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Register a new userUncovering the hidden geometry behind metabolic networks
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Metabolism is a fascinating cell machinery underlying life and disease and genome-scale reconstructions provide us with a captivating view of its complexity. However, deciphering the relationship between metabolic structure and function remains a major challenge. In particular, turning observed structural regularities into organizing principles underlying systemic functions is a crucial task that can be significantly addressed after endowing complex network representations of metabolism with the notion of geometric distance. Here, we design a cartographic map of metabolic networks by embedding them into a simple geometry that provides a natural explanation for their observed network topology and that codifies node proximity as a measure of hidden structural similarities. We assume a simple and general connectivity law that gives more probability of interaction to metabolite/reaction pairs which are closer in the hidden space. Remarkably, we find an astonishing congruency between the architecture of E. coli and human cell metabolisms and the underlying geometry. In addition, the formalism unveils a backbone-like structure of connected biochemical pathways on the basis of a quantitative cross-talk. Pathways thus acquire a new perspective which challenges their classical view as self-contained functional units.
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An important goal of medical research is to develop methods to recover the loss of cellular function due to mutations and other defects. Many approaches based on gene therapy aim to repair the defective gene or to insert genes with compensatory function. Here, we propose an alternative, network-based strategy that aims to restore biological function by forcing the cell to either bypass the functions affected by the defective gene, or to compensate for the lost function. Focusing on the metabolism of single-cell organisms, we computationally study mutants that lack an essential enzyme, and thus are unable to grow or have a significantly reduced growth rate. We show that several of these mutants can be turned into viable organisms through additional gene deletions that restore their growth rate. In a rather counterintuitive fashion, this is achieved via additional damage to the metabolic network. Using flux balance-based approaches, we identify a number of synthetically viable gene pairs, in which the removal of one enzyme-encoding gene results in a nonviable phenotype, while the deletion of a second enzyme-encoding gene rescues the organism. The systematic network-based identification of compensatory rescue effects may open new avenues for genetic interventions.
Understanding the system level adaptive changes taking place in an organism in response to variations in the environment is a key issue of contemporary biology. Current modeling approaches such as the constraint-based flux balance analyses (FBA) have proved highly successful in analyzing the capabilities of cellular metabolism, including its capacity to predict deletion phenotypes, the ability to calculate the relative flux values of metabolic reactions and the properties of alternate optimal growth states. Here, we use FBA to thoroughly assess the activity of the Escherichia coli, Helicobacter pylori, and Saccharomyces cerevisiae metabolism in 30,000 diverse simulated environments. We identify a set of metabolic reactions forming a connected metabolic core that carry non-zero fluxes under all growth conditions, and whose flux variations are highly correlated. Furthermore, we find that the enzymes catalyzing the core reactions display a considerably higher fraction of phenotypic essentiality and evolutionary conservation than those catalyzing non-core reactions. Cellular metabolism is characterized by a large number of species-specific conditionally-active reactions organized around an evolutionary conserved always active metabolic core. Finally, we find that most current antibiotics interfering with the bacterial metabolism target the core enzymes, indicating that our findings may have important implications for antimicrobial drug target discovery.
The metabolic network of a living cell involves several hundreds or thousands of interconnected biochemical reactions. Previous research has shown that under realistic conditions only a fraction of these reactions is concurrently active in any given cell. This is partially determined by nutrient availability, but is also strongly dependent on the metabolic function and network structure. Here, we establish rigorous bounds showing that the fraction of active reactions is smaller (rather than larger) in metabolic networks evolved or engineered to optimize a specific metabolic task, and we show that this is largely determined by the presence of thermodynamically irreversible reactions in the network. We also show that the inactivation of a certain number of reactions determined by irreversibility can generate a cascade of secondary reaction inactivations that propagates through the network. The mathematical results are complemented with numerical simulations of the metabolic networks of the bacterium Escherichia coli and of human cells, which show, counterintuitively, that even the maximization of the total reaction flux in the network leads to a reduced number of active reactions.
Metabolic networks are known to be scale free but the evolutionary origin of this structural property is not clearly understood. One way of studying the dynamical process is to compare the metabolic networks of species that have arisen at different points in evolution and hence are related to each other to varying extents. We have compared the reaction sets of each metabolite across and within 15 groups of species. For a given pair of species and a given metabolite, the number $Delta k$ of reactions of the metabolite that appear in the metabolic network of only one species and not the other is a measure of the distance between the two networks. While $Delta k$ is small within groups of related species and large across groups, we find its probability distribution to be $sim (Delta k)^{-gamma}$ where $gamma$ is a universal exponent that is the same within and across groups. This exponent equals, upto statistical uncertainties, the exponent $gamma$ in the scale free degree distribution $sim k^{-gamma}$. We argue that this, as well as our finding that $Delta k$ is approximately linearly correlated with the degree $k$ of the metabolite, is evidence of a `proportionate change process in evolution. We also discuss some molecular mechanisms that might be responsible for such an evolutionary process.
We consider the problem of inferring the probability distribution of flux configurations in metabolic network models from empirical flux data. For the simple case in which experimental averages are to be retrieved, data are described by a Boltzmann-like distribution ($propto e^{F/T}$) where $F$ is a linear combination of fluxes and the `temperature parameter $Tgeq 0$ allows for fluctuations. The zero-temperature limit corresponds to a Flux Balance Analysis scenario, where an objective function ($F$) is maximized. As a test, we have inverse modeled, by means of Boltzmann learning, the catabolic core of Escherichia coli in glucose-limited aerobic stationary growth conditions. Empirical means are best reproduced when $F$ is a simple combination of biomass production and glucose uptake and the temperature is finite, implying the presence of fluctuations. The scheme presented here has the potential to deliver new quantitative insight on cellular metabolism. Our implementation is however computationally intensive, and highlights the major role that effective algorithms to sample the high-dimensional solution space of metabolic networks can play in this field.
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