It is recently proposed that directed passage of ligand on the surface of enzymes may play an important role in the process of enzyme activity, as a result of decreasing the required steps of random walking of the ligand toward the active site. Here, we revisited the approach applied by others, where a cellular automaton is designed to simulate the behavior of a ligand molecule traveling toward the active site of an enzyme. Since a cellular automaton plane is topologically equivalent to a torus surface, we recommended the use of a 'double cellular automata' to model globular proteins. With the boundary conditions applied, our model is topologically identical to a sphere. It was shown that using this model, even fewer steps are needed for a molecule to attend the active site. This assumption can lead to more realistic results in the modeling of surfaces with spherical topology. (c) 2005 Elsevier Inc. All rights reserved.