  We simulate the evolution of model protein sequences subject to mutations. A
mutation is considered neutral if it conserves 1) the structure of the ground
state, 2) its thermodynamic stability and 3) its kinetic accessibility. All
other mutations are considered lethal and are rejected. We adopt a lattice
model, amenable to a reliable solution of the protein folding problem. We prove
the existence of extended neutral networks in sequence space -- sequences can
evolve until their similarity with the starting point is almost the same as for
random sequences. Furthermore, we find that the rate of neutral mutations has a
broad distribution in sequence space. Due to this fact, the substitution
process is overdispersed (the ratio between variance and mean is larger than
one). This result is in contrast with the simplest model of neutral evolution,
which assumes a Poisson process for substitutions, and in qualitative agreement
with biological data.
