Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.

The eigenvalues and eigenvectors of the molecular dynamics propagator (or transfer operator) contain the essential information about the molecular thermodynamics and kinetics. This includes the stationary distribution, the metastable states, and state-to-state transition rates. Here, we present a variational approach for computing these dominant eigenvalues and eigenvectors. This approach is analogous to the variational approach used for computing stationary states in quantum mechanics. A corresponding method of linear variation is formulated. It is shown that the matrices needed for the linear variation method are correlation matrices that can be estimated from simple MD simulations for a given basis set. The method proposed here is thus to first define a basis set able to capture the relevant conformational transitions, then compute the respective correlation matrices, and then to compute their dominant eigenvalues and eigenvectors, thus obtaining the key ingredients of the slow kinetics.

The identification of metastable states of a molecule plays an important role in the interpretation of molecular simulation data because the free-energy surface, the relative populations in this landscape, and ultimately also the dynamics of the molecule under study can be described in terms of these states. We compare the results of three different geometric cluster algorithms (neighbor algorithm, K-medoids algorithm, and common-nearest-neighbor algorithm) among each other and to the results of a kinetic cluster algorithm. First, we demonstrate the characteristics of each of the geometric cluster algorithms using five two-dimensional data sets. Second, we analyze the molecular dynamics data of a beta-heptapeptide in methanol--a molecule that exhibits a distinct folded state, a structurally diverse unfolded state, and a fast folding/unfolding equilibrium--using both geometric and kinetic cluster algorithms. We find that geometric clustering strongly depends on the algorithm used and that the density based common-nearest-neighbor algorithm is the most robust of the three geometric cluster algorithms with respect to variations in the input parameters and the distance metric. When comparing the geometric cluster results to the metastable states of the beta-heptapeptide as identified by kinetic clustering, we find that in most cases the folded state is identified correctly but the overlap of geometric clusters with further metastable states is often at best approximate.

The membrane permeability of cyclic peptides and peptidomimetics, which are generally larger and more complex than typical drug molecules, is likely strongly influenced by the conformational behavior of these compounds in polar and apolar environments. The size and complexity of peptides often limit their bioavailability, but there are known examples of peptide natural products such as cyclosporin A (CsA) that can cross cell membranes by passive diffusion. CsA is an undecapeptide with seven methylated backbone amides. Its crystal structure shows a "closed" twisted β-pleated sheet conformation with four intramolecular hydrogen bonds that is also observed in NMR measurements of CsA in chloroform. When binding to its target cyclophilin, on the other hand, CsA adopts an "open" conformation without intramolecular hydrogen bonds. In this study, we attempted to sample the complete conformational space of CsA in chloroform and in water by molecular dynamics simulations in order to better understand its conformational behavior in these two environments and to rationalize the good membrane permeability of CsA observed experimentally. From 10 μs molecular dynamics simulations in each solvent, Markov state models were constructed to characterize the metastable conformational states. The model in chloroform is compared to nuclear Overhauser effect NMR spectroscopy data reported in this study and taken from the literature. The conformational landscapes in the two solvents show significant overlap but also clearly distinct features.

Cyclization and selected backbone N-methylations are found to be often necessary but not sufficient conditions for peptidic drugs to have a good bioavailability. Thus, the design of cyclic peptides with good passive membrane permeability and good solubility remains a challenge. The backbone scaffold of a recently published series of cyclic decapeptides with six selected backbone N-methylations was designed to favor the adoption of a closed conformation with β-turns and four transannular hydrogen bonds. Although this conformation was indeed adopted by the peptides as determined by NMR measurements, substantial differences in the membrane permeability were observed. In this work, we aim to rationalize the impact of discrete side chain modifications on membrane permeability for six of these cyclic decapeptides. The thermodynamic and kinetic properties were investigated using molecular dynamics simulations and Markov state modeling in water and chloroform. The study highlights the influence that side-chain modifications can have on the backbone conformation. Peptides with a d-proline in the β-turns were more likely to adopt, even in water, the closed conformation with transannular hydrogen bonds, which facilitates transition through the membrane. The population of the closed conformation in water was found to correlate positively with PAMPA log P e.