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Thermal stability of solitons in protein $α$-helices

Protein$α$-helices provide an ordered biological environment that is conducive to soliton-assisted energy transport. The nonlinear interaction between amide I excitons and phonon deformations induced in the hydrogen-bonded lattice of peptide groups leads to self-trapping of the amide I energy, thereby creating a localized quasiparticle (soliton) that persists at zero temperature. The presence of thermal noise, however, could destabilize the protein soliton and dissipate its energy within a finite lifetime. In this work, we have computationally solved the system of stochastic differential equations that govern the quantum dynamics of protein solitons at physiological temperature, T=310 K, for either a single isolated $α$-helix spine of hydrogen bonded peptide groups or the full protein $α$-helix comprised of three parallel $α$-helix spines. The simulated stochastic dynamics revealed that although the thermal noise is detrimental for the single isolated $α$-helix spine, the cooperative action of three amide I exciton quanta in the full protein $α$-helix ensures soliton lifetime of over 30 ps, during which the amide I energy could be transported along the entire extent of an 18-nm-long $α$-helix. Thus, macromolecular protein complexes, which are built up of protein $α$-helices could harness soliton-assisted energy transport at physiological temperature. Because the hydrolysis of a single adenosine triphosphate molecule is able to initiate three amide I exciton quanta, it is feasible that multiquantal protein solitons subserve a variety of specialized physiological functions in living systems.