Accurate Calculation of Conformational Free Energy Differences in Explicit Water: The Confinement–Solvation Free Energy Approach

PME Switching in Confinement Simulations of Charged Solutes

The confinement method is a reaction coordinate-free enhanced sampling method for the calculation of conformational free energy differences. We show that in explicit solvent, artifacts occur when treating charged solutes. These artifacts are resolved by switching off the particle mesh Ewald (PME) method at the start of confinement. Calculations of the free energy cost of this switching converge rapidly, with small statistical error. The effectiveness and accuracy of confinement with PME switching is demonstrated by its application to a series of solutes of different charge; its ability to treat complex systems is illustrated by evaluating the free energy difference between B and Z-DNA.

Exploring ligands that target von Willebrand factor selectively under oxidizing conditions through docking and molecular dynamics simulations

The blood protein von Willebrand factor (VWF) is a large multimeric protein that, when activated, binds to blood platelets, tethering them to the site of vascular injury and initiating blood coagulation. This process is critical for the normal hemostatic response, but especially under inflammatory conditions, it is thought to be a major player in pathological thrombus formation. For this reason, VWF has been the target for the development of anti-thrombotic therapeutics. However, it is challenging to prevent pathological thrombus formation while still allowing normal physiological blood coagulation, as currently available anti-thrombotic therapeutics are known to cause unwanted bleeding, in particular intracranial hemorrhage. This work explores the possibility of inhibiting VWF selectively under the inflammatory conditions present during pathological thrombus formation. In particular, the A2 domain of VWF is known to inhibit the neighboring A1 domain from binding to the platelet surface receptor GpIbα, and this auto-inhibitory mechanism has been shown to be removed by oxidizing agents released during inflammation. Hence, finding drug molecules that bind at the interface between A1 and A2 only under oxidizing conditions could restore such an auto-inhibitory mechanism. Here, by using a combination of computational docking, molecular dynamics simulations, and free energy perturbation calculations, a ligand from the ZINC15 database was identified that binds at the A1A2 interface, with the interaction being stronger under oxidizing conditions. The results provide a framework for the discovery of drug molecules that bind to a protein selectively in the presence of inflammatory conditions.

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation

Computational studies play an increasingly important role in chemistry and biophysics, mainly thanks to improvements in hardware and algorithms. In drug discovery and development, computational studies can reduce the costs and risks of bringing a new medicine to market. Computational simulations are mainly used to optimize promising new compounds by estimating their binding affinity to proteins. This is challenging due to the complexity of the simulated system. To assess the present and future value of simulation for drug discovery, we review key applications of advanced methods for sampling complex free-energy landscapes at near nonergodicity conditions and for estimating the rate coefficients of very slow processes of pharmacological interest. We outline the statistical mechanics and computational background behind this research, including methods such as steered molecular dynamics and metadynamics. We review recent applications to pharmacology and drug discovery and discuss possible guidelines for the practitioner. Recent trends in machine learning are also briefly discussed. Thanks to the rapid development of methods for characterizing and quantifying rare events, simulation's role in drug discovery is likely to expand, making it a valuable complement to experimental and clinical approaches.

Solubility Advantage of Amorphous Ketoprofen. Thermodynamic and Kinetic Aspects by Molecular Dynamics and Free Energy Approaches

Thermodynamic and kinetic aspects of crystalline (c-KTP) and amorphous (a-KTP) ketoprofen dissolution in water have been investigated by molecular dynamics simulation focusing on free energy properties. Absolute free energies of all relevant species and phases have been determined by thermodynamic integration on a novel path, first connecting the harmonic to the anharmonic system Hamiltonian at low T and then extending the result to the temperature of interest. The free energy required to transfer one ketoprofen molecule from the crystal to the solution is in fair agreement with the experimental value. The absolute free energy of the amorphous form is 19.58 kJ/mol higher than for the crystal, greatly enhancing the ketoprofen concentration in water, although as a metastable species in supersaturated solution. The kinetics of the dissolution process has been analyzed by computing the free energy profile along a reaction coordinate bringing one ketoprofen molecule from the crystal or amorphous phase to the solvated state. This computation confirms that, compared to the crystal form, the dissolution rate is nearly 7 orders of magnitude faster for the amorphous form, providing one further advantage to the latter in terms of bioavailability. The problem of drug solubility, of great practical importance, is used here as a test bed for a refined method to compute absolute free energies, which could be of great interest in biophysics and drug discovery in particular.

Mapping saddles and minima on free energy surfaces using multiple climbing strings

Locating saddle points on free energy surfaces is key in characterizing multistate transition events in complicated molecular-scale systems. Because these saddle points represent transition states, determining minimum free energy pathways to these saddles and measuring their free energies relative to their connected minima are further necessary, for instance, to estimate transition rates. In this work, we propose a new multistring version of the climbing string method in collective variables to locate all saddles and corresponding pathways on free energy surfaces. The method uses dynamic strings to locate saddles and static strings to keep a history of prior strings converged to saddles. Interaction of the dynamic strings with the static strings is used to avoid the convergence to already-identified saddles. Additionally, because the strings approximate curves in collective-variable space, and we can measure free energy along each curve, identification of any saddle's two connected minima is guaranteed. We demonstrate this method to map the network of stationary points in the 2D and 4D free energy surfaces of alanine dipeptide and alanine tripeptide, respectively.

Harnessing complexity in molecular self-assembly using computer simulations

In molecular self-assembly, hundreds of thousands of freely-diffusing molecules associate to form ordered and functional architectures in the absence of an actuator. This intriguing phenomenon plays a critical role in biology and has become a powerful tool for the fabrication of advanced nanomaterials. Due to the limited spatial and temporal resolutions of current experimental techniques, computer simulations offer a complementary strategy to explore self-assembly with atomic resolution. Here, we review recent computational studies focusing on both thermodynamic and kinetic aspects. As we shall see, thermodynamic approaches based on modeling and statistical mechanics offer initial guidelines to design nanostructures with modest computational effort. Computationally more intensive analyses based on molecular dynamics simulations and kinetic network models (KNMs) reach beyond it, opening the door to the rational design of self-assembly pathways. Current limitations of these methodologies are discussed. We anticipate that the synergistic use of thermodynamic and kinetic analyses based on computer simulations will provide an important contribution to the de novo design of self-assembly.

Computation of Hemagglutinin Free Energy Difference by the Confinement Method

Hemagglutinin (HA) mediates membrane fusion, a crucial step during influenza virus cell entry. How many HAs are needed for this process is still subject to debate. To aid in this discussion, the confinement free energy method was used to calculate the conformational free energy difference between the extended intermediate and postfusion state of HA. Special care was taken to comply with the general guidelines for free energy calculations, thereby obtaining convergence and demonstrating reliability of the results. The energy that one HA trimer contributes to fusion was found to be 34.2 ± 3.4kBT, similar to the known contributions from other fusion proteins. Although computationally expensive, the technique used is a promising tool for the further energetic characterization of fusion protein mechanisms. Knowledge of the energetic contributions per protein, and of conserved residues that are crucial for fusion, aids in the development of fusion inhibitors for antiviral drugs.

Determinants of Alanine Dipeptide Conformational Equilibria on Graphene and Hydroxylated Derivatives

Understanding the interaction of carbon nanomaterials with proteins is essential for determining the potential effects of these materials on health and in the design of biotechnology based on them. Here we leverage explicit-solvent molecular simulation and multidimensional free-energy calculations to investigate how adsorption to carbon nanomaterial surfaces affects the conformational equilibrium of alanine dipeptide, a widely used model of protein backbone structure. We find that the two most favorable structures of alanine dipeptide on graphene (or large carbon nanotubes) correspond to the two amide linkages lying in the same plane, flat against the surface, rather than the nonplanar α-helix-like and β-sheet-like conformations that predominate in aqueous solution. On graphenic surfaces, the latter conformations are metastable and most often correspond to amide-π stacking of the N-terminal amide. The calculations highlight the key role of amide-π interactions in determining the conformational equilibrium. Lesser but significant contributions from hydrogen bonding to the high density interfacial water layer or to the hydroxy groups of hydroxylated graphene also define the most favorable conformations. This work should yield insight on the influence of carbon nanotubes, graphene, and their functionalized derivatives on protein structure.

Computational Approaches to the Chemical Equilibrium Constant in Protein-ligand Binding

The physiological role played by protein-ligand recognition has motivated the development of several computational approaches to the ligand binding affinity. Some of them, termed rigorous, have a strong theoretical foundation but involve too much computation to be generally useful. Some others alleviate the computational burden by introducing strong approximations and/or empirical calibrations, which also limit their general use. Most importantly, there is no straightforward correlation between the predictive power and the level of approximation introduced. Here, we present a general framework for the quantitative interpretation of protein-ligand binding based on statistical mechanics. Within this framework, we re-derive self-consistently the fundamental equations of some popular approaches to the binding constant and pinpoint the inherent approximations. Our analysis represents a first step towards the development of variants with optimum accuracy/efficiency ratio for each stage of the drug discovery pipeline.

Balancing Accuracy and Cost of Confinement Simulations by Interpolation and Extrapolation of Confinement Energies

Improvements to the confinement method for the calculation of conformational free energy differences are presented. By taking advantage of phase space overlap between simulations at different frequencies, significant gains in accuracy and speed are reached. The optimal frequency spacing for the simulations is obtained from extrapolations of the confinement energy, and relaxation time analysis is used to determine time steps, simulation lengths, and friction coefficients. At postprocessing, interpolation of confinement energies is used to significantly reduce discretization errors in the calculation of conformational free energies. The efficiency of this protocol is illustrated by applications to alanine n-peptides and lactoferricin. For the alanine-n-peptide, errors were reduced between 2- and 10-fold and sampling times between 8- and 67-fold, while for lactoferricin the long sampling times at low frequencies were reduced 10-100-fold.

Calculation of the Local Free Energy Landscape in the Restricted Region by the Modified Tomographic Method

The free energy landscape is the most important information in the study of the reaction mechanisms of the molecules. However, it is difficult to calculate. In a large collective variable space, a molecule must take a long time to obtain the sufficient sampling during the simulation. To save the calculation quantity, decreasing the sampling region and constructing the local free energy landscape is required in practice. However, the restricted region in the collective variable space may have an irregular shape. Simply restricting one or more collective variables of the molecule cannot satisfy the requirement. In this paper, we propose a modified tomographic method to perform the simulation. First, it divides the restricted region by some hyperplanes and connects the centers of hyperplanes together by a curve. Second, it forces the molecule to sample on the curve and the hyperplanes in the simulation and calculates the free energy data on them. Finally, all the free energy data are combined together to form the local free energy landscape. Without consideration of the area outside the restricted region, this free energy calculation can be more efficient. By this method, one can further optimize the path quickly in the collective variable space.

Assessment of Mutational Effects on Peptide Stability through Confinement Simulations

The evaluation of free energy differences between specific states of a system is of fundamental interest in the study of (bio)chemical systems. Herein, we examine the use of the recently introduced confinement method (CM) to evaluate relative free energy changes upon protein/peptide mutations. CM is a path-independent technique that involves the transformation of a configurational state of the system into an ideal crystal permitting the direct computation of free energy differences. We illustrate the method by evaluating the differential stabilities between native and mutant sequences of a model peptide that has been extensively characterized by experimental approaches, the GB1 hairpin. We show a good correlation between calculated and experimental relative stabilities and discuss other possible applications of this method in the context of complex molecular conversions.

Predicting molecular self-assembly at surfaces: a statistical thermodynamics and modeling approach

A self-consistent framework based on modeling and statistical mechanics for the theoretical interpretation of self-assembly at surfaces and interfaces is presented.