A Comprehensive Analysis of Allostery in 14-3-3 $\zeta$ Docking Proteins using the Spatial Convolution Model (SCM)

Abstract

The Spatial Convolution Model (SCM) analyzes allostery based on the spatial evolution of the docking protein elastic media, whereby convolution of the media in response to wave propagation is solved as a function of Z fluctuations and backbone vibration modes. We show that although the elastic media is a complex three-dimensional structure allostery behaves as if it occurs along a stretched oscillating string, where inhomogeneities along the string effect local entropies responsible for ligand binding and transduction of allosteric waves. To identify inhomogeneities along the string, we ignored local density and tension changes during wave propagation and resolved helix wave and physical properties by applying molecular string and beam bending theories. Importantly, we show that allostery occurs at three major scales and that propagation of standing waves create a rolling entropy which drives entropy transfers between fields. Conversion of resonance energy to quantum harmonic oscillators allowed us to consider effects of damping and interactions with the surrounding media as well as to model effects of residue interaction strength on entropy transfer.