  Assuming a steady-state condition within a cell, metabolic fluxes satisfy an
under-determined linear system of stoichiometric equations. Characterizing the
space of fluxes that satisfy such equations along with given bounds (and
possibly additional relevant constraints) is considered of utmost importance
for the understanding of cellular metabolism. Extreme values for each
individual flux can be computed with Linear Programming (as Flux Balance
Analysis), and their marginal distributions can be approximately computed with
Monte-Carlo sampling. Here we present an approximate analytic method for the
latter task based on Expectation Propagation equations that does not involve
sampling and can achieve much better predictions than other existing analytic
methods. The method is iterative, and its computation time is dominated by one
matrix inversion per iteration. With respect to sampling, we show through
extensive simulation that it has some advantages including computation time,
and the ability to efficiently fix empirically estimated distributions of
fluxes.
