Statistical analysis of the fractal gating motions of the enzyme acetylcholinesterase

The enzyme acetylcholinesterase has an active site that is accessible only by a “gorge” or main channel from the surface, and perhaps by secondary channels such as the “back door.” Molecular-dynamics simulations show that these channels are too narrow most of the time to admit substrate or other small molecules. Binding of substrates is therefore “gated” by structural fluctuations of the enzyme. Here, we analyze the fluctuations of these possible channels, as observed in the 10.8-ns trajectory of the simulation. The probability density function of the gorge proper radius (defined in the text) was calculated. A double-peak feature of the function was discovered and therefore two states with a threshold were identified. The relaxation (transition probability) functions of these two states were also calculated. The results 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.