Statistical analysis of the fractal gating motions of the enzyme acetylcholinesterase - art. no. 041902

The enzyme acetylcholinesterase has an active site that is accessible only by a "gorge" or main channel from the surface, and perhaps by secondary cha nnels such as the "back door." Molecular-dynamics simulations show that the se channels are too narrow most of the time to admit substrate or other sma ll molecules. Binding of substrates is therefore "gated" by structural fluc tuations of the enzyme. Here, we analyze the fluctuations of these possible channels, as observed in the 10.8-ns trajectory of the simulation. The pro bability density function of the gorge proper radius (defined in the text) was calculated. A double-peak feature of the function was discovered and th erefore two states with a threshold were identified. The relaxation (transi tion probability) functions of these two states were also calculated. The r esults revealed a power-law decay trend and an oscillation around it, which show properties of fractal dynamics with a ''complex exponent.'' The cross correlation of potential energy versus proper radius was also investigated . We discuss possible physical models behind the fractal protein dynamics: the dynamic hierarchical model for glassy systems is evaluated in detail.