Figure 4:
Solution spaces from steady state fluxes are anisotropic, that is, long in some directions and short in others. This impedes the ability of any sampling algorithm taking a random direction to evenly explore the full feasible set (artificial centering hit-and-run (ACHR) algorithm). The CHRR (coordinate hit-and-run with rounding) algorithm first rounds the solution space based on the maximum volume ellipsoid. Then, the rounded solution space is uniformly sampled using a provably efficient coordinate hit-and-run random walk. Finally, the samples are projected back onto the anisotropic feasible set. This leads to a more distributed uniform sampling, so that the converged sampling distributions for the selected reactions become smoother. As an example, for both sampling distributions, the parameters were defined as: nSkip = 8 × (dim(fluxSpace))2, nSarnples = 1000.