  Model-based prediction of stochastic noise in biomolecular reactions often
resorts to approximation with unknown precision. As a result, unexpected
stochastic fluctuation causes a headache for the designers of biomolecular
circuits. This paper proposes a convex optimization approach to quantifying the
steady state moments of molecular copy counts with theoretical rigor. We show
that the stochastic moments lie in a convex semi-algebraic set specified by
linear matrix inequalities. Thus, the upper and the lower bounds of some
moments can be computed by a semidefinite program. Using a protein dimerization
process as an example, we demonstrate that the proposed method can precisely
predict the mean and the variance of the copy number of the monomer protein.
