Directed Ligand Passage over the Surface of Diffusion-Controlled Enzymes: A Cellular Automata Model

Abstract

Abstract. The rate-limiting step of some enzymatic reactions is a physical step, i.e. diffusion. The efficiency of such reactions can be improved through an increase in the arrival rate of the substrate molecules, e.g. by a directed passage of substrate (ligand) to active site after its random encounter with the enzyme surface. Herein, we introduce a cellular automata model simulating the ligand passage over the protein surface to its destined active site. The system is simulated using the lattice gas automata with probabilistic transition rules. Different distributions of amino acids over the protein surface are examined. For each distribution, the hydration pattern is achieved and the mean number of iteration steps needed for the ligand to arrive at the active site calculated. Comparison of results indicates that the rate at which ligand arrives at the active site is clearly affected by the distribution of amino acids outside the active side. Such a process can facilitate the ligand diffusion towards the active site thereby enhancing the efficiency of the enzyme action.

Evolution of ‘Ligand‐Diffusion Chreodes’ on Protein‐Surface Models: A Genetic‐Algorithm Study

“…These patterns are evolved merely with the consideration of mutations, and without crossover (i.e., crossover rate ¼ 0). Note that these patterns match well with the chreodes hypothesized to be present in previous studies [7] [9 -11]. Fig.…”

“…-To eliminate the effect of outliers, we decided to use median instead of mean. We simulated the travel of a ligand toward an active site with the assumptions described in [11], with two differences: 1) in contrast to previous works [7] [9 -11], we assumed that the number of H 2 O molecules are constant, proportional to the hydropathical value of each cell. Therefore, our simulations only consider the most probable states for the chreodes and it is constant.…”