Flux balance analysis with or without molecular crowding fails to predict two thirds of experimentally observed epistasis in yeast.

Computational predictions of double gene knockout effects by flux balance analysis (FBA) have been used to characterized genome-wide patterns of epistasis in microorganisms. However, it is unclear how in silico predictions are related to in vivo epistasis, as FBA predicted only a minority of experimentally observed genetic interactions between non-essential metabolic genes in yeast. Here, we perform a detailed comparison of yeast experimental epistasis data to predictions generated with different constraint-based metabolic modeling algorithms. The tested methods comprise standard FBA; a variant of MOMA, which was specifically designed to predict fitness effects of non-essential gene knockouts; and two alternative implementations of FBA with macro-molecular crowding, which account approximately for enzyme kinetics. The number of interactions uniquely predicted by one method is typically larger than its overlap with any alternative method. Only 20% of negative and 10% of positive interactions jointly predicted by all methods are confirmed by the experimental data; almost all unique predictions appear to be false. More than two thirds of epistatic interactions are undetectable by any of the tested methods. The low prediction accuracies indicate that the physiology of yeast double metabolic gene knockouts is dominated by processes not captured by current constraint-based analysis methods.

Machine learning applied to enzyme turnover numbers reveals protein structural correlates and improves metabolic models.

Knowing the catalytic turnover numbers of enzymes is essential for understanding the growth rate, proteome composition, and physiology of organisms, but experimental data on enzyme turnover numbers is sparse and noisy. Here, we demonstrate that machine learning can successfully predict catalytic turnover numbers in Escherichia coli based on integrated data on enzyme biochemistry, protein structure, and network context. We identify a diverse set of features that are consistently predictive for both in vivo and in vitro enzyme turnover rates, revealing novel protein structural correlates of catalytic turnover. We use our predictions to parameterize two mechanistic genome-scale modelling frameworks for proteome-limited metabolism, leading to significantly higher accuracy in the prediction of quantitative proteome data than previous approaches. The presented machine learning models thus provide a valuable tool for understanding metabolism and the proteome at the genome scale, and elucidate structural, biochemical, and network properties that underlie enzyme kinetics.

Alleles of a gene differ in pleiotropy, often mediated through currency metabolite production, in E. coli and yeast metabolic simulations.

A major obstacle to the mapping of genotype-phenotype relationships is pleiotropy, the tendency of mutations to affect seemingly unrelated traits. Pleiotropy has major implications for evolution, development, ageing, and disease. Except for disease data, pleiotropy is almost exclusively estimated from full gene knockouts. However, most deleterious alleles segregating in natural populations do not fully abolish gene function, and the degree to which a polymorphism reduces protein function may influence the number of traits it affects. Utilizing genome-scale metabolic models for Escherichia coli and Saccharomyces cerevisiae, we show that most fitness-reducing full gene knockouts of metabolic genes in these fast-growing microbes have pleiotropic effects, i.e., they compromise the production of multiple biomass components. Alleles of the same metabolic enzyme-encoding gene with increasingly reduced enzymatic function typically affect an increasing number of biomass components. This increasing pleiotropy is often mediated through effects on the generation of currency metabolites such as ATP or NADPH. We conclude that the physiological effects observed in full gene knockouts of metabolic genes will in most cases not be representative for alleles with only partially reduced enzyme capacity or expression level.

CycleFreeFlux: efficient removal of thermodynamically infeasible loops from flux distributions.

MOTIVATION: Constraint-based metabolic modeling methods such as Flux Balance Analysis (FBA) are routinely used to predict metabolic phenotypes, e.g. growth rates, ATP yield or the fitness of gene knockouts. One frequent difficulty of constraint-based solutions is the inclusion of thermodynamically infeasible loops (or internal cycles), which add nonbiological fluxes to the predictions. RESULTS: We propose a simple postprocessing of constraint-based solutions, which removes internal cycles from any given flux distribution [Formula: see text] without disturbing other fluxes not involved in the loops. This new algorithm, termed CycleFreeFlux, works by minimizing the sum of absolute fluxes [Formula: see text] while (i) conserving the exchange fluxes and (ii) using the fluxes of the original solution to bound the new flux distribution. This strategy reduces internal fluxes until at least one reaction of every possible internal cycle is inactive, a necessary and sufficient condition for the thermodynamic feasibility of a flux distribution. If alternative representations of the input flux distribution in terms of elementary flux modes exist that differ in their inclusion of internal cycles, then CycleFreeFlux is biased towards solutions that maintain the direction given by [Formula: see text] and towards solutions with lower total flux [Formula: see text]. Our method requires only one additional linear optimization, making it computationally very efficient compared to alternative strategies. AVAILABILITY AND IMPLEMENTATION: We provide freely available R implementations for the enumeration of thermodynamically infeasible cycles as well as for cycle-free FBA solutions, flux variability calculations and random sampling of solution spaces. CONTACT: lercher@cs.uni-duesseldorf.de.

Sybil--efficient constraint-based modelling in R.

BACKGROUND: Constraint-based analyses of metabolic networks are widely used to simulate the properties of genome-scale metabolic networks. Publicly available implementations tend to be slow, impeding large scale analyses such as the genome-wide computation of pairwise gene knock-outs, or the automated search for model improvements. Furthermore, available implementations cannot easily be extended or adapted by users. RESULTS: Here, we present sybil, an open source software library for constraint-based analyses in R; R is a free, platform-independent environment for statistical computing and graphics that is widely used in bioinformatics. Among other functions, sybil currently provides efficient methods for flux-balance analysis (FBA), MOMA, and ROOM that are about ten times faster than previous implementations when calculating the effect of whole-genome single gene deletions in silico on a complete E. coli metabolic model. CONCLUSIONS: Due to the object-oriented architecture of sybil, users can easily build analysis pipelines in R or even implement their own constraint-based algorithms. Based on its highly efficient communication with different mathematical optimisation programs, sybil facilitates the exploration of high-dimensional optimisation problems on small time scales. Sybil and all its dependencies are open source. Sybil and its documentation are available for download from the comprehensive R archive network (CRAN).