Proteins are molecular machines that carry out essential functions in the living cell. Since the structure and dynamics are crucial for a protein’s functional mechanism, a detailed knowledge of the protein’s conformation and conformational landscape at atomic level provides an ultimate description of its exact function. Establishing a fundamental understanding of proteins is vital to elucidate the causes of human diseases, so that potential cures and efficient drugs can be designed. An increasingly accurate computational modelling of protein molecules is, in many aspects, able to produce quantitative insights into their thermodynamic and mechanistic properties that are difficult to probe in laboratory experiments.

However, despite the rapid progress in the development of molecular simulation, there are still two limiting factors, (1), the current molecular mechanics force fields alone are not sufficient to provide an accurate structural and dynamical description of certain properties of proteins, (2), it is difficult to obtain correct statistical weights of the samples generated, due to lack of equilibrium sampling. In this dissertation I present several new methodologies based on Monte Carlo sampling methods to address these two problems.

First of all, a novel technique has been developed for reliably estimating diffusion coefficients for use in the enhanced sampling of molecular simulations. A broad applicability of this method is illustrated by studying various simulation problems such as protein folding and aggregation. Second, by combining Monte Carlo sampling with a flexible probabilistic model of NMR chemical shifts, a series of simulation strategies are developed to accelerate the equilibrium sampling of free energy landscapes of proteins. Finally, a novel approach is presented to predict the structure of a functional amyloid protein, by using intramolecular evolutionary restrains in Monte Carlo simulations.