Spin dynamics calculations applied to systems of potential biological significance

Magnetic fields interact with biological systems, often in unexplored and surprising ways. In this thesis I develop and employ a range of quantum mechanical spin dynamics tools for simulating these magnetic spin interactions, modelling a diverse set of systems of potential biological relevance. Nuclear spins in calcium phosphates known as Posner molecules form the basis of a proposed mechanism for human neural processing. This theory requires that phosphorus nuclei in different Posner molecules become entangled and remain so for periods far longer than typical nuclear spin relaxation times. In Chapter 3 I model the coherent and relaxation spin dynamics of this molecule, deriving a strict upper bound on the entanglement lifetime and arguing that other relaxation effects will further limit this lifetime. Spin relaxation is also relevant to studies into the chemical compass sense possessed by migratory birds. Certain evidence indicates that a flavin-superoxide radical pair may be better suited for detecting the Earth’s magnetic field than the flavin-tryptophan system more commonly assumed. Studies into this alternative radical pair often ignore the particularly rapid electron spin relaxation expected for superoxide. In Chapter 4 I simulate the sensitivity of this superoxide radical pair to an Earth-strength magnetic field, deriving a set of strict conditions on the local environment and molecular dynamics of the radicals that will need to be satisfied if it does play a role in geomagnetic sensing. In Chapter 5 I simulate the effect of a magnetic field on the electrocatalytic reduction of carbon dioxide, demonstrating that an experimentally observed field effect cannot be accounted for by the mechanism originally proposed. By including spin relaxation, I am able to fit the experimental results and derive a set of physically reasonable parameters that quantitatively account for the observed field effect. In many systems these observed magnetic effects are of a relatively small magnitude. In Chapter 6 I examine autocatalysis in oscillating chemical reactions as a means of amplifying weak field effects. A minute change in one of the rate constants for the initiation step in a model oscillating system that involves a radical pair is found to produce a dramatically large change in the amplitude of reaction intermediate oscillations.