Comparison of thermodynamic integration and Bennett acceptance ratio for calculating relative protein‐ligand binding free energies

The performances of Bennett's acceptance ratio method and thermodynamic integration (TI) for the calculation of free energy differences in protein simulations are compared. For the latter, the standard trapezoidal rule, Simpson's rule, and Clenshaw‐Curtis integration are used as numerical integration methods. We evaluate the influence of the number and definition of intermediate states on the precision, accuracy, and efficiency of the free energy calculations. Our results show that non‐equidistantly spaced intermediate states are in some cases beneficial for the TI methods. Using several combinations of softness parameters and the λ power dependence, it is shown that these benefits are strongly dependent on the shape of the integrand. Although TI is more user‐friendly due to its simplicity, it was found that Bennett's acceptance ratio method is the more efficient method. It is also the least dependent on the choice of the intermediate states, making it more robust than TI. © 2013 Wiley Periodicals, Inc.     

A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6

Successive parameterizations of the GROMOS force field have been used successfully to simulate biomolecular systems over a long period of time. The continuing expansion of computational power with time makes it possible to compute ever more properties for an increasing variety of molecular systems with greater precision. This has led to recurrent parameterizations of the GROMOS force field all aimed at achieving better agreement with experimental data. Here we report the results of the latest, extensive reparameterization of the GROMOS force field. In contrast to the parameterization of other biomolecular force fields, this parameterization of the GROMOS force field is based primarily on reproducing the free enthalpies of hydration and apolar solvation for a range of compounds. This approach was chosen because the relative free enthalpy of solvation between polar and apolar environments is a key property in many biomolecular processes of interest, such as protein folding, biomolecular association, membrane formation, and transport over membranes. The newest parameter sets, 53A5 and 53A6, were optimized by first fitting to reproduce the thermodynamic properties of pure liquids of a range of small polar molecules and the solvation free enthalpies of amino acid analogs in cyclohexane (53A5). The partial charges were then adjusted to reproduce the hydration free enthalpies in water (53A6). Both parameter sets are fully documented, and the differences between these and previous parameter sets are discussed.     

Modifying the OPLS-AA force field to improve hydration free energies for several amino acid side chains using new atomic charges and an off-plane charge model for aromatic residues

The hydration free energies of amino acid side chains are an important determinant of processes that involve partitioning between different environments, including protein folding, protein complex formation, and protein-membrane interactions. Several recent papers have shown that calculated hydration free energies for polar and aromatic residues (Trp, His, Tyr, Asn, Gln, Asp, Glu) in several common molecular dynamics force fields differ significantly from experimentally measured values. We have attempted to improve the hydration energies for these residues by modifying the partial charges of the OPLS-AA force field based on natural population analysis of density functional theory calculations. The resulting differences between calculated hydration free energies and experimental results for the seven side chain analogs are less than 0.1 kcal/mol. Simulations of the synthetic Trp-rich peptide Trpzip2 show that the new charges lead to significantly improved geometries for interacting Trp-side chains. We also investigated an off-plane charge model for aromatic rings that more closely mimics their electronic configuration. This model results in an improved free energy of hydration for Trp and a somewhat altered benzene-sodium potential of mean force with a more favorable energy for direct benzene-sodium contact.     

Combination of COSMOmic and molecular dynamics simulations for the calculation of membrane–water partition coefficients

The importance of membrane‐water partition coefficients led to the recent extension of the conductor‐like screening model for realistic solvation (COSMO‐RS) to micelles and biomembranes termed COSMOmic. Compared to COSMO‐RS, this new approach needs structural information to account for the anisotropy of colloidal systems. This information can be obtained from molecular dynamics (MD) simulations. In this work, we show that this combination of molecular methods can efficiently be used to predict partition coefficients with good agreement to experimental data and enables screening studies. However, there is a discrepancy between the amount of data generated by MD simulations and the structural information needed for COSMOmic. Therefore, a new scheme is presented to extract data from MD trajectories for COSMOmic calculations. In particular, we show how to calculate the system structure from MD, the influence of lipid conformers, the relation to the COSMOmic layer size, and the water/lipid ratio impact. For a 1,2‐dimyristoyl‐sn‐glycero‐3‐phosphocholine (DMPC) bilayer, 66 partition coefficients for various solutes were calculated. Further, 52 partition coefficients for a 1‐palmitoyl‐2‐oleoyl‐sn‐glycero‐3‐phosphocholine (POPC) bilayer system were calculated. All these calculations were compared to experimental data. © 2013 Wiley Periodicals, Inc.     

Molecular dynamics simulations and free energy calculations on the enzyme 4‐hydroxyphenylpyruvate dioxygenase

4‐Hydroxyphenylpyruvate dioxygenase is a relevant target in both pharmaceutical and agricultural research. We report on molecular dynamics simulations and free energy calculations on this enzyme, in complex with 12 inhibitors for which experimental affinities were determined. We applied the thermodynamic integration approach and the more efficient one‐step perturbation. Even though simulations seem well converged and both methods show excellent agreement between them, the correlation with the experimental values remains poor. We investigate the effect of slight modifications on the charge distribution of these highly conjugated systems and find that accurate models can be obtained when using improved force field parameters. This study gives insight into the applicability of free energy methods and current limitations in force field parameterization. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Solvation free energies calculated using the GB/SA model: Sensitivity of results on charge sets,protocols, and force fields

The sensitivity of aqueous solvation free energies (SFEs), estimated using the GB/SA continuum solvent model, on charge sets, protocols, and force fields, was studied. Simple energy calculations using the GB/SA solvent model were performed on 11 monofunctional organic compounds. Results indicate that calculated SFEs are strongly dependent on the charge sets. Charges derived from electrostatic potential fitting to high level ab initio wave functions using the CHELPG procedure and “class IV” charges from AM1/CM1a or PM3/CM1p calculations yielded better results than the corresponding Mulliken charges. Calculated SFEs were similar to MC/FEP energies obtained in the presence of explicit TIP4P water. Further improvements were obtained by using GVB/6-31G** and MP2/6-31+G** (CHELPG) charge sets that included correlation effects. SFEs calculated using charge sets assigned by the OPLSA* force field gave the best results of all standard force fields (MM2*, MM3*, MMFF, AMBER*, and OPLSA*) implemented in MacroModel. Comparison of relative and absolute SFEs computed using either the GB/SA continuum model or MC/FEP calculations in the presence of explicit TIP4P water showed that, in general, relative SFEs can be estimated with greater accuracy. A second set of 20 mono- and difunctional molecules was also studied and relative SFEs estimated using energy minimization and thermodynamic cycle perturbation (TCP) protocols. SFEs calculated from TCP calculations using the GB/SA model were sensitive to bond lengths of dummy bonds (i.e., bonds involving dummy atoms). In such cases, keeping the bond lengths of dummy bonds close to the corresponding bond lengths of the starting structures improved the agreement of TCP-calculated SFEs with energy minimization results. Overall, these results indicate that GB/SA solvation free energy estimates from simple energy minimization calculations are of similar accuracy and value to those obtained using more elaborate TCP protocols. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 769–780, 1998     

Update on phosphate and charged post‐translationally modified amino acid parameters in the GROMOS force field

In this study, we propose newly derived parameters for phosphate ions in the context of the GROMOS force field parameter sets. The non‐bonded parameters used up to now lead to a hydration free energy, which renders the dihydrogen phosphate ion too hydrophobic when compared to experimentally derived values, making a reparametrization of the phosphate moiety necessary. Phosphate species are of great importance in biomolecular simulations not only because of their crucial role in the backbone of nucleic acids but also as they represent one of the most important types of post‐translational modifications to protein side‐chains and are an integral part in many lipids. Our re‐parametrization of the free dihydrogen phosphate (H PO ) and three derivatives (methyl phosphate, dimethyl phosphate, and phenyl phosphate) leads, in conjunction with the previously updated charged side‐chains in the GROMOS parameter set 54A8, to new nucleic acid backbone parameters and a 54A8 version of the widely used GROMOS protein post‐translational modification parameter set. © 2017 Wiley Periodicals, Inc.     

Net charge changes in the calculation of relative ligand‐binding free energies via classical atomistic molecular dynamics simulation

The calculation of binding free energies of charged species to a target molecule is a frequently encountered problem in molecular dynamics studies of (bio‐)chemical thermodynamics. Many important endogenous receptor‐binding molecules, enzyme substrates, or drug molecules have a nonzero net charge. Absolute binding free energies, as well as binding free energies relative to another molecule with a different net charge will be affected by artifacts due to the used effective electrostatic interaction function and associated parameters (e.g., size of the computational box). In the present study, charging contributions to binding free energies of small oligoatomic ions to a series of model host cavities functionalized with different chemical groups are calculated with classical atomistic molecular dynamics simulation. Electrostatic interactions are treated using a lattice‐summation scheme or a cutoff‐truncation scheme with Barker–Watts reaction‐field correction, and the simulations are conducted in boxes of different edge lengths. It is illustrated that the charging free energies of the guest molecules in water and in the host strongly depend on the applied methodology and that neglect of correction terms for the artifacts introduced by the finite size of the simulated system and the use of an effective electrostatic interaction function considerably impairs the thermodynamic interpretation of guest‐host interactions. Application of correction terms for the various artifacts yields consistent results for the charging contribution to binding free energies and is thus a prerequisite for the valid interpretation or prediction of experimental data via molecular dynamics simulation. Analysis and correction of electrostatic artifacts according to the scheme proposed in the present study should therefore be considered an integral part of careful free‐energy calculation studies if changes in the net charge are involved. © 2013 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Minimum MD simulation length required to achieve reliable results in free energy perturbation calculations: Case study of relative binding free energies of fructose‐1,6‐bisphosphatase inhibitors

In an attempt to establish the criteria for the length of simulation to achieve the desired convergence of free energy calculations, two studies were carried out on chosen complexes of FBPase‐AMP mimics. Calculations were performed for varied length of simulations and for different starting configurations using both conventional‐ and QM/MM‐FEP methods. The results demonstrate that for small perturbations, 1248 ps simulation time could be regarded a reasonable yardstick to achieve convergence of the results. As the simulation time is extended, the errors associated with free energy calculations also gradually tapers off. Moreover, when starting the simulation from different initial configurations of the systems, the results are not changed significantly, when performed for 1248 ps. This study carried on FBPase‐AMP mimics corroborates well with our previous successful demonstration of requirement of simulation time for solvation studies, both by conventional and ab initio FEP. The establishment of aforementioned criteria of simulation length serves a useful benchmark in drug design efforts using FEP methodologies, to draw a meaningful and unequivocal conclusion. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

On the Relative Merits of Equilibrium and Non‐Equilibrium Simulations for the Estimation of Free‐Energy Differences

The possibility of estimating equilibrium free‐energy profiles from multiple non‐equilibrium simulations using the fluctuation–dissipation theory or the relation proposed by Jarzynski has attracted much attention. Although the Jarzynski estimator has poor convergence properties for simulations far from equilibrium, corrections have been derived for cases in which the work is Gaussian distributed. Here, we examine the utility of corrections proposed by Gore and collaborators using a simple dissipative system as a test case. The system consists of a single methane‐like particle in explicit water. The Jarzynski equality is used to estimate the change in free energy associated with pulling the methane particle a distance of 3.9 nm at rates ranging from ～0.1 to 100 m s^?1. It is shown that although the corrections proposed by Gore and collaborators have excellent numerical performance, the profiles still converge slowly. Even when the corrections are applied in an ideal case where the work distribution is necessarily Gaussian, performing simulations under quasi‐equilibrium conditions is still most efficient. Furthermore, it is shown that even for a single methane molecule in water, pulling rates as low as 1 m s^?1 can be problematic. The implications of this finding for studies in which small molecules or even large biomolecules are pulled through inhomogeneous environments at similar pulling rates are discussed.     

Interaction identification of Zif268 and TATAZF proteins with GC‐/AT‐rich DNA sequence: A theoretical study

Molecular dynamics (MD) simulations for Zif268 (a zinc‐finger‐protein binding specifically to the GC‐rich DNA)‐d(A₁G₂C₃G₄T₅G₆G₇G₈C₉A₁₀C₁₁)₂ and TATA_ZF (a zinc‐finger‐protein recognizing the AT‐rich DNA)‐d(A₁C₂G₃C₄T₅A₆T₇A₈A₉A₁₀A₁₁G₁₂G₁₃)₂ complexes have been performed for investigating the DNA binding affinities and specific recognitions of zinc fingers to GC‐rich and AT‐rich DNA sequences. The binding free energies for the two systems have been further analyzed by using the molecular mechanics Poisson‐Boltzmann surface area (MM‐PBSA) method. The calculations of the binding free energies reveal that the affinity energy of Zif268‐DNA complex is larger than that of TATA_ZF‐DNA one. The affinity between the zinc‐finger‐protein and DNA is mainly driven by more favorable van‐der‐Waals and nonpolar/solvation interactions in both complexes. However, the affinity energy difference of the two binding systems is mainly caused by the difference of van‐der‐Waals interactions and entropy components. The decomposition analysis of MM‐PBSA free energies on each residue of the proteins predicts that the interactions between the residues with the positive charges and DNA favor the binding process; while the interactions between the residues with the negative charges and DNA behave in the opposite way. The interhydrogen‐bonds at the protein‐DNA interface and the induced intrafinger hydrogen bonds between the residues of protein for the Zif268‐DNA complex have been identified at some key contact sites. However, only the interhydrogen‐bonds between the residues of protein and DNA for TATA_ZF‐DNA complex have been found. The interactions of hydrogen‐bonds, electrostatistics and van‐der‐Waals type at some new contact sites have been identified. Moreover, the recognition characteristics of the two studied zinc‐finger‐proteins have also been discussed. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

OBGMX: A web‐based generator of GROMACS topologies for molecular and periodic systems using the universal force field

OBGMX is a web service providing topologies for the GROMACS molecular dynamics software package according to the Universal Force Field, as implemented in the Open Babel package. OBGMX can deal with molecular and periodic systems. The geometrical parameters appearing in the potential energy functions for the bonded interactions can be set to those measured in the input configuration. The performance of OBGMX in reproducing the structure of periodic systems is analyzed by calculating the root mean‐squared displacements of optimized configurations of a large set of metal–organic frameworks. OBGMX is available at http://software‐lisc.fbk.eu/obgmx/ . © 2012 Wiley Periodicals, Inc.     

Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water

A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit‐solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build‐up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of β‐D ‐glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build‐up protocol, even for relatively short build‐up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones). © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

The role of protein “Stability patches” in molecular recognition: A case study of the human growth hormone‐receptor complex

Dynamic characteristics of protein surfaces are among the factors determining their functional properties, including their potential participation in protein‐protein interactions. The presence of clusters of static residues—“stability patches” (SPs)—is a characteristic of protein surfaces involved in intermolecular recognition. The mechanism, by with SPs facilitate molecular recognition, however, remains unclear. Analyzing the surface dynamic properties of the growth hormone and of its high‐affinity variant we demonstrated that reshaping of the SPs landscape may be among the factors accountable for the improved affinity of this variant to the receptor. We hypothesized that SPs facilitate molecular recognition by moderating the conformational entropy of the unbound state, diminishing enthalpy–entropy compensation upon binding, and by augmenting the favorable entropy of desolvation. SPs mapping emerges as a valuable tool for investigating the structural basis of the stability of protein complexes and for rationalizing experimental approaches, such as affinity maturation, aimed at improving it. © 2015 Wiley Periodicals, Inc.