Statistical epistasis is a generic feature of gene regulatory networks

Genome-Wide Epistatic Network Analyses of Semantic Fluency in Older Adults

Semantic fluency impairment has been attributed to a wide range of neurocognitive and psychiatric conditions, especially in the older population. Moderate heritability estimates on semantic fluency were obtained from both twin and family-based studies suggesting genetic contributions to the observed variation across individuals. Currently, effort in identifying the genetic variants underlying the heritability estimates for this complex trait remains scarce. Using the semantic fluency scale and genome-wide SNP genotype data from the Long Life Family Study (LLFS), we performed a genome-wide association study (GWAS) and epistasis network analysis on semantic fluency in 2289 individuals aged over 60 years from the American LLFS cohorts and replicated the findings in 1129 individuals aged over 50 years from the Danish LLFS cohort. In the GWAS, two SNPs with genome-wide significance (rs3749683, p = 2.52 × 10-8; rs880179, p = 4.83 × 10-8) mapped to the CMYAS gene on chromosome 5 were detected. The epistasis network analysis identified five modules as significant (4.16 × 10-5 < p < 7.35 × 10-3), of which two were replicated (p < 3.10 × 10-3). These two modules revealed significant enrichment of tissue-specific gene expression in brain tissues and high enrichment of GWAS catalog traits, e.g., obesity-related traits, blood pressure, chronotype, sleep duration, and brain structure, that have been reported to associate with verbal performance in epidemiological studies. Our results suggest high tissue specificity of genetic regulation of gene expression in brain tissues with epistatic SNP networks functioning jointly in modifying individual verbal ability and cognitive performance.

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.

Progress and opportunities through use of genomics in animal production

The rearing of farmed animals is a vital component of global food production systems, but its impact on the environment, human health, animal welfare, and biodiversity is being increasingly challenged. Developments in genetic and genomic technologies have had a key role in improving the productivity of farmed animals for decades. Advances in genome sequencing, annotation, and editing offer a means not only to continue that trend, but also, when combined with advanced data collection, analytics, cloud computing, appropriate infrastructure, and regulation, to take precision livestock farming (PLF) and conservation to an advanced level. Such an approach could generate substantial additional benefits in terms of reducing use of resources, health treatments, and environmental impact, while also improving animal health and welfare.

The limits of normal approximation for adult height

Adult height inspired the first biometrical and quantitative genetic studies and is a test-case trait for understanding heritability. The studies of height led to formulation of the classical polygenic model, that has a profound influence on the way we view and analyse complex traits. An essential part of the classical model is an assumption of additivity of effects and normality of the distribution of the residuals. However, it may be expected that the normal approximation will become insufficient in bigger studies. Here, we demonstrate that when the height of hundreds of thousands of individuals is analysed, the model complexity needs to be increased to include non-additive interactions between sex, environment and genes. Alternatively, the use of log-normal approximation allowed us to still use the additive effects model. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait.

Emergence and propagation of epistasis in metabolic networks

Epistasis is often used to probe functional relationships between genes, and it plays an important role in evolution. However, we lack theory to understand how functional relationships at the molecular level translate into epistasis at the level of whole-organism phenotypes, such as fitness. Here, I derive two rules for how epistasis between mutations with small effects propagates from lower- to higher-level phenotypes in a hierarchical metabolic network with first-order kinetics and how such epistasis depends on topology. Most importantly, weak epistasis at a lower level may be distorted as it propagates to higher levels. Computational analyses show that epistasis in more realistic models likely follows similar, albeit more complex, patterns. These results suggest that pairwise inter-gene epistasis should be common, and it should generically depend on the genetic background and environment. Furthermore, the epistasis coefficients measured for high-level phenotypes may not be sufficient to fully infer the underlying functional relationships.

Gene-Environment Interaction: A Variable Selection Perspective

Gene-environment interactions have important implications for elucidating the genetic basis of complex diseases beyond the joint function of multiple genetic factors and their interactions (or epistasis). In the past, G × E interactions have been mainly conducted within the framework of genetic association studies. The high dimensionality of G × E interactions, due to the complicated form of environmental effects and the presence of a large number of genetic factors including gene expressions and SNPs, has motivated the recent development of penalized variable selection methods for dissecting G × E interactions, which has been ignored in the majority of published reviews on genetic interaction studies. In this article, we first survey existing studies on both gene-environment and gene-gene interactions. Then, after a brief introduction to the variable selection methods, we review penalization and relevant variable selection methods in marginal and joint paradigms, respectively, under a variety of conceptual models. Discussions on strengths and limitations, as well as computational aspects of the variable selection methods tailored for G × E studies, have also been provided.

Selecting Closely-Linked SNPs Based on Local Epistatic Effects for Haplotype Construction Improves Power of Association Mapping

Genome-wide association studies (GWAS) have gained central importance for the identification of candidate loci underlying complex traits. Single nucleotide polymorphism (SNP) markers are mostly used as genetic variants for the analysis of genotype-phenotype associations in populations, but closely linked SNPs that are grouped into haplotypes are also exploited. The benefit of haplotype-based GWAS approaches vs. SNP-based approaches is still under debate because SNPs in high linkage disequilibrium provide redundant information. To overcome some constraints of the commonly-used haplotype-based GWAS in which only consecutive SNPs are considered for haplotype construction, we propose a new method called functional haplotype-based GWAS (FH GWAS). FH GWAS is featured by combining SNPs into haplotypes based on the additive and epistatic effects among SNPs. Such haplotypes were termed functional haplotypes (FH). As shown by simulation studies, the FH GWAS approach clearly outperformed the SNP-based approach unless the minor allele frequency of the SNPs making up the haplotypes is low and the linkage disequilibrium between them is high. Applying FH GWAS for the trait flowering time in a large Arabidopsis thaliana population with whole-genome sequencing data revealed its potential empirically. FH GWAS identified all candidate regions which were detected in SNP-based and two other haplotype-based GWAS approaches. In addition, a novel region on chromosome 4 was solely detected by FH GWAS. Thus both the results of our simulation and empirical studies demonstrate that FH GWAS is a promising method and superior to the SNP-based approach even if almost complete genotype information is available.

Changes in gene expression predictably shift and switch genetic interactions

Non-additive interactions between mutations occur extensively and also change across conditions, making genetic prediction a difficult challenge. To better understand the plasticity of genetic interactions (epistasis), we combine mutations in a single protein performing a single function (a transcriptional repressor inhibiting a target gene). Even in this minimal system, genetic interactions switch from positive (suppressive) to negative (enhancing) as the expression of the gene changes. These seemingly complicated changes can be predicted using a mathematical model that propagates the effects of mutations on protein folding to the cellular phenotype. More generally, changes in gene expression should be expected to alter the effects of mutations and how they interact whenever the relationship between expression and a phenotype is nonlinear, which is the case for most genes. These results have important implications for understanding genotype-phenotype maps and illustrate how changes in genetic interactions can often—but not always—be predicted by hierarchical mechanistic models.

Non-additive genetic interactions are plastic and can complicate genetic prediction. Here, using deep mutagenesis of the lambda repressor, Li et al. reveal that changes in gene expression can alter the strength and direction of genetic interactions between mutations in many genes and develop mathematical models for predicting them.

Epistasis regulates the developmental stability of the mouse craniofacial shape

Fluctuating asymmetry is a classic concept linked to organismal development. It has traditionally been used as a measure of developmental instability, which is the inability of an organism to buffer environmental fluctuations during development. Developmental stability has a genetic component that influences the final phenotype of the organism and can lead to congenital disorders. According to alternative hypotheses, this genetic component might be either the result of additive genetic effects or a by-product of developmental gene networks. Here we present a genome-wide association study of the genetic architecture of fluctuating asymmetry of the skull shape in mice. Geometric morphometric methods were applied to quantify fluctuating asymmetry: we estimated fluctuating asymmetry as Mahalanobis distances to the mean asymmetry, correcting first for genetic directional asymmetry. We applied the marginal epistasis test to study epistasis among genomic regions. Results showed no evidence of additive effects but several interacting regions significantly associated with fluctuating asymmetry. Among the candidate genes overlapping these interacting regions we found an over-representation of genes involved in craniofacial development. A gene network is likely to be associated with skull developmental stability, and genes originally described as buffering genes (e.g., Hspa2) might occupy central positions within these networks, where regulatory elements may also play an important role. Our results constitute an important step in the exploration of the molecular roots of developmental stability and the first empirical evidence about its genetic architecture.

Layers of Cryptic Genetic Variation Underlie a Yeast Complex Trait

To better understand cryptic genetic variation, Lee et al. comprehensively map the genetic basis of a trait that is typically suppressed in a yeast cross. By determining how three different genetic perturbations give rise...

Cryptic genetic variation may be an important contributor to heritable traits, but its extent and regulation are not fully understood. Here, we investigate the cryptic genetic variation underlying a Saccharomyces cerevisiae colony phenotype that is typically suppressed in a cross of the laboratory strain BY4716 (BY) and a derivative of the clinical isolate 322134S (3S). To do this, we comprehensively dissect the trait’s genetic basis in the BYx3S cross in the presence of three different genetic perturbations that enable its expression. This allows us to detect and compare the specific loci that interact with each perturbation to produce the trait. In total, we identify 21 loci, all but one of which interact with just a subset of the perturbations. Beyond impacting which loci contribute to the trait, the genetic perturbations also alter the extent of additivity, epistasis, and genotype–environment interaction among the detected loci. Additionally, we show that the single locus interacting with all three perturbations corresponds to the coding region of the cell surface gene FLO11. While nearly all of the other remaining loci influence FLO11 transcription in cis or trans, the perturbations tend to interact with loci in different pathways and subpathways. Our work shows how layers of cryptic genetic variation can influence complex traits. Here, these layers mainly represent different regulatory inputs into the transcription of a single key gene.

The genetic landscape of a physical interaction

A key question in human genetics and evolutionary biology is how mutations in different genes combine to alter phenotypes. Efforts to systematically map genetic interactions have mostly made use of gene deletions. However, most genetic variation consists of point mutations of diverse and difficult to predict effects. Here, by developing a new sequencing-based protein interaction assay – deepPCA – we quantified the effects of >120,000 pairs of point mutations on the formation of the AP-1 transcription factor complex between the products of the FOS and JUN proto-oncogenes. Genetic interactions are abundant both in cis (within one protein) and trans (between the two molecules) and consist of two classes – interactions driven by thermodynamics that can be predicted using a three-parameter global model, and structural interactions between proximally located residues. These results reveal how physical interactions generate quantitatively predictable genetic interactions.

Proteins, the molecular workhorses of the cell, are made of small units called amino acids attached together like the links of a chain. Each protein is composed of a unique combination of amino acids, which is determined by a specific sequence of DNA called a gene. A change in a gene – a mutation – can create a variation in the protein it codes for, for instance by swapping a type of amino acid for another. Different mutations in the same gene can alter a protein in different ways. Some of these changes are harmless, but other can hinder how the protein performs its role. For example, a small change in the structure of a protein could affect how it will bind to other molecules.

It is possible for people to have identical mutations in the same genes, but experience different consequences. For instance, two persons could carry the same disease-inducing mutation, but one has a severe version of the condition and the other only mild symptoms. One reason is that changes in other genes cancel out or enhance the effect of a mutation. This phenomenon is known as a genetic interaction and it remains poorly understood, especially at the molecular level.

Here, Diss and Lehner developed a method, called deepPCA, to study the consequences of mutations in proteins in the laboratory. The experiments focused on two human genes which code for two proteins that normally attach to each other. Two mutations were artificially created, either one in each gene, or two in one of them. Diss and Lehner then examined how strongly the two mutated proteins could still attach to each other. By repeating this process with over 120,000 different pairs of mutations, it became possible to study how one mutation can have different effects depending on the presence of other mutations in the same protein or in the binding partner.

Overall, Diss and Lehner found that genetic interactions are the result of two mechanisms. In the first one, the two mutations together cause specific structural changes that modify how proteins bind to each other. In the second one, the changes solely depend on the magnitude of the initial, thermodynamic effects of individual mutations, but not on their specific physical and chemical properties. To predict the consequences of this second type of genetic interactions, knowing the identity or the exact effects of the two mutations is not necessary.

Understanding and predicting genetic interactions is important to develop personalized medicine, where treatments are tailored based on the genetic make up of an individual. This knowledge will also help to study how genes have evolved together.

Estimation of Sobol's Sensitivity Indices under Generalized Linear Models

We derive explicit formulas for Sobol's sensitivity indices (SSIs) under the generalized linear models (GLMs) with independent or multivariate normal inputs. We argue that the main-effect SSIs provide a powerful tool for variable selection under GLMs with identity links under polynomial regressions. We also show via examples that the SSI-based variable selection results are similar to the ones obtained by the random forest algorithm but without the computational burden of data permutation. Finally, applying our results to the problem of gene network discovery, we identify though the SSI analysis of a public microarray dataset several novel higher-order gene-gene interactions missed out by the more standard inference methods. The relevant functions for SSI analysis derived here under GLMs with identity, log, and logit links are implemented and made available in the R package SobolSensitivity.

Modifiers of the Genotype-Phenotype Map: Hsp90 and Beyond

Disruption of certain genes alters the heritable phenotypic variation among individuals. Research on the chaperone Hsp90 has played a central role in determining the genetic basis of this phenomenon, which may be important to evolution and disease. Key studies have shown that Hsp90 perturbation modifies the effects of many genetic variants throughout the genome. These modifications collectively transform the genotype–phenotype map, often resulting in a net increase or decrease in heritable phenotypic variation. Here, we summarize some of the foundational work on Hsp90 that led to these insights, discuss a framework for interpreting this research that is centered upon the standard genetics concept of epistasis, and propose major questions that future studies in this area should address.

Why and how genetic canalization evolves in gene regulatory networks

Background

Genetic canalization reflects the capacity of an organism’s phenotype to remain unchanged in spite of mutations. As selection on genetic canalization is weak and indirect, whether or not genetic canalization can reasonably evolve in complex genetic architectures is still an open question. In this paper, we use a quantitative model of gene regulatory network to describe the conditions in which substantial canalization is expected to emerge in a stable environment.

Results

Through an individual-based simulation framework, we confirmed that most parameters associated with the network topology (complexity and size of the network) have less influence than mutational parameters (rate and size of mutations) on the evolution of genetic canalization. We also established that selecting for extreme phenotypic optima (nil or full gene expression) leads to much higher canalization levels than selecting for intermediate expression levels. Overall, constrained networks evolve less canalization than networks in which some genes could evolve freely (i.e. without direct stabilizing selection pressure on gene expression).

Conclusions

Taken together, these results lead us to propose a two-fold mechanism involved in the evolution of genetic canalization in gene regulatory networks: the shrinkage of mutational target (useless genes are virtually removed from the network) and redundancy in gene regulation (so that some regulatory factors can be lost without affecting gene expression).

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-016-0801-2) contains supplementary material, which is available to authorized users.

Gene-Environment Interactions in Stress Response Contribute Additively to a Genotype-Environment Interaction

How combinations of gene-environment interactions collectively give rise to genotype-environment interactions is not fully understood. To shed light on this problem, we genetically dissected an environment-specific poor growth phenotype in a cross of two budding yeast strains. This phenotype is detectable when certain segregants are grown on ethanol at 37°C (‘E37’), a condition that differs from the standard culturing environment in both its carbon source (ethanol as opposed to glucose) and temperature (37°C as opposed to 30°C). Using recurrent backcrossing with phenotypic selection, we identified 16 contributing loci. To examine how these loci interact with each other and the environment, we focused on a subset of four loci that together can lead to poor growth in E37. We measured the growth of all 16 haploid combinations of alleles at these loci in all four possible combinations of carbon source (ethanol or glucose) and temperature (30 or 37°C) in a nearly isogenic population. This revealed that the four loci act in an almost entirely additive manner in E37. However, we also found that these loci have weaker effects when only carbon source or temperature is altered, suggesting that their effect magnitudes depend on the severity of environmental perturbation. Consistent with such a possibility, cloning of three causal genes identified factors that have unrelated functions in stress response. Thus, our results indicate that polymorphisms in stress response can show effects that are intensified by environmental stress, thereby resulting in major genotype-environment interactions when multiple of these variants co-occur.

Determining the genetic and molecular mechanisms that give rise to genotype-environment interaction (‘GxE’) is important for many areas of biology, including agriculture, evolution, and medicine. To help advance knowledge regarding this topic, we dissect the genetic basis of an example of GxE in which certain Saccharomyces cerevisiae cross progeny show extremely poor growth specifically on ethanol at 37°C. This environment differs from the standard condition used for culturing budding yeast in both its carbon source (ethanol as opposed to glucose) and temperature (37°C as opposed to 30°C). We provide evidence that poor growth on ethanol at 37°C is caused by a number of predominantly additive loci that individually exhibit gene-environment interactions with both carbon source and temperature. These loci show their largest effects when carbon source and temperature are simultaneously modified, indicating their effect magnitudes may be influenced by the severity of environmental stress. Consistent with this possibility, we clone three causal genes and find they encode functionally unrelated components of stress response. Our work suggests that polymorphisms in stress response can contribute additively to genotype-environment interactions that vary in intensity across conditions in a stress level-dependent manner.

Genetic assimilation: a review of its potential proximate causes and evolutionary consequences

BACKGROUND

Most, if not all, organisms possess the ability to alter their phenotype in direct response to changes in their environment, a phenomenon known as phenotypic plasticity. Selection can break this environmental sensitivity, however, and cause a formerly environmentally induced trait to evolve to become fixed through a process called genetic assimilation. Essentially, genetic assimilation can be viewed as the evolution of environmental robustness in what was formerly an environmentally sensitive trait. Because genetic assimilation has long been suggested to play a key role in the origins of phenotypic novelty and possibly even new species, identifying and characterizing the proximate mechanisms that underlie genetic assimilation may advance our basic understanding of how novel traits and species evolve.

SCOPE

This review begins by discussing how the evolution of phenotypic plasticity, followed by genetic assimilation, might promote the origins of new traits and possibly fuel speciation and adaptive radiation. The evidence implicating genetic assimilation in evolutionary innovation and diversification is then briefly considered. Next, the potential causes of phenotypic plasticity generally and genetic assimilation specifically are examined at the genetic, molecular and physiological levels and approaches that can improve our understanding of these mechanisms are described. The review concludes by outlining major challenges for future work.

CONCLUSIONS

Identifying and characterizing the proximate mechanisms involved in phenotypic plasticity and genetic assimilation promises to help advance our basic understanding of evolutionary innovation and diversification.

Survival of the Curviest: Noise-Driven Selection for Synergistic Epistasis

A major goal of human genetics is to elucidate the genetic architecture of human disease, with the goal of fueling improvements in diagnosis and the understanding of disease pathogenesis. The degree to which epistasis, or non-additive effects of risk alleles at different loci, accounts for common disease traits is hotly debated, in part because the conditions under which epistasis evolves are not well understood. Using both theory and evolutionary simulation, we show that the occurrence of common diseases (i.e. unfit phenotypes with frequencies on the order of 1%) can, under the right circumstances, be expected to be driven primarily by synergistic epistatic interactions. Conditions that are necessary, collectively, for this outcome include a strongly non-linear phenotypic landscape, strong (but not too strong) selection against the disease phenotype, and "noise" in the genotype-phenotype map that is both environmental (extrinsic, time-correlated) and developmental (intrinsic, uncorrelated) and, in both cases, neither too little nor too great. These results suggest ways in which geneticists might identify, a priori, those disease traits for which an "epistatic explanation" should be sought, and in the process better focus ongoing searches for risk alleles.

Epistatic interaction between common AGT G(-6)A (rs5051) and AGTR1 A1166C (rs5186) variants contributes to variation in kidney size at birth

Low nephron number has been recognised as an important cardiovascular risk factor and recently a strong correlation between renal mass and nephron number has been demonstrated in newborns. The aim of this study was to investigate individual, as well as combined, effects of common variants of genes which encode for major components of the renin-angiotensin system (REN G10601A, AGT G(-6)A, ACE I/D, AGTR1 A1166C) on kidney size in healthy, full-term newborns. A significant additive main effect of the ACE I/D polymorphism, as well as an additive-by-additive interaction between AGT G(-6)A and AGTR1 A1166C variants, were found. The variance attributed to the epistatic effect was 27.9 ml(2)/m(4), which accounted for 73.8% of the interaction variance (37.8 ml(2)/m(4)), 66.4% of the genetic variance (42.0 ml(2)/m(4)) and 4.4% to the total phenotypic variance (628 ml(2)/m(4)). No other statistically significant main or epistatic effects were detected. Our results highlight the importance of considering gene-gene interactions as part of the genetic architecture of congenital nephron number, even when the loci do not show significant single locus effects. Unravelling the genetic determinants of low nephron number, along with early molecular screening, may well help to identify children at risk for cardiovascular disease.

Transcriptional Derepression Uncovers Cryptic Higher-Order Genetic Interactions

Disruption of certain genes can reveal cryptic genetic variants that do not typically show phenotypic effects. Because this phenomenon, which is referred to as ‘phenotypic capacitance’, is a potential source of trait variation and disease risk, it is important to understand how it arises at the genetic and molecular levels. Here, we use a cryptic colony morphology trait that segregates in a yeast cross to explore the mechanisms underlying phenotypic capacitance. We find that the colony trait is expressed when a mutation in IRA2, a negative regulator of the Ras pathway, co-occurs with specific combinations of cryptic variants in six genes. Four of these genes encode transcription factors that act downstream of the Ras pathway, indicating that the phenotype involves genetically complex changes in the transcriptional regulation of Ras targets. We provide evidence that the IRA2 mutation reveals the phenotypic effects of the cryptic variants by disrupting the transcriptional silencing of one or more genes that contribute to the trait. Supporting this role for the IRA2 mutation, deletion of SFL1, a repressor that acts downstream of the Ras pathway, also reveals the phenotype, largely due to the same cryptic variants that were detected in the IRA2 mutant cross. Our results illustrate how higher-order genetic interactions among mutations and cryptic variants can result in phenotypic capacitance in specific genetic backgrounds, and suggests these interactions might reflect genetically complex changes in gene expression that are usually suppressed by negative regulation.

Some genetic polymorphisms have phenotypic effects that are masked under most conditions, but can be revealed by mutations or environmental change. The genetic and molecular mechanisms that suppress and uncover these cryptic genetic variants are important to understand. Here, we show that a single mutation in a yeast cross causes a major phenotypic change through its genetic interactions with two specific combinations of cryptic variants in six genes. This result suggests that in some cases cryptic variants themselves play roles in revealing their own phenotypic effects through their genetic interactions with each other and the mutations that reveal them. We also demonstrate that most of the genes harboring cryptic variation in our system are transcription factors, a finding that supports an important role for perturbation of gene regulatory networks in the uncovering of cryptic variation. As a final part of our study, we interrogate how a mutation exposes combinations of cryptic variants and obtain evidence that it does so by disrupting the silencing of one or more genes that must be expressed for the cryptic variants to exert their effects. To prove this point, we delete the transcriptional repressor that mediates this silencing and demonstrate that this deletion reveals a similar set of cryptic variants to the ones that were discovered in the initial mutant background. These findings advance our understanding of the genetic and molecular mechanisms that reveal cryptic variation.

Wiring for independence: positive feedback motifs facilitate individuation of traits in development and evolution

Independent selection response of a trait is contingent on the availability of genetic variation that is not entangled with other traits. Mechanistically, such variational individuation in spite of shared genome results from gene regulation. Changes that increase individuation of traits are likely caused by gene regulatory changes. Yet the effect of regulatory evolution on population variation is understudied. Trait individuation also occurs during development. Developmental differentiation involves two stages-induction of differentiation and the maintenance of differentiated fate. The corresponding gene regulatory transition involves the feed-forward and the regulated feedback motifs. Here we consider analogous transition pattern at the evolutionary scale, establishing an autonomous regulatory sub-network involved in the independent trait variation. A population genetic simulation of regulated feedback loop dynamics under small perturbations shows a decoupling of variation in gene expression between the upstream gene and the responding downstream gene. We furthermore observe that the ranges of dynamics that can be generated by feedback and feed-forward networks overlap. Such phenotypic overlap enables genetic accessibility of network-specific expression dynamics. We suggest that feedback topology may eventually confer selective advantage leading from a gradual process to threshold individuation, i.e., the emergence of a novel trait.

Capacitating epistasis--detection and role in the genetic architecture of complex traits

Here, we discuss the potential role of capacitating epistasis in the genetic architecture of complex traits. Two alternative methods for identifying such gene-gene interactions in genetic association studies-mapping of variance controlling loci and the variance plane ratio (VPR) method-are introduced. An overview of the theoretical foundation of the methods is presented together with a discussion on their implementation and available software for performing these analyses. We conclude by highlighting a few examples of capacitating epistasis described in the literature and its potential impacts on the genetics of complex traits.

Higher-order genetic interactions and their contribution to complex traits

The contribution of genetic interactions involving three or more loci to complex traits is poorly understood. These higher-order genetic interactions (HGIs) are difficult to detect in genetic mapping studies, therefore, few examples of them have been described. However, the lack of data on HGIs should not be misconstrued as proof that this class of genetic effect is unimportant. To the contrary, evidence from model organisms suggests that HGIs frequently influence genetic studies and contribute to many complex traits. Here, we review the growing literature on HGIs and discuss the future of research on this topic.

Estimating directional epistasis

Epistasis, i.e., the fact that gene effects depend on the genetic background, is a direct consequence of the complexity of genetic architectures. Despite this, most of the models used in evolutionary and quantitative genetics pay scant attention to genetic interactions. For instance, the traditional decomposition of genetic effects models epistasis as noise around the evolutionarily-relevant additive effects. Such an approach is only valid if it is assumed that there is no general pattern among interactions—a highly speculative scenario. Systematic interactions generate directional epistasis, which has major evolutionary consequences. In spite of its importance, directional epistasis is rarely measured or reported by quantitative geneticists, not only because its relevance is generally ignored, but also due to the lack of simple, operational, and accessible methods for its estimation. This paper describes conceptual and statistical tools that can be used to estimate directional epistasis from various kinds of data, including QTL mapping results, phenotype measurements in mutants, and artificial selection responses. As an illustration, I measured directional epistasis from a real-life example. I then discuss the interpretation of the estimates, showing how they can be used to draw meaningful biological inferences.

Genomic correlates of relationship QTL involved in fore- versus hind limb divergence in mice

Divergence of serially homologous elements of organisms is a common evolutionary pattern contributing to increased phenotypic complexity. Here, we study the genomic intervals affecting the variational independence of fore- and hind limb traits within an experimental mouse population. We use an advanced intercross of inbred mouse strains to map the loci associated with the degree of autonomy between fore- and hind limb long bone lengths (loci affecting the relationship between traits, relationship quantitative trait loci [rQTL]). These loci have been proposed to interact locally with the products of pleiotropic genes, thereby freeing the local trait from the variational constraint due to pleiotropic mutations. Using the known polymorphisms (single nucleotide polymorphisms [SNPs]) between the parental strains, we characterized and compared the genomic regions in which the rQTL, as well as their interaction partners (intQTL), reside. We find that these two classes of QTL intervals harbor different kinds of molecular variation. SNPs in rQTL intervals more frequently reside in limb-specific cis-regulatory regions than SNPs in intQTL intervals. The intQTL loci modified by the rQTL, in contrast, show the signature of protein-coding variation. This result is consistent with the widely accepted view that protein-coding mutations have broader pleiotropic effects than cis-regulatory polymorphisms. For both types of QTL intervals, the underlying candidate genes are enriched for genes involved in protein binding. This finding suggests that rQTL effects are caused by local interactions among the products of the causal genes harbored in rQTL and intQTL intervals. This is the first study to systematically document the population-level molecular variation underlying the evolution of character individuation.

Evolutionary constraints in variable environments, from proteins to networks

Environmental changes can not only trigger a regulatory response, but also impose evolutionary pressures that can modify the underlying regulatory network. Here, we review recent approaches that are beginning to disentangle this complex interplay between regulatory and evolutionary responses. Systematic genetic reconstructions have shown how evolutionary constraints arise from epistatic interactions between mutations in fixed environments. This approach is now being extended to more complex environments and systems. The first results suggest that epistasis is affected dramatically by environmental changes and, hence, can profoundly affect the course of evolution. Thus, external environments not only define the selection of favored phenotypes, but also affect the internal constraints that can limit the evolution of these phenotypes. These findings also raise new questions relating to the conditions for evolutionary transitions and the evolutionary potential of regulatory networks.

Cryptic genetic variation: evolution's hidden substrate

Cryptic genetic variation (CGV) is invisible under normal conditions, but it can fuel evolution when circumstances change. In theory, CGV can represent a massive cache of adaptive potential or a pool of deleterious alleles that are in need of constant suppression. CGV emerges from both neutral and selective processes, and it may inform about how human populations respond to change. CGV facilitates adaptation in experimental settings, but does it have an important role in the real world? Here, we review the empirical support for widespread CGV in natural populations, including its potential role in emerging human diseases and the growing evidence of its contribution to evolution.

Genetic regulatory network motifs constrain adaptation through curvature in the landscape of mutational (co)variance

Systems biology is accumulating a wealth of understanding about the structure of genetic regulatory networks, leading to a more complete picture of the complex genotype-phenotype relationship. However, models of multivariate phenotypic evolution based on quantitative genetics have largely not incorporated a network-based view of genetic variation. Here we model a set of two-node, two-phenotype genetic network motifs, covering a full range of regulatory interactions. We find that network interactions result in different patterns of mutational (co)variance at the phenotypic level (the M-matrix), not only across network motifs but also across phenotypic space within single motifs. This effect is due almost entirely to mutational input of additive genetic (co)variance. Variation in M has the effect of stretching and bending phenotypic space with respect to evolvability, analogous to the curvature of space-time under general relativity, and similar mathematical tools may apply in each case. We explored the consequences of curvature in mutational variation by simulating adaptation under divergent selection with gene flow. Both standing genetic variation (the G-matrix) and rate of adaptation are constrained by M, so that G and adaptive trajectories are curved across phenotypic space. Under weak selection the phenotypic mean at migration-selection balance also depends on M.

Monotonicity is a key feature of genotype-phenotype maps

It was recently shown that monotone gene action, i.e., order-preservation between allele content and corresponding genotypic values in the mapping from genotypes to phenotypes, is a prerequisite for achieving a predictable parent-offspring relationship across the whole allele frequency spectrum. Here we test the consequential prediction that the design principles underlying gene regulatory networks are likely to generate highly monotone genotype-phenotype maps. To this end we present two measures of the monotonicity of a genotype-phenotype map, one based on allele substitution effects, and the other based on isotonic regression. We apply these measures to genotype-phenotype maps emerging from simulations of 1881 different 3-gene regulatory networks. We confirm that in general, genotype-phenotype maps are indeed highly monotonic across network types. However, regulatory motifs involving incoherent feedforward or positive feedback, as well as pleiotropy in the mapping between genotypes and gene regulatory parameters, are clearly predisposed for generating non-monotonicity. We present analytical results confirming these deep connections between molecular regulatory architecture and monotonicity properties of the genotype-phenotype map. These connections seem to be beyond reach by the classical distinction between additive and non-additive gene action.

Evolutionary systems biology: what it is and why it matters

Evolutionary systems biology (ESB) is a rapidly growing integrative approach that has the core aim of generating mechanistic and evolutionary understanding of genotype-phenotype relationships at multiple levels. ESB's more specific objectives include extending knowledge gained from model organisms to non-model organisms, predicting the effects of mutations, and defining the core network structures and dynamics that have evolved to cause particular intracellular and intercellular responses. By combining mathematical, molecular, and cellular approaches to evolution, ESB adds new insights and methods to the modern evolutionary synthesis, and offers ways in which to enhance its explanatory and predictive capacities. This combination of prediction and explanation marks ESB out as a research manifesto that goes further than its two contributing fields. Here, we summarize ESB via an analysis of characteristic research examples and exploratory questions, while also making a case for why these integrative efforts are worth pursuing.

Effect of regulatory architecture on broad versus narrow sense heritability

Additive genetic variance (VA ) and total genetic variance (VG ) are core concepts in biomedical, evolutionary and production-biology genetics. What determines the large variation in reported VA /VG ratios from line-cross experiments is not well understood. Here we report how the VA /VG ratio, and thus the ratio between narrow and broad sense heritability (h(2) /H(2) ), varies as a function of the regulatory architecture underlying genotype-to-phenotype (GP) maps. We studied five dynamic models (of the cAMP pathway, the glycolysis, the circadian rhythms, the cell cycle, and heart cell dynamics). We assumed genetic variation to be reflected in model parameters and extracted phenotypes summarizing the system dynamics. Even when imposing purely linear genotype to parameter maps and no environmental variation, we observed quite low VA /VG ratios. In particular, systems with positive feedback and cyclic dynamics gave more non-monotone genotype-phenotype maps and much lower VA /VG ratios than those without. The results show that some regulatory architectures consistently maintain a transparent genotype-to-phenotype relationship, whereas other architectures generate more subtle patterns. Our approach can be used to elucidate these relationships across a whole range of biological systems in a systematic fashion.

Congruence of additive and non-additive effects on gene expression estimated from pedigree and SNP data

There is increasing evidence that heritable variation in gene expression underlies genetic variation in susceptibility to disease. Therefore, a comprehensive understanding of the similarity between relatives for transcript variation is warranted--in particular, dissection of phenotypic variation into additive and non-additive genetic factors and shared environmental effects. We conducted a gene expression study in blood samples of 862 individuals from 312 nuclear families containing MZ or DZ twin pairs using both pedigree and genotype information. From a pedigree analysis we show that the vast majority of genetic variation across 17,994 probes is additive, although non-additive genetic variation is identified for 960 transcripts. For 180 of the 960 transcripts with non-additive genetic variation, we identify expression quantitative trait loci (eQTL) with dominance effects in a sample of 339 unrelated individuals and replicate 31% of these associations in an independent sample of 139 unrelated individuals. Over-dominance was detected and replicated for a trans association between rs12313805 and ETV6, located 4MB apart on chromosome 12. Surprisingly, only 17 probes exhibit significant levels of common environmental effects, suggesting that environmental and lifestyle factors common to a family do not affect expression variation for most transcripts, at least those measured in blood. Consistent with the genetic architecture of common diseases, gene expression is predominantly additive, but a minority of transcripts display non-additive effects.

Genetic and environmental factors affecting cryptic variations in gene regulatory networks

BACKGROUND

Cryptic genetic variation (CGV) is considered to facilitate phenotypic evolution by producing visible variations in response to changes in the internal and/or external environment. Several mechanisms enabling the accumulation and release of CGVs have been proposed. In this study, we focused on gene regulatory networks (GRNs) as an important mechanism for producing CGVs, and examined how interactions between GRNs and the environment influence the number of CGVs by using individual-based simulations.

RESULTS

Populations of GRNs were allowed to evolve under various stabilizing selections, and we then measured the number of genetic and phenotypic variations that had arisen. Our results showed that CGVs were not depleted irrespective of the strength of the stabilizing selection for each phenotype, whereas the visible fraction of genetic variation in a population decreased with increasing strength of selection. On the other hand, increasing the number of different environments that individuals encountered within their lifetime (i.e., entailing plastic responses to multiple environments) suppressed the accumulation of CGVs, whereas the GRNs with more genes and interactions were favored in such heterogeneous environments.

CONCLUSIONS

Given the findings that the number of CGVs in a population was largely determined by the size (order) of GRNs, we propose that expansion of GRNs and adaptation to novel environments are mutually facilitating and sustainable sources of evolvability and hence the origins of biological diversity and complexity.

Use of pleiotropy to model genetic interactions in a population

Systems-level genetic studies in humans and model systems increasingly involve both high-resolution genotyping and multi-dimensional quantitative phenotyping. We present a novel method to infer and interpret genetic interactions that exploits the complementary information in multiple phenotypes. We applied this approach to a population of yeast strains with randomly assorted perturbations of five genes involved in mating. We quantified pheromone response at the molecular level and overall mating efficiency. These phenotypes were jointly analyzed to derive a network of genetic interactions that mapped mating-pathway relationships. To determine the distinct biological processes driving the phenotypic complementarity, we analyzed patterns of gene expression to find that the pheromone response phenotype is specific to cellular fusion, whereas mating efficiency was a combined measure of cellular fusion, cell cycle arrest, and modifications in cellular metabolism. We applied our novel method to global gene expression patterns to derive an expression-specific interaction network and demonstrate applicability to global transcript data. Our approach provides a basis for interpretation of genetic interactions and the generation of specific hypotheses from populations assayed for multiple phenotypes.

Parallel advances in genotype and phenotype measurement technologies are yielding large-scale, multidimensional datasets that can potentially decipher the genetic etiology of complex traits. Understanding these data will require methods that combine the experimental power of molecular biology and the quantitative power of statistical genetics. In this work, we describe a novel approach that uses the complementary information encoded by multiple phenotypes in conjunction with genetic data to map genetic interaction networks in terms of quantitative variant-to-variant and variant-to-phenotype influences. We tested this method using a population of yeast strains with random combinations of five genetic mutations and derived an interaction network using molecular and colony-level assays of mating phenotypes. Distinct biological processes that underlie the two phenotypes were identified with gene expression analysis, validating the method's ability to exploit complementary biological information in multiple phenotypes. Our method generates data-driven models and testable hypotheses of how the genetic variation in a population combines to affect complex traits. It is designed to be flexible and scalable for application to populations with extensive genetic diversity.

From sequence to consequence and back

The genotype-phenotype relation is at the core of theoretical biology. It is argued why a mathematically based explanatory structure of this relation is in principle possible, and why it has to embrace both sequence to consequence and consequence to sequence phenomena. It is suggested that the primary role of DNA in the chain of causality is that its presence allows a living system to induce perturbations of its own dynamics as a function of its own system state or phenome, i.e. it capacitates living systems to self-transcend beyond those morphogenetic limits that exist for non-living open physical systems in general. Dynamic models bridging genotypes with phenotypic variation in a causally cohesive way are shown to provide explanations of genetic phenomena that go well beyond the explanatory domains of statistically oriented genetics theory construction. A theory originally proposed by Rupert Riedl, which implies that the morphospace that is reachable by the standing genetic variation in a population is quite restricted due to systemic constraints, is shown to provide a foundation for a mathematical conceptualization of numerous evolutionary phenomena associated with the phenotypic consequence to sequence relation. The paper may be considered a call to arms to mathematicians and the mathematically inclined to rise to the challenge of developing new formalisms capable of dealing with the deep defining characteristics of living systems.

Genetic variation in the Yolk protein expression network of Drosophila melanogaster: sex-biased negative correlations with longevity

One of the persistent problems in biology is understanding how genetic variation contributes to phenotypic variation. Associations at many levels have been reported, and yet causal inference has remained elusive. We propose to rely on the knowledge of causal relationships established by molecular biology approaches. The existing molecular knowledge forms a firm backbone upon which hypotheses connecting genetic variation, transcriptional variation and phenotypic variation can be built. The sex determination pathway is a well-established molecular network, with the Yolk protein 1-3 (Yp) genes as the most downstream target. Our analyses reveal that genetic variation in expression for genes known to be upstream in the pathway explains variation in downstream targets. Relationships differ between the two sexes, and each Yp has a distinct transcriptional pattern. Yp expression is significantly negatively correlated with longevity, an important life history trait, for both males and females.

Parameters in dynamic models of complex traits are containers of missing heritability

Polymorphisms identified in genome-wide association studies of human traits rarely explain more than a small proportion of the heritable variation, and improving this situation within the current paradigm appears daunting. Given a well-validated dynamic model of a complex physiological trait, a substantial part of the underlying genetic variation must manifest as variation in model parameters. These parameters are themselves phenotypic traits. By linking whole-cell phenotypic variation to genetic variation in a computational model of a single heart cell, incorporating genotype-to-parameter maps, we show that genome-wide association studies on parameters reveal much more genetic variation than when using higher-level cellular phenotypes. The results suggest that letting such studies be guided by computational physiology may facilitate a causal understanding of the genotype-to-phenotype map of complex traits, with strong implications for the development of phenomics technology.

Despite an ever-increasing number of genome locations reported to be associated with complex human diseases or quantitative traits, only a small proportion of phenotypic variations in a typical quantitative trait can be explained by the discovered variants. We argue that this problem can partly be resolved by combining the statistical methods of quantitative genetics with computational biology. We demonstrate this for the in silico genotype-to-phenotype map of a model heart cell in conjunction with publically accessible genomic data. We show that genome wide association studies (GWAS) on model parameters identify more causal variants and can build better prediction models for the higher-level phenotypes than by performing GWAS on the higher-level phenotypes themselves. Since model parameters are in principle measurable physiological phenotypes, our findings suggest that development of future phenotyping technologies could be guided by mathematical models of the biological systems being targeted.

Model Misinterpretation within Biology: Phenotypes, Statistics, Networks, and Inference

Models of myriad forms are rapidly becoming central to biology. These range from statistical models that are fundamental to the interpretation of experimental results to ordinary differential equation models that attempt to describe the results in a mechanistic format. Models will be more and more essential to biologists but this growing importance requires all model users to become more sophisticated about what is in a model and how that limits the usability of the model. This review attempts to relay the potential pitfalls that can lie within a model.

Evolutionary systems biology: historical and philosophical perspectives on an emerging synthesis

Systems biology (SB) is at least a decade old now and maturing rapidly. A more recent field, evolutionary systems biology (ESB), is in the process of further developing system-level approaches through the expansion of their explanatory and potentially predictive scope. This chapter will outline the varieties of ESB existing today by tracing the diverse roots and fusions that make up this integrative project. My approach is philosophical and historical. As well as examining the recent origins of ESB, I will reflect on its central features and the different clusters of research it comprises. In its broadest interpretation, ESB consists of five overlapping approaches: comparative and correlational ESB; network architecture ESB; network property ESB; population genetics ESB; and finally, standard evolutionary questions answered with SB methods. After outlining each approach with examples, I will examine some strong general claims about ESB, particularly that it can be viewed as the next step toward a fuller modern synthesis of evolutionary biology (EB), and that it is also the way forward for evolutionary and systems medicine. I will conclude with a discussion of whether the emerging field of ESB has the capacity to combine an even broader scope of research aims and efforts than it presently does.

Genotype-Phenotype Map Characteristics of an In silico Heart Cell

Understanding the causal chain from genotypic to phenotypic variation is a tremendous challenge with huge implications for personalized medicine. Here we argue that linking computational physiology to genetic concepts, methodology, and data provides a new framework for this endeavor. We exemplify this causally cohesive genotype–phenotype (cGP) modeling approach using a detailed mathematical model of a heart cell. In silico genetic variation is mapped to parametric variation, which propagates through the physiological model to generate multivariate phenotypes for the action potential and calcium transient under regular pacing, and ion currents under voltage clamping. The resulting genotype-to-phenotype map is characterized using standard quantitative genetic methods and novel applications of high-dimensional data analysis. These analyses reveal many well-known genetic phenomena like intralocus dominance, interlocus epistasis, and varying degrees of phenotypic correlation. In particular, we observe penetrance features such as the masking/release of genetic variation, so that without any change in the regulatory anatomy of the model, traits may appear monogenic, oligogenic, or polygenic depending on which genotypic variation is actually present in the data. The results suggest that a cGP modeling approach may pave the way for a computational physiological genomics capable of generating biological insight about the genotype–phenotype relation in ways that statistical-genetic approaches cannot.

Computational modeling of interactions between multiple myeloma and the bone microenvironment

Multiple Myeloma (MM) is a B-cell malignancy that is characterized by osteolytic bone lesions. It has been postulated that positive feedback loops in the interactions between MM cells and the bone microenvironment form reinforcing ‘vicious cycles’, resulting in more bone resorption and MM cell population growth in the bone microenvironment. Despite many identified MM-bone interactions, the combined effect of these interactions and their relative importance are unknown. In this paper, we develop a computational model of MM-bone interactions and clarify whether the intercellular signaling mechanisms implemented in this model appropriately drive MM disease progression. This new computational model is based on the previous bone remodeling model of Pivonka et al. [1], and explicitly considers IL-6 and MM-BMSC (bone marrow stromal cell) adhesion related pathways, leading to formation of two positive feedback cycles in this model. The progression of MM disease is simulated numerically, from normal bone physiology to a well established MM disease state. Our simulations are consistent with known behaviors and data reported for both normal bone physiology and for MM disease. The model results suggest that the two positive feedback cycles identified for this model are sufficient to jointly drive the MM disease progression. Furthermore, quantitative analysis performed on the two positive feedback cycles clarifies the relative importance of the two positive feedback cycles, and identifies the dominant processes that govern the behavior of the two positive feedback cycles. Using our proposed quantitative criteria, we identify which of the positive feedback cycles in this model may be considered to be ‘vicious cycles’. Finally, key points at which to block the positive feedback cycles in MM-bone interactions are identified, suggesting potential drug targets.

Genomic analysis of QTLs and genes altering natural variation in stochastic noise

Quantitative genetic analysis has long been used to study how natural variation of genotype can influence an organism's phenotype. While most studies have focused on genetic determinants of phenotypic average, it is rapidly becoming understood that stochastic noise is genetically determined. However, it is not known how many traits display genetic control of stochastic noise nor how broadly these stochastic loci are distributed within the genome. Understanding these questions is critical to our understanding of quantitative traits and how they relate to the underlying causal loci, especially since stochastic noise may be directly influenced by underlying changes in the wiring of regulatory networks. We identified QTLs controlling natural variation in stochastic noise of glucosinolates, plant defense metabolites, as well as QTLs for stochastic noise of related transcripts. These loci included stochastic noise QTLs unique for either transcript or metabolite variation. Validation of these loci showed that genetic polymorphism within the regulatory network alters stochastic noise independent of effects on corresponding average levels. We examined this phenomenon more globally, using transcriptomic datasets, and found that the Arabidopsis transcriptome exhibits significant, heritable differences in stochastic noise. Further analysis allowed us to identify QTLs that control genomic stochastic noise. Some genomic QTL were in common with those altering average transcript abundance, while others were unique to stochastic noise. Using a single isogenic population, we confirmed that natural variation at ELF3 alters stochastic noise in the circadian clock and metabolism. Since polymorphisms controlling stochastic noise in genomic phenotypes exist within wild germplasm for naturally selected phenotypes, this suggests that analysis of Arabidopsis evolution should account for genetic control of stochastic variance and average phenotypes. It remains to be determined if natural genetic variation controlling stochasticity is equally distributed across the genomes of other multi-cellular eukaryotes.

Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance

In quantitative genetics, the degree of resemblance between parents and offspring is described in terms of the additive variance (V(A)) relative to genetic (V(G)) and phenotypic (V(P)) variance. For populations with extreme allele frequencies, high V(A)/V(G) can be explained without considering properties of the genotype-phenotype (GP) map. We show that randomly generated GP maps in populations with intermediate allele frequencies generate far lower V(A)/V(G) values than empirically observed. The main reason is that order-breaking behaviour is ubiquitous in random GP maps. Rearrangement of genotypic values to introduce order-preservation for one or more loci causes a dramatic increase in V(A)/V(G). This suggests the existence of order-preserving design principles in the regulatory machinery underlying GP maps. We illustrate this feature by showing how the ubiquitously observed monotonicity of dose-response relationships gives much higher V(A)/V(G) values than a unimodal dose-response relationship in simple gene network models.

High-dimensional variance partitioning reveals the modular genetic basis of adaptive divergence in gene expression during reproductive character displacement

Although adaptive change is usually associated with complex changes in phenotype, few genetic investigations have been conducted on adaptations that involve sets of high-dimensional traits. Microarrays have supplied high-dimensional descriptions of gene expression, and phenotypic change resulting from adaptation often results in large-scale changes in gene expression. We demonstrate how genetic analysis of large-scale changes in gene expression generated during adaptation can be accomplished by determining high-dimensional variance partitioning within classical genetic experimental designs. A microarray experiment conducted on a panel of recombinant inbred lines (RILs) generated from two populations of Drosophila serrata that have diverged in response to natural selection, revealed genetic divergence in 10.6% of 3762 gene products examined. Over 97% of the genetic divergence in transcript abundance was explained by only 12 genetic modules. The two most important modules, explaining 50% of the genetic variance in transcript abundance, were genetically correlated with the morphological traits that are known to be under selection. The expression of three candidate genes from these two important genetic modules was assessed in an independent experiment using qRT-PCR on 430 individuals from the panel of RILs, and confirmed the genetic association between transcript abundance and morphological traits under selection.

Molecular mechanisms of epistasis within and between genes

'Disease-causing' mutations do not cause disease in all individuals. One possible important reason for this is that the outcome of a mutation can depend upon other genetic variants in a genome. These epistatic interactions between mutations occur both within and between molecules, and studies in model organisms show that they are extremely prevalent. However, epistatic interactions are still poorly understood at the molecular level, and consequently difficult to predict de novo. Here I provide an overview of our current understanding of the molecular mechanisms that can cause epistasis, and areas where more research is needed. A more complete understanding of epistasis will be vital for making accurate predictions about the phenotypes of individuals.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

Background

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function.

Results

Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops.

Conclusions

HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

A modelling framework for the analysis of artificial-selection time series

Artificial-selection experiments constitute an important source of empirical information for breeders, geneticists and evolutionary biologists. Selected characters can generally be shifted far from their initial state, sometimes beyond what is usually considered as typical inter-specific divergence. A careful analysis of the data collected during such experiments may thus reveal the dynamical properties of the genetic architecture that underlies the trait under selection. Here, we propose a statistical framework describing the dynamics of selection-response time series. We highlight how both phenomenological models (which do not make assumptions on the nature of genetic phenomena) and mechanistic models (explaining the temporal trends in terms of e.g. mutations, epistasis or canalization) can be used to understand and interpret artificial-selection data. The practical use of the models and their implementation in a software package are demonstrated through the analysis of a selection experiment on the shape of the wing in Drosophila melanogaster.