Du, B. | Search bioRxiv

bioRxiv2018

Temperature-dependent estimation of Gibbs energies using an updated group contribution method

Reaction equilibrium constants determine the mass action ratios necessary to drive flux through metabolic pathways. Group contribution methods offer a way to estimate reaction equilibrium constants at wide coverage across the metabolic network. Here, we present an updated group contribution method with: 1) additional curated thermodynamic data used in fitting; and 2) capabilities to calculate equilibrium constants as a function of temperature. We first collected and curated aqueous thermo-dynamic data, including reaction equilibrium constants, enthalpies of reaction, Gibbs free energies of formation, enthalpies of formation, entropies change of formation of compounds, and proton and metal ion binding constants. We further estimated magnesium binding constants for 618 compounds using a linear regression model validated against measured data. Next, we formulated the calculation of equilibrium constants as a function of temperature and calculated necessary parameters, including standard entropy change of formation ({Delta}f S{circ}) and standard entropy change of reaction ({Delta}rS{circ}), using a model based on molecular properties. The median absolute errors in estimating {Delta}f S{circ} and {Delta}rS{circ} were 0.010 kJ/K/mol and 0.018 kJ/K/mol, respectively. The efforts here fill in gaps for thermodynamic calculations under various conditions, specifically different temperatures and metal ion concentrations. These results support the study of thermodynamic driving forces underlying the metabolic function of organisms living under diverse conditions.

biophysics↗

bioRxiv2017

Topological and Kinetic Determinants of the Modal Matrices of Dynamic Models of Metabolism

Linear analysis of kinetic models of metabolism can help in understanding the dynamic response of metabolic networks. Central to linear analysis of these models are two key matrices: the Jacobian matrix (J) and its modal matrix (M-1). The modal matrix contains dynamically independent motions of the kinetic model, and it is sparse in practice. Understanding the sparsity structure of the modal matrix provides insight into metabolic network dynamics. In this study, we analyze the relationship between J and M-1. First, we show that diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures within M-1. Dominant diagonal elements in J approximate the eigenvalues corresponding to these simple modes, in which a single metabolite is driven back to its reference state on a characteristic timescale. Second, we analyze more complicated mode structures in M-1, in which two or more variables move in a certain ratio relative to one another on defined time scales. We show that complicated modes originate from sub-matrices of topologically connected elements of similar magnitude in J. Third, we describe the origin of these mode structure features based on the network stoichiometric matrix S and the reaction kinetic gradient matrix G. We demonstrate that the topologically-connected reaction sensitivities of similar magnitude in G play a central role in determining the mode structure. Ratios of these reaction sensitivities represent equilibrium balances of half reactions that are defined by linearization of the bilinear mass action rate laws followed by enzymatic reactions. These half-reaction equilibrium ratios are key determinants of modal structure for both simple and complicated modes. The work presented here helps to establish a foundation for understanding the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions.

systems biology↗