We examine an application of the Gillespie algorithm to simulating spatially inhomogeneous reaction-diffusion systems in mesoscopic volumes such as cells and microchambers. The method involves discretizing the chamber into elements and modeling the diffusion of chemical species by the movement of molecules between neighboring elements. These transitions are expressed in the form of a set of reactions which are added to the chemical system. The derivation of the rates of these diffusion reactions is by comparison with a finite volume discretization of the heat equation on an unevenly spaced grid. The diffusion coefficient of each species is allowed to be inhomogeneous in space, including discontinuities. The resulting system is solved by the Gillespie algorithm using the fast direct method. We show that in an appropriate limit the method reproduces exact solutions of the heat equation for a purely diffusive system and the nonlinear reaction-rate equation describing the cubic autocatalytic reaction.

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BackgroundEnteric Escherichia coli survives the highly acidic environment of the stomach through multiple acid resistance (AR) mechanisms. The most effective system, AR2, decarboxylates externally-derived glutamate to remove cytoplasmic protons and excrete GABA. The first described system, AR1, does not require an external amino acid. Its mechanism has not been determined. The regulation of the multiple AR systems and their coordination with broader cellular metabolism has not been fully explored.ResultsWe utilized a combination of ChIP-Seq and gene expression analysis to experimentally map the regulatory interactions of four TFs: nac, ntrC, ompR, and csiR. Our data identified all previously in vivo confirmed direct interactions and revealed several others previously inferred from gene expression data. Our data demonstrate that nac and csiR directly modulate AR, and leads to a regulatory network model in which all four TFs participate in coordinating acid resistance, glutamate metabolism, and nitrogen metabolism. This model predicts a novel mechanism for AR1 by which the decarboxylation enzymes of AR2 are used with internally derived glutamate. This hypothesis makes several testable predictions that we confirmed experimentally.ConclusionsOur data suggest that the regulatory network underlying AR is complex and deeply interconnected with the regulation of GABA and glutamate metabolism, nitrogen metabolism. These connections underlie and experimentally validated model of AR1 in which the decarboxylation enzymes of AR2 are used with internally derived glutamate.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0376-y) contains supplementary material, which is available to authorized users.

The reconstruction and analysis of genome-scale metabolic models constitutes a powerful systems biology approach, with applications ranging from basic understanding of genotype-phenotype mapping to solving biomedical and environmental problems. However, the biological insight obtained from these models is limited by multiple heterogeneous sources of uncertainty, which are often difficult to quantify. Here we review the major sources of uncertainty and survey existing approaches developed for representing and addressing them. A unified formal characterization of these uncertainties through probabilistic approaches and ensemble modeling will facilitate convergence towards consistent reconstruction pipelines, improved data integration algorithms, and more accurate assessment of predictive capacity.

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