CONFORMATION CHANGES AND PROTEIN FOLDING INDUCED BY ϕ⁴ INTERACTION

Abstract

A model to describe the mechanism of conformational dynamics in protein based on matter interactions using lagrangian approach and imposing certain symmetry breaking is proposed. Both conformation changes of proteins and the injected non-linear sources are represented by the bosonic lagrangian with an additional φ 4 interaction for the sources. In the model the spring tension of protein representing the internal hydrogen bonds is realized as the interactions between individual amino acids and nonlinear sources. The folding pathway is determined by the strength of nonlinear sources that propagate through the protein backbone. It is also shown that the model reproduces the results in some previous works.

The Statistical Properties of Protein Folding in the 4 Theory

“…Having the total lagrangian in Eq. (1) at hand, one can derive immediately respective EOMs using Euler-Lagrange equation in term of ψ and φ [3],…”

“…On the other hand, some previous studies have shown that the nonlinear excitations could play an important role in conformational dynamics of protein backbone by decreasing the effective binding rigidity of a biopolymer chain leading to a buckling instability of the chain [2]. The results motivate us to develop a model describing the conformational changes of protein based on the φ 4 theory [3]. The model is actually inspired by some previous models which attempt to reproduce the protein folding using nonlinear Schrödinger hamiltonian with the additional tension-like force [4,5].…”

“…2. It is then followed by the short derivation of relevant equation of motions (EOMs) as done in [3] and showing the refined numerical simulation of folding process within the model. In Sec.…”

Field Theory Approach in the Dynamics of Biomatter

“…Similar to the previous case, the model adopts the φ 4 lagrangian but with additional interactions 15 ,…”

“…(10) can be evaluated analytically using the Gaussian integral. This can be accomplished by rewriting it in term of Gaussian integral using the Fourier representation of Green's function to obtain the master equation 15 ,…”