  The reaction-diffusion master equation (RDME) is a standard modelling
approach for understanding stochastic and spatial chemical kinetics. An
inherent assumption is that molecules are point-like. Here we introduce the
crowded reaction-diffusion master equation (cRDME) which takes into account
volume exclusion effects on stochastic kinetics due to a finite molecular
radius. We obtain an exact closed form solution of the RDME and of the cRDME
for a general chemical system in equilibrium conditions. The difference between
the two solutions increases with the ratio of molecular diameter to the
compartment length scale. We show that an increase in molecular crowding can
(i) lead to deviations from the classical inverse square root law for the
noise-strength; (ii) flip the skewness of the probability distribution from
right to left-skewed; (iii) shift the equilibrium of bimolecular reactions so
that more product molecules are formed; (iv) strongly modulate the Fano factors
and coefficients of variation. These crowding-induced effects are found to be
particularly pronounced for chemical species not involved in chemical
conservation laws.Finally we show that statistics obtained using the vRDME are
in good agreement with those obtained from Brownian dynamics with excluded
volume interactions.
