A comparison of Monte Carlo sampling methods for metabolic network models

Abstract

Reaction rates (fluxes) in a metabolic network can be analyzed using constraint-based modeling which imposes a steady state assumption on the system. In a deterministic formulation of the problem the steady state assumption has to be fulfilled exactly, and the observed fluxes are included in the model without accounting for experimental noise. One can relax the steady state constraint, and also include experimental noise in the model, through a stochastic formulation of the problem. Uniform sampling of fluxes, feasible in both the deterministic and stochastic formulation, can provide us with statistical properties of the metabolic network, such as marginal flux probability distributions. In this study we give an overview of both the deterministic and stochastic formulation of the problem, and of available Monte Carlo sampling methods for sampling the corresponding solution space. We apply the ACHR, OPTGP, CHRR and Gibbs sampling algorithms to ten metabolic networks and evaluate their convergence, consistency and efficiency. The coordinate hit-and-run with rounding (CHRR) is found to perform best among the algorithms suitable for the deterministic formulation. A desirable property of CHRR is its guaranteed distributional convergence. Among the three other algorithms, ACHR has the largest consistency with CHRR for genome scale models. For the stochastic formulation, the Gibbs sampler is the only method appropriate for sampling at genome scale. However, our analysis ranks it as less efficient than the samplers used for the deterministic formulation.

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“…We thus opted to perform further analysis only on these models. Since the basic version of flux balance analysis (FBA) is unable to provide unique solutions, we opted to analyse the activity of the observed metabolic reactions using flux sampling using the artificial centering hit-and-run (ACHR) algorithm [50] . It was performed on the models extracted with the FASTCORE algorithm to obtain the mean values of reaction fluxes in each of the models.…”

“…To assess the dynamical response of the models, we performed flux sampling using the artificial centering hit-and-run (ACHR) algorithm [50] on the extracted models. 1000 flux samples were generated for each of the models, and the mean flux of each reaction was used to identify the reactions that are either down- or up-regulated in pairwise comparisons of specific factors (diet, gender, and genotype) according to Spearman’s rank correlation.…”

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“…Despite its simplicity and the genuine uniform distribution that it provides, this algorithm cannot be used with high dimensional spaces and irregular shaped polytopes given that the fraction of rejected samples increases dramatically with the number of metabolic fluxes considered in the network. Other algorithms have been (and are still) developed to circumvent this problem [41,42]. Among the oldest and simplest methods, hit-and-run algorithms [43] consist of Markov Chain Monte Carlo methods that sample the convex polytope via some specific random walk.…”

“…Regarding these criteria, refs. [41,42] have shown that CHRR outperforms ACHR and OPTGP. Recently, refs.…”