A stochastic finite element model for the dynamics of globular proteins

This thesis concerns a novel coarse graining method for the simulation of the globular proteins. Conventional simulation methods such as molecular dynamics cannot
generate sufficient times to reach the important timescales that govern the biology of large biological systems like molecular motors. To address this, I have developed a
new coarse graining algorithm drawing on the techniques of continuum mechanics and finite element analysis to build a new simulation technique. The novel part of this algorithm is that the fluctuation dissipation relation for the system can be derived and solved locally. This avoids the need to invert a global resistance matrix to solve for the thermal noise component of the system and reduces the computational expense of the algorithm per time step. I have validated this coarse grained model by performing a variety of tests on the numerical code including spatial and temporal convergence tests using Fourier analysis and beam bending theory. In addition compliance with the equipartition theorem has been confirmed.
One key advantage of this method over atomistic techniques is that the coarse grained method does not require any atomic information ab intio. Thus, this method can interface with low resolution imaging techniques such as Small Angle X-Ray Scattering and Cryo-Electron Microscopy. In this thesis, I show how to construct a finite element mesh from both of these sources and run simulations to replicate the results from Small Angle X-Ray Scattering and Cryo-Electron Microscopy experiments. In more detail, I have taken a structure obtained using Small Angle X-ray Scattering, ran simulations and checked that the dynamics do not affect the average X-Ray scattering curve. Furthermore, using experimentally obtained structures and dynamics of the molecular motor dynein I have run simulations to find the elastic parameters that match the experimental data to map the overall dynamics of the dynein motor.