MOTIVATION: Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). RESULTS: Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs. AVAILABILITY AND IMPLEMENTATION: The software is implemented in Matlab, and is provided as supplementary information . CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The field of systems biology thrives upon the use of models to organize biological knowledge and make predictions of complex processes that are hard to measure. When attempting to generate model descriptions for metabolic systems, one arrives at a crossroads. A variety of mathematical explanations are available for metabolic data with varying degrees of resolution from simple to complex. Biological modelers often rely upon subjective arguments to choose one framework over another. While there is no universal rule to determine the absolute utility of a model, certain metrics founded on information theoretical principles, demonstrate promise in providing a coherent, rational, and objective basis for addressing this model selection problem in systems biology. A model seeks to capture the regularity in biological data. Models that best capture regularity in data without excessive complexity are the most useful for applications in optimization and control. To demonstrate the efficacy of such an approach, several metabolic model selection scenarios are investigated. This work develops the argument that information theoretic model selection metrics should be extended to nonnested model comparison applications in systems biology. It also makes a novel comparison of kinetic, constraint-based, and cybernetic models of metabolism based not only on model accuracy, but also model complexity. The results show the strengths of lumped hybrid cybernetic model (L-HCM) and flux balance analysis (FBA) for applications in steady state flux prediction. Also, the hybrid cybernetic model's (HCM) merit in the modeling of dynamic changes in fluxes is also established.

In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the "off" state, and the other at the high end representing the "on" state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the "off" state and the other in the "on" state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model.