Elasticity sampling links thermodynamics to metabolic control

Metabolic networks can be turned into kinetic models in a predefined steady state by sampling the reaction elasticities in this state. Elasticities for many reversible rate laws can be computed from the reaction Gibbs free energies, which are determined by the state, and from physically unconstrained saturation values. Starting from a network structure with allosteric regulation and consistent metabolic fluxes and concentrations, one can sample the elasticities, compute the control coefficients, and reconstruct a kinetic model with consistent reversible rate laws. Some of the model variables are manually chosen, fitted to data, or optimised, while the others are computed from them. The resulting model ensemble allows for probabilistic predictions, for instance, about possible dynamic behaviour. By adding more data or tighter constraints, the predictions can be made more precise. Model variants differing in network structure, flux distributions, thermodynamic forces, regulation, or rate laws can be realised by different model ensembles and compared by significance tests. The thermodynamic forces have specific effects on flux control, on the synergisms between enzymes, and on the emergence and propagation of metabolite fluctuations. Large kinetic models could help to simulate global metabolic dynamics and to predict the effects of enzyme inhibition, differential expression, genetic modifications, and their combinations on metabolic fluxes. MATLAB code for elasticity sampling is freely available

Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle

Structural Kinetic Modeling of Metabolic Networks

To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit kinetic modeling based on differential equations is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a detailed and quantitative account of the dynamical capabilities of metabolic systems, without requiring any explicit information about the particular functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible, or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a systematic statistical exploration of the comprehensive parameter space. The method is applied to two paradigmatic examples: The glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.Comment: 14 pages, 8 figures (color

Metabolic Futile Cycles and Their Functions: A Systems Analysis of Energy and Control

It has long been hypothesized that futile cycles in cellular metabolism are involved in the regulation of biochemical pathways. Following the work of Newsholme and Crabtree, we develop a quantitative theory for this idea based on open-system thermodynamics and metabolic control analysis. It is shown that the {\it stoichiometric sensitivity} of an intermediary metabolite concentration with respect to changes in steady-state flux is governed by the effective equilibrium constant of the intermediate formation, and the equilibrium can be regulated by a futile cycle. The direction of the shift in the effective equilibrium constant depends on the direction of operation of the futile cycle. High stoichiometric sensitivity corresponds to ultrasensitivity of an intermediate concentration to net flow through a pathway; low stoichiometric sensitivity corresponds to super-robustness of concentration with respect to changes in flux. Both cases potentially play important roles in metabolic regulation. Futile cycles actively shift the effective equilibrium by expending energy; the magnitude of changes in effective equilibria and sensitivities is a function of the amount of energy used by a futile cycle. This proposed mechanism for control by futile cycles works remarkably similarly to kinetic proofreading in biosynthesis. The sensitivity of the system is also intimately related to the rate of concentration fluctuations of intermediate metabolites. The possibly different roles of the two major mechanisms for cellular biochemical regulation, namely reversible chemical modifications via futile cycles and shifting equilibrium by macromolecular binding, are discussed.Comment: 11 pages, 5 figure

Enzyme economy in metabolic networks

Metabolic systems are governed by a compromise between metabolic benefit and enzyme cost. This hypothesis and its consequences can be studied by kinetic models in which enzyme profiles are chosen by optimality principles. In enzyme-optimal states, active enzymes must provide benefits: a higher enzyme level must provide a metabolic benefit to justify the additional enzyme cost. This entails general relations between metabolic fluxes, reaction elasticities, and enzyme costs, the laws of metabolic economics. The laws can be formulated using economic potentials and loads, state variables that quantify how metabolites, reactions, and enzymes affect the metabolic performance in a steady state. Economic balance equations link them to fluxes, reaction elasticities, and enzyme levels locally in the network. Economically feasible fluxes must be free of futile cycles and must lead from lower to higher economic potentials, just like thermodynamics makes them lead from higher to lower chemical potentials. Metabolic economics provides algebraic conditions for economical fluxes, which are independent of the underlying kinetic models. It justifies and extends the principle of minimal fluxes and shows how to construct kinetic models in enzyme-optimal states, where all enzymes have a positive influence on the metabolic performance

Systems approaches to modelling pathways and networks.

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