Kinetic distance and kinetic maps from molecular dynamics simulation

Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine

Molecular dynamics simulations data of the twenty encoded amino acids in different force fields

We present extensive all-atom Molecular Dynamics (MD) simulation data of the twenty encoded amino acids in explicit water, simulated with different force fields. The termini of the amino acids have been capped to ensure that the dynamics of the Φ and ψ torsion angles are analogues to the dynamics within a peptide chain. We use representatives of each of the four major force field families: AMBER ff-99SBILDN [1], AMBER ff-03 [2], OPLS-AA/L [3], CHARMM27 [4] and GROMOS43a1 [5,6]. Our data represents a library and test bed for method development for MD simulations and for force fields development. Part of the data set has been previously used for comparison of the dynamic properties of force fields (Vitalinietal.,2015) [7] and for the construction of peptide basis functions for the variational approach to molecular kinetics [8]

A basis set for peptides for the variational approach to conformational kinetics

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

Reversible Markov chain estimation using convex-concave programming

We present a convex-concave reformulation of the reversible Markov chain estimation problem and outline an efficient numerical scheme for the solution of the resulting problem based on a primal-dual interior point method for monotone variational inequalities. Extensions to situations in which information about the stationary vector is available can also be solved via the convex- concave reformulation. The method can be generalized and applied to the discrete transition matrix reweighting analysis method to perform inference from independent chains with specified couplings between the stationary probabilities. The proposed approach offers a significant speed-up compared to a fixed-point iteration for a number of relevant applications.Comment: 17pages, 2 figure

Pattern formation in binary fluid mixtures induced by short-range competing interactions

Molecular dynamics simulations and integral equation calculations of a simple equimolar mixture of diatomic molecules and monomers interacting via attractive and repulsive short-range potentials show the existence of pattern formation (microheterogeneity), mostly due to depletion forces away from the demixing region. Effective site-site potentials extracted from the pair correlation functions using an inverse Monte Carlo approach and an integral equation inversion procedure exhibit the features characteristic of a short-range attractive and long-range repulsive potential. When charges are incorporated into the model, this becomes a coarse grained representation of a room temperature ionic liquid, and as expected, intermediate range order becomes more pronounced and stable

Dynamic Properties of Force Fields

Molecular-dynamics simulations are increasingly used to study dynamic properties of biological systems. With this development, the ability of force fields to successfully predict relaxation timescales and the associated conformational exchange processes moves into focus. We assess to what extent the dynamic properties of model peptides (Ac-A-NHMe, Ac-V-NHMe, AVAVA, A10) differ when simulated with different force fields (AMBER ff99SB-ILDN, AMBER ff03, OPLS-AA/L, CHARMM27, and GROMOS43a1). The dynamic properties are extracted using Markov state models. For single-residue models (Ac-A-NHMe, Ac-V-NHMe), the slow conformational exchange processes are similar in all force fields, but the associated relaxation timescales differ by up to an order of magnitude. For the peptide systems, not only the relaxation timescales, but also the conformational exchange processes differ considerably across force fields. This finding calls the significance of dynamic interpretations of molecular-dynamics simulations into question