phbuilder: A Tool for Efficiently Setting up Constant pH Molecular Dynamics Simulations in GROMACS.

Constant pH molecular dynamics (MD) is a powerful technique that allows the protonation state of residues to change dynamically, thereby enabling the study of pH dependence in a manner that has not been possible before. Recently, a constant pH implementation was incorporated into the GROMACS MD package. Although this implementation provides good accuracy and performance, manual modification and the preparation of simulation input files are required, which can be complicated, tedious, and prone to errors. To simplify and automate the setup process, we present phbuilder, a tool that automatically prepares constant pH MD simulations for GROMACS by modifying the input structure and topology as well as generating the necessary parameter files. phbuilder can prepare constant pH simulations from both initial structures and existing simulation systems, and it also provides functionality for performing titrations and single-site parametrizations of new titratable group types. The tool is freely available at www.gitlab.com/gromacs-constantph. We anticipate that phbuilder will make constant pH simulations easier to set up, thereby making them more accessible to the GROMACS user community.

On the Path to Optimal Alchemistry.

Alchemical free energy calculations have become a standard and widely used tool, in particular for calculating and comparing binding affinities of drugs. Although methods to compute such free energies have improved significantly over the last decades, the choice of path between the end states of interest is usually still the same as two decades ago. We will show that there is a fundamentally arbitrary, implicit choice of parametrization of this path. To address this, the notion of the length of a path or a metric is required. A metric recently introduced in the context of the accelerated weight histogram method also proves to be very useful here. We demonstrate that this metric can not only improve the efficiency of sampling along a given path, but that it can also be used to improve the actual choice of path. For a set of relevant use cases, the combination of these improvements can increase the efficiency of alchemical free energy calculations by up to a factor 16.

Skin permeability prediction with MD simulation sampling spatial and alchemical reaction coordinates.

A molecular-level understanding of skin permeation may rationalize and streamline product development, and improve quality and control, of transdermal and topical drug delivery systems. It may also facilitate toxicity and safety assessment of cosmetics and skin care products. Here, we present new molecular dynamics simulation approaches that make it possible to efficiently sample the free energy and local diffusion coefficient across the skin's barrier structure to predict skin permeability and the effects of chemical penetration enhancers. In particular, we introduce a new approach to use two-dimensional reaction coordinates in the accelerated weight histogram method, where we combine sampling along spatial coordinates with an alchemical perturbation virtual coordinate. We present predicted properties for 20 permeants, and demonstrate how our approach improves correlation with ex vivo/in vitro skin permeation data. For the compounds included in this study, the obtained log KPexp-calc mean square difference was 0.9 cm2 h-2.

Best Practices in Constant pH MD Simulations: Accuracy and Sampling.

Various approaches have been proposed to include the effect of pH in molecular dynamics (MD) simulations. Among these, the λ-dynamics approach proposed by Brooks and co-workers [Kong, X.; Brooks III, C. L. J. Chem. Phys. 1996, 105, 2414-2423] can be performed with little computational overhead and hfor each typeence be used to routinely perform MD simulations at microsecond time scales, as shown in the accompanying paper [Aho, N. et al. J. Chem. Theory Comput. 2022, DOI: 10.1021/acs.jctc.2c00516]. At such time scales, however, the accuracy of the molecular mechanics force field and the parametrization becomes critical. Here, we address these issues and provide the community with guidelines on how to set up and perform long time scale constant pH MD simulations. We found that barriers associated with the torsions of side chains in the CHARMM36m force field are too high for reaching convergence in constant pH MD simulations on microsecond time scales. To avoid the high computational cost of extending the sampling, we propose small modifications to the force field to selectively reduce the torsional barriers. We demonstrate that with such modifications we obtain converged distributions of both protonation and torsional degrees of freedom and hence consistent pKa estimates, while the sampling of the overall configurational space accessible to proteins is unaffected as compared to normal MD simulations. We also show that the results of constant pH MD depend on the accuracy of the correction potentials. While these potentials are typically obtained by fitting a low-order polynomial to calculated free energy profiles, we find that higher order fits are essential to provide accurate and consistent results. By resolving problems in accuracy and sampling, the work described in this and the accompanying paper paves the way to the widespread application of constant pH MD beyond pKa prediction.

Scalable Constant pH Molecular Dynamics in GROMACS.

Molecular dynamics (MD) computer simulations are used routinely to compute atomistic trajectories of complex systems. Systems are simulated in various ensembles, depending on the experimental conditions one aims to mimic. While constant energy, temperature, volume, and pressure are rather straightforward to model, pH, which is an equally important parameter in experiments, is more difficult to account for in simulations. Although a constant pH algorithm based on the λ-dynamics approach by Brooks and co-workers [Kong, X.; Brooks III, C. L. J. Chem. Phys.1996, 105, 2414-2423] was implemented in a fork of the GROMACS molecular dynamics program, uptake has been rather limited, presumably due to the poor scaling of that code with respect to the number of titratable sites. To overcome this limitation, we implemented an alternative scheme for interpolating the Hamiltonians of the protonation states that makes the constant pH molecular dynamics simulations almost as fast as a normal MD simulation with GROMACS. In addition, we implemented a simpler scheme, called multisite representation, for modeling side chains with multiple titratable sites, such as imidazole rings. This scheme, which is based on constraining the sum of the λ-coordinates, not only reduces the complexity associated with parametrizing the intramolecular interactions between the sites but also is easily extendable to other molecules with multiple titratable sites. With the combination of a more efficient interpolation scheme and multisite representation of titratable groups, we anticipate a rapid uptake of constant pH molecular dynamics simulations within the GROMACS user community.

Heterogeneous parallelization and acceleration of molecular dynamics simulations in GROMACS.

The introduction of accelerator devices such as graphics processing units (GPUs) has had profound impact on molecular dynamics simulations and has enabled order-of-magnitude performance advances using commodity hardware. To fully reap these benefits, it has been necessary to reformulate some of the most fundamental algorithms, including the Verlet list, pair searching, and cutoffs. Here, we present the heterogeneous parallelization and acceleration design of molecular dynamics implemented in the GROMACS codebase over the last decade. The setup involves a general cluster-based approach to pair lists and non-bonded pair interactions that utilizes both GPU and central processing unit (CPU) single instruction, multiple data acceleration efficiently, including the ability to load-balance tasks between CPUs and GPUs. The algorithm work efficiency is tuned for each type of hardware, and to use accelerators more efficiently, we introduce dual pair lists with rolling pruning updates. Combined with new direct GPU-GPU communication and GPU integration, this enables excellent performance from single GPU simulations through strong scaling across multiple GPUs and efficient multi-node parallelization.

Riemann metric approach to optimal sampling of multidimensional free-energy landscapes.

Exploring the free-energy landscape along reaction coordinates or system parameters λ is central to many studies of high-dimensional model systems in physics, e.g., large molecules or spin glasses. In simulations this usually requires sampling conformational transitions or phase transitions, but efficient sampling is often difficult to attain due to the roughness of the energy landscape. For Boltzmann distributions, crossing rates decrease exponentially with free-energy barrier heights. Thus, exponential acceleration can be achieved in simulations by applying an artificial bias along λ tuned such that a flat target distribution is obtained. A flat distribution is, however, an ambiguous concept unless a proper metric is used and is generally suboptimal. Here we propose a multidimensional Riemann metric, which takes the local diffusion into account, and redefine uniform sampling such that it is invariant under nonlinear coordinate transformations. We use the metric in combination with the accelerated weight histogram method, a free-energy calculation and sampling method, to adaptively optimize sampling toward the target distribution prescribed by the metric. We demonstrate that for complex problems, such as molecular dynamics simulations of DNA base-pair opening, sampling uniformly according to the metric, which can be calculated without significant computational overhead, improves sampling efficiency by 50%-70%.

Permeability and ammonia selectivity in aquaporin TIP2;1: linking structure to function.

Aquaporin TIP2;1 is a protein channel permeable to both water and ammonia. The structural origin of ammonia selectivity remains obscure, but experiments have revealed that a double mutation renders it impermeable to ammonia without affecting water permeability. Here, we aim to reproduce and explain these observations by performing an extensive mutational study using microsecond long molecular dynamics simulations, applying the two popular force fields CHARMM36 and Amber ff99SB-ILDN. We calculate permeabilities and free energies along the channel axis for ammonia and water. For one force field, the permeability of the double mutant decreases by a factor of 2.5 for water and 4 for ammonia, increasing water selectivity by a factor of 1.6. We attribute this effect to decreased entropy of water in the pore, due to the observed increase in pore-water interactions and narrower pore. Additionally, we observe spontaneous opening and closing of the pore on the cytosolic side, which suggests a gating mechanism for the pore. Our results show that sampling methods and simulation times are sufficient to delineate even subtle effects of mutations on structure and function and to capture important long-timescale events, but also underline the importance of improving models further.

Sequence dependency of canonical base pair opening in the DNA double helix.

The flipping-out of a DNA base from the double helical structure is a key step of many cellular processes, such as DNA replication, modification and repair. Base pair opening is the first step of base flipping and the exact mechanism is still not well understood. We investigate sequence effects on base pair opening using extensive classical molecular dynamics simulations targeting the opening of 11 different canonical base pairs in two DNA sequences. Two popular biomolecular force fields are applied. To enhance sampling and calculate free energies, we bias the simulation along a simple distance coordinate using a newly developed adaptive sampling algorithm. The simulation is guided back and forth along the coordinate, allowing for multiple opening pathways. We compare the calculated free energies with those from an NMR study and check assumptions of the model used for interpreting the NMR data. Our results further show that the neighboring sequence is an important factor for the opening free energy, but also indicates that other sequence effects may play a role. All base pairs are observed to have a propensity for opening toward the major groove. The preferred opening base is cytosine for GC base pairs, while for AT there is sequence dependent competition between the two bases. For AT opening, we identify two non-canonical base pair interactions contributing to a local minimum in the free energy profile. For both AT and CG we observe long-lived interactions with water and with sodium ions at specific sites on the open base pair.

Direct-Space Corrections Enable Fast and Accurate Lorentz-Berthelot Combination Rule Lennard-Jones Lattice Summation.

Long-range lattice summation techniques such as the particle-mesh Ewald (PME) algorithm for electrostatics have been revolutionary to the precision and accuracy of molecular simulations in general. Despite the performance penalty associated with lattice summation electrostatics, few biomolecular simulations today are performed without it. There are increasingly strong arguments for moving in the same direction for Lennard-Jones (LJ) interactions, and by using geometric approximations of the combination rules in reciprocal space, we have been able to make a very high-performance implementation available in GROMACS. Here, we present a new way to correct for these approximations to achieve exact treatment of Lorentz-Berthelot combination rules within the cutoff, and only a very small approximation error remains outside the cutoff (a part that would be completely ignored without LJ-PME). This not only improves accuracy by almost an order of magnitude but also achieves absolute biomolecular simulation performance that is an order of magnitude faster than any other available lattice summation technique for LJ interactions. The implementation includes both CPU and GPU acceleration, and its combination with improved scaling LJ-PME simulations now provides performance close to the truncated potential methods in GROMACS but with much higher accuracy.

GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit.

MOTIVATION: Molecular simulation has historically been a low-throughput technique, but faster computers and increasing amounts of genomic and structural data are changing this by enabling large-scale automated simulation of, for instance, many conformers or mutants of biomolecules with or without a range of ligands. At the same time, advances in performance and scaling now make it possible to model complex biomolecular interaction and function in a manner directly testable by experiment. These applications share a need for fast and efficient software that can be deployed on massive scale in clusters, web servers, distributed computing or cloud resources. RESULTS: Here, we present a range of new simulation algorithms and features developed during the past 4 years, leading up to the GROMACS 4.5 software package. The software now automatically handles wide classes of biomolecules, such as proteins, nucleic acids and lipids, and comes with all commonly used force fields for these molecules built-in. GROMACS supports several implicit solvent models, as well as new free-energy algorithms, and the software now uses multithreading for efficient parallelization even on low-end systems, including windows-based workstations. Together with hand-tuned assembly kernels and state-of-the-art parallelization, this provides extremely high performance and cost efficiency for high-throughput as well as massively parallel simulations. AVAILABILITY: GROMACS is an open source and free software available from http://www.gromacs.org. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Probing microscopic material properties inside simulated membranes through spatially resolved three-dimensional local pressure fields and surface tensions.

Cellular lipid membranes are spatially inhomogeneous soft materials. Materials properties such as pressure and surface tension thus show important microscopic-scale variation that is critical to many biological functions. We present a means to calculate pressure and surface tension in a 3D-resolved manner within molecular-dynamics simulations and show how such measurements can yield important insight. We also present the first corrections to local virial and pressure fields to account for the constraints typically used in lipid simulations that otherwise cause problems in highly oriented systems such as bilayers. Based on simulations of an asymmetric bacterial ion channel in a POPC bilayer, we demonstrate how 3D-resolved pressure can probe for both short-range and long-range effects from the protein on the membrane environment. We also show how surface tension is a sensitive metric for inter-leaflet equilibrium and can be used to detect even subtle imbalances between bilayer leaflets in a membrane-protein simulation. Since surface tension is known to modulate the function of many proteins, this effect is an important consideration for predictions of ion channel function. We outline a strategy by which our local pressure measurements, which we make available within a version of the GROMACS simulation package, may be used to design optimally equilibrated membrane-protein simulations.

Lennard-Jones Lattice Summation in Bilayer Simulations Has Critical Effects on Surface Tension and Lipid Properties.

The accuracy of electrostatic interactions in molecular dynamics advanced tremendously with the introduction of particle-mesh Ewald (PME) summation almost 20 years ago. Lattice summation electrostatics is now the de facto standard for most types of biomolecular simulations, and in particular, for lipid bilayers, it has been a critical improvement due to the large charges typically present in zwitterionic lipid headgroups. In contrast, Lennard-Jones interactions have continued to be handled with increasingly longer cutoffs, partly because few alternatives have been available despite significant difficulties in tuning cutoffs and parameters to reproduce lipid properties. Here, we present a new Lennard-Jones PME implementation applied to lipid bilayers. We confirm that long-range contributions are well approximated by dispersion corrections in simple systems such as pentadecane (which makes parameters transferable), but for inhomogeneous and anisotropic systems such as lipid bilayers there are large effects on surface tension, resulting in up to 5.5% deviations in area per lipid and order parameters-far larger than many differences for which reparameterization has been attempted. We further propose an approximation for combination rules in reciprocal space that significantly reduces the computational cost of Lennard-Jones PME and makes accurate treatment of all nonbonded interactions competitive with simulations employing long cutoffs. These results could potentially have broad impact on important applications such as membrane proteins and free energy calculations.

The free energy barrier for arginine gating charge translation is altered by mutations in the voltage sensor domain.

The gating of voltage-gated ion channels is controlled by the arginine-rich S4 helix of the voltage-sensor domain moving in response to an external potential. Recent studies have suggested that S4 moves in three to four steps to open the conducting pore, thus visiting several intermediate conformations during gating. However, the exact conformational changes are not known in detail. For instance, it has been suggested that there is a local rotation in the helix corresponding to short segments of a 3(10)-helix moving along S4 during opening and closing. Here, we have explored the energetics of the transition between the fully open state (based on the X-ray structure) and the first intermediate state towards channel closing (C1), modeled from experimental constraints. We show that conformations within 3 Å of the X-ray structure are obtained in simulations starting from the C1 model, and directly observe the previously suggested sliding 3(10)-helix region in S4. Through systematic free energy calculations, we show that the C1 state is a stable intermediate conformation and determine free energy profiles for moving between the states without constraints. Mutations indicate several residues in a narrow hydrophobic band in the voltage sensor contribute to the barrier between the open and C1 states, with F233 in the S2 helix having the largest influence. Substitution for smaller amino acids reduces the transition cost, while introduction of a larger ring increases it, largely confirming experimental activation shift results. There is a systematic correlation between the local aromatic ring rotation, the arginine barrier crossing, and the corresponding relative free energy. In particular, it appears to be more advantageous for the F233 side chain to rotate towards the extracellular side when arginines cross the hydrophobic region.

310-helix conformation facilitates the transition of a voltage sensor S4 segment toward the down state.

The activation of voltage-gated ion channels is controlled by the S4 helix, with arginines every third residue. The x-ray structures are believed to reflect an open-inactivated state, and models propose combinations of translation, rotation, and tilt to reach the resting state. Recently, experiments and simulations have independently observed occurrence of 3(10)-helix in S4. This suggests S4 might make a transition from α- to 3(10)-helix in the gating process. Here, we show 3(10)-helix structure between Q1 and R3 in the S4 segment of a voltage sensor appears to facilitate the early stage of the motion toward a down state. We use multiple microsecond-steered molecular simulations to calculate the work required for translating S4 both as α-helix and transformed to 3(10)-helix. The barrier appears to be caused by salt-bridge reformation simultaneous to R4 passing the F233 hydrophobic lock, and it is almost a factor-two lower with 3(10)-helix. The latter facilitates translation because R2/R3 line up to face E183/E226, which reduces the requirement to rotate S4. This is also reflected in a lower root mean-square deviation distortion of the rest of the voltage sensor. This supports the 3(10) hypothesis, and could explain some of the differences between the open-inactivated- versus activated-states.

Ion pairing in aqueous electrolyte solutions with biologically relevant anions.

We performed molecular simulations to study ion pairing in aqueous solutions. Our results indicate that ion specific interactions of Li(+), Na(+), and K(+) with the dimethyl phosphate anion are solvent-mediated. The same mechanism applies to carboxylate ions, as has been illustrated in earlier simulations of aqueous alkali acetate solutions. Contact ion pairs play only a minor role--or no role at all--in determining the solution structure and ion specific thermodynamics of these systems. On the basis of the Kirkwood-Buff theory of solution we furthermore show that the well-known reversal of the Hofmeister series of salt activity coefficients, comparing chloride or bromide with dimethyl phosphate or acetate, is caused by changing from a contact pairing mechanism in the former system to a solvent-mediated interaction mechanism in the latter system.

SHAKE parallelization.

SHAKE is a widely used algorithm to impose general holonomic constraints during molecular simulations. By imposing constraints on stiff degrees of freedom that require integration with small time steps (without the constraints) we are able to calculate trajectories with time steps larger by approximately a factor of two. The larger time step makes it possible to run longer simulations. Another approach to extend the scope of Molecular Dynamics is parallelization. Parallelization speeds up the calculation of the forces between the atoms and makes it possible to compute longer trajectories with better statistics for thermodynamic and kinetic averages. A combination of SHAKE and parallelism is therefore highly desired. Unfortunately, the most widely used SHAKE algorithm (of bond relaxation) is inappropriate for parallelization and alternatives are needed. The alternatives must minimize communication, lead to good load balancing, and offer significantly better performance than the bond relaxation approach. The algorithm should also scale with the number of processors. We describe the theory behind different implementations of constrained dynamics on parallel systems, and their implementation on common architectures.

Driving forces for adsorption of amphiphilic peptides to the air-water interface.

We have studied the partitioning of amphiphilic peptides at the air-water interface. The free energy of adsorption from bulk to interface was calculated by determining the potential of mean force via atomistic molecular dynamics simulations. To this end a method is introduced to restrain or constrain the center of mass of a group of molecules in a periodic system. The model amphiphilic peptides are composed of alternating valine and asparagine residues. The decomposition of the free energy difference between the bulk and interface is studied for different peptide block lengths. Our analysis revealed that for short amphiphilic peptides the surface driving force dominantly stems from the dehydration of hydrophobic side chains. The only opposing force is associated with the loss of orientational freedom of the peptide at the interface. For the peptides studied, the free energy difference scales linearly with the size of the molecule, since the peptides mainly adopt extended conformations both in bulk and at the interface. The free energy difference depends strongly on the water model, which can be rationalized through the hydration thermodynamics of hydrophobic solutes. Finally, we measured the reduction of the surface tension associated with complete coverage of the interface with peptides.

Chain packing in polycarbonate glasses.

Chain packing in homogeneous blends of carbonate (13)C-labeled bisphenol A polycarbonate with either (i) CF(3)-labeled bisphenol A polycarbonate or (ii) ring-F-labeled bisphenol A polycarbonate has been characterized using (13)C{(19)F} rotational-echo double-resonance (REDOR) nuclear magnetic resonance. In both blends, the (13)C observed spin was at high concentration, and the (19)F dephasing or probe spin was at low concentration. In this situation, an analysis in terms of a distribution of isolated heteronuclear pairs of spins is valid. Nearest-neighbor separation of (13)C and (19)F labels was determined by accurately mapping the initial dipolar evolution using a shifted-pulse version of REDOR. Based on the results of this experiment, the average distance from a ring-fluorine to the nearest (13)C=O is more than 1.2 A greater than the corresponding CF(3)-(13)C=O distance. Next-nearest and more-distant-neighbor separations of labels were measured in a 416-rotor-cycle constant-time version of REDOR for both blends. Statistically significant local order was established for the nearest-neighbor labels in the methyl-labeled blend. These interchain packing results are in qualitative agreement with predictions based on coarse-grained simulations of a specially adapted model for bisphenol A polycarbonate. The model itself has been previously used to determine static and dynamic properties of polycarbonate with results in good agreement with those from rheological and neutron scattering experiments.