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.