Cellular signaling networks have evolved to cope with intrinsic fluctuations,
coming from the small numbers of constituents, and the environmental noise.
Stochastic chemical kinetics equations govern the way biochemical networks
process noisy signals. The essential difficulty associated with the master
equation approach to solving the stochastic chemical kinetics problem is the
enormous number of ordinary differential equations involved. In this work, we
show how to achieve tremendous reduction in the dimensionality of specific
reaction cascade dynamics by solving variationally an equivalent quantum field
theoretic formulation of stochastic chemical kinetics. The present formulation
avoids cumbersome commutator computations in the derivation of evolution
equations, making more transparent the physical significance of the variational
method. We propose novel time-dependent basis functions which work well over a
wide range of rate parameters. We apply the new basis functions to describe
stochastic signaling in several enzymatic cascades and compare the results so
obtained with those from alternative solution techniques. The variational
ansatz gives probability distributions that agree well with the exact ones,
even when fluctuations are large and discreteness and nonlinearity are
important. A numerical implementation of our technique is many orders of
magnitude more efficient computationally compared with the traditional Monte
Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure