Exploration of high dimensional free energy landscapes by a combination of temperature-accelerated sliced sampling and parallel biasing

Buckets Instead of Umbrellas for Enhanced Sampling and Free Energy Calculations

Umbrella sampling has been a workhorse for free energy calculations in molecular simulations for several decades. In conventional umbrella sampling, restraining bias potentials are strategically applied along one or several collective variables. Major drawbacks associated with this method are the requirement of a large number of bias windows and the poor sampling of the transverse coordinates. In this work, we propose an alternate formalism that departs from the traditional umbrella sampling to mitigate these issues, where we replace umbrella-type restraining bias potentials with bucket-type wall potentials. This modification permits one to formulate an efficient computational strategy leveraging wall potentials and metadynamics sampling. This new method, called "bucket sampling", can significantly reduce the computational cost of obtaining converged high-dimensional free energy surfaces. Extensions of the proposed method with temperature acceleration and replica exchange solute tempering are also demonstrated.

Comprehensive Analysis of Coupled Proline Cis-Trans States in Bradykinin Using ωBP-REMD Simulations

It is well-known that proline (Pro) cis-trans isomerization plays a decisive role in the folding and stabilization of proteins. The conformational coupling between isomerization states of different Pro residues in proteins during conformational adaptation processes is not well understood. In the present work, we investigate the coupled cis-trans isomerization of three Pro residues using bradykinin (BK), a partially unstructured nonapeptide hormone, as a model system. We use a recently developed enhanced-sampling molecular dynamics method (ω-bias potential replica exchange molecular dynamics; ωBP-REMD) that allows us to exhaustively sample all combinations of Pro isomer states and obtain converged probability densities of all eight state combinations within 885 ns ωBP-REMD simulations. In agreement with experiment, the all-trans state is seen to be the preferred isomer of zwitterionic aqueous BK. In about a third of its structures, this state presents the characteristic C-terminal β-turn conformation; however, other isomer combinations also contribute significantly to the structural ensemble. Unbiased probabilities can be projected onto the peptide bond dihedral angles of the three Pro residues. This unveils the interdependence of the individual Pro isomerization states, i.e., a possible coupling of the different Pro isomers. The cis/trans equilibrium of a Pro residue can change by up to 2.5 kcal·mol-1, depending on the isomerization state of other Pro residues. For example, for Pro7, the simulations indicate that its cis state becomes favored compared to its trans state when Pro2 is switched from the trans state to the cis state. Our findings demonstrate the efficiency of the ωBP-REMD methodology and suggest that the coupling of Pro isomerization states may play an even more decisive role in larger folded proteins subject to more conformational restraints.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Temperature Accelerated Sliced Sampling to Probe Ligand Dissociation from Protein

Modeling ligand unbinding in proteins to estimate the free energy of binding and probing the mechanism presents several challenges. They primarily pertain to the entropic bottlenecks resulting from protein and solvent conformations. While exploring the unbinding processes using enhanced sampling techniques, very long simulations are required to sample all of the conformational states as the system gets trapped in local free energy minima along transverse coordinates. Here, we demonstrate that temperature accelerated sliced sampling (TASS) is an ideal approach to overcome some of the difficulties faced by conventional sampling methods in studying ligand unbinding. Using TASS, we study the unbinding of avibactam inhibitor molecules from the Class C β-lactamase (CBL) active site. Extracting CBL-avibactam unbinding free energetics, unbinding pathways, and identifying critical interactions from the TASS simulations are demonstrated.