Electrostatics in Mesoscale Simulations of Biological Membranes using the Hybrid Particle-Field Approach

I develop and apply an iterative method to solve a general Poisson equation in Fourier space, with a variable dielectric. The iterative method is implemented in the molecular dynamics software HylleraasMD, using the Hamiltonian hPF formalism. First, I benchmark the iterative method with known cases. The method reproduces the electrostatic potential from an analytically constructed charge number density. When comparing with the Coulomb interaction of point particles, the iterative method yields reasonable magnitudes in force and energy, and momentum and energy are conserved. In addition, the method reproduces the behaviour of a 5mM electrolytic solution, with ideal monovalent ions dissolved in a biphase of liquid oil and water. Secondly, I simulate systems of Lipid A and Lipid Re with divalent counter-ions in the NVT ensemble, applying two constant dielectric values and two variable dielectric func- tions. Results are benchmarked with density profiles of united-atom simulations of the same systems. Model membranes of Lipid A and Lipid Re are in agreement with the reference membrane, except for low relative dielectric values, implying screening from polar moieties is necessary to preserve a lamellar bilayer. Lastly, I optimize Flory Huggins mixing parameters with Bayesian optimization, for Lipid A. Optimization increase R2-fitness and reduce RMSE-scores, with no significant differ- ences between trajectories for chosen dielectric parameters. Transferred to Lipid Re, optimized parameters give an improvement in R2 and RMSE compared to unoptimized parameters sets, except for the oligosaccharide chain, which is not present in Lipid A