Long-range donor-acceptor electron transport mediated by α helices

Abstract

We study the long-range electron and energy transfer mediated by a polaron on an α-helix polypeptide chain coupled to donor and acceptor molecules at opposite ends of the chain. We show that for specific parameters of the system, an electron initially located on the donor can tunnel onto the α-helix, forming a polaron which then travels to the other extremity of the polypeptide chain where it is captured by the acceptor. We consider three families of couplings between the donor, acceptor and the chain, and show that one of them can lead to a 90% efficiency of the electron transport from donor to acceptor. We also show that this process remains stable at physiological temperatures in the presence of thermal fluctuations in the system.

Thermal stability of solitons in protein $α$-helices

“…In the model of the full protein α-helix, however, the presence of Q = 3 amide I quanta ensures a cooperative stabilizing effect upon the formed soliton for a time period over 30 ps, which is long enough for the soliton to traverse the full extent of an α-helix with n max = 40 lattice sites. Thus, our computational results establish that multiquantal solitons in full protein α-helices with three α-helix spines possess the required thermal stability in order to support energy transportation in proteins of living systems [48,63]. This robustness against thermal noise of the generalized Davydov model with lateral coupling also lends indirect support for the predicted importance of topological solitons for protein folding in relation to their biological function [64,65].…”

“…The observed thermal stability of the three-spine model with lateral coupling is corroborated by recent computational study by Brizhik and collaborators [48], where an elaborate spiral protein lattice with greater number of lateral couplings is considered. In the latter model, each peptide group is coupled to 6 neighboring peptide groups in the spiral, whereas in our three-spine Hamiltonian (25), each peptide group is coupled to only 4 neighboring peptide groups.…”

“…Because we were still able to obtain extended soliton lifetime, we consider our three-spine Hamiltonian as the minimal model that guarantees thermal stability. Further inclusion of additional (diagonal) lateral couplings can only reinforce the model against thermal noise [48].…”

Quantum transport and utilization of free energy in protein α-helices

“…In this work, we model only a single hydrogen-bonded spine in the protein α-helix, rather than the 3-spine structure of the entire helix. In realistic protein α-helices, the quantum dynamics of amide I energy in the 3-spine structure will also depend on inter-spine interactions and may give rise to complicated multihump solitons [82,83], which the current study does not consider. For a single α-helix spine of hydrogen-bonded peptide groups, the generalized Davydov Hamiltonian is a sum of three parts Ĥ = Ĥex + Ĥph + Ĥint (1) respectively for amide I excitons Ĥex , hydrogen-bonded lattice phonons Ĥph , and excitonphonon interaction Ĥint .…”

Exact analytical solution of a novel modified nonlinear Schrödinger equation: Solitary quantum waves on a lattice

“…To interpret the solution (24), we begin by deriving () as a model of the dynamics of a quantum mechanical exciton when coupled to a lattice. The theoretical principles of exciton‐lattice interaction were founded in the 1930s, and have been important in condensed matter physics for their relevance to superconductivity, conducting polymers and bioelectronics 25–29 . The method of deriving the NLSE or its variants by taking a exciton‐lattice system to a continuum limit was first presented by Davydov, 4 and has since been employed in many studies; details can be found in some excellent reviews 30,31 .…”