Book Description

We developed theories and algorithms for two coarse-grained implicit solvent models that can be deployed within a multiscale framework to enable computational studies of large-scale protein-protein associations. The first model is a residue level alpha-carbon bead model intended for simulating proteins at close range during formation of encounter complexes. This model introduces a novel forcefield term to model directional backbone hydrogen bond semi-explicitly, as well as a fourth bead flavor in its sequence-dependence to better represent the spectrum of residue-residue attractive interactions. We showed that the introduction of the orientation-dependent hydrogen bonding term resulted in more stable and realistic alpha helices and beta sheets. In addition, the addition of a fourth bead flavor reduces energetic frustrations and competition from misfolded states. The overall model showed increased folding cooperativity, and a greater structural faithfulness to experimentally solved structures. The computational efficiency of the model has also permitted us to develop molecular models of the Alzheimer's A-beta 1-40 fibril to study nucleation and elongation, providing a good proof-of-concept and laying the foundation for applications to other protein-protein assembly processes. The second model is a protein level model intended for simulating proteins during diffusional search. It treats proteins as rigid bodies interacting solely through long-range electrostatics. We first described the theory and implementation of a novel method, Poisson-Boltzmann Semi-Analytical Method (PB-SAM), to model electrostatic interactions by efficiently solving the linearized Poisson-Boltzmann equation (PBE). This novel method combines advantages of analytical and boundary element methods by representing the macromolecular surface realistically as a collection of overlapping spheres, for which polarization charges can then be iteratively solved using analytical multipole method. Unlike finite difference solvers, PB-SAM is not constrained spatially by the box size, making it suitable for simulating dynamics. We showed that this method realizes better accuracy at reduced cost relative to either finite difference or boundary element PBE solvers. We derived expressions for force and torque that account for mutual polarization in both the zero and first order derivative of the surface charges, and incorporated the complete PB-SAM method into a protein level Brownian dynamics simulation algorithm. We demonstrated for the first time dynamic propagation of multiple Brownian particles with accurate accounting of mutual polarization effects for successive timesteps, using a model system of two monomers of brome mosaic virus (PDB code: 1YC6). While PB-SAM enable us to model mutual polarization effects in systems of hitherto inaccessible spatial dimensions, we can further reduce the computation time through parallelization, faster linear algebra operations, optimizing convergence criteria and polarization cutoffs, and approximating mutual polarization effects from analytical models. Finally, we discussed multiscale strategies to connect the two models described above for large-scale protein assembly studies. The two models can be employed successively in a novel nested variant of the Northrup-Allison-McCammon formalism to compute bi-molecular kinetics rates. The kinetic parameters can in turn be inputs to chemical master equations or stochastic simulations. Such multiscale modeling can be used to determine kinetics rates and the order of association, and help investigate how changing physical interactions can alter the association rates, and consequently control overall sequences of association.