Department of Mathematics, University of Bergen, Bergen, Norway.
PLoS One. 2020 Jul 1;15(7):e0235393. doi: 10.1371/journal.pone.0235393. eCollection 2020.
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.
反应速率（通量）在代谢网络中可以使用约束建模进行分析，该方法对系统施加稳态假设。在问题的确定性表述中，必须严格满足稳态假设，并且观察到的通量包含在模型中，而不考虑实验噪声。可以通过问题的随机表述来放宽稳态约束，并将实验噪声纳入模型。通量的均匀采样在确定性和随机表述中都是可行的，可以为我们提供代谢网络的统计特性，例如边际通量概率分布。在这项研究中，我们概述了问题的确定性和随机表述，以及用于采样相应解空间的可用蒙特卡罗采样方法。我们将 ACHR、OPTGP、CHRR 和吉布斯采样算法应用于十个代谢网络，并评估它们的收敛性、一致性和效率。坐标命中和运行（CHRR）算法在适合确定性表述的算法中表现最佳。CHRR 的一个理想特性是其有保证的分布收敛性。在其他三个算法中，ACHR 与 CHRR 的一致性最大，适用于基因组规模的模型。对于随机表述，吉布斯采样器是唯一适合在基因组规模上采样的方法。然而，我们的分析将其排在用于确定性表述的采样器之后，认为它效率较低。
