  Thermodynamic constraints on reactions directions are inherent in the
structure of a given biochemical network. However, concrete procedures for
determining feasible reaction directions for large-scale metabolic networks are
not well established. This work introduces a systematic approach to compute
reaction directions, which are constrained by mass balance and thermodynamics,
for genome-scale networks. In addition, it is shown that the nonconvex solution
space constrained by physicochemical constraints can be approximated by a set
of linearized subspaces in which mass and thermodynamic balance are guaranteed.
The developed methodology can be used to {\it ab initio} predict reaction
directions of genome-scale networks based solely on the network stoichoimetry.
