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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.

SUBMITTER: Fallahi S

PROVIDER: S-EPMC7329079 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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A comparison of Monte Carlo sampling methods for metabolic network models.

Fallahi Shirin S Skaug Hans J HJ Alendal Guttorm G

PloS one 20200701 7

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 samp ...[more]

PMID: 32609776

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Project description:In diffusion MRI analysis, advances in biophysical multi-compartment modeling have gained popularity over the conventional Diffusion Tensor Imaging (DTI), because they can obtain a greater specificity in relating the dMRI signal to underlying cellular microstructure. Biophysical multi-compartment models require a parameter estimation, typically performed using either the Maximum Likelihood Estimation (MLE) or the Markov Chain Monte Carlo (MCMC) sampling. Whereas, the MLE provides only a point estimate of the fitted model parameters, the MCMC recovers the entire posterior distribution of the model parameters given in the data, providing additional information such as parameter uncertainty and correlations. MCMC sampling is currently not routinely applied in dMRI microstructure modeling, as it requires adjustment and tuning, specific to each model, particularly in the choice of proposal distributions, burn-in length, thinning, and the number of samples to store. In addition, sampling often takes at least an order of magnitude, more time than non-linear optimization. Here we investigate the performance of the MCMC algorithm variations over multiple popular diffusion microstructure models, to examine whether a single, well performing variation could be applied efficiently and robustly to many models. Using an efficient GPU-based implementation, we showed that run times can be removed as a prohibitive constraint for the sampling of diffusion multi-compartment models. Using this implementation, we investigated the effectiveness of different adaptive MCMC algorithms, burn-in, initialization, and thinning. Finally we applied the theory of the Effective Sample Size, to the diffusion multi-compartment models, as a way of determining a relatively general target for the number of samples needed to characterize parameter distributions for different models and data sets. We conclude that adaptive Metropolis methods increase MCMC performance and select the Adaptive Metropolis-Within-Gibbs (AMWG) algorithm as the primary method. We furthermore advise to initialize the sampling with an MLE point estimate, in which case 100 to 200 samples are sufficient as a burn-in. Finally, we advise against thinning in most use-cases and as a relatively general target for the number of samples, we recommend a multivariate Effective Sample Size of 2,200.

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A comparison of Monte Carlo sampling methods for metabolic network models.

Publications

A comparison of Monte Carlo sampling methods for metabolic network models.

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