A variety of proteins have been shown to aggregate to form amyloid fibrils on system size scales ranging from hundreds to many thousands of protein monomers, and on timescales ranging from minutes to hours to years. Given that the current state of the art for molecular dynamics simulations of proteins lies in the millisecond timescale regime for single proteins, it is self-evident that in order to model the complete aggregation dynamics of amyloid fibrils forming from a set of monomers, a particularly aggressive coarse-graining of the system is necessary. To this end, we have developed a mathematical model for fibrillization whereby all spatial effects are coarse-grained by embedding them into a graph theoretical topological representation where the energetics of interactions between monomers are governed by a network Hamiltonian. Using this network Hamiltonian as a force field, we have developed a computational methodology for simulating amyloid fibril formation that is capable of simulating the formation of amyloid fibrils from an initial condition comprised of 1000 fully dissociated protein monomers. Our computational methodology consists of two distinct simulation techniques. One simulation method is based in Markov Chain Monte Carlo (MCMC) sampling, where upon sufficient mixing, the method samples a thermodynamic distribution of aggregation states, returning an ensemble of high probability, i.e. thermodynamically stable, aggregation states. The other simulation method, a kinetic sampling method, carries out time-dependent dynamics of aggregation in network space. Additional analysis of all amyloid fibril structures in the protein data bank (PDB), also carried out by these authors, has indicated that all known amyloid fibril structures in the PDB fall under 5 different topological motifs. Our computational methodology can be parameterized to recapitulate the formation of all 5 fibril types from fully dissociated protein monomers. This presentation will include an overview of the statistical mechanical formalism pertaining to our network Hamiltonian, a brief explanation of the network analysis carried out on the PDB structures, and explanations and demonstrations of our aggregation simulation methodology.

Topological coarse-graining: Building ultra efficient computer models of aggregation using network Hamiltonians

2019 Fall National Meeting

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