Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration.

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.

Quantitative assignment of reaction directionality in a multicompartmental human metabolic reconstruction.

Reaction directionality is a key constraint in the modeling of genome-scale metabolic networks. We thermodynamically constrained reaction directionality in a multicompartmental genome-scale model of human metabolism, Recon 1, by calculating, in vivo, standard transformed reaction Gibbs energy as a function of compartment-specific pH, electrical potential, and ionic strength. We show that compartmental pH is an important determinant of thermodynamically determined reaction directionality. The effects of pH on transport reaction thermodynamics are only seen to their full extent when metabolites are represented as pseudoisomer groups of multiple protonated species. We accurately predict the irreversibility of 387 reactions, with detailed propagation of uncertainty in input data, and manually curate the literature to resolve conflicting directionality assignments. In at least half of all cases, a prediction of a reversible reaction directionality is due to the paucity of compartment-specific quantitative metabolomic data, with remaining cases due to uncertainty in estimation of standard reaction Gibbs energy. This study points to the pressing need for 1), quantitative metabolomic data, and 2), experimental measurement of thermochemical properties for human metabolites.

A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks.

We derive a convex optimization problem on a steady-state nonequilibrium 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.

Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism.

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.

Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide.

Biochemical network reconstructions have become popular tools in systems biology. Metabolicnetwork reconstructions are biochemically, genetically, and genomically (BiGG) structured databases of biochemical reactions and metabolites. They contain information such as exact reaction stoichiometry, reaction reversibility, and the relationships between genes, proteins, and reactions. Network reconstructions have been used extensively to study the phenotypic behavior of wild-type and mutant stains under a variety of conditions, linking genotypes with phenotypes. Such phenotypic simulations have allowed for the prediction of growth after genetic manipulations, prediction of growth phenotypes after adaptive evolution, and prediction of essential genes. Additionally, because network reconstructions are organism specific, they can be used to understand differences between organisms of species in a functional context.There are different types of reconstructions representing various types of biological networks (metabolic, regulatory, transcription/translation). This chapter serves as an introduction to metabolic and regulatory network reconstructions and models and gives a complete description of the core Escherichia coli metabolic model. This model can be analyzed in any computational format (such as MATLAB or Mathematica) based on the information given in this chapter. The core E. coli model is a small-scale model that can be used for educational purposes. It is meant to be used by senior undergraduate and first-year graduate students learning about constraint-based modeling and systems biology. This model has enough reactions and pathways to enable interesting and insightful calculations, but it is also simple enough that the results of such calculations can be understoodeasily.

Quantitative assignment of reaction directionality in constraint-based models of metabolism: application to Escherichia coli.

Constraint-based modeling is an approach for quantitative prediction of net reaction flux in genome-scale biochemical networks. In vivo, the second law of thermodynamics requires that net macroscopic flux be forward, when the transformed reaction Gibbs energy is negative. We calculate the latter by using (i) group contribution estimates of metabolite species Gibbs energy, combined with (ii) experimentally measured equilibrium constants. In an application to a genome-scale stoichiometric model of Escherichia coli metabolism, iAF1260, we demonstrate that quantitative prediction of reaction directionality is increased in scope and accuracy by integration of both data sources, transformed appropriately to in vivo pH, temperature and ionic strength. Comparison of quantitative versus qualitative assignment of reaction directionality in iAF1260, assuming an accommodating reactant concentration range of 0.02-20mM, revealed that quantitative assignment leads to a low false positive, but high false negative, prediction of effectively irreversible reactions. The latter is partly due to the uncertainty associated with group contribution estimates. We also uncovered evidence that the high intracellular concentration of glutamate in E. coli may be essential to direct otherwise thermodynamically unfavorable essential reactions, such as the leucine transaminase reaction, in an anabolic direction.