An extension to the metabolic control theory taking into account correlations between enzyme concentrations

The genotype-phenotype relationship and evolutionary genetics in the light of the Metabolic Control Analysis

Metabolic control analysis has long been used as a systemic model of the genotype-phenotype (GP) relationship. By considering kinetic parameters and enzyme concentrations as reflecting the genotype level and metabolic fluxes or pools as phenotypes related to fitness, MCA has given a biological basis to the relationship between these two levels. The non-linear and concave relationship between enzymes and fluxes can account for common genetic effects that reductionist approaches have been powerless to explain, such as the dominance of active alleles over less active alleles, the various types of epistasis and heterosis, and reveals the structural links between these genetic effects. The summation property of the flux control coefficients accounts for the L-shaped distribution of Quantitative Trait Locus (QTL) effects, irrespective of other possible causes. Metabolic models of response to selection results in evolutionary scenarios that are markedly different from those derived from the classical infinitesimal model of quantitative genetics. In particular, evolution towards selective neutrality appears to be a consequence of the diminishing return of the flux-enzyme relationship. In this paper, we survey the historical and recent achievements of MCA in genetics, quantitative genetics and evolution, focusing on epistasis and the evolution of flux in relation to enzyme concentrations.

Evolution of enzyme levels in metabolic pathways: A theoretical approach. Part 2

Metabolism is essential for cell function and adaptation. Because of their central role in metabolism, kinetic parameters and enzyme concentrations are under constant selective pressure to adapt the fluxes of the metabolic networks to the needs of the organism. In line with various studies dealing with enzyme evolution, we recently developed a model of the evolution of enzyme concentrations under selection for increased flux, considered as a proxy for fitness (Coton et al., 2022). With this model, taking into account two realistic cellular constraints, competition for resources and co-regulation, we determined the evolutionary equilibria and range of neutral variations of enzyme concentrations. In this article, we expanded this model by considering that the enzymes in a pathway can belong to different co-regulation groups. We determined the equilibria and showed that the constraints modify the adaptive landscape by limiting the number of independent dimensions. We also showed that any trade-off between enzyme concentrations is sufficient to limit the flux and relax selection for increasing the concentration of other enzymes. Even though this model is based on simplifying assumptions, the complexity of the relationship between enzyme concentrations prevents the formal analysis of the range of neutral variation of enzyme concentrations. However, we could show that selection for maximizing the flux results in selective neutrality for all enzymes regardless the constraints applied, giving generality to the prediction of Hartl et al. (1985).

Evolution of enzyme levels in metabolic pathways: A theoretical approach

The central role of metabolism in cell functioning and adaptation has given rise to countless studies on the evolution of enzyme-coding genes and network topology. However, very few studies have addressed the question of how enzyme concentrations change in response to positive selective pressure on the flux, considered a proxy of fitness. In particular, the way cellular constraints, such as resource limitations and co-regulation, affect the adaptive landscape of a pathway under selection has never been analyzed theoretically. To fill this gap, we developed a model of the evolution of enzyme concentrations that combines metabolic control theory and an adaptive dynamics approach, and integrates possible dependencies between enzyme concentrations. We determined the evolutionary equilibria of enzyme concentrations and their range of neutral variation, and showed that they differ with the properties of the enzymes, the constraints applied to the system and the initial enzyme concentrations. Simulations of long-term evolution confirmed all analytical and numerical predictions, even though we relaxed the simplifying assumptions used in the analytical treatment.

Heterosis Is a Systemic Property Emerging From Non-linear Genotype-Phenotype Relationships: Evidence From in Vitro Genetics and Computer Simulations

Heterosis, the superiority of hybrids over their parents for quantitative traits, represents a crucial issue in plant and animal breeding as well as evolutionary biology. Heterosis has given rise to countless genetic, genomic and molecular studies, but has rarely been investigated from the point of view of systems biology. We hypothesized that heterosis is an emergent property of living systems resulting from frequent concave relationships between genotypic variables and phenotypes, or between different phenotypic levels. We chose the enzyme-flux relationship as a model of the concave genotype-phenotype (GP) relationship, and showed that heterosis can be easily created in the laboratory. First, we reconstituted in vitro the upper part of glycolysis. We simulated genetic variability of enzyme activity by varying enzyme concentrations in test tubes. Mixing the content of "parental" tubes resulted in "hybrids," whose fluxes were compared to the parental fluxes. Frequent heterotic fluxes were observed, under conditions that were determined analytically and confirmed by computer simulation. Second, to test this model in a more realistic situation, we modeled the glycolysis/fermentation network in yeast by considering one input flux, glucose, and two output fluxes, glycerol and acetaldehyde. We simulated genetic variability by randomly drawing parental enzyme concentrations under various conditions, and computed the parental and hybrid fluxes using a system of differential equations. Again we found that a majority of hybrids exhibited positive heterosis for metabolic fluxes. Cases of negative heterosis were due to local convexity between certain enzyme concentrations and fluxes. In both approaches, heterosis was maximized when the parents were phenotypically close and when the distributions of parental enzyme concentrations were contrasted and constrained. These conclusions are not restricted to metabolic systems: they only depend on the concavity of the GP relationship, which is commonly observed at various levels of the phenotypic hierarchy, and could account for the pervasiveness of heterosis.

Only one health, and so many omics

The development of new approaches based on wide profiling methods in studying biological and medical systems is bringing large amounts of data on a daily basis. The causes of complex diseases have been directed to the genome examination bringing formidable knowledge. We can study genome, but also proteome, exome, transcriptome, epigenome, metabolome, and newcomers too such as microbiome, connectome and exposome. The title of this editorial is paraphrasing the famous saying of Victor Schlichter from Buenos Aires children hospital in Argentina who said "How unfair! Only one health, and so many diseases". Today there is indeed a whole lot of omics. We think that we are lucky to have all the omics possible, but we also wanted to stress the importance of future holistic approach in integrating the knowledge omics has rewarded us.

Linking post-translational modifications and variation of phenotypic traits

Enzymes can be post-translationally modified, leading to isoforms with different properties. The phenotypic consequences of the quantitative variability of isoforms have never been studied. We used quantitative proteomics to dissect the relationships between the abundances of the enzymes and isoforms of alcoholic fermentation, metabolic traits, and growth-related traits in Saccharomyces cerevisiae. Although the enzymatic pool allocated to the fermentation proteome was constant over the culture media and the strains considered, there was variation in abundance of individual enzymes and sometimes much more of their isoforms, which suggests the existence of selective constraints on total protein abundance and trade-offs between isoforms. Variations in abundance of some isoforms were significantly associated to metabolic traits and growth-related traits. In particular, cell size and maximum population size were highly correlated to the degree of N-terminal acetylation of the alcohol dehydrogenase. The fermentation proteome was found to be shaped by human selection, through the differential targeting of a few isoforms for each food-processing origin of strains. These results highlight the importance of post-translational modifications in the diversity of metabolic and life-history traits.

Sex linkage, sex-specific selection, and the role of recombination in the evolution of sexually dimorphic gene expression

Sex-biased genes--genes that are differentially expressed within males and females--are nonrandomly distributed across animal genomes, with sex chromosomes and autosomes often carrying markedly different concentrations of male- and female-biased genes. These linkage patterns are often gene- and lineage-dependent, differing between functional genetic categories and between species. Although sex-specific selection is often hypothesized to shape the evolution of sex-linked and autosomal gene content, population genetics theory has yet to account for many of the gene- and lineage-specific idiosyncrasies emerging from the empirical literature. With the goal of improving the connection between evolutionary theory and a rapidly growing body of genome-wide empirical studies, we extend previous population genetics theory of sex-specific selection by developing and analyzing a biologically informed model that incorporates sex linkage, pleiotropy, recombination, and epistasis, factors that are likely to vary between genes and between species. Our results demonstrate that sex-specific selection and sex-specific recombination rates can generate, and are compatible with, the gene- and species-specific linkage patterns reported in the genomics literature. The theory suggests that sexual selection may strongly influence the architectures of animal genomes, as well as the chromosomal distribution of fixed substitutions underlying sexually dimorphic traits.

Systemic properties of metabolic networks lead to an epistasis-based model for heterosis

The genetic and molecular approaches to heterosis usually do not rely on any model of the genotype-phenotype relationship. From the generalization of Kacser and Burns' biochemical model for dominance and epistasis to networks with several variable enzymes, we hypothesized that metabolic heterosis could be observed because the response of the flux towards enzyme activities and/or concentrations follows a multi-dimensional hyperbolic-like relationship. To corroborate this, we used the values of systemic parameters accounting for the kinetic behaviour of four enzymes of the upstream part of glycolysis, and simulated genetic variability by varying in silico enzyme concentrations. Then we "crossed" virtual parents to get 1,000 hybrids, and showed that best-parent heterosis was frequently observed. The decomposition of the flux value into genetic effects, with the help of a novel multilocus epistasis index, revealed that antagonistic additive-by-additive epistasis effects play the major role in this framework of the genotype-phenotype relationship. This result is consistent with various observations in quantitative and evolutionary genetics, and provides a model unifying the genetic effects underlying heterosis.

DATE analysis: A general theory of biological change applied to microarray data

In contrast to conventional data mining, which searches for specific subsets of genes (extensive variables) to correlate with specific phenotypes, DATE analysis correlates intensive state variables calculated from the same datasets. At the heart of DATE analysis are two biological equations of state not dependent on genetic pathways. This result distinguishes DATE analysis from other bioinformatics approaches. The dimensionless state variable F quantifies the relative overall cellular activity of test cells compared to well-chosen reference cells. The variable pi(i) is the fold-change in the expression of the ith gene of test cells relative to reference. It is the fraction phi of the genome undergoing differential expression-not the magnitude pi-that controls biological change. The state variable phi is equivalent to the control strength of metabolic control analysis. For tractability, DATE analysis assumes a linear system of enzyme-connected networks and exploits the small average contribution of each cellular component. This approach was validated by reproducible values of the state variables F, RNA index, and phi calculated from random subsets of transcript microarray data. Using published microarray data, F, RNA index, and phi were correlated with: (1) the blood-feeding cycle of the malaria parasite, (2) embryonic development of the fruit fly, (3) temperature adaptation of Killifish, (4) exponential growth of cultured S. pneumoniae, and (5) human cancers. DATE analysis was applied to aCGH data from the great apes. A good example of the power of DATE analysis is its application to genomically unstable cancers, which have been refractory to data mining strategies.

Simplified modelling of metabolic pathways for flux prediction and optimization: lessons from an in vitro reconstruction of the upper part of glycolysis

Explicit modelling of metabolic networks relies on well-known mathematical tools and specialized computer programs. However, identifying and estimating the values of the very numerous enzyme parameters inherent to the models remain a tedious and difficult task, and the rate equations of the reactions are usually not known in sufficient detail. A way to circumvent this problem is to use 'non-mechanistic' models, which may account for the behaviour of the systems with a limited number of parameters. Working on the first part of glycolysis reconstituted in vitro, we showed how to derive, from titration experiments, values of effective enzyme activity parameters that do not include explicitly any of the classical kinetic constants. With a maximum of only two parameters per enzyme, this approach produced very good estimates for the flux values, and enabled us to determine the optimization conditions of the system, i.e. to calculate the set of enzyme concentrations that maximizes the flux. This fast and easy method should be valuable in the context of integrative biology or for metabolic engineering, where the challenge is to deal with the dramatic increase in the number of parameters when the systems become complex.