Threshold-dominated regulation hides genetic variation in gene expression networks

<p>Abstract</p> <p>Background</p> <p>In dynamical models with feedback and sigmoidal response functions, some or all variables have thresholds around which they regulate themselves or other variables. A mathematical analysis has shown that when the dose-response functions approach binary or on/off responses, any variable with an equilibrium value close to one of its thresholds is very robust to parameter perturbations of a homeostatic state. We denote this threshold robustness. To check the empirical relevance of this phenomenon with response function steepnesses ranging from a near on/off response down to Michaelis-Menten conditions, we have performed a simulation study to investigate the degree of threshold robustness in models for a three-gene system with one downstream gene, using several logical input gates, but excluding models with positive feedback to avoid multistationarity. Varying parameter values representing functional genetic variation, we have analysed the coefficient of variation (<it>CV</it>) of the gene product concentrations in the stable state for the regulating genes in absolute terms and compared to the <it>CV </it>for the unregulating downstream gene. The sigmoidal or binary dose-response functions in these models can be considered as phenomenological models of the aggregated effects on protein or mRNA expression rates of all cellular reactions involved in gene expression.</p> <p>Results</p> <p>For all the models, threshold robustness increases with increasing response steepness. The <it>CV</it>s of the regulating genes are significantly smaller than for the unregulating gene, in particular for steep responses. The effect becomes less prominent as steepnesses approach Michaelis-Menten conditions. If the parameter perturbation shifts the equilibrium value too far away from threshold, the gene product is no longer an effective regulator and robustness is lost. Threshold robustness arises when a variable is an active regulator around its threshold, and this function is maintained by the feedback loop that the regulator necessarily takes part in and also is regulated by. In the present study all feedback loops are negative, and our results suggest that threshold robustness is maintained by negative feedback which necessarily exists in the homeostatic state.</p> <p>Conclusion</p> <p>Threshold robustness of a variable can be seen as its ability to maintain an active regulation around its threshold in a homeostatic state despite external perturbations. The feedback loop that the system necessarily possesses in this state, ensures that the robust variable is itself regulated and kept close to its threshold. Our results suggest that threshold regulation is a generic phenomenon in feedback-regulated networks with sigmoidal response functions, at least when there is no positive feedback. Threshold robustness in gene regulatory networks illustrates that hidden genetic variation can be explained by systemic properties of the genotype-phenotype map.</p

Can we always sweep the details of RNA-processing under the carpet?

RNA molecules follow a succession of enzyme-mediated processing steps from transcription until maturation. The participating enzymes, for example the spliceosome for mRNAs and Drosha and Dicer for microRNAs, are also produced in the cell and their copy-numbers fluctuate over time. Enzyme copy-number changes affect the processing rate of the substrate molecules; high enzyme numbers increase the processing probability, low enzyme numbers decrease it. We study different RNA processing cascades where enzyme copy-numbers are either fixed or fluctuate. We find that for fixed enzyme-copy numbers the substrates at steady-state are Poisson-distributed, and the whole RNA cascade dynamics can be understood as a single birth-death process of the mature RNA product. In this case, solely fluctuations in the timing of RNA processing lead to variation in the number of RNA molecules. However, we show analytically and numerically that when enzyme copy-numbers fluctuate, the strength of RNA fluctuations increases linearly with the RNA transcription rate. This linear effect becomes stronger as the speed of enzyme dynamics decreases relative to the speed of RNA dynamics. Interestingly, we find that under certain conditions, the RNA cascade can reduce the strength of fluctuations in the expression level of the mature RNA product. Finally, by investigating the effects of processing polymorphisms we show that it is possible for the effects of transcriptional polymorphisms to be enhanced, reduced, or even reversed. Our results provide a framework to understand the dynamics of RNA processing

Arvbarhet og biologisk systemdynamikk

The concept of heritability is rooted in the observation that relatives resemble one another more than expected by chance. Narrow-sense heritability is defined as the proportion of phenotypic variance that is attributable to additive genetic variation (i.e. where an allele substitution has the same effect irrespective of the rest of the genotype), while broad-sense heritability denotes the proportion of phenotypic variance caused by genetic variation including non-additive effects. Both concepts have been highly instrumental in evolutionary biology, production biology and biomedical research for several decades. However, this successful instrumental use should not be equated with deep understanding of how underlying biology shapes narrow- and broad-sense heritability. Nor does it guarantee that these statistical definitions and associated methodology are optimally suited to deal with the recent floods of biological data. Seeking a deeper understanding of the relationship between narrow- and broad-sense heritability in terms of biological mechanisms, I simulated genetic variation in dynamic models of biological systems. A striking result was that the ratio between narrow-sense and broad-sense heritability depended strongly on the type of regulatory architecture involved. Applying the same approach to an ensemble of gene regulatory network models, I showed that monotonicity features of genotype-to-phenotype maps reveal deep connections between molecular regulatory architecture and heritability aspects; connections that do not materialize from the classical distinction between additive, dominant and epistatic gene actions. Lastly, I addressed why genome-wide association studies (GWAS) have failed to identify much of the genetic variation underlying highly heritable traits. By linking computational physiology to GWAS, one can do GWAS on lower-level phenotypes that are mathematically related to each other through a dynamic model. This allows much more precise identification of the causal genetic variation, coupled with understanding of its function.Begrepet arvbarhet gjenspeiler det faktum at slektninger jevnt over ligner mer på hverandre enn på andre individer. Arvbarhet i smal forstand defineres som andelen av fenotypisk varians som kan tilskrives additive effekter av genetisk variasjon (altså der en allel-substitusjon har samme effekt uavhengig av resten av genotypen), mens arvbarhet i vid forstand betegner den samlede andelen som skyldes både additive og ikke-additive effekter. Begge begrepene har vist seg nyttige i evolusjonsbiologi, produksjonsbiologi og biomedisinsk forskning over flere tiår. Denne nytten som verktøy er imidlertid ikke ensbetydende med dyp innsikt i hvordan de to typene av arvbarhet formes av underliggende biologi. Det er heller ikke selvsagt at disse statistisk baserte definisjonene og metodene vil være de beste til å møte dagens flom av nye biologiske data. I mitt doktorgradsarbeid har jeg belyst hvordan forholdet mellom arvbarhet i smal og vid forstand henger sammen med biologiske mekanismer, gjennom å simulere genetisk variasjon i dynamiske modeller av fysiologiske systemer. Et slående resultat var at den regulatoriske arkitekturen til systemet har mye å si for forholdstallet mellom arvbarhet i smal og vid forstand. På lignende vis studerte jeg arvbarhet i et knippe modeller av genregulatoriske nettverk med ulike grader av monotonitet i den matematiske sammenhengen mellom genotype og fenotype. Dette avdekket dype bånd mellom arvbarhetsmønstre og molekylær regulatorisk arkitektur; sammenhenger som ikke er åpenbare ut fra det klassiske skillet mellom additive, dominante og epistatiske gen-effekter. Til sist tok jeg for meg svakheter ved dagens statistiske metoder for å forklare hvordan variasjon i sterkt arvbare trekk styres av genetiske forskjeller mellom individer. Såkalte hel-genom-assosiasjons-studier (genome-wide association studies, GWAS) påviser ofte en mengde relevante loci med genetisk variasjon, men disse forklarer likevel bare en liten del av den observerte arvbarheten i overordnede trekk som f.eks. kroppshøyde eller sjukdomsforekomst. En mer lovende tilnærming er å koble matematisk fysiologi til GWAS. Jeg viser at man ved å gjøre GWAS på lavnivå-fenotyper som er matematisk forbundet gjennom en dynamisk modell, kan identifisere den årsaksbestemmende genetiske variasjonen langt mer presist og samtidig øke forståelsen av dennes funksjon

A Developmental Systems Perspective on Epistasis: Computational Exploration of Mutational Interactions in Model Developmental Regulatory Networks

The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns) depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks). Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/− feedback) and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs) epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected) networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1) the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2) the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks

Allele Interaction – Single Locus Genetics Meets Regulatory Biology

Background: Since the dawn of genetics, additive and dominant gene action in diploids have been defined by comparison of heterozygote and homozygote phenotypes. However, these definitions provide little insight into the underlying intralocus allelic functional dependency and thus cannot serve directly as a mediator between genetics theory and regulatory biology, a link that is sorely needed. Methodology/Principal Findings: We provide such a link by distinguishing between positive, negative and zero allele interaction at the genotype level. First, these distinctions disclose that a biallelic locus can display 18 qualitatively different allele interaction sign motifs (triplets of +, – and 0). Second, we show that for a single locus, Mendelian dominance is not related to heterozygote allele interaction alone, but is actually a function of the degrees of allele interaction in all the three genotypes. Third, we demonstrate how the allele interaction in each genotype is directly quantifiable in gene regulatory models, and that there is a unique, one-to-one correspondence between the sign of autoregulatory feedback loops and the sign of the allele interactions. Conclusion/Significance: The concept of allele interaction refines single locus genetics substantially, and it provides a direct link between classical models of gene action and gene regulatory biology. Together with available empirical data, our results indicate that allele interaction can be exploited experimentally to identify and explain intricate intra- and inter-locu

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

From sequence to consequence and back

AbstractThe 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

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

Incorporating Existing Network Information into Gene Network Inference

One methodology that has met success to infer gene networks from gene expression data is based upon ordinary differential equations (ODE). However new types of data continue to be produced, so it is worthwhile to investigate how to integrate these new data types into the inference procedure. One such data is physical interactions between transcription factors and the genes they regulate as measured by ChIP-chip or ChIP-seq experiments. These interactions can be incorporated into the gene network inference procedure as a priori network information. In this article, we extend the ODE methodology into a general optimization framework that incorporates existing network information in combination with regularization parameters that encourage network sparsity. We provide theoretical results proving convergence of the estimator for our method and show the corresponding probabilistic interpretation also converges. We demonstrate our method on simulated network data and show that existing network information improves performance, overcomes the lack of observations, and performs well even when some of the existing network information is incorrect. We further apply our method to the core regulatory network of embryonic stem cells utilizing predicted interactions from two studies as existing network information. We show that including the prior network information constructs a more closely representative regulatory network versus when no information is provided

Influence of Modularity and Regularity on Disparity of Atelostomata Sea Urchins

A modularity approach is used to study disparity rates and evolvability of sea urchins belonging to the Atelostomata superorder. For this purpose, the pentameric sea urchin architecture is partitioned into modular spatial components and the interference between modules is quantified using areas and a measurement of the regularity of the spatial partitions. This information is used to account for the variability through time (disparity) and potential for morphological variation and evolution (evolvability) in holasteroid echinoids. We obtain that regular partitions of the space produce modules with high modular integrity, whereas irregular partitions produce low modular integrity; the former ones are related with high morphological disparity (facilitation hypothesis). Our analysis also suggests that a pentameric body plan with low regularity rates in Atelostomata reflects a stronger modular integration among modules than within modules, which could favors bilaterality against radial symmetry. Our approach constitutes a theoretical platform to define and quantify spatial organization in partitions of the space that can be related to modules in a morphological analysis