Project description:We introduce a number of computationally inexpensive modifications to the MM/PBSA and MM/GBSA estimators for binding free energies, which are based on average receptor-ligand interaction energies in simulations of a noncovalent complex, to improve the treatment of entropy: second- and higher-order terms in a cumulant expansion and a confining potential on ligand external degrees of freedom. We also consider a filter for snapshots where ligands have drifted from the initial binding pose. The variations were tested on six sets of systems for which binding modes and free energies have previously been experimentally determined. For some data sets, none of the tested estimators led to results significantly correlated with measured free energies. In data sets with nontrivial correlation, a ligand RMSD cutoff of 3 Å and a second-order truncation of the cumulant expansion was found to be comparable or better than the average interaction energy by several statistical metrics.
Project description:The binding of gold nanoparticles capped with N-(2-mercaptopropionyl)glycine (Au@tiopronin) with double-stranded DNA has been investigated and quantified in terms of free energies by using two different approaches. The first approach follows the DNA conformational changes induced by gold nanoparticles using the CD technique. The second methodology consists in the use of pyrene-1-carboxaldehyde as a fluorescent probe. This second procedure implies the determination of the "true" free energy of binding of the probe with DNA, after corrections through solubility measurements. Working at different salt concentrations, the nonelectrostatic and electrostatic components of the binding free energy have been separated. The results obtained revealed that the binding is of nonelectrostatic character, fundamentally. The procedure used in this work could be extended to quantify the binding affinity of other AuNPs/DNA systems.
Project description:Here we present a novel, end-point method using the dead-end-elimination and A* algorithms to efficiently and accurately calculate the change in free energy, enthalpy, and configurational entropy of binding for ligand-receptor association reactions. We apply the new approach to the binding of a series of human immunodeficiency virus (HIV-1) protease inhibitors to examine the effect ensemble reranking has on relative accuracy as well as to evaluate the role of the absolute and relative ligand configurational entropy losses upon binding in affinity differences for structurally related inhibitors. Our results suggest that most thermodynamic parameters can be estimated using only a small fraction of the full configurational space, and we see significant improvement in relative accuracy when using an ensemble versus single-conformer approach to ligand ranking. We also find that using approximate metrics based on the single-conformation enthalpy differences between the global minimum energy configuration in the bound as well as unbound states also correlates well with experiment. Using a novel, additive entropy expansion based on conditional mutual information, we also analyze the source of ligand configurational entropy loss upon binding in terms of both uncoupled per degree of freedom losses as well as changes in coupling between inhibitor degrees of freedom. We estimate entropic free energy losses of approximately +24 kcal/mol, 12 kcal/mol of which stems from loss of translational and rotational entropy. Coupling effects contribute only a small fraction to the overall entropy change (1-2 kcal/mol) but suggest differences in how inhibitor dihedral angles couple to each other in the bound versus unbound states. The importance of accounting for flexibility in drug optimization and design is also discussed.
Project description:BackgroundBinding free energy and binding hot spots at protein-protein interfaces are two important research areas for understanding protein interactions. Computational methods have been developed previously for accurate prediction of binding free energy change upon mutation for interfacial residues. However, a large number of interrupted and unimportant atomic contacts are used in the training phase which caused accuracy loss.ResultsThis work proposes a new method, ?ACVASA, to predict the change of binding free energy after alanine mutations. ?ACVASA integrates accessible surface area (ASA) and our newly defined ? contacts together into an atomic contact vector (ACV). A ? contact between two atoms is a direct contact without being interrupted by any other atom between them. A ? contact's potential contribution to protein binding is also supposed to be inversely proportional to its ASA to follow the water exclusion hypothesis of binding hot spots. Tested on a dataset of 396 alanine mutations, our method is found to be superior in classification performance to many other methods, including Robetta, FoldX, HotPOINT, an ACV method of ? contacts without ASA integration, and ACVASA methods (similar to ?ACVASA but based on distance-cutoff contacts). Based on our data analysis and results, we can draw conclusions that: (i) our method is powerful in the prediction of binding free energy change after alanine mutation; (ii) ? contacts are better than distance-cutoff contacts for modeling the well-organized protein-binding interfaces; (iii) ? contacts usually are only a small fraction number of the distance-based contacts; and (iv) water exclusion is a necessary condition for a residue to become a binding hot spot.Conclusions?ACVASA is designed using the advantages of both ? contacts and water exclusion. It is an excellent tool to predict binding free energy changes and binding hot spots after alanine mutation.
Project description:Advanced lead-free energy storage ceramics play an indispensable role in next-generation pulse power capacitors market. Here, an ultrahigh energy storage density of ~ 13.8 J cm-3 and a large efficiency of ~ 82.4% are achieved in high-entropy lead-free relaxor ferroelectrics by increasing configuration entropy, named high-entropy strategy, realizing nearly ten times growth of energy storage density compared with low-entropy material. Evolution of energy storage performance and domain structure with increasing configuration entropy is systematically revealed for the first time. The achievement of excellent energy storage properties should be attributed to the enhanced random field, decreased nanodomain size, strong multiple local distortions, and improved breakdown field. Furthermore, the excellent frequency and fatigue stability as well as charge/discharge properties with superior thermal stability are also realized. The significantly enhanced comprehensive energy storage performance by increasing configuration entropy demonstrates that high entropy is an effective but convenient strategy to design new high-performance dielectrics, promoting the development of advanced capacitors .
Project description:The weighted histogram analysis method (WHAM) is routinely used for computing free energies and expectations from multiple ensembles. Existing derivations of WHAM require observations to be discretized into a finite number of bins. Yet, WHAM formulas seem to hold even if the bin sizes are made arbitrarily small. The purpose of this article is to demonstrate both the validity and value of the multi-state Bennet acceptance ratio (MBAR) method seen as a binless extension of WHAM. We discuss two statistical arguments to derive the MBAR equations, in parallel to the self-consistency and maximum likelihood derivations already known for WHAM. We show that the binless method, like WHAM, can be used not only to estimate free energies and equilibrium expectations, but also to estimate equilibrium distributions. We also provide a number of useful results from the statistical literature, including the determination of MBAR estimators by minimization of a convex function. This leads to an approach to the computation of MBAR free energies by optimization algorithms, which can be more effective than existing algorithms. The advantages of MBAR are illustrated numerically for the calculation of absolute protein-ligand binding free energies by alchemical transformations with and without soft-core potentials. We show that binless statistical analysis can accurately treat sparsely distributed interaction energy samples as obtained from unmodified interaction potentials that cannot be properly analyzed using standard binning methods. This suggests that binless multi-state analysis of binding free energy simulations with unmodified potentials offers a straightforward alternative to the use of soft-core potentials for these alchemical transformations.
Project description:The binding of proteins and ligands is generally associated with the loss of translational, rotational, and conformational entropy. In many cases, however, the net entropy change due to binding is positive. To develop a deeper understanding of the energetics of entropically driven protein-ligand binding, we calculated the absolute binding free energies and binding entropies for two HIV-1 protease inhibitors Nelfinavir and Amprenavir using the double-decoupling method with molecular dynamics simulations in explicit solvent. For both ligands, the calculated absolute binding free energies are in general agreement with experiments. The statistical error in the computed ΔG(bind) due to convergence problem is estimated to be ≥2 kcal/mol. The decomposition of free energies indicates that, although the binding of Nelfinavir is driven by nonpolar interaction, Amprenavir binding benefits from both nonpolar and electrostatic interactions. The calculated absolute binding entropies show that (1) Nelfinavir binding is driven by large entropy change and (2) the entropy of Amprenavir binding is much less favorable compared with that of Nelfinavir. Both results are consistent with experiments. To obtain qualitative insights into the entropic effects, we decomposed the absolute binding entropy into different contributions based on the temperature dependence of free energies along different legs of the thermodynamic pathway. The results suggest that the favorable entropic contribution to binding is dominated by the ligand desolvation entropy. The entropy gain due to solvent release from binding site appears to be more than offset by the reduction of rotational and vibrational entropies upon binding.
Project description:Free energy drives a wide range of molecular processes such as solvation, binding, chemical reactions and conformational change. Given the central importance of binding, a wide range of methods exist to calculate it, whether based on scoring functions, machine-learning, classical or electronic structure methods, alchemy, or explicit evaluation of energy and entropy. Here we present a new energy-entropy (EE) method to calculate the host-guest binding free energy directly from molecular dynamics (MD) simulation. Entropy is evaluated using Multiscale Cell Correlation (MCC) which uses force and torque covariance and contacts at two different length scales. The method is tested on a series of seven host-guest complexes in the SAMPL8 (Statistical Assessment of the Modeling of Proteins and Ligands) "Drugs of Abuse" Blind Challenge. The EE-MCC binding free energies are found to agree with experiment with an average error of 0.9 kcal mol-1. MCC makes clear the origin of the entropy changes, showing that the large loss of positional, orientational, and to a lesser extent conformational entropy of each binding guest is compensated for by a gain in orientational entropy of water released to bulk, combined with smaller decreases in vibrational entropy of the host, guest and contacting water.
Project description:We previously developed the direct interaction approximation (DIA) method to estimate the protein-ligand binding free energy (DG). The DIA method estimates the DG value based on the direct van der Waals and electrostatic interaction energies between the protein and the ligand. In the current study, the effect of the entropy of the ligand was introduced with protein dynamic properties by molecular dynamics simulations, and the interaction between each residue of the protein and the ligand was also weighted considering the hydration of each residue. The molecular dynamics simulation of the apo target protein gave the hydration effect of each residue, under the assumption that the residues, which strongly bind the water molecules, are important in the protein-ligand binding. These two effects improved the reliability of the DIA method. In fact, the parameters used in the DIA became independent of the target protein. The averaged error of DG estimation was 1.3 kcal/mol and the correlation coefficient between the experimental DG value and the calculated DG value was 0.75.