  Constraint-based modeling has been widely used on metabolic networks
analysis, such as biosynthetic prediction and flux optimization. The linear
constraints, like mass conservation constraint, reversibility constraint,
biological capacity constraint, can be imposed on linear algorithms. However,
recently a non-linear constraint based on the second thermodynamic law, known
as "loop law", has emerged and challenged the existing algorithms. Proven to be
unfeasible with linear solutions, this non-linear constraint has been
successfully imposed on the sampling process. In this place, Monte - Carlo
sampling with Metropolis criterion and Simulated Annealing has been introduced
to optimize the Biomass synthesis of genome scale metabolic network of
Helicobacter pylori (iIT341 GSM / GPR) under mass conservation constraint,
biological capacity constraint, and thermodynamic constraints including
reversibility and "loop law". The sampling method has also been employed to
optimize a non-linear objective function, the Biomass synthetic rate, which is
unified by the total income number of reducible electrons. To verify whether a
sample contains internal loops, an automatic solution has been developed based
on solving a set of inequalities. In addition, a new type of pathway has been
proposed here, the Futile Pathway, which has three properties: 1) its mass flow
could be self-balanced; 2) it has exchange reactions; 3) it is independent to
the biomass synthesis. To eliminate the fluxes of the Futile Pathways in the
sampling results, a linear programming based method has been suggested and the
results have showed improved correlations among the reaction fluxes in the
pathways related to Biomass synthesis.
