Characterizing the capabilities, criticalities and response to perturbations of genome-scale metabolic networks is a basic problem with important applications. A key question concerns the identification of the potentially most harmful knockouts. The
integration of combinatorial methods with sampling techniques to explore the space of viable flux states may provide crucial insights on this issue. We assess the replaceability of every metabolic conversion in the human red blood cell by enumerating the alternative paths from substrate to product, obtaining a complete map of the potential damage of single enzymopathies. Sampling the space of optimal flux states in the healthy and in the mutated cell reveals both correlations and complementarity between topologic and dynamical aspects.
Understanding the organization of reaction fluxes in cellular metabolism from the stoichiometry and the topology of the underlying biochemical network is a central issue in systems biology. In this task, it is important to devise reasonable approxima
tion schemes that rely on the stoichiometric data only, because full-scale kinetic approaches are computationally affordable only for small networks (e.g. red blood cells, about 50 reactions). Methods commonly employed are based on finding the stationary flux configurations that satisfy mass-balance conditions for metabolites, often coupling them to local optimization rules (e.g. maximization of biomass production) to reduce the size of the solution space to a single point. Such methods have been widely applied and have proven able to reproduce experimental findings for relatively simple organisms in specific conditions. Here we define and study a constraint-based model of cellular metabolism where neither mass balance nor flux stationarity are postulated, and where the relevant flux configurations optimize the global growth of the system. In the case of E. coli, steady flux states are recovered as solutions, though mass-balance conditions are violated for some metabolites, implying a non-zero net production of the latter. Such solutions furthermore turn out to provide the correct statistics of fluxes for the bacterium E. coli in different environments and compare well with the available experimental evidence on individual fluxes. Conserved metabolic pools play a key role in determining growth rate and flux variability. Finally, we are able to connect phenomenological gene essentiality with `frozen fluxes (i.e. fluxes with smaller allowed variability) in E. coli metabolism.
We study a simplified, solvable model of a fully-connected metabolic network with constrained quenched disorder to mimic the conservation laws imposed by stoichiometry on chemical reactions. Within a spin-glass type of approach, we show that in prese
nce of a conserved metabolic pool the flux state corresponding to maximal growth is stationary independently of the pool size. In addition, and at odds with the case of unconstrained networks, the volume of optimal flux configurations remains finite, indicating that the frustration imposed by stoichiometric constraints, while reducing growth capabilities, confers robustness and flexibility to the system. These results have a clear biological interpretation and provide a basic, fully analytical explanation to features recently observed in real metabolic networks.
We explore the effect of discounting and experimentation in a simple model of interacting adaptive agents. Agents belong to either of two types and each has to decide whether to participate a game or not, the game being profitable when there is an ex
cess of players of the other type. We find the emergence of large fluctuations as a result of the onset of a dynamical instability which may arise discontinuously (increasing the discount factor) or continuously (decreasing the experimentation rate). The phase diagram is characterized in detail and noise amplification close to a bifurcation point is identified as the physical mechanism behind the instability.
