BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale
Fig 2
Graphical illustration of Artificial centering Metropolis sampling (AcMet) behind the BayFlux software package.
The AcMet algorithm is used to sample the phase space and find the probability for each flux profile (see Eq (1), and Algorithm 1). Each frame illustrates a step in the AcMet algorithm, shown in only two dimensions for simplicity. The black outline represents the feasible flux phase space (a polytope), as determined by the genome scale model stoichiometric matrix. 1. Center identification. Initial ‘edge points’ are identified on the edges of the flux space by minimizing and maximizing each reaction. A running average of all samples is maintained as the ‘center’ and a series of samples are taken, always moving the current point in a direction determined by the current center and one of the edge points. Once a direction is determined, a sample is chosen from the uniform distribution within the allowable bounds, and all samples are accepted. Sufficient samples are collected to obtain a stable center. 2. Metropolis sampling. Once a stable center is identified, the center is locked, and all previous samples are discarded. New proposed samples are collected in the same manner as step 1., but without updating the center. 3. Reject low probability samples. Samples are accepted or rejected probabilistically based on the ratio of the likelihood of the data given the new sample, divided by the likelihood of the data given the current sample, L(data|new sample)/L(data|current sample). All higher likelihood samples are accepted. 4. If a sample is rejected, back up a step. If a sample is rejected, it is discarded, and the sampler is moved back to the previous sample location, and records an additional sample at the previous location. 5. If a sample is accepted, continue. If a sample is accepted, it is recorded and more samples are collected, just as in step 1, but without updating the center. 6. Halt and report posterior probability. After a sufficient number of samples are collected, they are used to describe the posterior probability distribution. See Materials and methods for further details.