Fast and Accurate Multidimensional Free Energy Integration

Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation

We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.

Mechanism of proton-powered c-ring rotation in a mitochondrial ATP synthase

Proton-powered c-ring rotation in mitochondrial ATP synthase is crucial to convert the transmembrane protonmotive force into torque to drive the synthesis of adenosine triphosphate (ATP). Capitalizing on recent cryo-EM structures, we aim at a structural and energetic understanding of how functional directional rotation is achieved. We performed multi-microsecond atomistic simulations to determine the free energy profiles along the c-ring rotation angle before and after the arrival of a new proton. Our results reveal that rotation proceeds by dynamic sliding of the ring over the a-subunit surface, during which interactions with conserved polar residues stabilize distinct intermediates. Ordered water chains line up for a Grotthuss-type proton transfer in one of these intermediates. After proton transfer, a high barrier prevents backward rotation and an overall drop in free energy favors forward rotation, ensuring the directionality of c-ring rotation required for the thermodynamically disfavored ATP synthesis. The essential arginine of the a-subunit stabilizes the rotated configuration through a salt bridge with the c-ring. Overall, we describe a complete mechanism for the rotation step of the ATP synthase rotor, thereby illuminating a process critical to all life at atomic resolution.

Molecular Dynamics Simulations of Ion Permeation in Human Voltage-Gated Sodium Channels

The recent determination of cryo-EM structures of voltage-gated sodium (Na_v) channels has revealed many details of these proteins. However, knowledge of ionic permeation through the Na_v pore remains limited. In this work, we performed atomistic molecular dynamics (MD) simulations to study the structural features of various neuronal Na_v channels based on homology modeling of the cryo-EM structure of the human Na_v1.4 channel and, in addition, on the recently resolved configuration for Na_v1.2. In particular, single Na⁺ permeation events during standard MD runs suggest that the ion resides in the inner part of the Na_v selectivity filter (SF). On-the-fly free energy parametrization (OTFP) temperature-accelerated molecular dynamics (TAMD) was also used to calculate two-dimensional free energy surfaces (FESs) related to single/double Na⁺ translocation through the SF of the homology-based Na_v1.2 model and the cryo-EM Na_v1.2 structure, with different realizations of the DEKA filter domain. These additional simulations revealed distinct mechanisms for single and double Na⁺ permeation through the wild-type SF, which has a charged lysine in the DEKA ring. Moreover, the configurations of the ions in the SF corresponding to the metastable states of the FESs are specific for each SF motif. Overall, the description of these mechanisms gives us new insights into ion conduction in human Na_v cryo-EM-based and cryo-EM configurations that could advance understanding of these systems and how they differ from potassium and bacterial Na_v channels.

Enhancing sampling with free-energy calculations

In recent years, considerable progress has been made to enhance sampling and help address biological questions, including, but not limited to conformational transitions in biomolecules and protein-ligand reversible binding, hitherto intractable by brute-force computer simulations. Many of these advances result from the development of a palette of methods aimed at exploring rare events through reliable free-energy calculations. The advent of new, often conceptually related methods has also rendered difficult the choice of the best suited option for a given problem. Here, we focus on geometrical transformations and algorithms designed to enhance sampling along adequately chosen progress variables, tracing their theoretical foundations, and showing how they are connected and can be blended together for improved performance.

Consistent Picture of Phosphate-Divalent Cation Binding from Models with Implicit and Explicit Electronic Polarization

The binding of divalent cations to the ubiquitous phosphate group is essential for a number of key biological processes, such as DNA compaction, RNA folding, or interactions of some proteins with membranes. Yet, probing their binding sites, modes, and associated binding free energy is a challenge for both experiments and simulations. In simulations, standard force fields strongly overestimate the interaction between phosphate groups and divalent cations. Here, we examine how different strategies to include electronic polarization effects in force fields─implicitly, through the use of scaled charges or pair-specific Lennard-Jones parameters, or explicitly, with the polarizable force fields Drude and AMOEBA─capture the interactions of a model phosphate compound, dimethyl phosphate, with calcium and magnesium divalent cations. We show that both implicit and explicit approaches, when carefully parameterized, are successful in capturing the overall binding free energy and that common trends emerge from the comparison of different simulation approaches. Overall, the binding is very moderate, slightly weaker for Ca²⁺ than Mg²⁺, and the solvent-shared ion pair is slightly more stable than the contact monodentate ion pair. The bidentate ion pair is higher in energy (or even fully unstable for Mg²⁺). Our results thus suggest practical ways to capture the divalent cations with biomolecular phosphate groups in complex biochemical systems. In particular, the computational efficiency of implicit models makes them ideally suited for large-scale simulations of biological assemblies, with improved accuracy compared to state-of-the-art fixed-charge force fields.

Human Learning for Molecular Simulations: The Collective Variables Dashboard in VMD

The Collective Variables Dashboard is a software tool for real-time, seamless exploration of molecular structures and trajectories in a customizable space of collective variables. The Dashboard arises from the integration of the Collective Variables Module (also known as Colvars) with the visualization software VMD, augmented with a fully discoverable graphical interface offering interactive workflows for the design and analysis of collective variables. Typical use cases include a priori design of collective variables for enhanced sampling and free energy simulations as well as analysis of any type of simulation or collection of structures in a collective variable space. A combination of those cases commonly occurs when preliminary simulations, biased or unbiased, reveal that an optimized set of collective variables is necessary to improve sampling in further simulations. Then the Dashboard provides an efficient way to intuitively explore the space of likely collective variables, validate them on existing data, and use the resulting collective variable definitions directly in further biased simulations using the Collective Variables Module. Visualization of biasing energies and forces is proposed to help analyze or plan biased simulations. We illustrate the use of the Dashboard on two applications: discovering coordinates to describe ligand unbinding from a protein binding site and designing volume-based variables to bias the hydration of a transmembrane pore.

Pyranose Ring Puckering Thermodynamics for Glycan Monosaccharides Associated with Vertebrate Proteins

The conformational properties of carbohydrates can contribute to protein structure directly through covalent conjugation in the cases of glycoproteins and proteoglycans and indirectly in the case of transmembrane proteins embedded in glycolipid-containing bilayers. However, there continue to be significant challenges associated with experimental structural biology of such carbohydrate-containing systems. All-atom explicit-solvent molecular dynamics simulations provide a direct atomic resolution view of biomolecular dynamics and thermodynamics, but the accuracy of the results depends on the quality of the force field parametrization used in the simulations. A key determinant of the conformational properties of carbohydrates is ring puckering. Here, we applied extended system adaptive biasing force (eABF) all-atom explicit-solvent molecular dynamics simulations to characterize the ring puckering thermodynamics of the ten common pyranose monosaccharides found in vertebrate biology (as represented by the CHARMM carbohydrate force field). The results, along with those for idose, demonstrate that the CHARMM force field reliably models ring puckering across this diverse set of molecules, including accurately capturing the subtle balance between 4C1 and 1C4 chair conformations in the cases of iduronate and of idose. This suggests the broad applicability of the force field for accurate modeling of carbohydrate-containing vertebrate biomolecules such as glycoproteins, proteoglycans, and glycolipids.