Probing Translocation in Mutants of the Anthrax Channel: Atomically Detailed Simulations with Milestoning

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

Structural Mechanism of ω-Currents in a Mutated Kv7.2 Voltage Sensor Domain from Molecular Dynamics Simulations

Activation of voltage-gated ion channels is regulated by conformational changes of the voltage sensor domains (VSDs), four water- and ion-impermeable modules peripheral to the central, permeable pore domain. Anomalous currents, defined as ω-currents, have been recorded in response to mutations of residues on the VSD S4 helix and associated with ion fluxes through the VSDs. In humans, gene defects in the potassium channel Kv7.2 result in a broad range of epileptic disorders, from benign neonatal seizures to severe epileptic encephalopathies. Experimental evidence suggests that the R207Q mutation in S4, associated with peripheral nerve hyperexcitability, induces ω-currents at depolarized potentials, but the fine structural details are still elusive. In this work, we use atom-detailed molecular dynamics simulations and a refined model structure of the Kv7.2 VSD in the active conformation in a membrane/water environment to study the effect of R207Q and four additional mutations of proven clinical importance. Our results demonstrate that the R207Q mutant shows the most pronounced increase of hydration in the internal VSD cavity, a feature favoring the occurrence of ω-currents. Free energy and kinetics calculations of sodium permeation through the native and mutated VSD indicate as more favorable the formation of a cationic current in the latter. Overall, our simulations establish a mechanistic linkage between genetic variations and their physiological outcome, by providing a computational description that includes both thermodynamic and kinetic features of ion permeation associated with ω-currents.

Milestoning: An Efficient Approach for Atomically Detailed Simulations of Kinetics in Biophysics

Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.

Kinetics and free energy of ligand dissociation using weighted ensemble milestoning

We consider the recently developed weighted ensemble milestoning (WEM) scheme [D. Ray and I. Andricioaei, J. Chem. Phys. 152, 234114 (2020)] and test its capability of simulating ligand-receptor dissociation dynamics. We performed WEM simulations on the following host-guest systems: Na⁺/Cl^- ion pair and 4-hydroxy-2-butanone ligand with FK506 binding protein. As a proof of principle, we show that the WEM formalism reproduces the Na⁺/Cl^- ion pair dissociation timescale and the free energy profile obtained from long conventional MD simulation. To increase the accuracy of WEM calculations applied to kinetics and thermodynamics in protein-ligand binding, we introduced a modified WEM scheme called weighted ensemble milestoning with restraint release (WEM-RR), which can increase the number of starting points per milestone without adding additional computational cost. WEM-RR calculations obtained a ligand residence time and binding free energy in agreement with experimental and previous computational results. Moreover, using the milestoning framework, the binding time and rate constants, dissociation constants, and committor probabilities could also be calculated at a low computational cost. We also present an analytical approach for estimating the association rate constant (k_on) when binding is primarily diffusion driven. We show that the WEM method can efficiently calculate multiple experimental observables describing ligand-receptor binding/unbinding and is a promising candidate for computer-aided inhibitor design.