A Basis Set for Peptides for the Variational Approach to Conformational Kinetics

Abstract

Although Markov state models have proven to be powerful tools in resolving the complex features of biomolecular kinetics, the discretization of the conformational space has been a bottleneck since the advent of the method. A recently introduced variational approach, which uses basis functions instead of crisp conformational states, opened up a route to construct kinetic models in which the discretization error can be controlled systematically. Here, we develop and test a basis set for peptides to be used in the variational approach. The basis set is constructed by combining local residue-centered kinetic modes that are obtained from kinetic models of terminally blocked amino acids. Using this basis set, we model the conformational kinetics of two hexapeptides with sequences VGLAPG and VGVAPG. Six basis functions are sufficient to represent the slow kinetic modes of these peptides. The basis set also allows for a direct interpretation of the slow kinetic modes without an additional clustering in the space of the dominant eigenvectors. Moreover, changes in the conformational kinetics due to the exchange of leucine in VGLAPG to valine in VGVAPG can be directly quantified by comparing histograms of the basis set expansion coefficients.

Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations

“…the variational approach (VA) to approximate the slow components of reversible Markov processes [51]. Due to its relevance for molecular dynamics, it has also been referred to as VA for molecular kinetics [52,53] or VA for conformation dynamics [52,54]. It has been known for many years that Markov state models are good approximations to molecular kinetics if their largest eigenvalues and eigenvectors approximate the eigenvalues and eigenfunctions of the Markov operator governing the full-phase space dynamics [18,34,55], moreover the first few eigenvalues and eigenvectors are sufficient to compute almost all stationary and kinetic quantities of interest [37,38,[56][57][58].…”

“…A VAbased metric has been defined which transforms the simulation data into a space in which Euclidean distance corresponds to kinetic distance [66,67]. The importance of meaningful basis sets has been discussed, and a basis for peptide dynamics has been proposed in [54].…”

Common Nearest Neighbor Clustering—A Benchmark

“…The transition matrix is however only a model of the true dynamics, and the approximation error depends sensitively on the discretization [56]. Recently, methods to discretize the dynamical propagator with respect to arbitrary ansatz functions have emerged [29,[57][58][59][60]. In core-set models [24][25][26]28], the state space is discretized into core sets, which do not fully partition the state space.…”

Communication: Consistent interpretation of molecular simulation kinetics using Markov state models biased with external information

“…Practically, this link is provided by Markov state models (MSMs), which describe the long-time dynamics of a system with a memoryless evolution of microstate transitions. The methodology for constructing MSMs directly from simulations has been extensively developed [26][27][28][29][30][31][32][33][34] and MSMs are routinely employed to elucidate complex simulated processes, e.g., protein folding [35][36][37][38][39][40] and protein-ligand binding. [41][42][43][44][45] Additionally, recent work 46 has applied MSMs to identify a) Electronic mail: rudzinski@mpip-mainz.mpg.de various discrepancies in the dynamical properties generated by different AA force fields.…”