Obstructions to Sampling Qualitative Properties.

Background: Sampling methods have proven to be a very efficient and intuitive method to understand properties of complicated spaces that cannot easily be computed using deterministic methods. Therefore, sampling methods became a popular tool in the applied sciences.

Results: Here, we show that sampling methods are not an appropriate tool to analyze qualitative properties of complicated spaces unless RP = NP. We illustrate these results on the example of the thermodynamically feasible flux space of genome-scale metabolic networks and show that with artificial centering hit and run (ACHR) not all reactions that can have variable flux rates are sampled with variables flux rates. In particular a uniform sample of the flux space would not sample the flux variabilities completely.

Conclusion: We conclude that unless theoretical convergence results exist, qualitative results obtained from sampling methods should be considered with caution and if possible double checked using a deterministic method.