Polaron Dynamics in the Alpha Helix: Models of Electron Transport in Hydrogen-Bonded Polypeptides

Abstract

In this thesis, I present two mathematical models which are capable of explaining the phenomenon of directed electron transport in α-helical regions of protein macromolecules. The models are built upon the framework of polaron theory, which originated in condensed matter physics, and which I argue is applicable to biophysical systems such as an extra electron interacting electromagnetically with peptide units in an α-helix. The two models concern the electron’s coupling to, respectively, picosecond-scale intrapeptide oscillators and nanosecond-scale hydrogen bond phonons in the α-helix. I show that the models permit the auto-localisation of the electron in stationary polaron states, and that certain electromagnetic fields cause the polaron to propagate along the polypeptide, transporting the electron in a solitonic manner. Taking effects of the cell environment into account, I demonstrate that stochastic forces arising from thermal fluctuations can enhance the electron transport, and that the stability of the polaron dynamics exhibit contrasting degrees of tolerance to temperature in the two models. When interpreting my results, I describe their biological implications, as well as the physical realisability of the models’ forcing parameters. In particular, I establish that some electromagnetic fields which can facilitate directed electron transport are intrinsic physical features of the cell.