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

The limitations of phenotype prediction in metabolism

Phenotype prediction is at the center of many questions in biology. Prediction is often achieved by determining statistical associations between genetic and phenotypic variation, ignoring the exact processes that cause the phenotype. Here, we present a framework based on genome-scale metabolic reconstructions to reveal the mechanisms behind the associations. We calculated a polygenic score (PGS) that identifies a set of enzymes as predictors of growth, the phenotype. This set arises from the synergy of the functional mode of metabolism in a particular setting and its evolutionary history, and is suitable to infer the phenotype across a variety of conditions. We also find that there is optimal genetic variation for predictability and demonstrate how the linear PGS can still explain phenotypes generated by the underlying nonlinear biochemistry. Therefore, the explicit model interprets the black box statistical associations of the genotype-to-phenotype map and helps to discover what limits the prediction in metabolism.

Quantitative Operating Principles of Yeast Metabolism during Adaptation to Heat Stress

Microorganisms evolved adaptive responses to survive stressful challenges in ever-changing environments. Understanding the relationships between the physiological/metabolic adjustments allowing cellular stress adaptation and gene expression changes being used by organisms to achieve such adjustments may significantly impact our ability to understand and/or guide evolution. Here, we studied those relationships during adaptation to various stress challenges in Saccharomyces cerevisiae, focusing on heat stress responses. We combined dozens of independent experiments measuring whole-genome gene expression changes during stress responses with a simplified kinetic model of central metabolism. We identified alternative quantitative ranges for a set of physiological variables in the model (production of ATP, trehalose, NADH, etc.) that are specific for adaptation to either heat stress or desiccation/rehydration. Our approach is scalable to other adaptive responses and could assist in developing biotechnological applications to manipulate cells for medical, biotechnological, or synthetic biology purposes.

Using a system of differential equations that models cattle growth to uncover the genetic basis of complex traits

The interplay between dynamic models of biological systems and genomics is based on the assumption that genetic variation of the complex trait (i.e., outcome of model behavior) arises from component traits (i.e., model parameters) in lower hierarchical levels. In order to provide a proof of concept of this statement for a cattle growth model, we ask whether model parameters map genomic regions that harbor quantitative trait loci (QTLs) already described for the complex trait. We conducted a genome-wide association study (GWAS) with a Bayesian hierarchical LASSO method in two parameters of the Davis Growth Model, a system of three ordinary differential equations describing DNA accretion, protein synthesis and degradation, and fat synthesis. Phenotypic and genotypic data were available for 893 Nellore (Bos indicus) cattle. Computed values for parameter k₁ (DNA accretion rate) ranged from 0.005 ± 0.003 and for α (constant for energy for maintenance requirement) 0.134 ± 0.024. The expected biological interpretation of the parameters is confirmed by QTLs mapped for k₁ and α. QTLs within genomic regions mapped for k₁ are expected to be correlated with the DNA pool: body size and weight. Single nucleotide polymorphisms (SNPs) which were significant for α mapped QTLs that had already been associated with residual feed intake, feed conversion ratio, average daily gain (ADG), body weight, and also dry matter intake. SNPs identified for k₁ were able to additionally explain 2.2% of the phenotypic variability of the complex ADG, even when SNPs for k₁ did not match the genomic regions associated with ADG. Although improvements are needed, our findings suggest that genomic analysis on component traits may help to uncover the genetic basis of more complex traits, particularly when lower biological hierarchies are mechanistically described by mathematical simulation models.

Comparing GWAS Results of Complex Traits Using Full Genetic Model and Additive Models for Revealing Genetic Architecture

Most of the genome-wide association studies (GWASs) for human complex diseases have ignored dominance, epistasis and ethnic interactions. We conducted comparative GWASs for total cholesterol using full model and additive models, which illustrate the impacts of the ignoring genetic variants on analysis results and demonstrate how genetic effects of multiple loci could differ across different ethnic groups. There were 15 quantitative trait loci with 13 individual loci and 3 pairs of epistasis loci identified by full model, whereas only 14 loci (9 common loci and 5 different loci) identified by multi-loci additive model. Again, 4 full model detected loci were not detected using multi-loci additive model. PLINK-analysis identified two loci and GCTA-analysis detected only one locus with genome-wide significance. Full model identified three previously reported genes as well as several new genes. Bioinformatics analysis showed some new genes are related with cholesterol related chemicals and/or diseases. Analyses of cholesterol data and simulation studies revealed that the full model performs were better than the additive-model performs in terms of detecting power and unbiased estimations of genetic variants of complex traits.

Network biology concepts in complex disease comorbidities

The co-occurrence of diseases can inform the underlying network biology of shared and multifunctional genes and pathways. In addition, comorbidities help to elucidate the effects of external exposures, such as diet, lifestyle and patient care. With worldwide health transaction data now often being collected electronically, disease co-occurrences are starting to be quantitatively characterized. Linking network dynamics to the real-life, non-ideal patient in whom diseases co-occur and interact provides a valuable basis for generating hypotheses on molecular disease mechanisms, and provides knowledge that can facilitate drug repurposing and the development of targeted therapeutic strategies.

Integrating Genomics with Nutrition Models to Improve the Prediction of Cattle Performance and Carcass Composition under Feedlot Conditions

Cattle body composition is difficult to model because several factors affect the composition of the average daily gain (ADG) of growing animals. The objective of this study was to identify commercial single nucleotide polymorphism (SNP) panels that could improve the predictability of days on feed (DOF) to reach a target United States Department of Agriculture (USDA) grade given animal, diet, and environmental information under feedyard conditions. The data for this study was comprised of crossbred heifers (n = 681) and steers (n = 836) from commercial feedyards. Eleven molecular breeding value (MBV) scores derived from SNP panels of candidate gene polymorphisms and two-leptin gene SNP (UASMS2 and E2FB) were evaluated. The empty body fat (EBF) and the shrunk body weight (SBW) at 28% EBF (AFSBW) were computed by the Cattle Value Discovery System (CVDS) model using hip height (EBF_HH and AFSBW_HH) or carcass traits (EBF_CT and AFSBW_CT) of the animals. The DOF_HH was calculated when AFSBW_HH and ADG_HH were used and DOF_CT was calculated when AFSBW_CT and ADG_CT were used. The CVDS estimates dry matter required (DMR) by individuals fed in groups when observed ADG and AFSBW are provided. The AFSBW_CT was assumed more accurate than the AFSBW_HH because it was computed using carcass traits. The difference between AFSBW_CT and AFSBW_HH, DOF_CT and DOF_HH, and DMR and dry matter intake (DMI) were regressed on the MBV scores and leptin gene SNP to explain the variation. Our results indicate quite a large range of correlations among MBV scores and model input and output variables, but MBV ribeye area was the most strongly correlated with the differences in DOF, AFSBW, and DMI by explaining 8, 13.2 and 6.5%, respectively, of the variation. This suggests that specific MBV scores might explain additional variation of input and output variables used by nutritional models in predicting individual animal performance.

Towards causally cohesive genotype-phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries

A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype-phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype-phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.

Causal drift, robust signaling, and complex disease

The phenotype of many regulatory circuits in which mutations can cause complex, polygenic diseases is to some extent robust to DNA mutations that affect circuit components. Here I demonstrate how such mutational robustness can prevent the discovery of genetic disease determinants. To make my case, I use a mathematical model of the insulin signaling pathway implicated in type 2 diabetes, whose signaling output is governed by 15 genetically determined parameters. Using multiple complementary measures of a parameter's importance for this phenotype, I show that any one disease determinant that is crucial in one genetic background will be virtually irrelevant in other backgrounds. In an evolving population that drifts through the parameter space of this or other robust circuits through DNA mutations, the genetic changes that can cause disease will vary randomly over time. I call this phenomenon causal drift. It means that mutations causing disease in one (human or non-human) population may have no effect in another population, and vice versa. Causal drift casts doubt on our ability to infer the molecular mechanisms of complex diseases from non-human model organisms.

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.

Missing heritability of common diseases and treatments outside the protein-coding exome

Genetic factors strongly influence risk of common human diseases and treatment outcomes but the causative variants remain largely unknown; this gap has been called the 'missing heritability'. We propose several hypotheses that in combination have the potential to narrow the gap. First, given a multi-stage path from wellness to disease, we propose that common variants under positive evolutionary selection represent normal variation and gate the transition between wellness and an 'off-well' state, revealing adaptations to changing environmental conditions. In contrast, genome-wide association studies (GWAS) focus on deleterious variants conveying disease risk, accelerating the path from off-well to illness and finally specific diseases, while common 'normal' variants remain hidden in the noise. Second, epistasis (dynamic gene-gene interactions) likely assumes a central role in adaptations and evolution; yet, GWAS analyses currently are poorly designed to reveal epistasis. As gene regulation is germane to adaptation, we propose that epistasis among common normal regulatory variants, or between common variants and less frequent deleterious variants, can have strong protective or deleterious phenotypic effects. These gene-gene interactions can be highly sensitive to environmental stimuli and could account for large differences in drug response between individuals. Residing largely outside the protein-coding exome, common regulatory variants affect either transcription of coding and non-coding RNAs (regulatory SNPs, or rSNPs) or RNA functions and processing (structural RNA SNPs, or srSNPs). Third, with the vast majority of causative variants yet to be discovered, GWAS rely on surrogate markers, a confounding factor aggravated by the presence of more than one causative variant per gene and by epistasis. We propose that the confluence of these factors may be responsible to large extent for the observed heritability gap.

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.

PGMRA: a web server for (phenotype x genotype) many-to-many relation analysis in GWAS

It has been proposed that single nucleotide polymorphisms (SNPs) discovered by genome-wide association studies (GWAS) account for only a small fraction of the genetic variation of complex traits in human population. The remaining unexplained variance or missing heritability is thought to be due to marginal effects of many loci with small effects and has eluded attempts to identify its sources. Combination of different studies appears to resolve in part this problem. However, neither individual GWAS nor meta-analytic combinations thereof are helpful for disclosing which genetic variants contribute to explain a particular phenotype. Here, we propose that most of the missing heritability is latent in the GWAS data, which conceals intermediate phenotypes. To uncover such latent information, we propose the PGMRA server that introduces phenomics--the full set of phenotype features of an individual--to identify SNP-set structures in a broader sense, i.e. causally cohesive genotype-phenotype relations. These relations are agnostically identified (without considering disease status of the subjects) and organized in an interpretable fashion. Then, by incorporating a posteriori the subject status within each relation, we can establish the risk surface of a disease in an unbiased mode. This approach complements-instead of replaces-current analysis methods. The server is publically available at http://phop.ugr.es/fenogeno.

Post-GWAS: where next? More samples, more SNPs or more biology?

The power of genome-wide association studies (GWAS) rests on several foundations: (i) there is a significant amount of additive genetic variation, (ii) individual causal polymorphisms often have sizable effects and (iii) they segregate at moderate-to-intermediate frequencies, or will be effectively 'tagged' by polymorphisms that do. Each of these assumptions has recently been questioned. (i) Why should genetic variation appear additive given that the underlying molecular networks are highly nonlinear? (ii) A new generation of relatedness-based analyses directs us back to the nearly infinitesimal model for effect sizes that quantitative genetics was long based upon. (iii) Larger effect causal polymorphisms are often low frequency, as selection might lead us to expect. Here, we review these issues and other findings that appear to question many of the foundations of the optimism GWAS prompted. We then present a roadmap emerging as one possible future for quantitative genetics. We argue that in future GWAS should move beyond purely statistical grounds. One promising approach is to build upon the combination of population genetic models and molecular biological knowledge. This combined treatment, however, requires fitting experimental data to models that are very complex, as well as accurate capturing of the uncertainty of resulting inference. This problem can be resolved through Bayesian analysis and tools such as approximate Bayesian computation-a method growing in popularity in population genetic analysis. We show a case example of anterior-posterior segmentation in Drosophila, and argue that similar approaches will be helpful as a GWAS augmentation, in human and agricultural research.

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.

Integrating knowledge representation and quantitative modelling in physiology

A wealth of potentially shareable resources, such as data and models, is being generated through the study of physiology by computational means. Although in principle the resources generated are reusable, in practice, few can currently be shared. A key reason for this disparity stems from the lack of consistent cataloguing and annotation of these resources in a standardised manner. Here, we outline our vision for applying community-based modelling standards in support of an automated integration of models across physiological systems and scales. Two key initiatives, the Physiome Project and the European contribution - the Virtual Phsysiological Human Project, have emerged to support this multiscale model integration, and we focus on the role played by two key components of these frameworks, model encoding and semantic metadata annotation. We present examples of biomedical modelling scenarios (the endocrine effect of atrial natriuretic peptide, and the implications of alcohol and glucose toxicity) to illustrate the role that encoding standards and knowledge representation approaches, such as ontologies, could play in the management, searching and visualisation of physiology models, and thus in providing a rational basis for healthcare decisions and contributing towards realising the goal of of personalized medicine.

Bridging the genotype-phenotype gap: what does it take?

The genotype-phenotype map (GP map) concept applies to any time point in the ontogeny of a living system. It is the outcome of very complex dynamics that include environmental effects, and bridging the genotype-phenotype gap is synonymous with understanding these dynamics. The context for this understanding is physiology, and the disciplinary goals of physiology do indeed demand the physiological community to seek this understanding. We claim that this task is beyond reach without use of mathematical models that bind together genetic and phenotypic data in a causally cohesive way. We provide illustrations of such causally cohesive genotype-phenotype models where the phenotypes span from gene expression profiles to development of whole organs. Bridging the genotype-phenotype gap also demands that large-scale biological ('omics') data and associated bioinformatics resources be more effectively integrated with computational physiology than is currently the case. A third major element is the need for developing a phenomics technology way beyond current state of the art, and we advocate the establishment of a Human Phenome Programme solidly grounded on biophysically based mathematical descriptions of human physiology.

Interpreting genetic effects through models of cardiac electromechanics

Multiscale models of cardiac electromechanics are being increasingly focused on understanding how genetic variation and environment underpin multiple disease states. In this paper we review the current state of the art in both the development of specific models and the physiological insights they have produced. This growing research body includes the development of models for capturing the effects of changes in function in both single and multiple proteins in both specific expression systems and in vivo contexts. Finally, the potential for using this approach for ultimately predicting phenotypes from genetic sequence information is discussed.

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.