**Markov State Models of Biomolecular Dynamics**

Molecular dynamics (MD) simulation are a well established method to assess the complex dynamics of biological macromolecules. Due
to their computational requirements, MD simulation are currently only able to generate simulation trajectories of a few microseconds
length - far less than would be required for a single trajectory to provide sufficient statistical information on probabilities and
rates for quantitatively describing the conformational equilibrium. Markov state models attack the sampling problem by extracting
statistical information from a large set of short trajectories that can be trivially distributed to many computers. When used in conjunction
with clusters containing modern graphics processors (GPUs), we can currently access processes occurring on timescales of up to milliseconds.
The statistical information obtained from many short trajectories is combined within an Markov state model (MSM). The MSM gives us a model of the most probable and
slowly-interconverting conformational states of a molecular system, and the transition rates between these states.

**Monte Carlo Methods for the Sampling of Rare Events **

The computational solution to problems in chemistry and
biology involves the characterization of high-dimensional systems. The appropriate
choice of algorithms to sample a given system is important in order to minimize the
number of energy evaluations needed and thereby reduce the computational cost. One of
the problems of the sampling process is the occurrence of rare events. If an energy
surface is composed of several low energy regions separated by high barriers, the
overall sampling efficiency is limited by the number of transitions between these
regions. Many approaches to address this difficulty can be found in literature.
Unfortunately for most of these approaches a rigorous mathematical derivation of
the improved efficiency is missing. Furthermore, there is a lack of systematic
comparison of methods. One reason for this is the deficiency of analytical measures
for the efficiency of algorithms

Empirical atomistic force fields are models of interactomic interactions. The accuracy of atomistic force fields depends on the complexity of the interatomic potential function as well as on the parametrization of the potential. In conventional force fields, the electrostatic potential is represented by atom-centered point charges. Point charges can be understood as the first term of multipole expansions, which converge with increasing number of terms towards the accurate representation of the molecular potential given by the electron density distribution. The distributed multipole analysis (DMA) can be used to obtain atomic multipole moments. Important points to consider are the orientation of the multipole moments and the conformational dependence of multipole parameters.