  As a widely used method in metabolic network studies, Monte-Carlo sampling in
the steady state flux space is known for its flexibility and convenience of
carrying out different purposes, simply by alternating constraints or objective
functions, or appending post processes. Recently the concept of a non-linear
constraint based on the second thermodynamic law, known as "Loop Law", is
challenging current sampling algorithms which will inevitably give rise to the
internal loops. A generalized method is proposed here to eradicate the
probability of the appearance of internal loops during sampling process. Based
on Artificial Centered Hit and Run (ACHR) method, each step of the new sampling
process will avoid entering "loop-forming" subspaces. This method has been
applied on the metabolic network of Helicobacter pylori with three different
objective functions: uniform sampling, optimizing biomass synthesis, optimizing
biomass synthesis efficiency over resources ingested. Comparison between
results from the new method and conventional ACHR method shows effective
elimination of loop fluxes without affecting non-loop fluxes.
