Innovation and robustness in complex regulatory gene networks

SCAR-6 elncRNA locus epigenetically regulates PROZ and modulates coagulation and vascular function

In this study, we characterize a novel lncRNA-producing gene locus that we name Syntenic Cardiovascular Conserved Region-Associated lncRNA-6 (scar-6) and functionally validate its role in coagulation and cardiovascular function. A 12-bp deletion of the scar-6 locus in zebrafish (scar-6gib007Δ12/Δ12) results in cranial hemorrhage and vascular permeability. Overexpression, knockdown and rescue with the scar-6 lncRNA modulates hemostasis in zebrafish. Molecular investigation reveals that the scar-6 lncRNA acts as an enhancer lncRNA (elncRNA), and controls the expression of prozb, an inhibitor of factor Xa, through an enhancer element in the scar-6 locus. The scar-6 locus suppresses loop formation between prozb and scar-6 sequences, which might be facilitated by the methylation of CpG islands via the prdm14-PRC2 complex whose binding to the locus might be stabilized by the scar-6 elncRNA transcript. Binding of prdm14 to the scar-6 locus is impaired in scar-6gib007Δ12/Δ12 zebrafish. Finally, activation of the PAR2 receptor in scar-6gib007Δ12/Δ12 zebrafish triggers NF-κB-mediated endothelial cell activation, leading to vascular dysfunction and hemorrhage. We present evidence that the scar-6 locus plays a role in regulating the expression of the coagulation cascade gene prozb and maintains vascular homeostasis.

Body plan evolvability: The role of variability in gene regulatory networks

Recent computational modeling of early fruit fly (Drosophila) development has characterized the degree to which gene regulation networks can be robust to natural variability. In the first few hours of development, broad spatial gradients of maternally derived transcription factors activate embryonic gap genes. These gap patterns determine the subsequent segmented insect body plan through pair-rule gene expression. Gap genes are expressed with greater spatial precision than the maternal patterns. Computational modeling of the gap-gap regulatory interactions provides a mechanistic understanding for this robustness to maternal variability in wild-type (WT) patterning. A long-standing question in evolutionary biology has been how a system which is robust, such as the developmental program creating any particular species' body plan, is also evolvable, i.e. how can a system evolve or speciate, if the WT form is strongly buffered and protected? In the present work, we use the WT model to explore the breakdown of such Waddington-type 'canalization'. What levels of variability will push the system out of the WT form; are there particular pathways in the gene regulatory mechanism which are more susceptible to losing the WT form; and when robustness is lost, what types of forms are most likely to occur (i.e. what forms lie near the WT)? Manipulating maternal effects in several different pathways, we find a common gap 'peak-to-step' pattern transition in the loss of WT. We discuss these results in terms of the evolvability of insect segmentation, and in terms of experimental perturbations and mutations which could test the model predictions. We conclude by discussing the prospects for using continuum models of pattern dynamics to investigate a wider range of evo-devo problems.

Non-Poissonian Bursts in the Arrival of Phenotypic Variation Can Strongly Affect the Dynamics of Adaptation

Modeling the rate at which adaptive phenotypes appear in a population is a key to predicting evolutionary processes. Given random mutations, should this rate be modeled by a simple Poisson process, or is a more complex dynamics needed? Here we use analytic calculations and simulations of evolving populations on explicit genotype-phenotype maps to show that the introduction of novel phenotypes can be "bursty" or overdispersed. In other words, a novel phenotype either appears multiple times in quick succession or not at all for many generations. These bursts are fundamentally caused by statistical fluctuations and other structure in the map from genotypes to phenotypes. Their strength depends on population parameters, being highest for "monomorphic" populations with low mutation rates. They can also be enhanced by additional inhomogeneities in the mapping from genotypes to phenotypes. We mainly investigate the effect of bursts using the well-studied genotype-phenotype map for RNA secondary structure, but find similar behavior in a lattice protein model and in Richard Dawkins's biomorphs model of morphological development. Bursts can profoundly affect adaptive dynamics. Most notably, they imply that fitness differences play a smaller role in determining which phenotype fixes than would be the case for a Poisson process without bursts.

Developing the genotype-to-phenotype relationship in evolutionary theory: A primer of developmental features

For decades, there have been repeated calls for more integration across evolutionary and developmental biology. However, critiques in the literature and recent funding initiatives suggest this integration remains incomplete. We suggest one way forward is to consider how we elaborate the most basic concept of development, the relationship between genotype and phenotype, in traditional models of evolutionary processes. For some questions, when more complex features of development are accounted for, predictions of evolutionary processes shift. We present a primer on concepts of development to clarify confusion in the literature and fuel new questions and approaches. The basic features of development involve expanding a base model of genotype-to-phenotype to include the genome, space, and time. A layer of complexity is added by incorporating developmental systems, including signal-response systems and networks of interactions. The developmental emergence of function, which captures developmental feedbacks and phenotypic performance, offers further model elaborations that explicitly link fitness with developmental systems. Finally, developmental features such as plasticity and developmental niche construction conceptualize the link between a developing phenotype and the external environment, allowing for a fuller inclusion of ecology in evolutionary models. Incorporating aspects of developmental complexity into evolutionary models also accommodates a more pluralistic focus on the causal importance of developmental systems, individual organisms, or agents in generating evolutionary patterns. Thus, by laying out existing concepts of development, and considering how they are used across different fields, we can gain clarity in existing debates around the extended evolutionary synthesis and pursue new directions in evolutionary developmental biology. Finally, we consider how nesting developmental features in traditional models of evolution can highlight areas of evolutionary biology that need more theoretical attention.

The duplication of genomes and genetic networks and its potential for evolutionary adaptation and survival during environmental turmoil

The importance of whole-genome duplication (WGD) for evolution is controversial. Whereas some view WGD mainly as detrimental and an evolutionary dead end, there is growing evidence that polyploidization can help overcome environmental change, stressful conditions, or periods of extinction. However, despite much research, the mechanistic underpinnings of why and how polyploids might be able to outcompete or outlive nonpolyploids at times of environmental upheaval remain elusive, especially for autopolyploids, in which heterosis effects are limited. On the longer term, WGD might increase both mutational and environmental robustness due to redundancy and increased genetic variation, but on the short-or even immediate-term, selective advantages of WGDs are harder to explain. Here, by duplicating artificially generated Gene Regulatory Networks (GRNs), we show that duplicated GRNs-and thus duplicated genomes-show higher signal output variation than nonduplicated GRNs. This increased variation leads to niche expansion and can provide polyploid populations with substantial advantages to survive environmental turmoil. In contrast, under stable environments, GRNs might be maladaptive to changes, a phenomenon that is exacerbated in duplicated GRNs. We believe that these results provide insights into how genome duplication and (auto)polyploidy might help organisms to adapt quickly to novel conditions and to survive ecological uproar or even cataclysmic events.

Eco-evolution from deep time to contemporary dynamics: The role of timescales and rate modulators

Eco-evolutionary dynamics, or eco-evolution for short, are often thought to involve rapid demography (ecology) and equally rapid heritable phenotypic changes (evolution) leading to novel, emergent system behaviours. We argue that this focus on contemporary dynamics is too narrow: Eco-evolution should be extended, first, beyond pure demography to include all environmental dimensions and, second, to include slow eco-evolution which unfolds over thousands or millions of years. This extension allows us to conceptualise biological systems as occupying a two-dimensional time space along axes that capture the speed of ecology and evolution. Using Hutchinson's analogy: Time is the 'theatre' in which ecology and evolution are two interacting 'players'. Eco-evolutionary systems are therefore dynamic: We identify modulators of ecological and evolutionary rates, like temperature or sensitivity to mutation, which can change the speed of ecology and evolution, and hence impact eco-evolution. Environmental change may synchronise the speed of ecology and evolution via these rate modulators, increasing the occurrence of eco-evolution and emergent system behaviours. This represents substantial challenges for prediction, especially in the context of global change. Our perspective attempts to integrate ecology and evolution across disciplines, from gene-regulatory networks to geomorphology and across timescales, from today to deep time.

Normalizing Input-Output Relationships of Cancer Networks for Reversion Therapy

Accumulated genetic alterations in cancer cells distort cellular stimulus-response (or input-output) relationships, resulting in uncontrolled proliferation. However, the complex molecular interaction network within a cell implicates a possibility of restoring such distorted input-output relationships by rewiring the signal flow through controlling hidden molecular switches. Here, a system framework of analyzing cellular input-output relationships in consideration of various genetic alterations and identifying possible molecular switches that can normalize the distorted relationships based on Boolean network modeling and dynamics analysis is presented. Such reversion is demonstrated by the analysis of a number of cancer molecular networks together with a focused case study on bladder cancer with in vitro experiments and patient survival data analysis. The origin of reversibility from an evolutionary point of view based on the redundancy and robustness intrinsically embedded in complex molecular regulatory networks is further discussed.

Speciation and development

Understanding general principles about the origin of species remains one of the foundational challenges in evolutionary biology. The genomic divergence between groups of individuals can spawn hybrid inviability and hybrid sterility, which presents a tantalizing developmental problem. Divergent developmental programs may yield either conserved or divergent phenotypes relative to ancestral traits, both of which can be responsible for reproductive isolation during the speciation process. The genetic mechanisms of developmental evolution involve cis- and trans-acting gene regulatory change, protein-protein interactions, genetic network structures, dosage, and epigenetic regulation, all of which also have roots in population genetic and molecular evolutionary processes. Toward the goal of demystifying Darwin's "mystery of mysteries," this review integrates microevolutionary concepts of genetic change with principles of organismal development, establishing explicit links between population genetic process and developmental mechanisms in the production of macroevolutionary pattern. This integration aims to establish a more unified view of speciation that binds process and mechanism.

Environment-dependent epistasis increases phenotypic diversity in gene regulatory networks

Mutations to gene regulatory networks can be maladaptive or a source of evolutionary novelty. Epistasis confounds our understanding of how mutations affect the expression patterns of gene regulatory networks, a challenge exacerbated by the dependence of epistasis on the environment. We used the toolkit of synthetic biology to systematically assay the effects of pairwise and triplet combinations of mutant genotypes on the expression pattern of a gene regulatory network expressed in Escherichia coli that interprets an inducer gradient across a spatial domain. We uncovered a preponderance of epistasis that can switch in magnitude and sign across the inducer gradient to produce a greater diversity of expression pattern phenotypes than would be possible in the absence of such environment-dependent epistasis. We discuss our findings in the context of the evolution of hybrid incompatibilities and evolutionary novelties.

Robustness and innovation in synthetic genotype networks

Genotype networks are sets of genotypes connected by small mutational changes that share the same phenotype. They facilitate evolutionary innovation by enabling the exploration of different neighborhoods in genotype space. Genotype networks, first suggested by theoretical models, have been empirically confirmed for proteins and RNAs. Comparative studies also support their existence for gene regulatory networks (GRNs), but direct experimental evidence is lacking. Here, we report the construction of three interconnected genotype networks of synthetic GRNs producing three distinct phenotypes in Escherichia coli. Our synthetic GRNs contain three nodes regulating each other by CRISPR interference and governing the expression of fluorescent reporters. The genotype networks, composed of over twenty different synthetic GRNs, provide robustness in face of mutations while enabling transitions to innovative phenotypes. Through realistic mathematical modeling, we quantify robustness and evolvability for the complete genotype-phenotype map and link these features mechanistically to GRN motifs. Our work thereby exemplifies how GRN evolution along genotype networks might be driving evolutionary innovation.

Gene regulatory networks with binary weights

An evolutionary computation framework to learn binary threshold networks is presented. Inspired by the recent trend of binary neural networks, where weights and activation thresholds are represented using 1 and -1 such that they can be stored in 1-bit instead of full precision, we explore this approach for gene regulatory network modeling. We test our method by inferring binary threshold networks of two regulatory network models: Quorum sensing systems in bacterium Paraburkholderia phytofirmans PsJN and the fission yeast cell-cycle. We considered differential evolution and particle swarm optimization for the simulations. Results for weights having only 1 and -1 values, and different activation thresholds are presented. Full binary threshold networks were found with minimum error (2 bits), whereas when the binary restriction is relaxed for the activation thresholds, networks with 0 bit error were found. .

Gene loss during a transition to multicellularity

Multicellular evolution is a major transition associated with momentous diversification of multiple lineages and increased developmental complexity. The volvocine algae comprise a valuable system for the study of this transition, as they span from unicellular to undifferentiated and differentiated multicellular morphologies despite their genomes being similar, suggesting multicellular evolution requires few genetic changes to undergo dramatic shifts in developmental complexity. Here, the evolutionary dynamics of six volvocine genomes were examined, where a gradual loss of genes was observed in parallel to the co-option of a few key genes. Protein complexes in the six species exhibited novel interactions, suggesting that gene loss could play a role in evolutionary novelty. This finding was supported by gene network modeling, where gene loss outpaces gene gain in generating novel stable network states. These results suggest gene loss, in addition to gene gain and co-option, may be important for the evolution developmental complexity.

The ensemble of gene regulatory networks at mutation-selection balance

The evolution of diverse phenotypes both involves and is constrained by molecular interaction networks. When these networks influence patterns of expression, we refer to them as gene regulatory networks (GRNs). Here, we develop a model of GRN evolution analogous to work from quasi-species theory, which is itself essentially the mutation-selection balance model from classical population genetics extended to multiple loci. With this GRN model, we prove that-across a broad spectrum of selection pressures-the dynamics converge to a stationary distribution over GRNs. Next, we show from first principles how the frequency of GRNs at equilibrium is related to the topology of the genotype network, in particular, via a specific network centrality measure termed the eigenvector centrality. Finally, we determine the structural characteristics of GRNs that are favoured in response to a range of selective environments and mutational constraints. Our work connects GRN evolution to quasi-species theory-and thus to classical populations genetics-providing a mechanistic explanation for the observed distribution of GRNs evolving in response to various evolutionary forces, and shows how complex fitness landscapes can emerge from simple evolutionary rules.

Exploring the expanse between theoretical questions and experimental approaches in the modern study of evolvability

Despite several decades of computational and experimental work across many systems, evolvability remains on the periphery with regards to its status as a widely accepted and regularly applied theoretical concept. Here we propose that its marginal status is partly a result of large gaps between the diverse but disconnected theoretical treatments of evolvability and the relatively narrower range of studies that have tested it empirically. To make this case, we draw on a range of examples-from experimental evolution in microbes, to molecular evolution in proteins-where attempts have been made to mend this disconnect. We highlight some examples of progress that has been made and point to areas where synthesis and translation of existing theory can lead to further progress in the still-new field of empirical measurements of evolvability.

Conflicting effects of recombination on the evolvability and robustness in neutrally evolving populations

Understanding the benefits and costs of recombination under different scenarios of evolutionary adaptation remains an open problem for theoretical and experimental research. In this study, we focus on finite populations evolving on neutral networks comprising viable and unfit genotypes. We provide a comprehensive overview of the effects of recombination by jointly considering different measures of evolvability and mutational robustness over a broad parameter range, such that many evolutionary regimes are covered. We find that several of these measures vary non-monotonically with the rates of mutation and recombination. Moreover, the presence of unfit genotypes that introduce inhomogeneities in the network of viable states qualitatively alters the effects of recombination. We conclude that conflicting trends induced by recombination can be explained by an emerging trade-off between evolvability on the one hand, and mutational robustness on the other. Finally, we discuss how different implementations of the recombination scheme in theoretical models can affect the observed dependence on recombination rate through a coupling between recombination and genetic drift.

Optimization of Transcription Factor Genetic Circuits

Transcription factors (TFs) affect the production of mRNAs. In essence, the TFs form a large computational network that controls many aspects of cellular function. This article introduces a computational method to optimize TF networks. The method extends recent advances in artificial neural network optimization. In a simple example, computational optimization discovers a four-dimensional TF network that maintains a circadian rhythm over many days, successfully buffering strong stochastic perturbations in molecular dynamics and entraining to an external day-night signal that randomly turns on and off at intervals of several days. This work highlights the similar challenges in understanding how computational TF and neural networks gain information and improve performance.

Genetic architecture of dispersal and local adaptation drives accelerating range expansions

Contemporary evolution has the potential to significantly alter biotic responses to global change, including range expansion dynamics and biological invasions. Models predicting range dynamics often make highly simplifying assumptions about the genetic architecture underlying relevant traits. However, genetic architecture defines evolvability and higher-order evolutionary processes, which determine whether evolution will be able to keep up with environmental change or not. Therefore, we here study the impact of the genetic architecture of dispersal and local adaptation, two central traits of high relevance for range expansions, on the dynamics and predictability of invasion into an environmental gradient, such as temperature. In our theoretical model we assume that dispersal and local adaptation traits result from the products of two noninteracting gene-regulatory networks (GRNs). We compare our model to simpler quantitative genetics models and show that in the GRN model, range expansions are accelerating and less predictable. We further find that accelerating dynamics in the GRN model are primarily driven by an increase in the rate of local adaptation to novel habitats which results from greater sensitivity to mutation (decreased robustness) and increased gene expression. Our results highlight how processes at microscopic scales, here within genomes, can impact the predictions of large-scale, macroscopic phenomena, such as range expansions, by modulating the rate of evolution.

A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and "ruggedness". As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population's evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.

Patterns of selection across gene regulatory networks

Gene regulatory networks (GRNs) are the core engine of organismal development. If we would like to understand the origin and diversification of phenotypes, it is necessary to consider the structure of GRNs in order to reconstruct the links between genetic mutations and phenotypic change. Much of the progress in evolutionary developmental biology, however, has occurred without a nuanced consideration of the evolution of functional relationships between genes, especially in the context of their broader network interactions. Characterizing and comparing GRNs across traits and species in a more detailed way will allow us to determine how network position influences what genes drive adaptive evolution. In this perspective paper, we consider the architecture of developmental GRNs and how positive selection strength may vary across a GRN. We then propose several testable models for these patterns of selection and experimental approaches to test these models.

Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution

The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.

Living systems are products of evolution, and their present forms reflect their evolutionary history. Thus, to investigate the particularity of the evolutionary process by computer simulations, an appropriate reference system is needed for comparison with the outcomes of evolutionary simulations. In this study, we considered a model of gene regulatory networks (GRNs). Our idea was to construct a reference ensemble comprising randomly generated GRNs. To produce GRNs with high fitness values, which are rare, we employed a “rare event sampling” method developed in statistical physics. In particular, we focused on the evolution of mutational robustness. Living systems do not lose viability readily, even when some genes are mutated. This trait, called mutational robustness, has developed throughout evolution, along with functionality. Using the abovementioned method, we found that mutational robustness resulting from evolution exceeded that of the reference set. Therefore, mutational robustness is enhanced by evolution. We also found that the emergence of a new phenotype was significantly delayed in evolution. Our results suggest that this delay is a consequence of the fact that mutationally robust GRNs are favored by evolution.

On the effects of the modularity of gene regulatory networks on phenotypic variability and its association with robustness

Biological adaptations depend on natural selection sorting out those individuals that exhibit characters fit to their environment. Selection, in turn, depends on the phenotypic variation present in a population. Thus, evolutionary outcomes depend, to a certain extent, on the kind of variation that organisms can produce through random genetic perturbation, that is, their phenotypic variability. Moreover, the properties of developmental mechanisms that produce the organisms affect their phenotypic variability. Two of these properties are modularity and robustness. Modularity is the degree to which interactions occur mostly within groups of the system's elements and scarcely between elements in different groups. Robustness is the propensity of a system to endure perturbations while preserving its phenotype. In this paper, we used a model of gene regulatory networks (GRNs) to study the relationship between modularity and robustness in developmental processes and how modularity affects the variation that random genetic mutations produce in the expression patterns of GRNs. Our results show that modularity and robustness are correlated in multifunctional GRNs and that selection for one of these properties affects the other as well. We contend that these observations may help to understand why modularity and robustness are widespread in biological systems. Additionally, we found that modular networks tend to produce new expression patterns with subtle changes localized in the expression of a few groups of genes. This effect in the phenotypic variability of modular GRNs may bear important consequences for adaptive evolution: it may help to adjust the expression of one group of genes at a time, with few alterations on other previously evolved expression patterns.

Redundancy-selection trade-off in phenotype-structured populations

Realistic fitness landscapes generally display a redundancy-fitness trade-off: highly fit trait configurations are inevitably rare, while less fit trait configurations are expected to be more redundant. The resulting sub-optimal patterns in the fitness distribution are typically described by means of effective formulations, where redundancy provided by the presence of neutral contributions is modelled implicitly, e.g. with a bias of the mutation process. However, the extent to which effective formulations are compatible with explicitly redundant landscapes is yet to be understood, as well as the consequences of a potential miss-match. Here we investigate the effects of such trade-off on the evolution of phenotype-structured populations, characterised by continuous quantitative traits. We consider a typical replication-mutation dynamics, and we model redundancy by means of two dimensional landscapes displaying both selective and neutral traits. We show that asymmetries of the landscapes will generate neutral contributions to the marginalised fitness-level description, that cannot be described by effective formulations, nor disentangled by the full trait distribution. Rather, they appear as effective sources, whose magnitude depends on the geometry of the landscape. Our results highlight new important aspects on the nature of sub-optimality. We discuss practical implications for rapidly mutant populations such as pathogens and cancer cells, where the qualitative knowledge of their trait and fitness distributions can drive disease management and intervention policies.

Gene network simulations provide testable predictions for the molecular domestication syndrome

The domestication of plant species lead to repeatable morphological evolution, often referred to as the phenotypic domestication syndrome. Domestication is also associated with important genomic changes, such as the loss of genetic diversity compared to adequately large wild populations, and modifications of gene expression patterns. Here, we explored theoretically the effect of a domestication-like scenario on the evolution of gene regulatory networks. We ran population genetics simulations in which individuals were featured by their genotype (an interaction matrix encoding a gene regulatory network) and their gene expressions, representing the phenotypic level. Our domestication scenario included a population bottleneck and a selection switch mimicking human-mediated directional and canalizing selection, i.e., change in the optimal gene expression level and selection towards more stable expression across environments. We showed that domestication profoundly alters genetic architectures. Based on four examples of plant domestication scenarios, our simulations predict (i) a drop in neutral allelic diversity, (ii) a change in gene expression variance that depends upon the domestication scenario, (iii) transient maladaptive plasticity, (iv) a deep rewiring of the gene regulatory networks, with a trend towards gain of regulatory interactions, and (v) a global increase in the genetic correlations among gene expressions, with a loss of modularity in the resulting coexpression patterns and in the underlying networks. We provide empirically testable predictions on the differences of genetic architectures between wild and domesticated forms. The characterization of such systematic evolutionary changes in the genetic architecture of traits contributes to define a molecular domestication syndrome.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

On the evolution and development of morphological complexity: A view from gene regulatory networks

How does morphological complexity evolve? This study suggests that the likelihood of mutations increasing phenotypic complexity becomes smaller when the phenotype itself is complex. In addition, the complexity of the genotype-phenotype map (GPM) also increases with the phenotypic complexity. We show that complex GPMs and the above mutational asymmetry are inevitable consequences of how genes need to be wired in order to build complex and robust phenotypes during development. We randomly wired genes and cell behaviors into networks in EmbryoMaker. EmbryoMaker is a mathematical model of development that can simulate any gene network, all animal cell behaviors (division, adhesion, apoptosis, etc.), cell signaling, cell and tissues biophysics, and the regulation of those behaviors by gene products. Through EmbryoMaker we simulated how each random network regulates development and the resulting morphology (i.e. a specific distribution of cells and gene expression in 3D). This way we obtained a zoo of possible 3D morphologies. Real gene networks are not random, but a random search allows a relatively unbiased exploration of what is needed to develop complex robust morphologies. Compared to the networks leading to simple morphologies, the networks leading to complex morphologies have the following in common: 1) They are rarer; 2) They need to be finely tuned; 3) Mutations in them tend to decrease morphological complexity; 4) They are less robust to noise; and 5) They have more complex GPMs. These results imply that, when complexity evolves, it does so at a progressively decreasing rate over generations. This is because as morphological complexity increases, the likelihood of mutations increasing complexity decreases, morphologies become less robust to noise, and the GPM becomes more complex. We find some properties in common, but also some important differences, with non-developmental GPM models (e.g. RNA, protein and gene networks in single cells).

Phenotypes to remember: Evolutionary developmental memory capacity and robustness

There is increased awareness of the possibility of developmental memories resulting from evolutionary learning. Genetic regulatory and neural networks can be modelled by analogous formalism raising the important question of productive analogies in principles, processes and performance. We investigate the formation and persistence of various developmental memories of past phenotypes asking how the number of remembered past phenotypes scales with network size, to what extent memories stored form by Hebbian-like rules, and how robust these developmental "devo-engrams" are against networks perturbations (graceful degradation). The analogy between neural and genetic regulatory networks is not superficial in that it allows knowledge transfer between fields that used to be developed separately from each other. Known examples of spectacular phenotypic radiations could partly be accounted for in such terms.

Multi-locus interactions and the build-up of reproductive isolation

All genes interact with other genes, and their additive effects and epistatic interactions affect an organism's phenotype and fitness. Recent theoretical and empirical work has advanced our understanding of the role of multi-locus interactions in speciation. However, relating different models to one another and to empirical observations is challenging. This review focuses on multi-locus interactions that lead to reproductive isolation (RI) through reduced hybrid fitness. We first review theoretical approaches and show how recent work incorporating a mechanistic understanding of multi-locus interactions recapitulates earlier models, but also makes novel predictions concerning the build-up of RI. These include high variance in the build-up rate of RI among taxa, the emergence of strong incompatibilities producing localized barriers to introgression, and an effect of population size on the build-up of RI. We then review recent experimental approaches to detect multi-locus interactions underlying RI using genomic data. We argue that future studies would benefit from overlapping methods like ancestry disequilibrium scans, genome scans of differentiation and analyses of hybrid gene expression. Finally, we highlight a need for further overlap between theoretical and empirical work, and approaches that predict what kind of patterns multi-locus interactions resulting in incompatibilities will leave in genome-wide polymorphism data. This article is part of the theme issue 'Towards the completion of speciation: the evolution of reproductive isolation beyond the first barriers'.

Genotype networks of 80 quantitative Arabidopsis thaliana phenotypes reveal phenotypic evolvability despite pervasive epistasis

We study the genotype-phenotype maps of 80 quantitative phenotypes in the model plant Arabidopsis thaliana, by representing the genotypes affecting each phenotype as a genotype network. In such a network, each vertex or node corresponds to an individual's genotype at all those genomic loci that affect a given phenotype. Two vertices are connected by an edge if the associated genotypes differ in exactly one nucleotide. The 80 genotype networks we analyze are based on data from genome-wide association studies of 199 A. thaliana accessions. They form connected graphs whose topography differs substantially among phenotypes. We focus our analysis on the incidence of epistasis (non-additive interactions among mutations) because a high incidence of epistasis can reduce the accessibility of evolutionary paths towards high or low phenotypic values. We find epistatic interactions in 67 phenotypes, and in 51 phenotypes every pairwise mutant interaction is epistatic. Moreover, we find phenotype-specific differences in the fraction of accessible mutational paths to maximum phenotypic values. However, even though epistasis affects the accessibility of maximum phenotypic values, the relationships between genotypic and phenotypic change of our analyzed phenotypes are sufficiently smooth that some evolutionary paths remain accessible for most phenotypes, even where epistasis is pervasive. The genotype network representation we use can complement existing approaches to understand the genetic architecture of polygenic traits in many different organisms.

Temporal encoding of bacterial identity and traits in growth dynamics

In biology, it is often critical to determine the identity of an organism and phenotypic traits of interest. Whole-genome sequencing can be useful for this but has limited power for trait prediction. However, we can take advantage of the inherent information content of phenotypes to bypass these limitations. We demonstrate, in clinical and environmental bacterial isolates, that growth dynamics in standardized conditions can differentiate between genotypes, even among strains from the same species. We find that for pairs of isolates, there is little correlation between genetic distance, according to phylogenetic analysis, and phenotypic distance, as determined by growth dynamics. This absence of correlation underscores the challenge in using genomics to infer phenotypes and vice versa. Bypassing this complexity, we show that growth dynamics alone can robustly predict antibiotic responses. These findings are a foundation for a method to identify traits not easily traced to a genetic mechanism.

Emergence of cooperative bistability and robustness of gene regulatory networks

Gene regulatory networks (GRNs) are complex systems in which many genes regulate mutually to adapt the cell state to environmental conditions. In addition to function, the GRNs possess several kinds of robustness. This robustness means that systems do not lose their functionality when exposed to disturbances such as mutations or noise, and is widely observed at many levels in living systems. Both function and robustness have been acquired through evolution. In this respect, GRNs utilized in living systems are rare among all possible GRNs. In this study, we explored the fitness landscape of GRNs and investigated how robustness emerged in highly-fit GRNs. We considered a toy model of GRNs with one input gene and one output gene. The difference in the expression level of the output gene between two input states, "on" and "off", was considered as fitness. Thus, the determination of the fitness of a GRN was based on how sensitively it responded to the input. We employed the multicanonical Monte Carlo method, which can sample GRNs randomly in a wide range of fitness levels, and classified the GRNs according to their fitness. As a result, the following properties were found: (1) Highly-fit GRNs exhibited bistability for intermediate input between "on" and "off". This means that such GRNs responded to two input states by using different fixed points of dynamics. This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. In other words, noise robustness is a byproduct of high fitness. (3) GRNs that were robust against mutations were not extremely rare among the highly-fit GRNs. This implies that mutational robustness is readily acquired through the evolutionary process. These properties are universal irrespective of the evolutionary pathway, because the results do not rely on evolutionary simulation.

Adaptation of turnip mosaic potyvirus to a specific niche reduces its genetic and environmental robustness

Robustness is the preservation of the phenotype in the face of genetic and environmental perturbations. It has been argued that robustness must be an essential fitness component of RNA viruses owed to their small and compacted genomes, high mutation rates and living in ever-changing environmental conditions. Given that genetic robustness might hamper possible beneficial mutations, it has been suggested that genetic robustness can only evolve as a side-effect of the evolution of robustness mechanisms specific to cope with environmental perturbations, a theory known as plastogenetic congruence. However, empirical evidences from different viral systems are contradictory. To test how adaptation to a particular environment affects both environmental and genetic robustness, we have used two strains of turnip mosaic potyvirus (TuMV) that differ in their degree of adaptation to Arabidopsis thaliana at a permissive temperature. We show that the highly adapted strain is strongly sensitive to the effect of random mutations and to changes in temperature conditions. In contrast, the non-adapted strain shows more robustness against both the accumulation of random mutations and drastic changes in temperature conditions. Together, these results are consistent with the predictions of the plastogenetic congruence theory, suggesting that genetic and environmental robustnesses may be two sides of the same coin for TuMV.

Using small samples to estimate neutral component size and robustness in the genotype-phenotype map of RNA secondary structure

In genotype-phenotype (GP) maps, the genotypes that map to the same phenotype are usually not randomly distributed across the space of genotypes, but instead are predominantly connected through one-point mutations, forming network components that are commonly referred to as neutral components (NCs). Because of their impact on evolutionary processes, the characteristics of these NCs, like their size or robustness, have been studied extensively. Here, we introduce a framework that allows the estimation of NC size and robustness in the GP map of RNA secondary structure. The advantage of this framework is that it only requires small samples of genotypes and their local environment, which also allows experimental realizations. We verify our framework by applying it to the exhaustively analysable GP map of RNA sequence length L = 15, and benchmark it against an existing method by applying it to longer, naturally occurring functional non-coding RNA sequences. Although it is specific to the RNA secondary structure GP map in the first place, our framework can probably be transferred and adapted to other sequence-to-structure GP maps.

Hsp90 and complex birth defects: A plausible mechanism for the interaction of genes and environment

How genes and environment interact to cause birth defects is not well understood, but key to developing new strategies to modify risk. The threshold model has been proposed to represent this complex interaction. This model stipulates that while environmental exposure or genetic mutation alone may not result in a defect, factors in combination increase phenotypic variability resulting in more individuals crossing the disease threshold where birth defects manifest. Many environmental factors that contribute to birth defects induce widespread cellular stress and misfolding of proteins. Yet, the impact of the stress response on the threshold model is not typically considered in discephering the etiology of birth defects. This mini-review will explore a potential mechanism for gene-environment interactions co-opted from studies of evolution. This model stipulates that heat shock proteins that mediate the stress response induced by environmental factors can influence the number of individuals that cross disease thresholds resulting in increased incidence of birth defects. Studies in the field of evolutionary biology have demonstrated that heat shock proteins and Hsp90 in particular provide a link between environmental stress, genotype and phenotype. Hsp90 is a highly expressed molecular chaperone that assists a wide variety of protein clients with folding and conformational changes needed for proper function. Hsp90 also chaperones client proteins with potentially deleterious amino acid changes to suppress variation caused by genetic mutations. However, upon exposure to stress, Hsp90 abandons its normal physiological clients and is diverted to assist with the misfolded protein response. This can impact the activity of signaling pathways that involve Hsp90 clients as well as unmask suppressed protein variation, essentially creating complex traits in a single step. In this capacity Hsp90 acts as an evolutionary capacitor allowing stored variation to accumulate and then become expressed in times of stress. This mechanism provides a substrate which natural selection can act upon at the population level allowing survival of the species with selective pressure. However, at the level of the individual, this mechanism can result in simultaneous expression of deleterious variants as well as reduced activity of a variety of Hsp90 chaperoned pathways, potentially shifting phenotypic variability over the disease threshold resulting in birth defects.

Genotype Components as Predictors of Phenotype in Model Gene Regulatory Networks

Models of gene regulatory networks (GRN) have proven useful for understanding many aspects of the highly complex behavior of biological control networks. Randomly generated non-Boolean networks were used in experimental simulations to generate data on dynamic phenotypes as a function of several genotypic parameters. We found that predictive relationships between some phenotypes and quantitative genotypic parameters such as number of network genes, interaction density, and initial condition could be derived depending on the strength of the topological (positional) genotype on specific phenotypes. We quantitated the strength of the topological genotype effect (TGE) on a number of phenotypes in multi-gene networks. For phenotypes with a low influence of topological genotype, derived and empirical relationships using quantitative genotype parameters were accurate in phenotypic outcomes. We found a number of dynamic network properties, including oscillation behaviors, that were largely dependent on genotype topology, and for which no such general quantitative relationships were determinable. It remains to be determined if these results are applicable to biological gene regulatory networks.

Model genotype-phenotype mappings and the algorithmic structure of evolution

Cancers are complex dynamic systems that undergo evolution and selection. Personalized medicine approaches in the clinic increasingly rely on predictions of tumour response to one or more therapies; these predictions are complicated by the inevitable evolution of the tumour. Despite enormous amounts of data on the mutational status of cancers and numerous therapies developed in recent decades to target these mutations, many of these treatments fail after a time due to the development of resistance in the tumour. The emergence of these resistant phenotypes is not easily predicted from genomic data, since the relationship between genotypes and phenotypes, termed the genotype-phenotype (GP) mapping, is neither injective nor functional. We present a review of models of this mapping within a generalized evolutionary framework that takes into account the relation between genotype, phenotype, environment and fitness. Different modelling approaches are described and compared, and many evolutionary results are shown to be conserved across studies despite using different underlying model systems. In addition, several areas for future work that remain understudied are identified, including plasticity and bet-hedging. The GP-mapping provides a pathway for understanding the potential routes of evolution taken by cancers, which will be necessary knowledge for improving personalized therapies.

Connecting the molecular function of microRNAs to cell differentiation dynamics

MicroRNAs form a class of short, non-coding RNA molecules which are essential for proper development in tissue-based plants and animals. To help explain their role in gene regulation, a number of mathematical and computational studies have demonstrated the potential canalizing effects of microRNAs. However, such studies have typically focused on the effects of microRNAs on only one or a few target genes. Consequently, it remains unclear how these small-scale effects add up to the experimentally observed developmental outcomes resulting from microRNA perturbation at the whole-genome level. To answer this question, we built a general computational model of cell differentiation to study the effect of microRNAs in genome-scale gene regulatory networks. Our experiments show that in large gene regulatory networks, microRNAs can control differentiation time without significantly changing steady-state gene expression profiles. This temporal regulatory role cannot be naturally replicated using protein-based transcription factors alone. While several microRNAs have been shown to regulate differentiation time in vivo, our findings provide a new explanation of how the cumulative molecular actions of individual microRNAs influence genome-scale cellular dynamics. Taken together, these results may help explain why tissue-based organisms exclusively depend on miRNA-mediated regulation, while their more primitive counterparts do not.

Developmental bias in horned dung beetles and its contributions to innovation, adaptation, and resilience

Developmental processes transduce diverse influences during phenotype formation, thereby biasing and structuring amount and type of phenotypic variation available for evolutionary processes to act on. The causes, extent, and consequences of this bias are subject to significant debate. Here we explore the role of developmental bias in contributing to organisms' ability to innovate, to adapt to novel or stressful conditions, and to generate well integrated, resilient phenotypes in the face of perturbations. We focus our inquiry on one taxon, the horned dung beetle genus Onthophagus, and review the role developmental bias might play across several levels of biological organization: (a) gene regulatory networks that pattern specific body regions; (b) plastic developmental mechanisms that coordinate body wide responses to changing environments and; (c) developmental symbioses and niche construction that enable organisms to build teams and to actively modify their own selective environments. We posit that across all these levels developmental bias shapes the way living systems innovate, adapt, and withstand stress, in ways that can alternately limit, bias, or facilitate developmental evolution. We conclude that the structuring contribution of developmental bias in evolution deserves further study to better understand why and how developmental evolution unfolds the way it does.

The causes of evolvability and their evolution

Evolvability is the ability of a biological system to produce phenotypic variation that is both heritable and adaptive. It has long been the subject of anecdotal observations and theoretical work. In recent years, however, the molecular causes of evolvability have been an increasing focus of experimental work. Here, we review recent experimental progress in areas as different as the evolution of drug resistance in cancer cells and the rewiring of transcriptional regulation circuits in vertebrates. This research reveals the importance of three major themes: multiple genetic and non-genetic mechanisms to generate phenotypic diversity, robustness in genetic systems, and adaptive landscape topography. We also discuss the mounting evidence that evolvability can evolve and the question of whether it evolves adaptively.

Phenotypes can be robust and evolvable if mutations have non-local effects on sequence constraints

The mapping between biological genotypes and phenotypes plays an important role in evolution, and understanding the properties of this mapping is crucial to determine the outcome of evolutionary processes. One of the most striking properties observed in several genotype-phenotype (GP) maps is the positive correlation between the robustness and evolvability of phenotypes. This implies that a phenotype can be strongly robust against mutations and at the same time evolvable to a diverse range of alternative phenotypes. Here, we examine the causes for this positive correlation by introducing two analytically tractable GP map models that follow the principles of real biological GP maps. The first model is based on gene-like GP maps, reflecting the way in which genetic sequences are organized into protein-coding genes, and the second one is based on the GP map of RNA secondary structure. For both models, we find that a positive correlation between phenotype robustness and evolvability only emerges if mutations at one sequence position can have non-local effects on the sequence constraints at another position. This highlights that non-local effects of mutations are closely related to the coexistence of robustness and evolvability in phenotypes, and are likely to be an important feature of many biological GP maps.

Adding levels of complexity enhances robustness and evolvability in a multilevel genotype-phenotype map

Robustness and evolvability are the main properties that account for the stability and accessibility of phenotypes. They have been studied in a number of computational genotype-phenotype maps. In this paper, we study a metabolic genotype-phenotype map defined in toyLIFE, a multilevel computational model that represents a simplified cellular biology. toyLIFE includes several levels of phenotypic expression, from proteins to regulatory networks to metabolism. Our results show that toyLIFE shares many similarities with other seemingly unrelated computational genotype-phenotype maps. Thus, toyLIFE shows a high degeneracy in the mapping from genotypes to phenotypes, as well as a highly skewed distribution of phenotypic abundances. The neutral networks associated with abundant phenotypes are highly navigable, and common phenotypes are close to each other in genotype space. All of these properties are remarkable, as toyLIFE is built on a version of the HP protein-folding model that is neither robust nor evolvable: phenotypes cannot be mutually accessed through point mutations. In addition, both robustness and evolvability increase with the number of genes in a genotype. Therefore, our results suggest that adding levels of complexity to the mapping of genotypes to phenotypes and increasing genome size enhances both these properties.

Developmental Bias and Evolution: A Regulatory Network Perspective

Phenotypic variation is generated by the processes of development, with some variants arising more readily than others-a phenomenon known as "developmental bias." Developmental bias and natural selection have often been portrayed as alternative explanations, but this is a false dichotomy: developmental bias can evolve through natural selection, and bias and selection jointly influence phenotypic evolution. Here, we briefly review the evidence for developmental bias and illustrate how it is studied empirically. We describe recent theory on regulatory networks that explains why the influence of genetic and environmental perturbation on phenotypes is typically not uniform, and may even be biased toward adaptive phenotypic variation. We show how bias produced by developmental processes constitutes an evolving property able to impose direction on adaptive evolution and influence patterns of taxonomic and phenotypic diversity. Taking these considerations together, we argue that it is not sufficient to accommodate developmental bias into evolutionary theory merely as a constraint on evolutionary adaptation. The influence of natural selection in shaping developmental bias, and conversely, the influence of developmental bias in shaping subsequent opportunities for adaptation, requires mechanistic models of development to be expanded and incorporated into evolutionary theory. A regulatory network perspective on phenotypic evolution thus helps to integrate the generation of phenotypic variation with natural selection, leaving evolutionary biology better placed to explain how organisms adapt and diversify.

Control of seminal fluid protein expression via regulatory hubs in Drosophila melanogaster

Highly precise, yet flexible and responsive coordination of expression across groups of genes underpins the integrity of many vital functions. However, our understanding of gene regulatory networks (GRNs) is often hampered by the lack of experimentally tractable systems, by significant computational challenges derived from the large number of genes involved or from difficulties in the accurate identification and characterization of gene interactions. Here we used a tractable experimental system in which to study GRNs: the genes encoding the seminal fluid proteins that are transferred along with sperm (the 'transferome') in Drosophila melanogaster fruit flies. The products of transferome genes are core determinants of reproductive success and, to date, only transcription factors have been implicated in the modulation of their expression. Hence, as yet, we know nothing about the post-transcriptional mechanisms underlying the tight, responsive and precise regulation of this important gene set. We investigated this omission in the current study. We first used bioinformatics to identify potential regulatory motifs that linked the transferome genes in a putative interaction network. This predicted the presence of putative microRNA (miRNA) 'hubs'. We then tested this prediction, that post-transcriptional regulation is important for the control of transferome genes, by knocking down miRNA expression in adult males. This abolished the ability of males to respond adaptively to the threat of sexual competition, indicating a regulatory role for miRNAs in the regulation of transferome function. Further bioinformatics analysis then identified candidate miRNAs as putative regulatory hubs and evidence for variation in the strength of miRNA regulation across the transferome gene set. The results revealed regulatory mechanisms that can underpin robust, precise and flexible regulation of multiple fitness-related genes. They also help to explain how males can adaptively modulate ejaculate composition.

Evolutionary potential of transcription factors for gene regulatory rewiring

Gene regulatory networks evolve through rewiring of individual components-that is, through changes in regulatory connections. However, the mechanistic basis of regulatory rewiring is poorly understood. Using a canonical gene regulatory system, we quantify the properties of transcription factors that determine the evolutionary potential for rewiring of regulatory connections: robustness, tunability and evolvability. In vivo repression measurements of two repressors at mutated operator sites reveal their contrasting evolutionary potential: while robustness and evolvability were positively correlated, both were in trade-off with tunability. Epistatic interactions between adjacent operators alleviated this trade-off. A thermodynamic model explains how the differences in robustness, tunability and evolvability arise from biophysical characteristics of repressor-DNA binding. The model also uncovers that the energy matrix, which describes how mutations affect repressor-DNA binding, encodes crucial information about the evolutionary potential of a repressor. The biophysical determinants of evolutionary potential for regulatory rewiring constitute a mechanistic framework for understanding network evolution.

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.

On the networked architecture of genotype spaces and its critical effects on molecular evolution

Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at the macroevolutionary, ecological and molecular level. Actually, when the complex architecture of genotype spaces is taken into account, the evolutionary dynamics of molecular populations becomes intrinsically non-uniform, sharing deep qualitative and quantitative similarities with slowly driven physical systems: nonlinear responses analogous to critical transitions, sudden state changes or hysteresis, among others. Furthermore, the phenotypic plasticity inherent to genotypes transforms classical fitness landscapes into multiscapes where adaptation in response to an environmental change may be very fast. The quantitative nature of adaptive molecular processes is deeply dependent on a network-of-networks multilayered structure of the map from genotype to function that we begin to unveil.

Cover-Encodings of Fitness Landscapes

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here, we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practical feasibility of our method is demonstrated by simulations of adaptive walks on the corresponding encoded landscapes which find the global minima for these problems.

It's not magic - Hsp90 and its effects on genetic and epigenetic variation

Canalization, or phenotypic robustness in the face of environmental and genetic perturbation, is an emergent property of living systems. Although this phenomenon has long been recognized, its molecular underpinnings have remained enigmatic until recently. Here, we review the contributions of the molecular chaperone Hsp90, a protein that facilitates the folding of many key regulators of growth and development, to canalization of phenotype - and de-canalization in times of stress - drawing on studies in eukaryotes as diverse as baker's yeast, mouse ear cress, and blind Mexican cavefish. Hsp90 is a hub of hubs that interacts with many so-called 'client proteins,' which affect virtually every aspect of cell signaling and physiology. As Hsp90 facilitates client folding and stability, it can epistatically suppress or enable the expression of genetic variants in its clients and other proteins that acquire client status through mutation. Hsp90's vast interaction network explains the breadth of its phenotypic reach, including Hsp90-dependent de novo mutations and epigenetic effects on gene regulation. Intrinsic links between environmental stress and Hsp90 function thus endow living systems with phenotypic plasticity in fluctuating environments. As environmental perturbations alter Hsp90 function, they also alter Hsp90's interaction with its client proteins, thereby re-wiring networks that determine the genotype-to-phenotype map. Ensuing de-canalization of phenotype creates phenotypic diversity that is not simply stochastic, but often has an underlying genetic basis. Thus, extreme phenotypes can be selected, and assimilated so that they no longer require environmental stress to manifest. In addition to acting on standing genetic variation, Hsp90 perturbation has also been linked to increased frequency of de novo variation and several epigenetic phenomena, all with the potential to generate heritable phenotypic change. Here, we aim to clarify and discuss the multiple means by which Hsp90 can affect phenotype and possibly evolutionary change, and identify their underlying common feature: at its core, Hsp90 interacts epistatically through its chaperone function with many other genes and their gene products. Its influence on phenotypic diversification is thus not magic but rather a fundamental property of genetics.