Analytical study on the generalized Davydov model in the alpha helical proteins

In this paper, we investigate the dynamics of a generalized Davydov model derived from an infinite chain of alpha helical protein molecules which contain three hydrogen bonding spines running almost parallel to the helical axis. Through the introduction of the auxiliary function, the bilinear form, one-, two- and three-soliton solutions for the generalized Davydov model are obtained firstly. Propagation and interactions of solitons have been investigated analytically and graphically. The amplitude of the soliton is only related to the complex parameter [Formula: see text] and real parameter [Formula: see text] with a range of [Formula: see text]. The velocity of the soliton is only related to the complex parameter [Formula: see text], real parameter [Formula: see text], lattice parameter [Formula: see text], and physical parameters [Formula: see text], [Formula: see text] and [Formula: see text]. Overtaking and head-on interactions of two and three solitons are presented. The common in the interactions of three solitons is the directions of the solitons change after the interactions. The soliton derived in this paper is expected to have potential applications in the alpha helical proteins.

On the diffusion of alpha-helical proteins in solvents

The winding probability function for a biopolymer diffusing in a crowded cell is obtained with the drift coefficient f(s) involving Bessel functions of general form f(s) = kJ2p+1 (νs). The variable s is the length along the chain and ν is a constant which can be used to simulate the frequency of appearance of a certain type of amino acid. Application of a particular case p = 3 to protein chains is carried out for different alpha helical proteins found in the Protein Data Bank (PDB). Analysis of our results leads us to an empirical formula that can be used to conveniently predict k/D and ν, where D is the diffusion coefficient of various α-helical proteins in solvents.