Calculation Of Free Energy Differences Research Articles

Calculation of relative free energy differences for the covalent hydration of organic compounds: A combined quantum mechanical and free energy perturbation study

AbstractThe relative free energy difference (ΔΔGhyd) for the reversible addition of water to two unsaturated molecules is accurately computed using a combination of ab initio quantum mechanical calculations and free energy perturbation methods. Initial attempts to calculate the absolute hydration free energy difference (ΔGhyd) for formaldehyde and trichloroacetaldehyde gave values that differed substantially from experimental results even after inclusion of electron correlation energy contributions using third‐order (MP3) and fourth‐order (MP4) Møller‐Plesset perturbation theory and QCISD(T) correlation methods at the 6‐31G** basis set level. Inaccuracies in ΔGhyd were attributed to errors in the calculation of both ΔGgas and ΔΔGsol. Gas phase quantum mechanical free energies (ΔGgas) varied significantly (2–3 kcal/mol) depending on the level of theory. Errors in ΔΔGsol were attributed to slow convergence of the calculations using the thermodynamic cycle perturbation (TCP) method with explicit solvent. These errors were minimized or canceled, however, when relative hydration free energy differences (ΔΔGhyd) were calculated using a combination of ab initio quantum mechanical calculations and free energy perturbation methods. Calculated values for a variety of aldehydes and ketones were consistent with experimental data. © 1995 John Wiley & Sons, Inc.

Molecular dynamics free energy calculation in four dimensions

A new method for the calculation of free energy differences by molecular dynamics simulations of molecular systems is presented. The main characteristic of the method is that the three-dimensional physical space is augmented by a further dimension. This allows the system to circumvent energy barriers in three-dimensional space. When simulating physical (three-dimensional) states, the dynamics along the 4th coordinate is uncoupled from the dynamics described with the original three coordinates. In the method presented here, free energy differences between physical states are determined using pathways leading over states where the dynamics along all four dimensions are coupled. Due to the barrier lowering in four dimensions, an increase of efficiency can be expected when low free energy physical states are separated by high barriers. The method is tested by application to an atomic liquid.

Calculation of electrostatic free energy differences with a time-saving approximate method

A method for obtaining approximate electrostatic free energy differences with molecular dynamics or Monte Carlo computer simulations is developed, which yields results that fall within 1 or 2 kcal/mol of those obtained from the corresponding thermodynamic integration calculations, while consuming less than half of the computer time. The method is based on the fact that, in most systems whose reactant and product states differ only in the charges assigned to the atoms, a linear response is observed as one state is transformed into the other. In other words, the transformation from reactant state to product state (or vice versa) may be thought of as the gradual application of a perturbation that the system responds to linearly

Calculation of Solvation Free-Energy Differences for Large Solute Change from Computer Simulations with Quadrature-Based Nearly Linear Thermodynamic Integration

Abstract The free-energy simulation methodology is reviewed from the point of view of calculating large free-energy differences. The advantages of the nearly linear thermodynamic integration based on Gaussian quadrature are highlighted and its performance is characterized on systems ranging from the Lennard-Jones fluid to the A to B transition of DNA oligomers. A technique for optimizing the runlength at each quadrature point is given. Examples for the sensitivity of the calculated free energy to the atomic charges used are also presented.

Calculation of solvation and binding free energy differences for folate-based inhibitors of the enzyme thymidylate synthase

The thermodynamic cycle perturbation approach, in conjunction with molecular dynamics simulations, has been used to calculate relative binding free energies for the closely related inhibitors 10-propargyl-5,8-dideazafolic acid (PDDF) and 10-formyl-5,8-dideazafolic acid (FDDF) to the binary complex consisting of the enzyme E. coli thymidylate synthase and 5-fluoro-2'-deoxyuridylate (FdUMP). The calculated difference in binding free energy (2.9 kcal/mol) is in good agreement with the experimentally observed preference for PDDF (3.75 kcal/mol)

Locally enhanced sampling in free energy calculations: Application of mean field approximation to accurate calculation of free energy differences

Mean field approximation is employed for accurate calculation of free energy differences. Significantly enhanced sampling is obtained for local changes. In an example for the mutation of a residue in a protein, the increase in the sampling yielded converged results at a significantly lower computational cost than the usual approach.

Binding of an antiviral agent to a sensitive and a resistant human rhinovirus. Computer simulation studies with sampling of amino acid side-chain conformations: II. Calculation of free-energy differences by thermodynamic integration

Thermodynamic-cycle perturbation theory and molecular dynamics simulations were used to calculate the difference in the free energy of binding of the antiviral compound WIN53338 to the wild-type human rhinovirus 14 and to a drug-resistant mutant of the virus in which valine 188 of the viral protein 1 is mutated to leucine. Because of the difficulty of achieving adequate sampling of all of the rotational isomers of amino acid side-chains in molecular dynamics simulations, an explicit treatment of the effects of the existence of multiple rotational isomers of residue 188 on the calculated free energies was used. The rotamers of residue 188 were first mapped by steric and energetic techniques as described in the accompanying article. Thermodynamic integration was then carried out during simulations of the virus, both with and without the antiviral compound bound, by mutating residue 188 while restraining its side-chain to one conformation. The contributions of the other rotamers of residue 188 to the free-energy changes for this mutation were then added to those calculated by thermodynamic integration as correction factors. Binding of WIN53338 to the wild-type virus was calculated to be favored over binding to the mutant virus by 1.7(±3.0) kcal/mol. This is consistent with experimental data which, if differences in activity are assumed to be due to differences in binding, indicate that the binding affinity of WIN53338 for the wild-type virus is at least 0.15 to 1.7 kcal/mol greater than for the mutant virus. Thermodynamic integration was also performed in the conventional manner without restraints and was found to give less accurate results.

Free energy thermodynamic integrations in molecular dynamics simulations using a noniterative method to include electronic polarization

Recently a method was proposed by the authors to include electric polarization in molecular dynamics simulations, using a noniterative procedure. Here it is shown that this method is particularly well suited for the calculation of free energy differences between systems that differ in polarizabilities.

Conformational flexibility in free energy simulations

Two approaches to accomplish efficient conformational sampling in free energy simulations of systems with internal flexibility are described. These methods combine standard thermodynamic perturbation or thermodynamic integration protocols for calculation of free energy differences with conformational free energy techniques. The application of the combined methodologies is illustrated for examples of aqueous hydration and relative enzyme inhibitor binding. It is demonstrated that flexibility has an influence on the calculated values of free energy changes.

Free energy perturbation calculations on binding and catalysis after mutating Asn 155 in subtilisin.

Site-directed mutagenesis is a very powerful approach to altering the biological functions of proteins, the structural stability of proteins and the interactions of proteins with other molecules. Several experimental studies in recent years have been directed at estimating the changes in catalytic properties, (rates of binding and catalysis) in site-directed mutants of enzymes compared to the native enzymes. Simulation approaches to the study of complex molecules have also become more powerful, in no small measure owing to the increase in computer power. These simulations have often allowed results of experiments to be rationalized and understood mechanistically. A new approach called the free-energy pertubation method, which uses statistical mechanics and molecular dynamics can often be used for quantitative calculation of free energy differences. We have applied such a technique to calculate the differential free energy of binding and free energy of activation for catalysis of a tripeptide substrate by native subtilisin and a subtilisin mutant (Asn 155----Ala 155). Our studies lead to a calculated difference in free energy of binding which is relatively small, but a calculated change in free energy of catalysis which is substantial. These energies are very close to those determined experimentally (J. A. Wells and D. A. Estell, personal communication), which were not known to us until the simulations were completed. This demonstrates the predictive power and utility of theoretical simulation methods in studies of the effects of site-specific mutagenesis on both enzyme binding and catalysis.

Calculation of free energy differences for water from computer simulations

Free energy differences for water at different temperatures have been calculated from Monte Carlo computer simulations using both ratio overlap and umbrella sampling methods. The problems of calculating precise values from these methods are discussed. Three models for water (ST2, TIPS2 and PE) have been used in these calculations which have been compared with experimental estimates for the configurational free energy. The importance of being able to predict accurate mean potential energies as well as accurate energy distributions is emphasised.

Simple pair distribution function theory for the calculation of Helmholtz free energy differences

A first order theory is developed for the calculation of Helmholtz energy differences. The theory is easy to use and requires only the well−known hard sphere pair distribution function and the pair intermolecular potential function for the species under considerationTriacC%%%%%ermolecular potential Lennard−Jones fluids and mixtures of Lennard−Jones fluids indicate that the theory has a domain of validity limited to molecules with nearly equal ε and σ values.

Quadrupole–quadrupole interactions in CO and N2: Effect on the thermodynamics of mixing

A first−order theory for the calculation of Helmholtz free energy differences is used to calculate the free energy (relative to an ideal gas at the same temperature and number density) of N2, CO, and their equimolar mixture. Results show that the superposition of the quadrupole−quadrupole interactions on the Lennard−Jones interactions does not provide an intermolecular potential model that quantitatively describes the mixing thermodynamics. However, such a model does appear to be an effective pair potential for CO. Additional calculations are presented that further establish the accuracy of the selected first−order theory.