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Register a new userFlux distribution in metabolic networks close to optimal biomass production
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Ginestra Bianconi
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We study a statistical model describing the steady state distribution of the fluxes in a metabolic network. The resulting model on continuous variables can be solved by the cavity method. In particular analytical tractability is possible solving the cavity equation over an ensemble of networks with the same degree distribution of the real metabolic network. The flux distribution that optimizes production of biomass has a fat tail with a power-law exponent independent on the structural properties of the underling network. These results are in complete agreement with the Flux-Balance-Analysis outcome of the same system and in qualitative agreement with the experimental results.
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A metabolic model can be represented as bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualisation of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae, and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for the other organisms.
We cast the metabolism of interacting cells within a statistical mechanics framework considering both, the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of high-dimensional spin vectors, whose values will be constrained by the stochiometry and the energy requirements of the metabolism. Within this picture, finding the phenotypic states of the population turns out to be equivalent to searching for the equilibrium states of a disordered spin model. We provide a general solution of this problem for arbitrary metabolic networks and interactions. We apply this solution to a simplified model of metabolism and to a complex metabolic network, the central core of the emph{E. coli}, and demonstrate that the combination of selective pressure and interactions define a complex phenotypic space. Cells may specialize in producing or consuming metabolites complementing each other at the population level and this is described by an equilibrium phase space with multiple minima, like in a spin-glass model.
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.
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.
In a recent paper [C. Marr, M. Mueller-Linow, and M.-T. Huett, Phys. Rev. E 75, 041917 (2007)] we discuss the pronounced potential of real metabolic network topologies, compared to randomized counterparts, to regularize complex binary dynamics. In their comment [P. Holme and M. Huss, arXiv:0705.4084v1], Holme and Huss criticize our approach and repeat our study with more realistic dynamics, where stylized reaction kinetics are implemented on sets of pairwise reactions. The authors find no dynamic difference between the reaction sets recreated from the metabolic networks and randomized counterparts. We reproduce the authors observation and find that their algorithm leads to a dynamical fragmentation and thus eliminates the topological information contained in the graphs. Hence, their approach cannot rule out a connection between the topology of metabolic networks and the ubiquity of steady states.
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