Simulating the evolution of signal transduction pathways

Pleiotropy alleviates the fitness costs associated with resource allocation trade-offs in immune signalling networks

Many genes and signalling pathways within plant and animal taxa drive the expression of multiple organismal traits. This form of genetic pleiotropy instigates trade-offs among life-history traits if a mutation in the pleiotropic gene improves the fitness contribution of one trait at the expense of another. Whether or not pleiotropy gives rise to conflict among traits, however, likely depends on the resource costs and timing of trait deployment during organismal development. To investigate factors that could influence the evolutionary maintenance of pleiotropy in gene networks, we developed an agent-based model of co-evolution between parasites and hosts. Hosts comprise signalling networks that must faithfully complete a developmental programme while also defending against parasites, and trait signalling networks could be independent or share a pleiotropic component as they evolved to improve host fitness. We found that hosts with independent developmental and immune networks were significantly more fit than hosts with pleiotropic networks when traits were deployed asynchronously during development. When host genotypes directly competed against each other, however, pleiotropic hosts were victorious regardless of trait synchrony because the pleiotropic networks were more robust to parasite manipulation, potentially explaining the abundance of pleiotropy in immune systems despite its contribution to life history trade-offs.

Pleiotropy alleviates the fitness costs associated with resource allocation trade-offs in immune signaling networks

Many genes and signaling pathways within plant and animal taxa drive the expression of multiple organismal traits. This form of genetic pleiotropy instigates trade-offs among life-history traits if a mutation in the pleiotropic gene improves the fitness contribution of one trait at the expense of another. Whether or not pleiotropy gives rise to conflict among traits, however, likely depends on the resource costs and timing of trait deployment during organismal development. To investigate factors that could influence the evolutionary maintenance of pleiotropy in gene networks, we developed an agent-based model of co-evolution between parasites and hosts. Hosts comprise signaling networks that must faithfully complete a developmental program while also defending against parasites, and trait signaling networks could be independent or share a pleiotropic component as they evolved to improve host fitness. We found that hosts with independent developmental and immune networks were significantly more fit than hosts with pleiotropic networks when traits were deployed asynchronously during development. When host genotypes directly competed against each other, however, pleiotropic hosts were victorious regardless of trait synchrony because the pleiotropic networks were more robust to parasite manipulation, potentially explaining the abundance of pleiotropy in immune systems despite its contribution to life history trade-offs.

Pleiotropy promotes the evolution of inducible immune responses in a model of host-pathogen coevolution

Components of immune systems face significant selective pressure to efficiently use organismal resources, mitigate infection, and resist parasitic manipulation. A theoretically optimal immune defense balances investment in constitutive and inducible immune components depending on the kinds of parasites encountered, but genetic and dynamic constraints can force deviation away from theoretical optima. One such potential constraint is pleiotropy, the phenomenon where a single gene affects multiple phenotypes. Although pleiotropy can prevent or dramatically slow adaptive evolution, it is prevalent in the signaling networks that compose metazoan immune systems. We hypothesized that pleiotropy is maintained in immune signaling networks despite slowed adaptive evolution because it provides some other advantage, such as forcing network evolution to compensate in ways that increase host fitness during infection. To study the effects of pleiotropy on the evolution of immune signaling networks, we used an agent-based modeling approach to evolve a population of host immune systems infected by simultaneously co-evolving parasites. Four kinds of pleiotropic restrictions on evolvability were incorporated into the networks, and their evolutionary outcomes were compared to, and competed against, non-pleiotropic networks. As the networks evolved, we tracked several metrics of immune network complexity, relative investment in inducible and constitutive defenses, and features associated with the winners and losers of competitive simulations. Our results suggest non-pleiotropic networks evolve to deploy highly constitutive immune responses regardless of parasite prevalence, but some implementations of pleiotropy favor the evolution of highly inducible immunity. These inducible pleiotropic networks are no less fit than non-pleiotropic networks and can out-compete non-pleiotropic networks in competitive simulations. These provide a theoretical explanation for the prevalence of pleiotropic genes in immune systems and highlight a mechanism that could facilitate the evolution of inducible immune responses.

In Silico Evolution of Biochemical Log-Response

Numerous biological systems are known to harbor a form of logarithmic behavior, from Weber's law to bacterial chemotaxis. Such a log-response allows for sensitivity to small relative variations of biochemical inputs over a large range of concentration values. Here we use a genetic algorithm to evolve biochemical networks displaying a logarithmic response. A quasi-perfect log-response implemented by the same core network evolves in a convergent way across our different in silico replications. The best network is able to fit a logarithm over 4 orders of magnitude with an accuracy of the order of 1%. At the heart of this network, we show that a logarithmic approximation may be implemented with one single nonlinear interaction, that can be interpreted either as multisite phosphorylations or as a ligand induced multimerization. We provide an analytical explanation for the effect and exhibit constraints on parameters. Biological log-response might thus be easier to implement than usually assumed.

Immune Signaling Networks: Sources of Robustness and Constrained Evolvability during Coevolution

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.

Reconstructing the genotype-to-fitness map for the bacterial chemotaxis network and its emergent behavioural phenotypes

The signal-transduction network responsible for chemotaxis in Escherichia coli has been characterised in extraordinary detail. Yet, relatively little is known about eco-evolutionary aspects of chemotaxis, such as how the network has been shaped by selection and to what extent natural populations may fine-tune their chemotactic behaviour to the ecological conditions. To address these questions, we here develop an evolutionary-systems-biology model of the chemotaxis network of E. coli, which we apply to estimate the resource accumulation rate (here used as a proxy for fitness) of wildtype and a large number of potential mutant genotypes. Mutant genotypes differ from the wildtype in the concentrations of one or more constituent proteins of the chemotaxis signalling network or in one or more of its kinetic parameters. To guarantee model consistency across the genotype space, we explicitly incorporated biochemical constraints that underly observed phenotypic trade-offs. The model was validated by reconstructing the phenotypic properties of several known mutant genotypes. We also characterised differences in the fitness distribution between genotypes, and reconstructed adaptive walks in genotype space for populations exposed to different environmental conditions. We found that the local fitness landscape is rugged, due to non-additive interactions between mutations. When selection has a consistent direction, just a few adaptive mutations are required to reach a local peak, and different local peaks can be reached by adaptive walks starting from the same initial genotype. However, when the direction of selection is fluctuating, evolutionary paths are much longer and genotype space is explored further. Longer adaptive walks were also observed when evolution was started from a low-fitness genotype such as a CheZ knockout mutant. In line with empirical observations, the initial ΔcheZ mutant did not respond to a step-down stimulus, but a dynamic response similar to the wildtype was recovered following the fixation of compensatory mutations.

Coevolutionary feedback elevates constitutive immune defence: a protein network model

Background

Organisms have evolved a variety of defence mechanisms against natural enemies, which are typically used at the expense of other life history components. Induced defence mechanisms impose minor costs when pathogens are absent, but mounting an induced response can be time-consuming. Therefore, to ensure timely protection, organisms may partly rely on constitutive defence despite its sustained cost that renders it less economical. Existing theoretical models addressing the optimal combination of constitutive versus induced defence focus solely on host adaptation and ignore the fact that the efficacy of protection depends on genotype-specific host-parasite interactions. Here, we develop a signal-transduction network model inspired by the invertebrate innate immune system, in order to address the effect of parasite coevolution on the optimal combination of constitutive and induced defence.

Results

Our analysis reveals that coevolution of parasites with specific immune components shifts the host’s optimal allocation from induced towards constitutive immunity. This effect is dependent upon whether receptors (for detection) or effectors (for elimination) are subjected to parasite counter-evolution. A parasite population subjected to a specific immune receptor can evolve heightened genetic diversity, which makes parasite detection more difficult for the hosts. We show that this coevolutionary feedback renders the induced immune response less efficient, forcing the hosts to invest more heavily in constitutive immunity. Parasites diversify to escape elimination by a specific effector too. However, this diversification does not alter the optimal balance between constitutive and induced defence: the reliance on constitutive defence is promoted by the receptor’s inability to detect, but not the effectors’ inability to eliminate parasites. If effectors are useless, hosts simply adapt to tolerate, rather than to invest in any defence against parasites. These contrasting results indicate that evolutionary feedback between host and parasite populations is a key factor shaping the selection regime for immune networks facing antagonistic coevolution.

Conclusion

Parasite coevolution against specific immune defence alters the prediction of the optimal use of defence, and the effect of parasite coevolution varies between different immune components.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-016-0667-3) contains supplementary material, which is available to authorized users.

BioJazz: in silico evolution of cellular networks with unbounded complexity using rule-based modeling

Systems biologists aim to decipher the structure and dynamics of signaling and regulatory networks underpinning cellular responses; synthetic biologists can use this insight to alter existing networks or engineer de novo ones. Both tasks will benefit from an understanding of which structural and dynamic features of networks can emerge from evolutionary processes, through which intermediary steps these arise, and whether they embody general design principles. As natural evolution at the level of network dynamics is difficult to study, in silico evolution of network models can provide important insights. However, current tools used for in silico evolution of network dynamics are limited to ad hoc computer simulations and models. Here we introduce BioJazz, an extendable, user-friendly tool for simulating the evolution of dynamic biochemical networks. Unlike previous tools for in silico evolution, BioJazz allows for the evolution of cellular networks with unbounded complexity by combining rule-based modeling with an encoding of networks that is akin to a genome. We show that BioJazz can be used to implement biologically realistic selective pressures and allows exploration of the space of network architectures and dynamics that implement prescribed physiological functions. BioJazz is provided as an open-source tool to facilitate its further development and use. Source code and user manuals are available at: http://oss-lab.github.io/biojazz and http://osslab.lifesci.warwick.ac.uk/BioJazz.aspx.

Evolution of bow-tie architectures in biology

Bow-tie or hourglass structure is a common architectural feature found in many biological systems. A bow-tie in a multi-layered structure occurs when intermediate layers have much fewer components than the input and output layers. Examples include metabolism where a handful of building blocks mediate between multiple input nutrients and multiple output biomass components, and signaling networks where information from numerous receptor types passes through a small set of signaling pathways to regulate multiple output genes. Little is known, however, about how bow-tie architectures evolve. Here, we address the evolution of bow-tie architectures using simulations of multi-layered systems evolving to fulfill a given input-output goal. We find that bow-ties spontaneously evolve when the information in the evolutionary goal can be compressed. Mathematically speaking, bow-ties evolve when the rank of the input-output matrix describing the evolutionary goal is deficient. The maximal compression possible (the rank of the goal) determines the size of the narrowest part of the network—that is the bow-tie. A further requirement is that a process is active to reduce the number of links in the network, such as product-rule mutations, otherwise a non-bow-tie solution is found in the evolutionary simulations. This offers a mechanism to understand a common architectural principle of biological systems, and a way to quantitate the effective rank of the goals under which they evolved.

Many biological systems show bow-tie (also called hourglass) architecture. A bow-tie means that a large number of inputs are converted to a small number of intermediates, which then fan out to generate a large number of outputs. For example, cells use a wide variety of nutrients; process them into 12 metabolic precursors, which are then used to make all of the cells biomass. Similar principles exist in biological signaling and in the information processing in the visual system. Despite the ubiquity of bow-tie structures in biology, there is no explanation of how they evolved. Here, we find that bow-ties spontaneously evolve when the information in the evolutionary goal they evolved to satisfy can be compressed. Mathematically, this means that the matrix representing the goal has deficient rank. The maximal compression possible determines the width of the bow-tie—the narrowest part in the network (equal to the rank of the goal matrix). This offers a mechanism to understand a common architectural principle of biological systems, and a way to quantitate the rank of the goals under which they evolved.

Elucidating the adaptation and temporal coordination of metabolic pathways using in-silico evolution

Cellular metabolism, the interconversion of small molecules by chemical reactions, is a tightly coordinated process that requires integration of diverse environmental and intracellular cues. While for many organisms the topology of the network of metabolic reactions is increasingly known, the regulatory principles that shape the network's adaptation to diverse and changing environments remain largely elusive. To investigate the principles of metabolic adaptation and regulation in metabolic pathways, we propose a computational approach based on in-silico evolution. Rather than analyzing existing regulatory schemes, we let a population of minimal, prototypical metabolic cells evolve rate constants and appropriate regulatory schemes that allow for optimal growth in static and fluctuating environments. Applying our approach to a small, but already sufficiently complex, minimal system reveals intricate transitions between metabolic modes. These results have implications for trade-offs in resource allocation. Going from static to varying environments, we show that for fluctuating nutrient availability, active metabolic regulation results in a significantly increased overall rate of metabolism.

Microbial evolution in vivo and in silico: methods and applications

Microbial evolution has been extensively studied in the past fifty years, which has lead to seminal discoveries that have shaped our understanding of evolutionary forces and dynamics. It is only recently however, that transformative technologies and computational advances have enabled a larger in-scale and in-depth investigation of the genetic basis and mechanistic underpinnings of evolutionary adaptation. In this review we focus on the strengths and limitations of in vivo and in silico techniques for studying microbial evolution in the laboratory, and we discuss how these complementary approaches can be integrated in a unifying framework for elucidating microbial evolution.

Evolution of transcription networks in response to temporal fluctuations

Organisms respond to changes in their environment over a wide range of biological and temporal scales. Such phenotypic plasticity can involve developmental, behavioral, physiological, and genetic shifts. The adaptive value of a plastic response is known to depend on the nature of the information that is available to the organism as well as the direct and indirect costs of the plastic response. We modeled the dynamic process of simple gene regulatory networks as they responded to temporal fluctuations in environmental conditions. We simulated the evolution of networks to determine when genes that function solely as transcription factors, with no direct function of their own, are beneficial to the function of the network. When there is perfect information about the environment and there is no timing information to be extracted then there is no advantage to adding pure transcription factor genes to the network. In contrast, when there is either timing information that can be extracted or only indirect information about the current state of the environment then additional transcription factor genes improve the evolved network fitness.

Phenotypic models of evolution and development: geometry as destiny

Quantitative models of development that consider all relevant genes typically are difficult to fit to embryonic data alone and have many redundant parameters. Computational evolution supplies models of phenotype with relatively few variables and parameters that allows the patterning dynamics to be reduced to a geometrical picture for how the state of a cell moves. The clock and wavefront model, that defines the phenotype of somitogenesis, can be represented as a sequence of two discrete dynamical transitions (bifurcations). The expression-time to space map for Hox genes and the posterior dominance rule are phenotypes that naturally follow from computational evolution without considering the genetics of Hox regulation.

Pareto evolution of gene networks: an algorithm to optimize multiple fitness objectives

The computational evolution of gene networks functions like a forward genetic screen to generate, without preconceptions, all networks that can be assembled from a defined list of parts to implement a given function. Frequently networks are subject to multiple design criteria that cannot all be optimized simultaneously. To explore how these tradeoffs interact with evolution, we implement Pareto optimization in the context of gene network evolution. In response to a temporal pulse of a signal, we evolve networks whose output turns on slowly after the pulse begins, and shuts down rapidly when the pulse terminates. The best performing networks under our conditions do not fall into categories such as feed forward and negative feedback that also encode the input-output relation we used for selection. Pareto evolution can more efficiently search the space of networks than optimization based on a single ad hoc combination of the design criteria.

Functional motifs in biochemical reaction networks

The signal-response characteristics of a living cell are determined by complex networks of interacting genes, proteins, and metabolites. Understanding how cells respond to specific challenges, how these responses are contravened in diseased cells, and how to intervene pharmacologically in the decision-making processes of cells requires an accurate theory of the information-processing capabilities of macromolecular regulatory networks. Adopting an engineer's approach to control systems, we ask whether realistic cellular control networks can be decomposed into simple regulatory motifs that carry out specific functions in a cell. We show that such functional motifs exist and review the experimental evidence that they control cellular responses as expected.

Reverse engineering of bacterial chemotaxis pathway via frequency domain analysis

Chemotaxis is defined as a behavior involving organisms sensing attractants or repellents and leading towards or away from them. Therefore, it is possible to reengineer chemotaxis network to control the movement of bacteria to our advantage. Understanding the design principles of chemotaxis pathway is a prerequisite and an important topic in synthetic biology. Here, we provide guidelines for chemotaxis pathway design by employing control theory and reverse engineering concept on pathway dynamic design. We first analyzed the mathematical models for two most important kinds of E. coli chemotaxis pathway—adaptive and non-adaptive pathways, and concluded that the control units of the pathway de facto function as a band-pass filter and a low-pass filter, respectively, by abstracting the frequency response properties of the pathways. The advantage of the band-pass filter is established, and we demonstrate how to tune the three key parameters of it—A (max amplification), ω₁ (down cut-off frequency) and ω₂ (up cut-off frequency) to optimize the chemotactic effect. Finally, we hypothesized a similar but simpler version of the dynamic pathway model based on the principles discovered and show that it leads to similar properties with native E. coli chemotactic behaviors. Our study provides an example of simulating and designing biological dynamics in silico and indicates how to make use of the native pathway's features in this process. Furthermore, the characteristics we discovered and tested through reverse engineering may help to understand the design principles of the pathway and promote the design of artificial chemotaxis pathways.

Robustness: mechanisms and consequences

Biological systems are robust to perturbation by mutations and environmental fluctuations. New data are shedding light on the biochemical and network-level mechanisms responsible for robustness. Robustness to mutation might have evolved as an adaptation to reduce the effect of mutations, as a congruent byproduct of adaptive robustness to environmental variation, or as an intrinsic property of biological systems selected for their primary functions. Whatever its mechanism or origin, robustness to mutation results in the accumulation of phenotypically cryptic genetic variation. Partial robustness can lead to pre-adaptation, and thereby might contribute to evolvability. The identification and characterization of phenotypic capacitors - which act as switches of the degree of robustness - are critical to understanding the mechanisms and consequences of robustness.

A framework for evolutionary systems biology

BACKGROUND

Many difficult problems in evolutionary genomics are related to mutations that have weak effects on fitness, as the consequences of mutations with large effects are often simple to predict. Current systems biology has accumulated much data on mutations with large effects and can predict the properties of knockout mutants in some systems. However experimental methods are too insensitive to observe small effects.

RESULTS

Here I propose a novel framework that brings together evolutionary theory and current systems biology approaches in order to quantify small effects of mutations and their epistatic interactions in silico. Central to this approach is the definition of fitness correlates that can be computed in some current systems biology models employing the rigorous algorithms that are at the core of much work in computational systems biology. The framework exploits synergies between the realism of such models and the need to understand real systems in evolutionary theory. This framework can address many longstanding topics in evolutionary biology by defining various 'levels' of the adaptive landscape. Addressed topics include the distribution of mutational effects on fitness, as well as the nature of advantageous mutations, epistasis and robustness. Combining corresponding parameter estimates with population genetics models raises the possibility of testing evolutionary hypotheses at a new level of realism.

CONCLUSION

EvoSysBio is expected to lead to a more detailed understanding of the fundamental principles of life by combining knowledge about well-known biological systems from several disciplines. This will benefit both evolutionary theory and current systems biology. Understanding robustness by analysing distributions of mutational effects and epistasis is pivotal for drug design, cancer research, responsible genetic engineering in synthetic biology and many other practical applications.

Parasites lead to evolution of robustness against gene loss in host signaling networks

Many biological networks can maintain their function against single gene loss. However, the evolutionary mechanisms responsible for such robustness remain unclear. Here, we demonstrate that antagonistic host–parasite interactions can act as a selective pressure driving the emergence of robustness against gene loss. Using a model of host signaling networks and simulating their coevolution with parasites that interfere with network function, we find that networks evolve both redundancy and specific architectures that allow them to maintain their response despite removal of proteins. We show that when the parasite pressure is removed, subsequent evolution can lead to loss of redundancy while architecture-based robustness is retained. Contrary to intuition, increased parasite virulence hampers evolution of robustness by limiting the generation of population level diversity in the host. However, when robustness emerges under high virulence, it tends to be stronger. These findings predict an increased presence of robustness mechanisms in biological networks operating under parasite interference. Conversely, the presence of such mechanisms could indicate current or past parasite interference.

Evolution of evolvability in gene regulatory networks

Gene regulatory networks are perhaps the most important organizational level in the cell where signals from the cell state and the outside environment are integrated in terms of activation and inhibition of genes. For the last decade, the study of such networks has been fueled by large-scale experiments and renewed attention from the theoretical field. Different models have been proposed to, for instance, investigate expression dynamics, explain the network topology we observe in bacteria and yeast, and for the analysis of evolvability and robustness of such networks. Yet how these gene regulatory networks evolve and become evolvable remains an open question.

An individual-oriented evolutionary model is used to shed light on this matter. Each individual has a genome from which its gene regulatory network is derived. Mutations, such as gene duplications and deletions, alter the genome, while the resulting network determines the gene expression pattern and hence fitness. With this protocol we let a population of individuals evolve under Darwinian selection in an environment that changes through time.

Our work demonstrates that long-term evolution of complex gene regulatory networks in a changing environment can lead to a striking increase in the efficiency of generating beneficial mutations. We show that the population evolves towards genotype-phenotype mappings that allow for an orchestrated network-wide change in the gene expression pattern, requiring only a few specific gene indels. The genes involved are hubs of the networks, or directly influencing the hubs. Moreover, throughout the evolutionary trajectory the networks maintain their mutational robustness. In other words, evolution in an alternating environment leads to a network that is sensitive to a small class of beneficial mutations, while the majority of mutations remain neutral: an example of evolution of evolvability.

A cell receives signals both from its internal and external environment and responds by changing the expression of genes. In this manner the cell adjusts to heat, osmotic pressures and other circumstances during its lifetime. Over long timescales, the network of interacting genes and its regulatory actions also undergo evolutionary adaptation. Yet how do such networks evolve and become adapted?

In this paper we describe the study of a simple model of gene regulatory networks, focusing solely on evolutionary adaptation. We let a population of individuals evolve, while the external environment changes through time. To ensure evolution is the only source of adaptation, we do not provide the individuals with a sensor to the environment. We show that the interplay between the long-term process of evolution and short-term gene regulation dynamics leads to a striking increase in the efficiency of creating well-adapted offspring. Beneficial mutations become more frequent, nevertheless robustness to the majority of mutations is maintained. Thus we demonstrate a clear example of the evolution of evolvability.

Evolution of taxis responses in virtual bacteria: non-adaptive dynamics

Bacteria are able to sense and respond to a variety of external stimuli, with responses that vary from stimuli to stimuli and from species to species. The best-understood is chemotaxis in the model organism Escherichia coli, where the dynamics and the structure of the underlying pathway are well characterised. It is not clear, however, how well this detailed knowledge applies to mechanisms mediating responses to other stimuli or to pathways in other species. Furthermore, there is increasing experimental evidence that bacteria integrate responses from different stimuli to generate a coherent taxis response. We currently lack a full understanding of the different pathway structures and dynamics and how this integration is achieved. In order to explore different pathway structures and dynamics that can underlie taxis responses in bacteria, we perform a computational simulation of the evolution of taxis. This approach starts with a population of virtual bacteria that move in a virtual environment based on the dynamics of the simple biochemical pathways they harbour. As mutations lead to changes in pathway structure and dynamics, bacteria better able to localise with favourable conditions gain a selective advantage. We find that a certain dynamics evolves consistently under different model assumptions and environments. These dynamics, which we call non-adaptive dynamics, directly couple tumbling probability of the cell to increasing stimuli. Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations. However, we find that stimulus scarcity and fluctuations during evolution results in complex pathway dynamics that result both in adaptive and non-adaptive dynamics depending on basal stimuli levels. Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components. The non-adaptive dynamics mediating taxis responses provide an explanation for experimental observations made in mutant strains of E. coli and in wild-type Rhodobacter sphaeroides that could not be explained with standard models. We speculate that such dynamics exist in other bacteria as well and play a role linking the metabolic state of the cell and the taxis response. The simplicity of mechanisms mediating such dynamics makes them a candidate precursor of more complex taxis responses involving adaptation. This study suggests a strong link between stimulus conditions during evolution and evolved pathway dynamics. When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances.

Here, we study how signalling networks mediating chemotaxis could have evolved. We simulated the evolution of virtual bacteria, which can explore their environment by alternating between swimming and tumbling. The tumbling frequency is dictated by the output of a signalling network that senses extracellular nutrient levels, while the bacteria's reproductive success is determined by their ability to find nutrients. Under conditions of abundant food, we find that bacteria quickly evolve signalling networks that enable effective chemotaxis, where increasing nutrient levels increase tumbling frequency. Our findings provide explanation for network dynamics underlying similar behaviour as observed in certain mutant strains of Escherichia coli and in other bacterial species. Conversely, wild-type E. coli respond to increasing nutrient levels by decreasing their tumbling frequency and adapting to constant attractant levels. We observe such adaptive network dynamics when we repeat evolutionary simulations under conditions of scarce food. These findings suggest that (i) adaptation is not necessary for effective chemotaxis, (ii) an ancestral minimal chemotaxis system could have used a simple coupling between the signalling network and the metabolic state, and (iii) environmental conditions are one of the determining factors for the evolution of adaptive responses.

Evolution of complex modular biological networks

Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their modularity of function, with modules defined as sets of genes that are strongly interconnected but whose function is separable from those of other modules. Here, we investigate the in silico evolution of modularity and robustness in complex artificial metabolic networks that encode an increasing amount of information about their environment while acquiring ubiquitous features of biological, social, and engineering networks, such as scale-free edge distribution, small-world property, and fault-tolerance. These networks evolve in environments that differ in their predictability, and allow us to study modularity from topological, information-theoretic, and gene-epistatic points of view using new tools that do not depend on any preconceived notion of modularity. We find that for our evolved complex networks as well as for the yeast protein–protein interaction network, synthetic lethal gene pairs consist mostly of redundant genes that lie close to each other and therefore within modules, while knockdown suppressor gene pairs are farther apart and often straddle modules, suggesting that knockdown rescue is mediated by alternative pathways or modules. The combination of network modularity tools together with genetic interaction data constitutes a powerful approach to study and dissect the role of modularity in the evolution and function of biological networks.

The modular organization of cells is not immediately obvious from the network of interacting genes, proteins, and molecules. A new window into cellular modularity is opened up by genetic data that identifies pairs of genes that interact either directly or indirectly to provide robustness to cellular function. Such pairs can map out the modular nature of a network if we understand how they relate to established mathematical clustering methods applied to networks to identify putative modules. We can test the relationship between genetically interacting pairs and modules on artificial data: large networks of interacting proteins and molecules that were evolved within an artificial chemistry and genetics, and that pass the standard tests for biological networks. Modularity evolves in these networks in order to deal with a multitude of functional goals, with a degree depending on environmental variability. Relationships between genetically interacting pairs and modules similar to those displayed by the artificial gene networks are found in the protein–protein interaction network of baker's yeast. The evolution of complex functional biological networks in silico provides an opportunity to develop and test new methods and tools to understand the complexity of biological systems at the network level.

Predictive behavior within microbial genetic networks

The homeostatic framework has dominated our understanding of cellular physiology. We question whether homeostasis alone adequately explains microbial responses to environmental stimuli, and explore the capacity of intracellular networks for predictive behavior in a fashion similar to metazoan nervous systems. We show that in silico biochemical networks, evolving randomly under precisely defined complex habitats, capture the dynamical, multidimensional structure of diverse environments by forming internal representations that allow prediction of environmental change. We provide evidence for such anticipatory behavior by revealing striking correlations of Escherichia coli transcriptional responses to temperature and oxygen perturbations-precisely mirroring the covariation of these parameters upon transitions between the outside world and the mammalian gastrointestinal tract. We further show that these internal correlations reflect a true associative learning paradigm, because they show rapid decoupling upon exposure to novel environments.

Emergence and maintenance of functional modules in signaling pathways

Background

While detection and analysis of functional modules in biological systems have received great attention in recent years, we still lack a complete understanding of how such modules emerge. One theory is that systems must encounter a varying selection (i.e. environment) in order for modularity to emerge. Here, we provide an alternative and simpler explanation using a realistic model of biological signaling pathways and simulating their evolution.

Results

These evolutionary simulations start with a homogenous population of a minimal pathway containing two effectors coupled to two signals via a single receptor. This population is allowed to evolve under a constant selection pressure for mediating two separate responses. Results of these evolutionary simulations show that under such a selective pressure, mutational processes easily lead to the emergence of pathways with two separate sub-pathways (i.e. modules) each mediating a distinct response only to one of the signals. Such functional modules are maintained as long as mutations leading to new interactions among existing proteins in the pathway are rare.

Conclusion

While supporting a neutralistic view for the emergence of modularity in biological systems, these findings highlight the relevant rate of different mutational processes and the distribution of functional pathways in the topology space as key factors for its maintenance.

The potential for signal integration and processing in interacting MAP kinase cascades

The cellular response to environmental stimuli requires biochemical information processing through which sensory inputs and cellular status are integrated and translated into appropriate responses by way of interacting networks of enzymes. One such network, the mitogen-activated protein (MAP) kinase cascade is a highly conserved signal transduction module that propagates signals from cell surface receptors to various cytosolic and nuclear targets by way of a phosphorylation cascade. We have investigated the potential for signal processing within a network of interacting feed-forward kinase cascades typified by the MAP kinase cascade. A genetic algorithm was used to search for sets of kinetic parameters demonstrating representative key input-output patterns of interest. We discuss two of the networks identified in our study, one implementing the exclusive-or function (XOR) and another implementing what we refer to as an in-band detector (IBD) or two-sided threshold. These examples confirm the potential for logic and amplitude-dependent signal processing in interacting MAP kinase cascades demonstrating limited cross-talk. Specifically, the XOR function allows the network to respond to either one, but not both signals simultaneously, while the IBD permits the network to respond exclusively to signals within a given range of strength, and to suppress signals below as well as above this range. The solution to the XOR problem is interesting in that it requires only two interacting pathways, crosstalk at only one layer, and no feedback or explicit inhibition. These types of responses are not only biologically relevant but constitute signal processing modules that can be combined to create other logical functions and that, in contrast to amplification, cannot be achieved with a single cascade or with two non-interacting cascades. Our computational results revealed surprising similarities between experimental data describing the JNK/MKK4/MKK7 pathway and the solution for the IBD that evolved from the genetic algorithm. The evolved IBD not only exhibited the required non-monotonic signal strength-response, but also demonstrated transient and sustained responses that properly reflected the input signal strength, dependence on both of the MAPKKs for signaling, phosphorylation site preferences by each of the MAPKKs, and both activation and inhibition resulting from the overexpression of one of the MAPKKs.

Evolution of complexity in signaling pathways

It is not clear how biological pathways evolve to mediate a certain physiological response and why they show a level of complexity that is generally above the minimum required to achieve such a response. One possibility is that pathway complexity increases due to the nature of evolutionary mechanisms. Here, we analyze this possibility by using mathematical models of biological pathways and evolutionary simulations. Starting with a population of small pathways of three proteins, we let the population evolve with mutations that affect pathway structure through duplication or deletion of existing proteins, deletion or creation of interactions among them, or addition of new proteins. Our simulations show that such mutational events, coupled with a selective pressure, leads to growth of pathways. These results indicate that pathways could be driven toward complexity via simple evolutionary mechanisms and that complexity can arise without any specific selective pressure for it. Furthermore, we find that the level of complexity that pathways evolve toward depends on the selection criteria. In general, we find that final pathway size tends to be lower when pathways evolve under stringent selection criteria. This leads to the counterintuitive conclusion that simple response requirements on a pathway would facilitate its evolution toward higher complexity.