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Conditions for duality between fluxes and concentrations in biochemical networks Fleming, Ronan MT ; ; Thiele, Ines et al in Journal of Theoretical Biology (2016), 409(21), 1-10 Detailed reference viewed: 244 (11 UL)Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels. Christian, Nils ; Skupin, Alexander ; et al in Journal of Theoretical Biology (2014), 343 A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical ... [more ▼] A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems. [less ▲] Detailed reference viewed: 235 (22 UL)Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration. Fleming, Ronan MT ; Thiele, Ines in Journal of Theoretical Biology (2012), 314 Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one ... [more ▼] Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to mimic this forcing. We provide a general formulation to force an arbitrary large kinetic model in a manner that is still consistent with the existence of a non-equilibrium steady state. We can guarantee the existence of a non-equilibrium steady state assuming only two conditions; that every reaction is mass balanced and that continuous kinetic reaction rate laws never lead to a negative molecule concentration. These conditions can be verified in polynomial time and are flexible enough to permit one to force a system away from equilibrium. With expository biochemical examples we show how reversible, mass balanced perpetual reaction(s), with thermodynamically infeasible kinetic parameters, can be used to perpetually force various kinetic models in a manner consistent with the existence of a steady state. Easily testable existence conditions are foundational for efforts to reliably compute non-equilibrium steady states in genome-scale biochemical kinetic models. [less ▲] Detailed reference viewed: 152 (12 UL)A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks Fleming, Ronan MT ; ; et al in Journal of Theoretical Biology (2012), 292 We derive a convex optimization problem on a steady-state no nequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the ... [more ▼] We derive a convex optimization problem on a steady-state no nequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a new variational principle for biochemical networks that can be implemented in a computationally tractable manner. We derive the Lagrange dual of the optimization problem and use strong duality to demonstrate that a biochemical analogue of Tellegen’s theorem holds at optimality. Each optimal flux is dependent on a free parameter that we relate to an elementary kinetic parameter when mass action kinetics is assumed. [less ▲] Detailed reference viewed: 137 (10 UL)Two-intermediate model to characterize the structure of fast-folding proteins ; ; Jurkowski, Wiktor et al in Journal of Theoretical Biology (2011), 283(1), 60-70 This paper introduces a new model that enables researchers to conduct protein folding simulations. A two-step in silico process is used in the course of structural analysis of a set of fast-folding ... [more ▼] This paper introduces a new model that enables researchers to conduct protein folding simulations. A two-step in silico process is used in the course of structural analysis of a set of fast-folding proteins. The model assumes an early stage (ES) that depends solely on the backbone conformation, as described by its geometrical properties--specifically, by the V-angle between two sequential peptide bond planes (which determines the radius of curvature, also called R-radius, according to a second-degree polynomial form). The agreement between the structure under consideration and the assumed model is measured in terms of the magnitude of dispersion of both parameters with respect to idealized values. The second step, called late-stage folding (LS), is based on the "fuzzy oil drop" model, which involves an external hydrophobic force field described by a three-dimensional Gauss function. The degree of conformance between the structure under consideration and its idealized model is expressed quantitatively by means of the Kullback-Leibler entropy, which is a measure of disparity between the observed and expected hydrophobicity distributions. A set of proteins, representative of the fast-folding group [less ▲] Detailed reference viewed: 95 (0 UL)Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism. Fleming, Ronan MT ; Thiele, Ines ; et al in Journal of Theoretical Biology (2010), 264(3), 683-92 The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for ... [more ▼] The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis. [less ▲] Detailed reference viewed: 157 (7 UL)Stochastic modelling of the eukaryotic heat shock response Mizera, Andrzej ; in Journal of Theoretical Biology (2010), 265(3), 455466 Detailed reference viewed: 80 (2 UL)Algebraic connectivity may explain the evolution of gene regulatory networks. ; May, Patrick ; in Journal of Theoretical Biology (2010), 267(1), 7-14 Gene expression is a result of the interplay between the structure, type, kinetics, and specificity of gene regulatory interactions, whose diversity gives rise to the variety of life forms. As the dynamic ... [more ▼] Gene expression is a result of the interplay between the structure, type, kinetics, and specificity of gene regulatory interactions, whose diversity gives rise to the variety of life forms. As the dynamic behavior of gene regulatory networks depends on their structure, here we attempt to determine structural reasons which, despite the similarities in global network properties, may explain the large differences in organismal complexity. We demonstrate that the algebraic connectivity, the smallest non-trivial eigenvalue of the Laplacian, of the directed gene regulatory networks decreases with the increase of organismal complexity, and may therefore explain the difference between the variety of analyzed regulatory networks. In addition, our results point out that, for the species considered in this study, evolution favours decreasing concentration of strategically positioned feed forward loops, so that the network as a whole can increase the specificity towards changing environments. Moreover, contrary to the existing results, we show that the average degree, the length of the longest cascade, and the average cascade length of gene regulatory networks cannot recover the evolutionary relationships between organisms. Whereas the dynamical properties of special subnetworks are relatively well understood, there is still limited knowledge about the evolutionary reasons for the already identified design principles pertaining to these special subnetworks, underlying the global quantitative features of gene regulatory networks of different organisms. The behavior of the algebraic connectivity, which we show valid on gene regulatory networks extracted from curated databases, can serve as an additional evolutionary principle of organism-specific regulatory networks. [less ▲] Detailed reference viewed: 98 (2 UL)Dynamical analysis of cellular networks based on the Green's function matrix Perumal, Thanneer Malai ; ; in Journal of Theoretical Biology (2009), 261(2), 248-59 The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential ... [more ▼] The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential equations (ODEs) have commonly been used to simulate dynamical behavior of cellular networks, to which a quantitative model analysis can be applied in order to gain biological insights. In this paper, we introduce a dynamical analysis based on the use of Green's function matrix (GFM) as sensitivity coefficients with respect to initial concentrations. In contrast to the classical (parametric) sensitivity analysis, the GFM analysis gives a dynamical, molecule-by-molecule insight on how system behavior is accomplished and complementarily how (impulse) signal propagates through the network. The knowledge gained will have application from model reduction and validation to drug discovery research in identifying potential drug targets, studying drug efficacy and specificity, and optimizing drug dosing and timing. The efficacy of the method is demonstrated through applications to common network motifs and a Fas-induced programmed cell death model in Jurkat T cell line. [less ▲] Detailed reference viewed: 79 (3 UL)Metabolic networks are NP-hard to reconstruct. ; ; May, Patrick et al in Journal of Theoretical Biology (2008), 254(4), 807-16 High-throughput data from various omics and sequencing techniques have rendered the automated metabolic network reconstruction a highly relevant problem. Our approach reflects the inherent probabilistic ... [more ▼] High-throughput data from various omics and sequencing techniques have rendered the automated metabolic network reconstruction a highly relevant problem. Our approach reflects the inherent probabilistic nature of the steps involved in metabolic network reconstruction. Here, the goal is to arrive at networks which combine probabilistic information with the possibility to obtain a small number of disconnected network constituents by reduction of a given preliminary probabilistic metabolic network. We define automated metabolic network reconstruction as an optimization problem on four-partite graph (nodes representing genes, enzymes, reactions, and metabolites) which integrates: (1) probabilistic information obtained from the existing process for metabolic reconstruction from a given genome, (2) connectedness of the raw metabolic network, and (3) clustering of components in the reconstructed metabolic network. The practical implications of our theoretical analysis refer to the quality of reconstructed metabolic networks and shed light on the problem of finding more efficient and effective methods for automated reconstruction. Our main contributions include: a completeness result for the defined problem, polynomial-time approximation algorithm, and an optimal polynomial-time algorithm for trees. Moreover, we exemplify our approach by the reconstruction of the sucrose biosynthesis pathway in Chlamydomonas reinhardtii. [less ▲] Detailed reference viewed: 96 (1 UL) |
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