Chaotic gene regulatory networks can be robust against mutations and noise

Robustness to mutations and noise has been shown to evolve through stabilizing selection for optimal phenotypes in model gene regulatory networks. The ability to evolve robust mutants is known to depend on the network architecture. How do the dynamical properties and state-space structures of networks with high and low robustness differ? Does selection operate on the global dynamical behavior of the networks? What kind of state-space structures are favored by selection? We provide damage propagation analysis and an extensive statistical analysis of state spaces of these model networks to show that the change in their dynamical properties due to stabilizing selection for optimal phenotypes is minor. Most notably, the networks that are most robust to both mutations and noise are highly chaotic. Certain properties of chaotic networks, such as being able to produce large attractor basins, can be useful for maintaining a stable gene-expression pattern. Our findings indicate that conventional measures of stability, such as damage propagation, do not provide much information about robustness to mutations or noise in model gene regulatory networks.     

Environmental Noise,Genetic Diversity and the Evolution of Evolvability and Robustness in Model Gene Networks

The ability of organisms to adapt and persist in the face of environmental change is accepted as a fundamental feature of natural systems. More contentious is whether the capacity of organisms to adapt (or “evolvability”) can itself evolve and the mechanisms underlying such responses. Using model gene networks, I provide evidence that evolvability emerges more readily when populations experience positively autocorrelated environmental noise (red noise) compared to populations in stable or randomly varying (white noise) environments. Evolvability was correlated with increasing genetic robustness to effects on network viability and decreasing robustness to effects on phenotypic expression; populations whose networks displayed greater viability robustness and lower phenotypic robustness produced more additive genetic variation and adapted more rapidly in novel environments. Patterns of selection for robustness varied antagonistically with epistatic effects of mutations on viability and phenotypic expression, suggesting that trade-offs between these properties may constrain their evolutionary responses. Evolution of evolvability and robustness was stronger in sexual populations compared to asexual populations indicating that enhanced genetic variation under fluctuating selection combined with recombination load is a primary driver of the emergence of evolvability. These results provide insight into the mechanisms potentially underlying rapid adaptation as well as the environmental conditions that drive the evolution of genetic interactions.     

Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.     

Characterization of stem cells and cancer cells on the basis of gene expression profile stability, plasticity, and robustness: dynamical systems theory of gene expressions under cell-cell interaction explains mutational robustness of differentiated cells and suggests how cancer cells emerge

Here I present and discuss a model that, among other things, appears able to describe the dynamics of cancer cell origin from the perspective of stable and unstable gene expression profiles. In identifying such aberrant gene expression profiles as lying outside the normal stable states attracted through development and normal cell differentiation, the hypothesis explains why cancer cells accumulate mutations, to which they are not robust, and why these mutations create a new stable state far from the normal gene expression profile space. Such cells are in strong contrast with normal cell types that appeared as an attractor state in the gene expression dynamical system under cell-cell interaction and achieved robustness to noise through evolution, which in turn also conferred robustness to mutation. In complex gene regulation networks, other aberrant cellular states lacking such high robustness are expected to remain, which would correspond to cancer cells.     

Selection for distinct gene expression properties favours the evolution of mutational robustness in gene regulatory networks

Mutational robustness is a genotype's tendency to keep a phenotypic trait with little and few changes in the face of mutations. Mutational robustness is both ubiquitous and evolutionarily important as it affects in different ways the probability that new phenotypic variation arises. Understanding the origins of robustness is specially relevant for systems of development that are phylogenetically widespread and that construct phenotypic traits with a strong impact on fitness. Gene regulatory networks are examples of this class of systems. They comprise sets of genes that, through cross‐regulation, build the gene activity patterns that define cellular responses, different tissues or distinct cell types. Several empirical observations, such as a greater robustness of wild‐type phenotypes, suggest that stabilizing selection underlies the evolution of mutational robustness. However, the role of selection in the evolution of robustness is still under debate. Computer simulations of the dynamics and evolution of gene regulatory networks have shown that selection for any gene activity pattern that is steady and self‐sustaining is sufficient to promote the evolution of mutational robustness. Here, I generalize this scenario using a computational model to show that selection for different aspects of a gene activity phenotype increases mutational robustness. Mutational robustness evolves even when selection favours properties that conflict with the stationarity of a gene activity pattern. The results that I present support an important role for stabilizing selection in the evolution of robustness in gene regulatory networks.     

Synthetic circuits reveal how mechanisms of gene regulatory networks constrain evolution

Phenotypic variation is the raw material of adaptive Darwinian evolution. The phenotypic variation found in organismal development is biased towards certain phenotypes, but the molecular mechanisms behind such biases are still poorly understood. Gene regulatory networks have been proposed as one cause of constrained phenotypic variation. However, most pertinent evidence is theoretical rather than experimental. Here, we study evolutionary biases in two synthetic gene regulatory circuits expressed in Escherichia coli that produce a gene expression stripe—a pivotal pattern in embryonic development. The two parental circuits produce the same phenotype, but create it through different regulatory mechanisms. We show that mutations cause distinct novel phenotypes in the two networks and use a combination of experimental measurements, mathematical modelling and DNA sequencing to understand why mutations bring forth only some but not other novel gene expression phenotypes. Our results reveal that the regulatory mechanisms of networks restrict the possible phenotypic variation upon mutation. Consequently, seemingly equivalent networks can indeed be distinct in how they constrain the outcome of further evolution.     

Evolution of robustness to noise and mutation in gene expression dynamics

Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these types of robustness? Robustness can be defined by the sharpness of the distribution of phenotype; the variance of phenotype distribution due to genetic variation gives a measure of 'genetic robustness', while that of isogenic individuals gives a measure of 'developmental robustness'. Through simulations of a simple stochastic gene expression network that undergoes mutation and selection, we show that in order for the network to acquire both types of robustness, the phenotypic variance induced by mutations must be smaller than that observed in an isogenic population. As the latter originates from noise in gene expression, this signifies that the genetic robustness evolves only when the noise strength in gene expression is larger than some threshold. In such a case, the two variances decrease throughout the evolutionary time course, indicating increase in robustness. The results reveal how noise that cells encounter during growth and development shapes networks' robustness to stochasticity in gene expression, which in turn shapes networks' robustness to mutation. The necessary condition for evolution of robustness, as well as the relationship between genetic and developmental robustness, is derived quantitatively through the variance of phenotypic fluctuations, which are directly measurable experimentally.     

Mapping the Fitness Landscape of Gene Expression Uncovers the Cause of Antagonism and Sign Epistasis between Adaptive Mutations

How do adapting populations navigate the tensions between the costs of gene expression and the benefits of gene products to optimize the levels of many genes at once? Here we combined independently-arising beneficial mutations that altered enzyme levels in the central metabolism of Methylobacterium extorquens to uncover the fitness landscape defined by gene expression levels. We found strong antagonism and sign epistasis between these beneficial mutations. Mutations with the largest individual benefit interacted the most antagonistically with other mutations, a trend we also uncovered through analyses of datasets from other model systems. However, these beneficial mutations interacted multiplicatively (i.e., no epistasis) at the level of enzyme expression. By generating a model that predicts fitness from enzyme levels we could explain the observed sign epistasis as a result of overshooting the optimum defined by a balance between enzyme catalysis benefits and fitness costs. Knowledge of the phenotypic landscape also illuminated that, although the fitness peak was phenotypically far from the ancestral state, it was not genetically distant. Single beneficial mutations jumped straight toward the global optimum rather than being constrained to change the expression phenotypes in the correlated fashion expected by the genetic architecture. Given that adaptation in nature often results from optimizing gene expression, these conclusions can be widely applicable to other organisms and selective conditions. Poor interactions between individually beneficial alleles affecting gene expression may thus compromise the benefit of sex during adaptation and promote genetic differentiation.     

The molecular and mathematical basis of Waddington's epigenetic landscape: A framework for post‐Darwinian biology?

The Neo-Darwinian concept of natural selection is plausible when one assumes a straightforward causation of phenotype by genotype. However, such simple 1:1 mapping must now give place to the modern concepts of gene regulatory networks and gene expression noise. Both can, in the absence of genetic mutations, jointly generate a diversity of inheritable randomly occupied phenotypic states that could also serve as a substrate for natural selection. This form of epigenetic dynamics challenges Neo-Darwinism. It needs to incorporate the non-linear, stochastic dynamics of gene networks. A first step is to consider the mathematical correspondence between gene regulatory networks and Waddington's metaphoric 'epigenetic landscape', which actually represents the quasi-potential function of global network dynamics. It explains the coexistence of multiple stable phenotypes within one genotype. The landscape's topography with its attractors is shaped by evolution through mutational re-wiring of regulatory interactions - offering a link between genetic mutation and sudden, broad evolutionary changes.     

Genes under weaker stabilizing selection increase network evolvability and rapid regulatory adaptation to an environmental shift

Regulatory networks play a central role in the modulation of gene expression, the control of cellular differentiation, and the emergence of complex phenotypes. Regulatory networks could constrain or facilitate evolutionary adaptation in gene expression levels. Here, we model the adaptation of regulatory networks and gene expression levels to a shift in the environment that alters the optimal expression level of a single gene. Our analyses show signatures of natural selection on regulatory networks that both constrain and facilitate rapid evolution of gene expression level towards new optima. The analyses are interpreted from the standpoint of neutral expectations and illustrate the challenge to making inferences about network adaptation. Furthermore, we examine the consequence of variable stabilizing selection across genes on the strength and direction of interactions in regulatory networks and in their subsequent adaptation. We observe that directional selection on a highly constrained gene previously under strong stabilizing selection was more efficient when the gene was embedded within a network of partners under relaxed stabilizing selection pressure. The observation leads to the expectation that evolutionarily resilient regulatory networks will contain optimal ratios of genes whose expression is under weak and strong stabilizing selection. Altogether, our results suggest that the variable strengths of stabilizing selection across genes within regulatory networks might itself contribute to the long‐term adaptation of complex phenotypes.     

Evolution of phenotypic fluctuation under host-parasite interactions

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important “environmental” factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness. Then, the robustness of the corresponding phenotype will be increased by reducing phenotypic fluctuations. Conversely, plasticity tends to evolve to avoid certain phenotypes that are attacked by parasites. By using a dynamic model of gene expression for the host, we investigate the evolution of the genotype-phenotype map and of phenotypic variances. If the host–parasite interaction is weak, the fittest phenotype of the host evolves to reduce phenotypic variances. In contrast, if there exists a sufficient degree of interaction, the phenotypic variances of hosts increase to escape parasite attacks. For the latter case, we found two strategies: if the noise in the stochastic gene expression is below a certain threshold, the phenotypic variance increases via genetic diversification, whereas above this threshold, it is increased mediated by noise-induced phenotypic fluctuation. We examine how the increase in the phenotypic variances caused by parasite interactions influences the growth rate of a single host, and observed a trade-off between the two. Our results help elucidate the roles played by noise and genetic mutations in the evolution of phenotypic fluctuation and robustness in response to host–parasite interactions.     

De Novo Evolution of Complex, Global and Hierarchical Gene Regulatory Mechanisms

Gene regulatory networks exhibit complex, hierarchical features such as global regulation and network motifs. There is much debate about whether the evolutionary origins of such features are the results of adaptation, or the by-products of non-adaptive processes of DNA replication. The lack of availability of gene regulatory networks of ancestor species on evolutionary timescales makes this a particularly difficult problem to resolve. Digital organisms, however, can be used to provide a complete evolutionary record of lineages. We use a biologically realistic evolutionary model that includes gene expression, regulation, metabolism and biosynthesis, to investigate the evolution of complex function in gene regulatory networks. We discover that: (i) network architecture and complexity evolve in response to environmental complexity, (ii) global gene regulation is selected for in complex environments, (iii) complex, inter-connected, hierarchical structures evolve in stages, with energy regulation preceding stress responses, and stress responses preceding growth rate adaptations and (iv) robustness of evolved models to mutations depends on hierarchical level: energy regulation and stress responses tend not to be robust to mutations, whereas growth rate adaptations are more robust and non-lethal when mutated. These results highlight the adaptive and incremental evolution of complex biological networks, and the value and potential of studying realistic in silico evolutionary systems as a way of understanding living systems.     

Evolution of Gene Regulatory Networks by Fluctuating Selection and Intrinsic Constraints

Various characteristics of complex gene regulatory networks (GRNs) have been discovered during the last decade, e.g., redundancy, exponential indegree distributions, scale-free outdegree distributions, mutational robustness, and evolvability. Although progress has been made in this field, it is not well understood whether these characteristics are the direct products of selection or those of other evolutionary forces such as mutational biases and biophysical constraints. To elucidate the causal factors that promoted the evolution of complex GRNs, we examined the effect of fluctuating environmental selection and some intrinsic constraining factors on GRN evolution by using an individual-based model. We found that the evolution of complex GRNs is remarkably promoted by fixation of beneficial gene duplications under unpredictably fluctuating environmental conditions and that some internal factors inherent in organisms, such as mutational bias, gene expression costs, and constraints on expression dynamics, are also important for the evolution of GRNs. The results indicate that various biological properties observed in GRNs could evolve as a result of not only adaptation to unpredictable environmental changes but also non-adaptive processes owing to the properties of the organisms themselves. Our study emphasizes that evolutionary models considering such intrinsic constraining factors should be used as null models to analyze the effect of selection on GRN evolution.     

Potential energy landscape and robustness of a gene regulatory network: toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers. It leads to the robustness of the biological basins of the gene switches. The technique used here is general and can be applied to explore the potential energy landscape of the gene networks.     

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.