Markov-chain Monte Carlo sampling (MCMC)

General concept

FBA-related methods are biased in that the author dictates a priori what the cell will do. However, unbiased methods like EFM and extreme pathway analysis cannot be used on genome scale models. MCMC sampling allows one to sample all feasible flux states for an organism.

Items to consider when implementing

In MCMC sampling, a non-uniform set of feasible flux distributions are selected and then iteratively moved throughout the solution space. It is essential to verify that the distribution of points converge upon a well-mixed state. Otherwise the sample points will not represent a uniform sampling of the solution space. This has been discussed in Bordbar, et al., Lewis, et al., and [ Schellenberger, et al.].

As sample points are randomly mixed in the solution space, mixing can be hindered by small step sizes if sample points are in tight corners of the solution space. This phenomenon is discussed in Li, et al.

Software packages with this method

Applications of interest

Thiele, et al. (2005) presented an algorithmic improvement using artificially-centered hit and run (ACHR sampling) to study the effects of several diseased in the cardiac mitochondrion.

Li, et al. (2009) showed that without a lower bound on biomass, the predicted growth rate initially decreases linearly while sample points mix, if they start from a point above the median growth rate from a well-sampled model. In addition, they coupled MCMC sampling with a model that balances noise with growth rate selection in evolving strains and showed that this modeled sub-optimal growth.

Bordbar, et al. (2010) used MCMC sampling to study how flux changes in tuberculosis after infecting a macrophage.

Lewis, et al. (2010) used MCMC sampling to study cell-type and brain region specific cell death in neurons and astrocytes in Alzheimer's disease.

Schellenberger, et al. (2011) presented a method, called ll-sampling to remove sample points from areas of the solution space that contain loop flux. While this method eliminates loop flux in sample points, it does not maintain sample uniformity.

Relevant references

Almaas E, Kovács B, Vicsek T, Oltvai ZN, Barabási AL. Global organization of metabolic fluxes in the bacterium Escherichia coli. Nature. 2004 Feb 26;427(6977):839-43.

Thiele I, Price ND, Vo TD, Palsson BØ. Candidate metabolic network states in human mitochondria. Impact of diabetes, ischemia, and diet. J Biol Chem. 2005 Mar 25;280(12):11683-95.

Li ZY, Xie ZW, Chen T, Ouyang Q. Noise effect in metabolic networks. Chinese Phys. B. 2009;18:5544.

Bordbar A, Lewis NE, Schellenberger J, Palsson BØ, Jamshidi N. Insight into human alveolar macrophage and M. tuberculosis interactions via metabolic reconstructions. Mol Syst Biol. 2010 Oct 19;6:422.

Lewis NE, Schramm G, Bordbar A, Schellenberger J, Andersen MP, Cheng JK, Patel N, Yee A, Lewis RA, Eils R, König R, Palsson BØ. Large-scale in silico modeling of metabolic interactions between cell types in the human brain. Nat Biotechnol. 2010 Dec;28(12):1279-85.

Schellenberger J, Lewis NE, Palsson BØ.Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophys J. 2011 Feb 2;100(3):544-53.

Related methods

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