Relative free-energy calculations for scaffold hopping-type transformations with an automated RE-EDS sampling procedure.

The calculation of relative free-energy differences between different compounds plays an important role in drug design to identify potent binders for a given protein target. Most rigorous methods based on molecular dynamics simulations estimate the free-energy difference between pairs of ligands. Thus, the comparison of multiple ligands requires the construction of a "state graph", in which the compounds are connected by alchemical transformations. The computational cost can be optimized by reducing the state graph to a minimal set of transformations. However, this may require individual adaptation of the sampling strategy if a transformation process does not converge in a given simulation time. In contrast, path-free methods like replica-exchange enveloping distribution sampling (RE-EDS) allow the sampling of multiple states within a single simulation without the pre-definition of alchemical transition paths. To optimize sampling and convergence, a set of RE-EDS parameters needs to be estimated in a pre-processing step. Here, we present an automated procedure for this step that determines all required parameters, improving the robustness and ease of use of the methodology. To illustrate the performance, the relative binding free energies are calculated for a series of checkpoint kinase 1 inhibitors containing challenging transformations in ring size, opening/closing, and extension, which reflect changes observed in scaffold hopping. The simulation of such transformations with RE-EDS can be conducted with conventional force fields and, in particular, without soft bond-stretching terms.

Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics.

Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multimethod approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable ("dry" and "wet") hydration states. The resulting dry-wet transition rates are then used in a spatially dependent multistate continuous-time Markov chain Brownian dynamics simulation and the related Fokker-Planck equation calculations of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semiquantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of nonequilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding vs. unbinding. Our study thus provides a significant step forward toward efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.

Volume-scaled common nearest neighbor clustering algorithm with free-energy hierarchy.

The combination of Markov state modeling (MSM) and molecular dynamics (MD) simulations has been shown in recent years to be a valuable approach to unravel the slow processes of molecular systems with increasing complexity. While the algorithms for intermediate steps in the MSM workflow such as featurization and dimensionality reduction have been specifically adapted to MD datasets, conventional clustering methods are generally applied to the discretization step. This work adds to recent efforts to develop specialized density-based clustering algorithms for the Boltzmann-weighted data from MD simulations. We introduce the volume-scaled common nearest neighbor (vs-CNN) clustering that is an adapted version of the common nearest neighbor (CNN) algorithm. A major advantage of the proposed algorithm is that the introduced density-based criterion directly links to a free-energy notion via Boltzmann inversion. Such a free-energy perspective allows a straightforward hierarchical scheme to identify conformational clusters at different levels of a generally rugged free-energy landscape of complex molecular systems.

Connecting dynamic reweighting Algorithms: Derivation of the dynamic reweighting family tree.

Thermally driven processes of molecular systems include transitions of energy barriers on the microsecond timescales and higher. Sufficient sampling of such processes with molecular dynamics simulations is challenging and often requires accelerating slow transitions using external biasing potentials. Different dynamic reweighting algorithms have been proposed in the past few years to recover the unbiased kinetics from biased systems. However, it remains an open question if and how these dynamic reweighting approaches are connected. In this work, we establish the link between the two main reweighting types, i.e., path-based and energy-based reweighting. We derive a path-based correction factor for the energy-based dynamic histogram analysis method, thus connecting the previously separate reweighting types. We show that the correction factor can be used to combine the advantages of path-based and energy-based reweighting algorithms: it is integrator independent, more robust, and at the same time able to reweight time-dependent biases. We can furthermore demonstrate the relationship between two independently derived path-based reweighting algorithms. Our theoretical findings are verified on a one-dimensional four-well system. By connecting different dynamic reweighting algorithms, this work helps to clarify the strengths and limitations of the different methods and enables a more robust usage of the combined types.

Affinity, kinetics, and pathways of anisotropic ligands binding to hydrophobic model pockets.

Using explicit-water molecular dynamics simulations of a generic pocket-ligand model, we investigate how chemical and shape anisotropy of small ligands influences the affinities, kinetic rates, and pathways for their association with hydrophobic binding sites. In particular, we investigate aromatic compounds, all of similar molecular size, but distinct by various hydrophilic or hydrophobic residues. We demonstrate that the most hydrophobic sections are in general desolvated primarily upon binding to the cavity, suggesting that specific hydration of the different chemical units can steer the orientation pathways via a "hydrophobic torque." Moreover, we find that ligands with bimodal orientation fluctuations have significantly increased kinetic barriers for binding compared to the kinetic barriers previously observed for spherical ligands due to translational fluctuations. We exemplify that these kinetic barriers, which are ligand specific, impact both binding and unbinding times for which we observe considerable differences between our studied ligands.

Curvature dependence of hydrophobic hydration dynamics.

We investigate the solute curvature dependence of water dynamics in the vicinity of hydrophobic spherical solutes using molecular dynamics simulations. For both the lateral and perpendicular diffusivity, as well as for H-bond kinetics of water in the first hydration shell, we find a nonmonotonic solute-size dependence, exhibiting extrema close to the well-known structural crossover length scale for hydrophobic hydration. Additionally, we find an apparent anomalous diffusion for water moving parallel to the surface of small solutes, which, however, can be explained by topology effects. Our findings regarding the intimate connection between solute curvature and water dynamics has implications for our understanding of hydration dynamics at heterogeneous biomolecular surfaces.

N-Glycosylation Enhances Conformational Flexibility of Protein Disulfide Isomerase Revealed by Microsecond Molecular Dynamics and Markov State Modeling.

Secreted proteins of eukaryotes are decorated with branched carbohydrate oligomers called glycans. This fact is only starting to be considered for in silico investigations of protein dynamics. Using all-atom molecular dynamics (MD) simulations and Markov state modeling (MSM), we unveil the influence of glycans on the conformational flexibility of the multidomain protein disulfide isomerase (PDI), which is a ubiquitous chaperone in the endoplasmic reticulum (ER). Yeast PDI (yPDI) from Saccharomyces cerevisiae is glycosylated at asparagine side chains and the knowledge of its five modified sites enables a realistic computational modeling. We compare simulations of glycosylated and unglycosylated yPDI and find that the presence of glycan-glycan and glycan-protein interactions influences the flexibility of PDI in different ways. For example, glycosylation reduces interdomain interactions, shifting the conformational ensemble toward more open, extended structures. In addition, we compare our results on yPDI with structural information of homologous proteins such as human PDI (hPDI), which is natively unglycosylated. Interestingly, hPDI lacks a surface recess that is present in yPDI. We find that glycosylation of yPDI facilitates its catalytic site to reach close to this surface recess. Hence, this might point to a possible functional relevance of glycosylation in yeast to act on substrates, while glycosylation seems redundant for the human homologous protein. We conclude that glycosylation is fundamental for protein dynamics, making it a necessity for a truthful representation of the flexibility and function in in silico studies of glycoproteins.

Glycan-protein interactions determine kinetics of N-glycan remodeling.

A hallmark of N-linked glycosylation in the secretory compartments of eukaryotic cells is the sequential remodeling of an initially uniform oligosaccharide to a site-specific, heterogeneous ensemble of glycostructures on mature proteins. To understand site-specific processing, we used protein disulfide isomerase (PDI), a model protein with five glycosylation sites, for molecular dynamics (MD) simulations and compared the result to a biochemical in vitro analysis with four different glycan processing enzymes. As predicted by an analysis of the accessibility of the N-glycans for their processing enzymes derived from the MD simulations, N-glycans at different glycosylation sites showed different kinetic properties for the processing enzymes. In addition, altering the tertiary structure of the glycoprotein PDI affected its N-glycan remodeling in a site-specific way. We propose that the observed differential N-glycan reactivities depend on the surrounding protein tertiary structure and lead to different glycan structures in the same protein through kinetically controlled processing pathways.

Principles for Tuning Hydrophobic Ligand-Receptor Binding Kinetics.

We investigate how to tune the rate of hydrophobic ligand-receptor association due to the role of solvent in adjustable receptor pockets by explicit-water molecular dynamics (MD) simulations. Our model considers the binding of a spherical ligand (key/guest) to a concave surface recess in a nonpolar wall as receptor (lock/host). We systematically modify the receptor's physicochemical properties in terms of geometry and dispersion attraction which, in turn, alter the water occupancy and fluctuations within the pocket. We demonstrate that even minor pocket modifications can lead to a significant acceleration of the water-mediated association. For example, the binding switches from comparably slow to fast if the binding pocket becomes only slightly deeper. We find that the degree of hydrophobicity, characterized by hydration occupancy and its fluctuations, clearly correlates with the binding times and, for instance, links the sudden acceleration to an abrupt increase in hydrophobicity. For a deeper analysis based on passage time theory, we quantify the intimate coupling between solvent fluctuations and the ligand's local dynamics and friction. The coupling exhibits substantial nonequilibrium effects and maximizes shortly before binding, which slows down the binding kinetics in all cases. In summary, we rationalize how the physicochemical properties of a nonpolar, concave binding site tune key-lock binding kinetics due to water-mediated forces and fluctuations. Our study thus complements the profound understanding of the solvent's influence in host-guest binding, which is essential for tailored solutions in catalysis and pharmaceutical applications.

Solvent Fluctuations Induce Non-Markovian Kinetics in Hydrophobic Pocket-Ligand Binding.

We investigate the impact of water fluctuations on the key-lock association kinetics of a hydrophobic ligand (key) binding to a hydrophobic pocket (lock) by means of a minimalistic stochastic model system. The latter describes the collective hydration behavior of the pocket by bimodal fluctuations of the water-pocket interface that dynamically couples to the diffusive motion of the approaching ligand via the hydrophobic interaction. This leads to a Markovian set of overdamped stochastic equations in 2D-coordinate-space spanned by the interface position and the ligand position. Numerical simulations demonstrate locally increased friction of the ligand, decelerated binding kinetics, and local non-Markovian (memory) effects in a reduced 1D-description along the ligand's reaction (distance) coordinate as found previously in explicit-water simulations. Our minimalistic model elucidates the origin of locally enhanced friction that can be traced back to long-time decays in the force-autocorrelation function induced by a spatially fluctuating interface-ligand interaction. Furthermore, we construct a generalized 1D-Langevin description of ligand binding including a spatially local memory function that reflects the dominant frequencies of the pocket wetting/dewetting process, enabling further interpretation and a semianalytical quantification of our results.

Confined Water Determines Transport Properties of Guest Molecules in Narrow Pores.

We computed the transport of methane through 1 nm wide slit-shaped pores carved out of solid substrates. Models for silica, magnesium oxide, and alumina were used as solid substrates. The pores were filled with water. The results show that the methane permeability through the hydrated pores is strongly dependent on the solid substrate. Detailed analysis of the simulated systems reveals that local properties of confined water, including its structure, and more importantly, evolution of solvation free energy and hydrogen bond structure are responsible for the pronounced differences observed. The simulations are extended to multicomponent systems representative of natural gas, containing methane, ethane, and H2S. The results show that all pores considered have high affinity for H2S, moderate affinity for methane, and low affinity for ethane. The H2S/methane transport selectivity through the hydrated alumina pore is comparable, or superior, to that reported for existing commercial membranes. A multiscale approach was then implemented to demonstrate that a Smoluchowski one-dimensional model is able to reproduce the molecular-level results for short pores when appropriate values for the local self-diffusion coefficients are used as input parameters. We propose that the model can be extended to predict methane transport through uniform hydrated pores of macroscopic length. When verified by experiments, our simulation results could have important implications in applications such as natural gas sweetening and predictions of methane migration through hydraulically fractured shale formations.