Long-time methods for Molecular Dynamics simulations: Markov State Models and Milestoning

In this thesis, the aim is to contribute to the development of long-time methods for molecular dynamics (MD) simulations such as the Milestoning method and Markov State Model (MSM), and their application to study the conformational dynamics of systems ranging from the small piezoelectric amyloid peptide diphenylalanine (FF) to much larger cancer-related systems such as the Abl and K-Ras proteins. Albeit all the progress in high-performance computing capacity, MD simulations of large systems with atomistic detail is computationally very expensive and requires advanced methods that can aid probing slow kinetics. Markov State Modelling and the Milestoning method are two fast developing novel and powerful computational approaches that can accurately capture molecular kinetics besides thermodynamics, and yet are relatively simple and easy to implement. The MSM approach relies of mapping the complex underlying dynamics of complex biomolecular systems on relatively simple networks with nodes corresponding to stable conformational states that are interconnected through Markovian transitions. The Milestoning method is useful where the sampling problem can be stated in terms of estimating the thermodynamics and kinetics along transition pathways that connect two known metastable states of the underlying molecular system. One could target the sampling in order to identify and characterize the most probable pathway(s) and the corresponding intermediate states that are relevant to the underlying reaction mechanism. Firstly, I showed that the thermodynamics and kinetics of the ensemble of conformations adopted by amyloid FF peptides solvated in explicit water molecules can be analysed in detail by using an efficient enhanced sampling method, replica exchange molecular dynamics (REMD), while simultaneously applying external electric fields and probing a range of temperatures. I also showed that even for such a small system, there could be possible artifacts arising from due to the coupling the exchange with external fields, and I proposed how to overcome these artifacts in our simulations. Next, I combined a reaction path algorithm with the theory and algorithm of Milestoning to study kinetics of the DFG flip and disassociation of Gleevec from the Abelson murine leukaemia viral oncogene homolog (Abl) kinase. This allowed me to probe the detailed mechanism for the unbinding transition, at a timescale longer than accessibly by conventional MD studies. This also allowed the accurate calculation of the slow underlying kinetic timescales from our sets of short atomistic MD trajectories, while sampling the unbinding pathway of Gleevec from Abl and providing detailed insight into the corresponding dissociation kinetics. Finally, using also sets of appropriately initialized yet relatively short trajectories, I analysed the underlying free energy landscape of K-Ras4B and unveiled new information on its underlying conformational states, and sheds new light on the activation/inactivation mechanism. This new MSM study of K-Ras, based on sets of short trajectories approach, unveils details underlying its equilibrium conformational kinetics, including the role of cancer-relevant mutations and the corresponding changes in activation/inactivation propensities.