Computational Estimation of Free Energy Using Fortran Code

ES/IS: Estimation of conformational free energy by combining dynamics simulations with explicit solvent with an implicit solvent continuum model

Energetics of Storage and Diffusion of Water and Cyclo-Octasulfur for a Nonpolar Cavity of RHCC Tetrabrachion by Molecular Dynamics Simulations

Calcium-dependent lectin I from Pseudomonas aeruginosa (PA-IL) binds specifically to oligosaccharides presenting an alpha-galactose residue at their nonreducing end, such as the disaccharides alphaGal1-2betaGalOMe, alphaGal1-3betaGalOMe, and alphaGal1-4betaGalOMe. This provides a unique model for studying the effect of the glycosidic linkage of the ligands on structure and thermodynamics of the complexes by means of experimental and theoretical tools. The structural features of PA-IL in complex with the three disaccharides were established by docking and molecular dynamics simulations and compared with those observed in available crystal structures, including PA-IL.alphaGal1-2betaGalOMe complex, which was solved at 2.4 A resolution and reported herein. The role of a structural bridge water molecule in the binding site of PA-IL was also elucidated through molecular dynamics simulations and free energy calculations. This water molecule establishes three very stable hydrogen bonds with O6 of nonreducing galactose, oxygen from Pro-51 main chain, and nitrogen from Gln-53 main chain of the lectin binding site. Binding free energies for PA-IL in complex with the three disaccharides were investigated, and the results were compared with the experimental data determined by titration microcalorimetry. When the bridge water molecule was included in the free energy calculations, the simulations predicted the correct binding affinity trends with the 1-2-linked disaccharide presenting three times stronger affinity ligand than the other two. These results highlight the role of the water molecule in the binding site of PA-IL and indicate that it should be taken into account when designing glycoderivatives active against P. aeruginosa adhesion.

Free energies of ferroelectric crystals from a microscopic approach

The eugenol functionalized B12N12 and B16N16 cages as potential inhibitors of TNF-α and HER2 receptors

Molecular dynamics simulations and molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free energy calculations were used to study the energetics of the binding of progesterone (PRG) and 5 beta-androstane-3,17-dione (5AD) to anti-PRG antibody DB3. Although the two steroids bind to DB3 in different orientations, their binding affinities are of the same magnitude, 1 nM for PRG and 8 nM for 5AD. The calculated relative binding free energy of the steroids, 8.8 kJ/mol, is in fair agreement with the experimental energy, 5.4 kJ/mol. In addition, computational alanine scanning was applied to study the role of selected amino acid residues of the ligand-binding site on the steroid cross-reactivity. The electrostatic and van der Waals components of the total binding free energies were found to favour more the binding of PRG, whereas solvation energies were more favourable for the binding of 5AD. The differences in the free energy components are due to the binding of the A rings of the steroids to different binding pockets: PRG is bound to a pocket in which electrostatic antibody-steroid interactions are dominating, whereas 5AD is bound to a pocket in which van der Waals and hydrophobic interactions dominate.

We describe a methodology to calculate the relative free energies of protein-peptide complex formation. The interaction energy was decomposed into nonpolar, electrostatic and entropic contributions. A free energy-surface area relationship served to calculate the nonpolar free energy term. The electrostatic free energy was calculated with the finite difference Poisson-Boltzmann method and the entropic contribution was estimated from the loss in the conformational entropy of the peptide side chains. We applied this methodology to a series of DnaK*peptide complexes. On the basis of the single known crystal structure of the peptide-binding domain of DnaK with a bound heptapeptide, we modeled ten other DnaK*heptapeptide complexes with experimentally measured K(d) values from 0.06 microM to 11 microM, using molecular dynamics to refine the structures of the complexes. Molecular dynamic trajectories, after equilibration, were used for calculating the energies with greater accuracy. The calculated relative binding free energies were compared with the experimentally determined free energies. Linear scaling of the calculated terms was applied to fit them to the experimental values. The calculated binding free energies were between -7.1 kcal/mol and - 9.4 kcal/mol with a correlation coefficient of 0.86. The calculated nonpolar contributions are mainly due to the central hydrophobic binding pocket of DnaK for three amino acid residues. Negative electrostatic fields generated by the protein increase the binding affinity for basic residues flanking the hydrophobic core of the peptide ligand. Analysis of the individual energy contributions indicated that the nonpolar contributions are predominant compared to the other energy terms even for peptides with low affinity and that inclusion of the change in conformational entropy of the peptide side chains does not improve the discriminative power of the calculation. The method seems to be useful for predicting relative binding energies of peptide ligands of DnaK and might be applicable to other protein-peptide systems, particularly if only the structure of one protein-ligand complex is available.

A few recent techniques to calculate free energies in the context of molecular dynamics simulations are discussed: temperature-accelerated molecular dynamics, which is a method to explore fast the important regions in the free energy landscape associated with a set of continuous collective variables without having to know where these regions are beforehand; the single sweep method, which is a variational method to interpolate the free energy globally given a set of mean forces (i.e., a set of gradients of the free energy) calculated at specific points, or centers, on the free energy landscape; and a Voronoi-based free energy method for the calculation of the free energy of the Voronoi tessellation associated with a set of centers. We also discuss how this last technique can be used in conjunction with the string method, and how kinetic information such as reaction rates can be calculated by milestoning using the edges of a Voronoi tessellation as milestones.

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures

<p>Computation predictions of organic crystal structure and thermodynamics are essential for material design, crystal engineering and drug development. However, accurate computational tools for organic crystal thermodynamics calculations are lacking, and experimental data set for validation of computational methods is limited. Most crystal structure predictions and stability calculations depend solely on potential energy, which is an insufficient representation of thermodynamics. This thesis proposes and validates both absolute and relative free energy calculation of small organic compounds, thus presenting an accurate computational tool that overcomes the shortcomings of potential-energy-based models.</p><p>The solubility of organic molecules can be computed from a thermodynamic cycle that decomposes standard state solubility into the sum of solid-vapor sublimation, i.e. thermodynamic stability of the crystal, and vapor-liquid solvation free energies ΔG°<sub>solubility</sub>=ΔG°<sub>sub</sub>+ΔG°<sub>solv</sub>. Crystal polymorphs have different ΔG°<sub>sub</sub> thus different solubility, which of critical importance to the pharmaceutical industry, however, robust computational methods to predict this quantity from first principles are lacking. Over the past few decades, alchemical simulation methods to compute solvation free energy using classical force fields have become widely used. However, analogous methods for determining the free energy of the sublimation/deposition phase transition are currently limited. This thesis describes an absolute thermodynamics approach based on growth of the asymmetric unit into a crystal via alchemy (GAUCHE). GAUCHE computes deposition free energy ΔG°<sub>dep</sub>=-ΔG°<sub>sub</sub>=ΔG°<sub>Vol</sub>+ΔG°<sub>Au</sub>+ΔG°<sub>Au→UG</sub> as the sum of an entropic term to account for compressing a 1 M vapor into the molar volume of the crystal asymmetric unit (V<sub>AU</sub>) plus two simulation steps. In the first simulation step, the deposition free energy ΔG°<sub>AU</sub> for a system composed of only N<sub>AU</sub> asymmetric unit (AU) molecule(s) is computed beginning from an arbitrary conformation in vacuum. In the second simulation step, the change in free energy ΔG°<sub>AU�UG</sub> to expand the asymmetric unit degrees of freedom into a unit cell (UC) composed of N<sub>UC</sub> independent molecules is computed. This latter step accounts for the favorable free energy of removing the constraint that every symmetry mate of the asymmetric unit has an identical conformation and intermolecular interactions. The current work is based on NVT simulations, which requires knowledge of the crystal space group and unit cell parameters from experiment, but not a priori knowledge of crystalline atomic coordinates. GAUCHE was applied to 5 organic molecules whose sublimation free energy has been measured experimentally, based on the polarizable AMOEBA force field and more than a microsecond of sampling per compound. The mean unsigned and root-mean-square errors were only 1.6 and 1.7 kcal/mol, respectively, which indicates that GAUCHE is capable of accurately predicting sublimation thermodynamics.</p><p>For polymorphic systems, we propose a relative thermodynamics approach, that is similar to the second simulation step of GAUCHE, where ΔG°<sub>P1→P2</sub> is calculated instead of ΔG°<sub>AU→UG</sub>. A relative approach reduces statistical uncertainty upon convergence compared to an absolute calculation; thus, it is more appropriate due to the thermodynamic stability difference between polymorphs are often fairly small. For our paracetamol test system, the experimental free energy difference was only 0.93 kcal/mol. Although both quantum and AMOEBA potential calculations predict the form II of paracetamol as more stable crystal form than form I, our relative free energy calculation predict the opposite stability ranking, which agrees with the experiment. Decomposition of free energy into entropy and enthalpy indicates that the favorable entropy change contributes to the greater thermodynamic stability of form I over form II. Although the exact magnitude of entropy and enthalpy changes differs across literature data as well as our data, the favorable entropic contribution is consistent. Further calculations over the temperature range from 100 to 308 K show the temperature dependence of free energy, which follows the parabolic trend observed in experiments. Our results show that our relative polymorph stability methods can accurately capture temperature dependence of free-energy-based stability ranking and overcome the limitations of potential-energy-based ranking. Thus, the importance of crystal structure predictions based on free energy can be further emphasized.</p>

Physics-based methods such as protein-ligand binding free energy calculations have been increasingly adopted in early-stage drug discovery to prioritize promising compounds for synthesis. However, the accuracy of these methods is highly dependent on the details of the calculation and choices made while preparing the ligands and protein ahead of running calculations. During ligand preparation, researchers typically assign partial atomic charges to each ligand atom using a specific ligand conformation for charge assignment, often the input conformer. While it is a well-known problem that partial charge assignment is dependent on conformation, little investigation has explored the downstream effects of varied partial charge assignment on free energy estimates. Preliminary benchmarks from the Open Free Energy Project show that generating partial charges from different input conformers leads to variation of up to kcal/mol in calculated relative binding free energies due to variation in partial charges alone. In this study, we more systematically explore this issue, investigating it in smaller systems using absolute hydration free energy calculations to reduce the degrees of freedom and sources of statistical error as compared to larger protein-ligand systems. We investigate how differences in partial charge generation (such as those caused by input conformer choice, partial charge engine, and hardware) may lead to differences in calculated absolute hydration free energy (AHFE) values. We demonstrate that supplying different input conformers to a partial charge engine can result in atomic partial charge discrepancies of up to 0.681 e, resulting in differences in calculated AHFE of kcal/mol. We find that even relatively small variations in partial charge assignment can result in notable differences in calculated AHFE. Thus, care should be taken when assigning partial charges to ensure reproducibility and accuracy of any resulting free energy calculations. We expect that these effects will be magnified in pharmaceutically relevant binding free energy calculations with additional degrees of freedom, more highly directional interactions than in water, and potentially more statistical error.

The outbreak caused by a coronavirus 2 has required quick and potential treatment strategies. The main protease enzyme Mpro plays an important role in the viral replication which renders it an important target for discovering SARS-CoV-2 inhibitors. In this study, 3D pharmacophore structure-based virtual screening and molecular docking were conducted using MOE and Bristol University Docking Engine (BUDE). Around 400,000 molecules of ZINC15 database were docked against the crystal structure of main protease, followed by 3D pharmacophore filtration. Six top-ranked hits (ZINC58717986, ZINC60399606, ZINC58662884, ZINC45988635, ZINC54706757 and ZINC17320595) were identified based on their strong spatial affinity and forming H-bonds with key residues H41, E166, Q189 and T190 of the binding pocket of Mpro SARS-CoV-2. The 6 hits subjected to molecular dynamics simulations for 100 ns followed by binding free energy calculations using MM-PBSA technique. Interestingly, three hits showed free binding energy (ΔGbinding) lower than tert-butyl N-[1-[(2S)-1-[[(2S)-4-(benzylamino)-3,4-dioxo-1-[(3S)-2-oxopyrrolidin-3-yl]butan-2-yl]amino]-3-cyclopropyl-1-oxopropan-2-yl]-2-oxopyridin-3-yl]carbamate (α-ketoamide 13 b) (ΔGbinding) −76.67 ± 0.5 kJ/mol which suggested their potential against SARS-CoV-2. The best binding free energy candidates, ZINC58717986 (ΔGbinding) −98.41 ± 0.7 kJ/mol. The second-best hit candidate, ZINC54706757 (ΔGbinding) −83.4 ± 0.6 kJ/mol and the third one ZINC17320595 (ΔGbinding) −78.85 ± 0.5 kJ/mol. Per residue decomposition free energy indicates H41, S46, H164, E166, D187, Q189 and Q192 are hot spot residues while residues M49, M165, L167 and P168 contribute to the hydrophobic interactions. The pharmacokinetic study suggests that the selected 6 hits possess drug-like properties. The 3D pharmacophore virtual screening, molecular dynamics and MM-PBSA approaches facilitated identification 3 promising hits with low free binding energy as SARS-CoV-2 inhibitors. Communicated by Ramaswamy H. Sarma

Computational methods for the study of enzymic reaction mechanisms. II. An overlapping mechanically embedded method for hybrid semi-empirical-QM/MM calculations

We present calculations of the absolute and relative binding free energies of complexation of streptavidin with biotin and its analogs by means of a thermodynamic free energy perturbation method implemented with molecular dynamics. Using the recently solved crystal structure of the streptavidin-biotin complex, biotin was mutated into a dummy molecule as well as thiobiotin and iminobiotin both in the protein and in solution. The calculated absolute binding free energy was dependent on the simulation model used. Encouragingly, the "best models" provided a reasonable semiquantitative reproduction (-20 to -22 kcal/mol) of the experimental free energy (-18.3 kcal/mol). Furthermore, the calculated results give clear insights into the binding nature of the protein-ligand complex, showing that the van der Waals energy dominates the electrostatic and hydrogen bonding energies in the binding of biotin by streptavidin. Specifically, the mutation of biotin into a dummy molecule in solution has a delta G (van der Waals) approximately -4 kcal/mol, due to the cancellation of dispersion and repulsion "cavity" effects. On the other hand, in the protein, a very small free energy price must be paid to create a cavity since one already exists and the mutation of biotin into a dummy molecule has a delta G (van der Waals) approximately 15 kcal/mol. These results are also consistent with the interpretation that the entropy increase to be expected from hydrophobic interactions from desolvation of biotin is counterbalanced by a decrease in entropy accompanying the formation of buried hydrogen bonds, which have been derived from the apparently conflicting experimental data. They provide an alternative interpretation of the reason for the extremely high affinity of the biotin-streptavidin interaction than that recently proposed by Weber et al. (J. Am. Chem. Soc. 114:3197, 1992). In the case of the relative binding free energies, the calculated values of 3.8 +/- 0.6 and 7.2 +/- 0.6 kcal/mol compare well with the experimental values of 3.6 and 6.2 kcal/mol for the perturbation of biotin to thiobiotin and iminobiotin, respectively in the related protein avidin. The calculations indicate that desolvation of the ligand is important in understanding the relative affinity of the ligands with the protein. The above successful simulations suggest that the molecular dynamics/free energy perturbation method is useful for understanding the energetic features affecting the binding between proteins and ligands, since it is generally difficult to determine these factors unambiguously by experiment.(ABSTRACT TRUNCATED AT 400 WORDS)

We have extended and applied a multicoordinate free energy method, chemical Monte Carlo/Molecular Dynamics (CMC/MD), to calculate the relative free energies of different amino acid side-chains. CMC/MD allows the calculation of the relative free energies for many chemical species from a single free energy calculation. We have previously shown its utility in host:guest chemistry (Pitera and Kollman, J Am Chem Soc 1998;120:7557-7567)1 and ligand design (Eriksson et al., J Med Chem 1999;42:868-881)2, and here demonstrate its utility in calculations of amino acid properties and protein stability. We first study the relative solvation free energies of N-methylated and acetylated alanine, valine, and serine amino acids. With careful inclusion of rotameric states, internal energies, and both the solution and vacuum states of the calculation, we calculate relative solvation free energies in good agreement with thermodynamic integration (TI) calculations. Interestingly, we find that a significant amount of the unfavorable solvation of valine seen in prior work (Sun et al., J Am Chem Soc 1992;114:6798-6801)3 is caused by restraining the backbone in an extended conformation. In contrast, the solvation free energy of serine is calculated to be less favorable than expected from experiment, due to the formation of a favorable intramolecular hydrogen bond in the vacuum state. These monomer calculations emphasize the need to accurately consider all significant conformations of flexible molecules in free energy calculations. This development of the CMC/MD method paves the way for computations of protein stability analogous to the biochemical technique of "exhaustive mutagenesis." We have carried out just such a calculation at position 133 of T4 lysozyme, where we use CMC/MD to calculate the relative stability of eight different side-chain mutants in a single free energy calculation. Our T4 calculations show good agreement with the prior free energy calculations of Veenstra et al. (Prot Eng 1997;10:789-807)4 and excellent agreement with the experiments of Mendel et al. (Science 1992;256:1798-1802).