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 $T\geq 0$ 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.
This paper serves as a framework for designing advanced models for drug action on metabolism. Drug treatment may affect metabolism by either enhancing or inhibiting metabolic reactions comprising a metabolic network. We introduce the concept of \textit{metabolic graphs}, a generalization of hypergraphs having specialized features common to metabolic networks. Linear-in-flux-expression (briefly LIFE) is a methodology for analyzing metabolic networks and simulating virtual patients. We extend LIFE dynamics to be compatible with metabolic graphs, including the more complex interactions of enhance…
Organisms have evolved a variety of mechanisms to cope with the unpredictability of environmental conditions, and yet mainstream models of metabolic regulation are typically based on strict optimality principles that do not account for uncertainty. This paper introduces a dynamic metabolic modelling framework that is a synthesis of recent ideas on resource allocation and the powerful optimal control formulation of Ramkrishna and colleagues. In particular, their work is extended based on the hypothesis that cellular resources are allocated among elementary flux modes according to the principle …
Carbon isotope labeling method is a standard metabolic engineering tool for flux quantification in living cells. To cope with the high dimensionality of isotope labeling systems, diverse algorithms have been developed to reduce the number of variables or operations in metabolic flux analysis (MFA), but lacks generalizability to non-stationary metabolic conditions. In this study, we present a stochastic simulation algorithm (SSA) derived from the chemical master equation of the isotope labeling system. This algorithm allows to compute the time evolution of isotopomer concentrations in non-stati…
A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community. Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subs…
Background: Genome-scale metabolic network models and constraint-based modeling techniques have become important tools for analyzing cellular metabolism. Thermodynamically infeasible cy-cles (TICs) causing unbounded metabolic flux ranges are often encountered. TICs satisfy the mass balance and directionality constraints but violate the second law of thermodynamics. Current prac-tices involve implementing additional constraints to ensure not only optimal but also loopless flux distributions. However, the mixed integer linear programming problems required to solve become computationally intracta…
The solution space of genome-scale models of cellular metabolism provides a map between physically viable flux configurations and cellular metabolic phenotypes described, at the most basic level, by the corresponding growth rates. By sampling the solution space of E. coli's metabolic network, we show that empirical growth rate distributions recently obtained in experiments at single-cell resolution can be explained in terms of a trade-off between the higher fitness of fast-growing phenotypes and the higher entropy of slow-growing ones. Based on this, we propose a minimal model for the evolutio…
Absolute concentration robustness (ACR) and concordance are novel concepts in the theory of robustness and stability within Chemical Reaction Network Theory. In this paper, we have extended Shinar and Feinberg's reaction network analysis approach to the insulin signaling system based on recent advances in decomposing reaction networks. We have shown that the network with 20 species, 35 complexes, and 35 reactions is concordant, implying at most one positive equilibrium in each of its stoichiometric compatibility class. We have obtained the system's finest independent decomposition consisting o…
One of the long-expected goals of genome-scale metabolic modeling is to evaluate the influence of the perturbed enzymes to the flux distribution. Both ordinary differential equation (ODE) models and the constraint-based models, like Flux balance analysis (FBA), lack of the room of performing metabolic control analysis (MCA) for large-scale networks. In this study, we developed a Hyper-Cube Shrink Algorithm (HCSA) to incorporate the enzymatic properties to the FBA model by introducing a pseudo reaction constrained by enzymatic parameters. Our algorithm was able to handle not only prediction of …
Constructing a Knowledge Base for Gene Regulatory Dynamics by Formal Concept Analysis Methods
University of Technology（德累斯顿工业大学）；Leibniz Institute for Natural Product Research and Infection Biology - Hans-Knöll-Institute (HKI)（莱布尼茨天然产物研究与感染生物学研究所——汉斯·克诺尔研究所（HKI））
Autocatalysis is a deceptively simple concept, referring to the situation that a chemical species $X$ catalyzes its own formation. From the perspective of chemical kinetics, autocatalysts show a regime of super-linear growth. Given a chemical reaction network, however, it is not at all straightforward to identify species that are autocatalytic in the sense that there is a sub-network that takes $X$ as input and produces more than one copy of $X$ as output. The difficulty arises from the need to distinguish autocatalysis e.g. from the superposition of a cycle that consumes and produces equal am…
