  The process of dimerization, in which two monomers bind to each other and
form a dimer, is common in nature. This process can be modeled using rate
equations, from which the average copy numbers of the reacting monomers and of
the product dimers can then be obtained. However, the rate equations apply only
when these copy numbers are large. In the limit of small copy numbers the
system becomes dominated by fluctuations, which are not accounted for by the
rate equations. In this limit one must use stochastic methods such as direct
integration of the master equation or Monte Carlo simulations. These methods
are computationally intensive and rarely succumb to analytical solutions. Here
we use the recently introduced moment equations which provide a highly
simplified stochastic treatment of the dimerization process. Using this
approach, we obtain an analytical solution for the copy numbers and reaction
rates both under steady state conditions and in the time-dependent case. We
analyze three different dimerization processes: dimerization without
dissociation, dimerization with dissociation and hetero-dimer formation. To
validate the results we compare them with the results obtained from the master
equation in the stochastic limit and with those obtained from the rate
equations in the deterministic limit. Potential applications of the results in
different physical contexts are discussed.
