  Several stochastic simulation algorithms (SSAs) have been recently proposed
for modelling reaction-diffusion processes in cellular and molecular biology.
In this paper, two commonly used SSAs are studied. The first SSA is an
on-lattice model described by the reaction-diffusion master equation. The
second SSA is an off-lattice model based on the simulation of Brownian motion
of individual molecules and their reactive collisions. In both cases, it is
shown that the commonly used implementation of bimolecular reactions (i.e. the
reactions of the form A + B -> C, or A + A -> C) might lead to incorrect
results. Improvements of both SSAs are suggested which overcome the
difficulties highlighted. In particular, a formula is presented for the
smallest possible compartment size (lattice spacing) which can be correctly
implemented in the first model. This implementation uses a new formula for the
rate of bimolecular reactions per compartment (lattice site).
