Modeling the evolution of complex genetic systems: the gene network family tree

CastNet: a systems-level sequence evolution simulator

BACKGROUND

Simulating DNA evolution has been done through coevolution-agnostic probabilistic frameworks for the past 3 decades. The most common implementation is by using the converse of the probabilistic approach used to infer phylogenies which, in the simplest form, simulates a single sequence at a time. However, biological systems are multi-genic, and gene products can affect each other's evolutionary paths through coevolution. These crucial evolutionary dynamics still remain to be simulated, and we believe that modelling them can lead to profound insights for comparative genomics.

RESULTS

Here we present CastNet, a genome evolution simulator that assumes each genome is a collection of genes with constantly evolving regulatory interactions in between them. The regulatory interactions produce a phenotype in the form of gene expression profiles, upon which fitness is calculated. A genetic algorithm is then used to evolve a population of such entities through a user-defined phylogeny. Importantly, the regulatory mutations are a response to sequence mutations, thus making a 1-1 relationship between the rate of evolution of sequences and of regulatory parameters. This is, to our knowledge, the first time the evolution of sequences and regulation have been explicitly linked in a simulation, despite there being a multitude of sequence evolution simulators, and a handful of models to simulate Gene Regulatory Network (GRN) evolution. In our test runs, we see a coevolutionary signal among genes that are active in the GRN, and neutral evolution in genes that are not included in the network, showing that selective pressures imposed on the regulatory output of the genes are reflected in their sequences.

CONCLUSION

We believe that CastNet represents a substantial step for developing new tools to study genome evolution, and more broadly, coevolutionary webs and complex evolving systems. This simulator also provides a new framework to study molecular evolution where sequence coevolution has a leading role.

Using phenotypic plasticity to understand the structure and evolution of the genotype-phenotype map

Deciphering the genotype-phenotype map necessitates relating variation at the genetic level to variation at the phenotypic level. This endeavour is inherently limited by the availability of standing genetic variation, the rate of spontaneous mutation to novo genetic variants, and possible biases associated with induced mutagenesis. An interesting alternative is to instead rely on the environment as a source of variation. Many phenotypic traits change plastically in response to the environment, and these changes are generally underlain by changes in gene expression. Relating gene expression plasticity to the phenotypic plasticity of more integrated organismal traits thus provides useful information about which genes influence the development and expression of which traits, even in the absence of genetic variation. We here appraise the prospects and limits of such an environment-for-gene substitution for investigating the genotype-phenotype map. We review models of gene regulatory networks, and discuss the different ways in which they can incorporate the environment to mechanistically model phenotypic plasticity and its evolution. We suggest that substantial progress can be made in deciphering this genotype-environment-phenotype map, by connecting theory on gene regulatory network to empirical patterns of gene co-expression, and by more explicitly relating gene expression to the expression and development of phenotypes, both theoretically and empirically.

Deviations of rational choice: an integrative explanation of the endowment and several context effects

People's choices are often found to be inconsistent with the assumptions of rational choice theory. Over time, several probabilistic models have been proposed that account for such deviations from rationality. However, these models have become increasingly complex and are often limited to particular choice phenomena. Here we introduce a network approach that explains a broad set of choice phenomena. We demonstrate that this approach can be used to compare different choice theories and integrates several choice mechanisms from established models. A basic setup implements bounded rationality, loss aversion, and inhibition in a natural fashion, which allows us to predict the occurrence of well-known choice phenomena, such as the endowment effect and the similarity, attraction, compromise, and phantom context effects. Our results show that this network approach provides a simple representation of complex choice behaviour, and can be used to gain a better understanding of how the many choice phenomena and key theoretical principles from different types of decision-making are connected.

Decanalizing thinking on genetic canalization

The concept of genetic canalization has had an abiding influence on views of complex-trait evolution. A genetically canalized system has evolved to become less sensitive to the effects of mutation. When a gene product that supports canalization is compromised, the phenotypic impacts of a mutation should be more pronounced. This expected increase in mutational effects not only has important consequences for evolution, but has also motivated strategies to treat disease. However, recent studies demonstrate that, when putative agents of genetic canalization are impaired, systems do not behave as expected. Here, we review the evidence that is used to infer whether particular gene products are agents of genetic canalization. Then we explain how such inferences often succumb to a converse error. We go on to show that several candidate agents of genetic canalization increase the phenotypic impacts of some mutations while decreasing the phenotypic impacts of others. These observations suggest that whether a gene product acts as a 'buffer' (lessening mutational effects) or a 'potentiator' (increasing mutational effects) is not a fixed property of the gene product but instead differs for the different mutations with which it interacts. To investigate features of genetic interactions that might predispose them toward buffering versus potentiation, we explore simulated gene-regulatory networks. Similarly to putative agents of genetic canalization, the gene products in simulated networks also modify the phenotypic effects of mutations in other genes without a strong overall tendency towards lessening or increasing these effects. In sum, these observations call into question whether complex traits have evolved to become less sensitive (i.e., are canalized) to genetic change, and the degree to which trends exist that predict how one genetic change might alter another's impact. We conclude by discussing approaches to address these and other open questions that are brought into focus by re-thinking genetic canalization.

On the role of sparseness in the evolution of modularity in gene regulatory networks

Modularity is a widespread property in biological systems. It implies that interactions occur mainly within groups of system elements. A modular arrangement facilitates adjustment of one module without perturbing the rest of the system. Therefore, modularity of developmental mechanisms is a major factor for evolvability, the potential to produce beneficial variation from random genetic change. Understanding how modularity evolves in gene regulatory networks, that create the distinct gene activity patterns that characterize different parts of an organism, is key to developmental and evolutionary biology. One hypothesis for the evolution of modules suggests that interactions between some sets of genes become maladaptive when selection favours additional gene activity patterns. The removal of such interactions by selection would result in the formation of modules. A second hypothesis suggests that modularity evolves in response to sparseness, the scarcity of interactions within a system. Here I simulate the evolution of gene regulatory networks and analyse diverse experimentally sustained networks to study the relationship between sparseness and modularity. My results suggest that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, sparseness amplifies the effects of forms of selection that, like selection for additional gene activity patterns, already produce an increase in modularity. That evolution of new gene activity patterns is frequent across evolution also supports that it is a major factor in the evolution of modularity. That sparseness is widespread across gene regulatory networks indicates that it may have facilitated the evolution of modules in a wide variety of cases.

Modular systems have performance and design advantages over non-modular systems. Thus, modularity is very important for the development of a wide range of new technological or clinical applications. Moreover, modularity is paramount to evolutionary biology since it allows adjusting one organismal function without disturbing other previously evolved functions. But how does modularity itself evolve? Here I analyse the structure of regulatory networks and follow simulations of network evolution to study two hypotheses for the origin of modules in gene regulatory networks. The first hypothesis considers that sparseness, a low number of interactions among the network genes, could be responsible for the evolution of modular networks. The second, that modules evolve when selection favours the production of additional gene activity patterns. I found that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, it enhances the effects of selection for multiple gene activity patterns. While selection for multiple patterns may be decisive in the evolution of modularity, that sparseness is widespread across gene regulatory networks suggests that its contributions should not be neglected.

Modelling the influence of parental effects on gene-network evolution

Understanding the importance of nongenetic heredity in the evolutionary process is a major topic in modern evolutionary biology. We modified a classical gene-network model by allowing parental transmission of gene expression and studied its evolutionary properties through individual-based simulations. We identified ontogenetic time (i.e. the time gene networks have to stabilize before being submitted to natural selection) as a crucial factor in determining the evolutionary impact of this phenotypic inheritance. Indeed, fast-developing organisms display enhanced adaptation and greater robustness to mutations when evolving in presence of nongenetic inheritance (NGI). In contrast, in our model, long development reduces the influence of the inherited state of the gene network. NGI thus had a negligible effect on the evolution of gene networks when the speed at which transcription levels reach equilibrium is not constrained. Nevertheless, simulations show that intergenerational transmission of the gene-network state negatively affects the evolution of robustness to environmental disturbances for either fast- or slow-developing organisms. Therefore, these results suggest that the evolutionary consequences of NGI might not be sought only in the way species respond to selection, but also on the evolution of emergent properties (such as environmental and genetic canalization) in complex genetic architectures.

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

In recent years, network models have been proposed as an alternative representation of psychometric constructs such as depression. In such models, the covariance between observables (e.g., symptoms like depressed mood, feelings of worthlessness, and guilt) is explained in terms of a pattern of causal interactions between these observables, which contrasts with classical interpretations in which the observables are conceptualized as the effects of a reflective latent variable. However, few investigations have been directed at the question how these different models relate to each other. To shed light on this issue, the current paper explores the relation between one of the most important network models-the Ising model from physics-and one of the most important latent variable models-the Item Response Theory (IRT) model from psychometrics. The Ising model describes the interaction between states of particles that are connected in a network, whereas the IRT model describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable. Despite the divergent backgrounds of the models, we show a broad equivalence between them and also illustrate several opportunities that arise from this connection.

Evolvability and robustness: A paradox restored

Evolvability and robustness are crucial for the origin and maintenance of complex organisms, but may not be simultaneously achievable as robust traits are also hard to change. Andreas Wagner has proposed a solution to this paradox by arguing that the many-to-few aspect of genotype-phenotype maps creates neutral networks of genotypes coding for the same phenotype. Phenotypes with large networks are genetically robust, but they may also have more neighboring phenotypes and thus higher evolvability. In this paper, we explore the generality of this idea by sampling large numbers of random genotype-phenotype maps for Boolean genotypes and phenotypes. We show that there is indeed a preponderance of positive correlations between the evolvability and robustness of phenotypes within a genotype-phenotype map, but also that there are negative correlations between average evolvability and robustness across maps. We interpret this as predicting a positive correlation across the phenotypic states of a character, but a negative correlation across characters. We also argue that evolvability and robustness tend to be negatively correlated when phenotypes are measured on ordinal or higher scale types. We conclude that Wagner's conjecture of a positive relation between robustness and evolvability is based on strict and somewhat unrealistic biological assumptions.

How evolution learns to generalise: Using the principles of learning theory to understand the evolution of developmental organisation

One of the most intriguing questions in evolution is how organisms exhibit suitable phenotypic variation to rapidly adapt in novel selective environments. Such variability is crucial for evolvability, but poorly understood. In particular, how can natural selection favour developmental organisations that facilitate adaptive evolution in previously unseen environments? Such a capacity suggests foresight that is incompatible with the short-sighted concept of natural selection. A potential resolution is provided by the idea that evolution may discover and exploit information not only about the particular phenotypes selected in the past, but their underlying structural regularities: new phenotypes, with the same underlying regularities, but novel particulars, may then be useful in new environments. If true, we still need to understand the conditions in which natural selection will discover such deep regularities rather than exploiting ‘quick fixes’ (i.e., fixes that provide adaptive phenotypes in the short term, but limit future evolvability). Here we argue that the ability of evolution to discover such regularities is formally analogous to learning principles, familiar in humans and machines, that enable generalisation from past experience. Conversely, natural selection that fails to enhance evolvability is directly analogous to the learning problem of over-fitting and the subsequent failure to generalise. We support the conclusion that evolving systems and learning systems are different instantiations of the same algorithmic principles by showing that existing results from the learning domain can be transferred to the evolution domain. Specifically, we show that conditions that alleviate over-fitting in learning systems successfully predict which biological conditions (e.g., environmental variation, regularity, noise or a pressure for developmental simplicity) enhance evolvability. This equivalence provides access to a well-developed theoretical framework from learning theory that enables a characterisation of the general conditions for the evolution of evolvability.

A striking feature of evolving organisms is their ability to acquire novel characteristics that help them adapt in new environments. The origin and the conditions of such ability remain elusive and is a long-standing question in evolutionary biology. Recent theory suggests that organisms can evolve designs that help them generate novel features that are more likely to be beneficial. Specifically, this is possible when the environments that organisms are exposed to share common regularities. However, the organisms develop robust designs that tend to produce what had been selected in the past and might be inflexible for future environments. The resolution comes from a recent theory introduced by Watson and Szathmáry that suggests a deep analogy between learning and evolution. Accordingly, here we utilise learning theory to explain the conditions that lead to more evolvable designs. We successfully demonstrate this by equating evolvability to the way humans and machines generalise to previously-unseen situations. Specifically, we show that the same conditions that enhance generalisation in learning systems have biological analogues and help us understand why environmental noise and the reproductive and maintenance costs of gene-regulatory connections can lead to more evolvable designs.