Markov state models (MSMs) and other related kinetic network models are frequently used to study the long-timescale dynamical behavior of biomolecular and materials systems. MSMs are often constructed bottom-up using brute-force molecular dynamics (MD) simulations when the model contains a large number of states and kinetic pathways that are not known a priori. However, the resulting network generally encompasses only parts of the configurational space, and regardless of any additional MD performed, several states and pathways will still remain missing. This implies that the duration for which the MSM can faithfully capture the true dynamics, which we term as the validity time for the MSM, is always finite and unfortunately much shorter than the MD time invested to construct the model. A general framework that relates the kinetic uncertainty in the model to the validity time, missing states and pathways, network topology, and statistical sampling is presented. Performing additional calculations for frequently-sampled states/pathways may not alter the MSM validity time. A new class of enhanced kinetic sampling techniques is introduced that aims at targeting rare states/pathways that contribute most to the uncertainty so that the validity time is boosted in an effective manner. Examples including straightforward 1D energy landscapes, lattice models, and biomolecular systems are provided to illustrate the application of the method. Developments presented here will be of interest to the kinetic Monte Carlo community as well.

This Letter demonstrates that using time-dependent Markov state models (TD-MSMs) one can obtain molecular-scale insights into force-extension curves for a variety of stretching experiments. A master-MSM constructed at a reference extension forms the basis for generating the required TD-MSM, i.e., the TD-MSM that is appropriate for the stretching experiment can be constructed from a single master-MSM. In addition, the availability of state-specific force models enable calculation of force-extension behavior in a variety of ensembles. Changes in the network topology upon stretching are related through a thermodynamic quantity termed the mechanical disposition. Proof-of-principle is provided using a stretched alanine decapeptide under a time-varying pulling force.

Extensive molecular dynamics simulations have been employed to probe the effects of salts on the kinetics and dynamics of early-stage aggregated structures of steric zipper peptides in water. The simulations reveal that the chemical identity and valency of cation in the salt play a crucial role in aggregate dynamics and morphology of the peptides. Sodium ions induce the most aggregated structures, but this is not replicated equivalently by potassium ions which are also monovalent. Divalent magnesium ions induce aggregation but to a lesser extent than that of sodium, and their interactions with the charged peptides are also significantly different. The aggregate morphology in the presence of monovalent sodium ions is a compact structure with interpenetrating peptides, which differs from the more loosely connected peptides in the presence of either potassium or magnesium ions. The different ways in which the cations effectively renormalize the charges of peptides are suggested to be the cause of the differential effects of different salts studied here. These simulations underscore the importance of understanding both the valency and nature of salts in biologically relevant aggregated structures.

A new class of rare event acceleration techniques based on steered molecular dynamics (SMD) simulations is introduced. A stretching force applied on a biomolecule causes it to access large end-to-end distances. Under these conditions the biomolecule undergoes rapid conformational changes that are rare at zero-force conditions. A theory describing kinetics of a biomolecule at various stretching forces is presented. Using the theory, a master-Markov state model (master-MSM) is constructed from rates frequently accessed over a small range of force conditions. The master-MSM is shown to be applicable over a wide range of force conditions. We demonstrate application of the theory to three different biomolecular systems, namely, deca-alanine, TBA (thrombin binding aptamer), and a RNA hairpin. The master-MSM is used to estimate the kinetics at zero-force conditions, i.e., on the unbiased free-energy landscape, resulting inasmuch as 2-6 orders-of-magnitude speed-up over standard molecular dynamics.