The Role of Aspherical Protein Shape: Dynamic Simulation of Ellipsoids - Marples, Callum (2019)
It was recently discovered that proteins, as well as their constituent amino acids, have aspect ratios that distribute around a value close to the Golden ratio, φ ≈ 1.618. In addition, it has long been known that proteins have an aspherical shape. However, reasons for evolution to favour such a shape have not been investigated. Therefore, in this thesis, possible reasons for proteins to favour a Golden shape are investigated. In order to do this, tri- axial ellipsoids were used as proxies for proteins, with diffusion and packing of ellipsoidal objects. In Chapter 1, the properties of the Golden ratio are discussed, and the relevant literature regarding protein shape, diffusion and packing reviewed. Chapter 2 outlines a Monte Carlo Brownian dynamics algorithm that was developed here to simulate the diffusion and packing of ellipsoidal particles, which interact via the Lennard-Jones potential. This simulation methodology includes two types of boundary: periodic boundary conditions, and a container that is itself ellipsoidal. In Chapter 3, diffusion of ellipsoids is investigated at various fixed volume fractions, using the method- ology of Chapter 2. It was found that the critical volume fraction, at which long-time self diffusion ceases, is greatest for ellipsoids of shape close to that of proteins. This implies that the shape of proteins offers optimal resistance to glass formation. Furthermore, the distribution of random contacts on the ellipsoid surface under diffusion was studied, necessitating the development of a fast means of calculating geodesic distances on the ellipsoid. It was found that the ellipsoidal shape of proteins gives rise to an anisotropic distri- bution of random collisions on their surface, with protein binding sites most common away from points of most probable contact, thus suggesting that an ellipsoidal shape helps to prevent aggregation of proteins. In Chapter 4, the algorithm of Chapter 2 is extended to simulate diffusion driven packing of ellipsoids, one result of which was a greater obtained volume fraction for ellipsoids than for spheres, consistent with previous work regarding ellipsoid packings. It was additionally found that packing of ellipsoids into a spherical container is more efficient than that inside an ellipsoid, with surface order- ing playing a key role in packing efficiency. This surface ordering was not found to occur for amino acids within proteins, due to the lack of a physi- cal boundary inducing torque. Chapter 5 investigates another phenomenon featuring the Golden ratio. Namely, that of quasicrystals, which are ordered arrangements of points in space without periodicity. The question of whether a protein quasicrystal can be made was investigated by identifying proteins that resemble a Golden rhombohedron as potential quasicrystal candidates.