0.01, * P < 0.0038, ** P < 0.001, *** P < 0.0001. Fig. 4. View largeDownload slide Coevolved Inducible hosts (N = 129) have more constrained network architectures than Coevolved Constitutive hosts (N = 1866) as revealed by 3-motif analysis. For 8 of 13 possible 3-motifs, Coevolved Inducible hosts had significantly or nearly significantly smaller variances in 3-motif prevalence than did Coevolved Constitutive hosts after Bonferroni correction (Brown–Forsythe test, P < 0.0038). + P < 0.01, * P < 0.0038, ** P < 0.001, *** P < 0.0001. Reduced variability in the network architectures of Coevolved Inducible hosts could have occurred for two reasons. First, perhaps the set of network architectures capable of producing robust inducible immunity is simply smaller than the set of network architectures capable of producing robust constitutive immunity. Alternatively, perhaps these two sets are of equal size, but the coevolution of a disrupting parasite renders many robust inducible network architectures unattainable by single mutational steps. To address these two hypotheses, we compared the network prevalence of 3-motifs in Coevolved Inducible hosts to their prevalence in those Evolved Inducible hosts which happened to achieve high robustness, even though it was not selected for during pure evolution. None of the 13 3-motifs differed significantly in the variance of their prevalences between these two groups (Brown–Forsythe tests), suggesting that Coevolved Inducible hosts spanned the full range of evolutionarily possible network architectures that produce robust inducible immunity. Thus, a coevolving signal-disrupting parasite did not prevent any specific robust inducible network architecture from arising. Instead, coevolving parasites simply constrained hosts to evolve toward a smaller set of network architectures. Decreased Total Connectivity, but Increased Detector-to-Effector Connectivity, Underlies Both Inducibility and Robustness Next we searched for network structures that underlie desirable features of immunity. Comparing Evolved Inducible networks to randomly generated, unevolved networks revealed structural properties conferring inducibility. Comparing Coevolved Inducible networks to Evolved Inducible networks revealed further structural properties that allow inducible immunity to also be robust against parasite disruption. Importantly, these comparisons revealed only the inducibility- and robustness-conferring properties that can arise through a (co)evolutionary process via stepwise mutations. Other inducibility- and/or robustness-conferring properties might be designed de novo, but are not (co)evolvable in this framework. In general, the (co)evolvable structural properties that allowed inducible immunity to be robust are exaggerations of the properties that allowed immunity to be inducible in the first place. Evolved Inducible networks were significantly less connected than unevolved networks (Wilcoxon rank-sum test, P < 2.2×10−16, effect size = 0.0392), and Coevolved Inducible networks were even less connected than Evolved Inducible networks (Wilcoxon rank-sum test, P < 7.3×10−16, effect size = 0.0714) (fig. 5A). Despite the decrease in total connectivity from unevolved to Evolved Inducible to Coevolved Inducible networks, this same progression witnessed an increase in connectivity specifically between the detector and effector. The number of short paths connecting the detector to the effector was greater in Evolved Inducible networks than in unevolved networks (Wilcoxon rank-sum test, P < 2.2×10−16, effect size = 1), and even greater in Coevolved Inducible networks (Wilcoxon rank-sum test, P < 2.2×10−16, effect size = 1) (fig. 5B). Similarly, the number of network edges that must be removed to completely decouple the effector from the detector was greater in Evolved Inducible networks than in unevolved networks (Wilcoxon rank-sum test, P < 2.2×10−16, effect size = 1), and even greater in Coevolved Inducible networks (Wilcoxon rank-sum test, P < 2.2×10−16, effect size = 1) (fig. 5C). Thus, these three network structural properties—low total connectivity, many short paths from the detector to the effector, and difficulty of decoupling the detector from the effector—underlie both inducibility and robustness. Fig. 5. View largeDownload slide Unevolved (N = 1979), Evolved Inducible (N = 1687), and Coevolved Inducible (N = 129) networks differ significantly in several key structural properties among the Most Common Hosts (MCHs) of different simulations. These measures are (A) connectivity, (B) shortest path number—the number of different directed paths of the shortest possible length from the detector to the effector, and (C) detector-to-effector cuts—the minimum number of edges that must be removed from the network to completely decouple the detector and effector. ***P < 10−15. Fig. 5. View largeDownload slide Unevolved (N = 1979), Evolved Inducible (N = 1687), and Coevolved Inducible (N = 129) networks differ significantly in several key structural properties among the Most Common Hosts (MCHs) of different simulations. These measures are (A) connectivity, (B) shortest path number—the number of different directed paths of the shortest possible length from the detector to the effector, and (C) detector-to-effector cuts—the minimum number of edges that must be removed from the network to completely decouple the detector and effector. ***P < 10−15. These findings suggest that once mutations accrue to confer inducibility on an immune network, more mutations of the same sort will also confer robustness to sabotage. This indicates that evolving robust inducible immunity requires traversing a vulnerable intermediate stage of merely inducible, nonrobust immunity. Supporting these conclusions, one type of host mutation—protein duplication—was consistently associated with each of the three network structural properties of robust inducible immunity (supplementary fig. S6C–E, Supplementary Material online). And yet, despite a predisposition to evolve these favorable network structures, host populations with high protein duplication probabilities attained robust inducible immunity significantly less often than host populations with low protein duplication probabilities (supplementary fig. S6B, Supplementary Material online). This is consistent with a vulnerable intermediate stage lying on the evolutionary path to robust inducible immunity. Discussion We modeled mutation and selection on protein networks underlying host immunity during pure evolution and coevolution with a signal-disrupting parasite, when the optimal immune strategy was defined a priori. The microscale individual interactions of our simulation model produced realistic macroscale evolutionary patterns, including Red Queen dynamics analogous to those observed experimentally (Decaestecker et al. 2007; Koskella and Lively 2009; Paterson et al. 2010; Hall et al. 2011). Moreover, the model selected for inducible immunity under both pure evolution and coevolution, as well as for robustness under coevolution, as intended. Thus, the network architectures observed here accord with previous work and enable fresh insights into the evolution of immune systems. Immune signaling networks that produced robust inducible immunity were sparsely connected overall, despite many short connections from the detector to the effector (fig. 5). In practical terms, networks which are both inducible and robust consist of many parallel pathways of immune signaling with few connections among them (supplementary fig. S8, Supplementary Material online). These parallel pathways can be considered redundant modules of host defense. In this regard, our model supports the longstanding notion that modularity and redundancy are two design principles essential for robustness in complex biological (Kirschner and Gerhart 1998; Kitano 2004; Bergstrom and Antia 2006) and artificial (Simon 1996) systems. Moreover, this architectural pattern resembles the understanding of invertebrate innate immune signaling networks emerging from numerous transcriptomic and molecular studies. For example, the immune defenses of C. elegans have been characterized in terms of protein interaction pathways (Ewbank 2006) and gene expression patterns (Engelmann et al. 2011). Consistent with its history of coevolution with signal-disrupting parasites (Schulenberg and Ewbank 2004; Tenor et al. 2004; Dunbar et al. 2012), C. elegans possesses exactly the immune network architecture our model predicts for robust inducible immunity: many parallel signaling pathways (Pukkila-Worley and Ausubel 2012), several of which participate in any given immune response (Alper et al. 2007). Thus, our model provides compelling in silico experimental evidence for network architectural properties thought to underlie robustness against targeted disruption in real biological systems. Our model also exposes the very process of network evolution by stepwise mutations as a constraint on optimal immunity. During coevolution with a signal-disrupting parasite, which forced hosts to evolve immunity that was robust, hosts were overwhelmingly likely to rely on suboptimal constitutive immunity rather than optimal inducible immunity. This occurred for two reasons, both of which involve the protein interaction networks that produced the observed immune dynamics. First, the set of (co)evolvable network architectures that produce robust inducible immunity is smaller than the set of network architectures that produce robust constitutive immunity. Because mutations were random, hosts approached and subsequently attained robust constitutive immunity more often than robust inducible immunity. Second, even rare evolution toward robust inducible immunity may require intermediate steps that are vulnerable to parasite sabotage. Hosts began simulations as randomly generated networks that were neither inducible nor robust—both properties had to be evolved. We found that the network structures producing robustness were exaggerations of the structures responsible for inducibility. Thus, once mutations accrued to confer inducibility on an immune network, more mutations of the same sort also conferred robustness—in short, inducibility evolved before robustness. Thus, even when random mutations did allow hosts to approach robust inducible immunity, this often proceeded through a vulnerable stage of nonrobust inducible immunity. As a result, each evolutionary approach to robust inducible immunity was easily blocked by coevolving parasites. Our model is not without limitations. For one thing, in nature, a host population faces many different parasite species. Immune signaling disruption strategies may be different among parasite species, but similar within a given parasite species. In our model, the host population faces only a single parasite species, but the parasite species can comprise many different disruption strategies and can entirely switch disruption strategies with a single mutation. In one sense, the variability and mutational freedom of the modeled parasites mimic the diversity of multiple parasite species, so that both natural and modeled hosts are selected to be robust against any kind of disruption to their immune signaling systems (Bergstrom and Antia 2006). In another sense, however, the natural and modeled scenarios are quite different. In nature, parasitic species can evolve to be more or less specialized on the host, but rarely do all parasite species specialize on the host at any given time. Meanwhile, in our model, the lone, highly variable parasite species does specialize entirely on the host. The net effect may be that natural host populations combat only a few disruption strategies at any given time, whereas the modeled host populations combat many different disruption strategies at one time, uniquely selecting for immune generalism in the model. In practice, however, our model did not differ from nature in this way: during any given generation, and often for many generations consecutively, a single disruption strategy dominated in the modeled parasite population (e.g., fig. 1C). Thus, at any given time in our model, the host population was not inundated with many different disruption strategies. Instead, as is expected in nature, only one or two were prevalent. Furthermore, in our model the level of diversity of disruption strategies in the parasite population decreased with decreasing parasite mutation probability (supplementary fig. S5B, Supplementary Material online). Even across a 1000-fold range of parasite mutation probabilities, the lower end of which severely restricted parasite diversity and curtailed any selection for immune generalism (supplementary fig. S5B, Supplementary Material online), host populations still predominantly failed to evolve optimal inducible immunity (supplementary fig. S5A, Supplementary Material online), upholding our key result. Another limitation of our model is that in nature, declining average absolute fitness in a population decreases effective population size, which in turn decreases the potential for new mutations to arise and rescue the population. This was not the case in our model, because host population size was fixed and host reproductive success was based solely on relative fitness. Host populations with low absolute fitness were therefore just as likely to undergo positive selection for a beneficial mutant. If anything, accounting for shrinking effective population size in our model would have strengthened our result that robust inducible immune networks are very unlikely to evolve by stepwise mutations under coevolution with a signal-disrupting parasite. Why, then, is inducible immunity so much more common in nature than in our model? In other words, how do immune network architectures like that of C. elegans—which could so rarely evolve in our model—evolve in nature? For one thing, networks in our model could not coopt entire prebuilt pathways from other, nonimmune networks, whereas this process may be important in nature. For example, several components of a molecular network underlying essential secretory processes have been coopted for use in immune responses in A. thaliana (Kwon et al. 2008). There is also evidence that the ERK, TGF-β, p38 MAP kinase, and insulin immune pathways of C. elegans were coopted from nonimmune pathways (Felix and Braendle 2010). More importantly, our model does not include recombination, due to the computational difficulties of melding distinct networks. Nonetheless, we recognize that the classic explanation for recombination is precisely that it allows host immunity to keep pace with parasites during coevolution (Jaenike 1978; Hamilton 1980). Indeed, recombination via sexual reproduction is necessary for the successful coevolution of C. elegans with parasitic adversaries (Morran et al. 2011), and it may have been the key that allowed C. elegans to evolve its robust immune network architecture noted above. Experimental coevolution of sexual C. elegans with parasites, combined with periodic transcriptional mapping of the C. elegans immune network, may shed light on the types (and pace) of network rewiring events which are impossible by stepwise mutations but required to successfully coevolve robust inducible immunity. Recombination often leads to the accumulation of redundant regulatory mechanisms (Lynch 2007), and unconnected redundant signaling pathways were essential to the robust inducible networks we observed. Thus, we predict that recombination allows hosts to more often escape the constraint of network assembly observed here, but does not introduce robust inducible network architectures that are qualitatively different from those we have already characterized. In sum, selection imposed by coevolving, subversive parasites occurs on the protein interaction networks underlying immunity, not on immune strategies themselves. This may prevent optimal immune strategies from evolving, and almost certainly limits the network architectures that can evolve to implement them. We found that redundant, parallel pathways with few interconnections is the most evolutionarily accessible network architecture that produces robust inducible immunity. Straightaway, this makes sense of numerous biological immune signaling pathways, which can seem bewildering when discovered and studied one by one. Moreover, for engineers of artificial systems, this erects a challenge to find other network architectures that are robust against targeted disruption and may not be accessible via evolution, but only by de novo design. Materials and Methods We simulated the evolution of a population of hosts, either with or without a coevolving parasite population. Each individual host is defined by its network of immune proteins. In a network, each vertex represents a protein. Each host has one detector protein, one effector protein, and multiple signaling proteins. An additional vertex representing a within-host parasite population (hereafter called the “parasite”) is added to a host network to simulate infection. Activating and deactivating interactions among the proteins and/or the parasite are represented by directed edges (supplementary fig. S1, Supplementary Material online). We implemented this by modifying a previously published modeling framework (Salathe and Soyer 2008), based on a widely used network dynamics model (Soyer et al. 2006). In this model, each vertex Pi of the network has a total concentration of 1, including both an active portion [Pi*] and an inactive portion [Pi], such that [Pi*] + [Pi] = 1. Here, i can represent the host’s detector protein, any of its signaling proteins, its effector protein, or the infecting parasite. There are three types of directed interactions among vertices: the active portion of vertex j may 1) activate the inactive portion of vertex i, 2) deactivate the active portion of vertex i, or 3) not affect vertex i at all. All interactions among proteins and/or the parasite follow the same form and are captured as follows: dPi*dt=Pi∑jki,jPj*-Pi*∑jli,jPj*, (1) where the coefficients ki,j are the values of the positive (activating) links from vertex j to vertex i, and the coefficients li,j are the absolute values of the negative (deactivating) links from vertex j to vertex i. Some edges of every network are fixed parameters of the model. When present, parasites activate their own growth with the parameter rpar, such that kpar, par = rpar. (Parameter values used in our main simulations, and justification from empirical literature, are provided in supplementary table S1, Supplementary Material online) When equation (1) is written for [Ppar*], the first term simplifies to logistic growth for the parasite, with growth rate rpar and carrying capacity 1.0. The parasite activates the host detector with perfect efficiency, such that kdet, par = 1.0. The host effector protein deactivates (kills) the parasite with perfect efficiency, such that lpar, eff = 1.0. No other host proteins may affect the parasite directly. The host detector and effector may not communicate directly, such that kdet, eff = ldet, eff = keff, det = leff, det = 0. Instead, the host detector and effector communicate via a subnetwork of signaling proteins, whose only restriction is that a signaler cannot activate or deactivate itself. Otherwise, edges between a signaler and the detector, effector, or another signaler take values between −1 and 1, and their existence and strength may be altered by mutations during evolutionary simulations. Within-Host Infections As previously mentioned, we simulate two different scenarios: pure host evolution independent of the parasite, and host–parasite coevolution. In the evolution scenario, every host is infected by a parasite once in each generation, and the parasite cannot affect any host protein (other than by triggering the detector). In the coevolution scenario, every host is also infected by a parasite once in each generation, and the parasite can also disrupt one of the host’s signaling proteins, either by down- or upregulating it. A downregulating parasite removes its target signaling protein from the host network: the active portion of the protein is set to 0, and all the edges involving that protein are removed from the host network. An upregulating parasite magnifies the activity of its target signaling protein: the active portion of the protein is set to 1, its incoming edges are removed to prevent subsequent deactivation, and its outgoing edges are doubled in strength to exacerbate its effect on the rest of the host’s network. In each generation of a simulation, each host experiences two phases (supplementary fig. S1, Supplementary Material online). During the preinfection phase, the parasite does not yet exist, and the active portion of each host protein is initialized to 0.5. Then the network reaches an equilibrium according to equation (1). Once equilibrium has been reached, the infection phase begins: the parasite is added to the network at a level of 0.5, and the network progresses to a new equilibrium. If the parasite is driven below a threshold of 1×10−4, it is considered cleared. The trajectories of each host protein level and the parasite level through these two phases define the “infection dynamics” of the host–parasite pair (supplementary fig. S2, Supplementary Material online). Host Selection Following Salathe and Soyer (2008), we use discrete, synchronized generations. We calculate a fitness value between 0 and 1 for each host in each generation to quantify the host’s immune network performance. Host fitness is conditional on three values from the infection dynamics (supplementary fig. S2, Supplementary Material online). The first is the equilibrium active portion of the host effector before infection, representing the cost of constitutive immunity. The second is the area under the parasite trajectory (normalized to a 0–1 scale), representing the cost of the duration and severity of infection. The third is the equilibrium active portion of the host effector protein after infection, representing the cost of lingering induced immunity. Host fitness is thus calculated as follows, Whost=e-Peff*pre+v·area+Peff*post, (2) where v is the damage potential of the parasite. Damage potential modulates the importance of the cost of infection to host fitness, relative to the costs of immunity. To create the next generation of hosts, individuals in the current generation are chosen to reproduce. The higher a host’s fitness relative to other hosts in the current generation, the more likely it is to be chosen. If a host’s fitness is <1×10−4, the host is considered dead and is not eligible to reproduce at all. Reproduction entails cloning the network of the original host and allowing for random mutations to occur with a given probability of 5×10−3 per signaling protein. We account for five types of host network mutations: 1) addition of a new edge between proteins (relative probability 0.25), 2) deletion of an existing edge between proteins (relative probability 0.25), 3) altering the strength of an existing edge between proteins (relative probability 0.3), 4) duplication of a protein and all its edges (relative probability 0.1), and 5) deletion of a protein and all of its edges (relative probability 0.1). In the pure evolution scenario, there are no distinct parasite types, and so the at-large parasite population (as opposed to within-host parasite populations) is not tracked. However, in the coevolution scenario, different parasite types are defined by different disruption strategies—either up- or downregulation of a target host signaling protein—and the at-large parasite population is explicitly tracked. Parasite fitness is conditional only on the duration and severity of infection, and is calculated as follows: Wparasite=e-2+v1-area. (3) Adding 2 to the damage potential insures that parasite fitness has the same range as host fitness. Parasite reproduction proceeds the same way as host reproduction, except that mutations occur with a fixed probability of 0.01. This is higher than the host mutation probability, as may be expected biologically. In the case of a mutation, the new parasite discards its original disruption strategy and chooses a new one at random. (Co)Evolutionary Simulations A simulation begins with a population of 1000 hosts, each one represented as a randomly generated network adhering to the connectivity rules above. Population size remains constant throughout the simulation. A simulation lasts 600 generations, enough for most simulations to achieve a stable evolutionary outcome. In each generation, every host is assigned a parasite, and infection dynamics are tracked for each host–parasite pair. From these dynamics we calculate fitnesses, and reproduction occurs to create the next generation, as described earlier. In the coevolution scenario, a simulation also begins with an at-large population of 1000 parasite types, each one randomly assigned a disruption strategy and a host. Model Output Analysis We track average host and parasite fitness, number of hosts and parasites surviving, abundances of parasite disruption strategies (in the coevolution scenario) and other statistics for each generation of each model run (supplementary table S2, Supplementary Material online). We also record the network architecture of the most common host type (MCH) in the host population after the final generation each simulation. For each MCH we calculate fitness after infection with a nondisrupting parasite, as well as robustness. We defined robustness as follows: robustness=Σiwi2sw0, (4) where s is the number of signaling proteins in the MCH network, the i are each of the possible disruption strategies that could affect the MCH (of which there are 2 s—up- or downregulation of each of the host’s signaling proteins), wi is the fitness of the MCH when infected by a parasite of disruption strategy i, and w0 is the fitness of the MCH when infected by a nondisrupting parasite. Finally, for each MCH we calculate several common metrics of network architecture (Pavlopoulos et al. 2011) (supplementary table S3, Supplementary Material online). Of these metrics, we report on four: Connectivity: The connectivity of a network is the number of existing edges divided by the maximum possible number of edges. Shortest path number: In each MCH, one or more paths along directed edges connect the detector to the effector. The path requiring the fewest edges is called the shortest path. The length of the shortest path is the number of edges it includes. The number of paths from the detector to the effector of this minimum length is the shortest path number. Detector-to-effector cuts: This is the minimum number of edges that can be removed from the network to completely decouple the effector from the detector. 3-motif prevalence: In a network of n vertices, n ≥ 3, a 3-motif is any of the 13 possible patterns of directed connections among a subset of three vertices (supplementary fig. S7, Supplementary Material online). Each 3-motif can be embedded in the larger network in numerous places, and the entire n-vertex network contains up to n3 = (n3) 3-motifs. Thus, the prevalence of a 3-motif in a given n-vertex network is the number of actual occurrences of that 3-motif divided by n3. The statistical tests used for all comparisons are noted in the text. The minimum measurable P value was 2.2×10−16, due to computational limits. Standard effect sizes are reported for tests comparing sample means. For the Brown–Forsythe test, which compares sample variances, the effect size reported is the difference in SD between the two samples. Software Evolutionary simulations were coded in Java and run using Eclipse Mars.2 Release (Version 4.5.2). All analyses were performed in RStudio Version 3.2.1. Supplementary Material Supplementary data are available at Molecular Biology and Evolution online. 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