Evaluation Of Free Energy Differences Research Articles

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.

1-Octanol/Water Partition Coefficients of n-Alkanes from Molecular Simulations of Absolute Solvation Free Energies.

The 1-octanol/water partition coefficient is an important thermodynamic variable usually employed to understand and quantify the partitioning of solutes between aqueous and organic phases. It finds widespread use in many empirical correlations to evaluate the environmental fate of pollutants as well as in the design of pharmaceuticals. The experimental evaluation of 1-octanol/water partition coefficients is an expensive and time-consuming procedure, and thus, theoretical estimation methods are needed, particularly when a physical sample of the solute may not yet be available, such as in pharmaceutical screening. 1-Octanol/water partition coefficients can be obtained from Gibbs free energies of solvation of the solute in both the aqueous and the octanol phases. The accurate evaluation of free energy differences remains today a challenging problem in computational chemistry. In order to study the absolute solvation Gibbs free energies in 1-octanol, a solvent that can mimic many properties of important biological systems, free energy calculations for n-alkanes in the range C1-C8 were performed using molecular simulation techniques, following the thermodynamic integration approach. In the first part of this paper, we test different force fields by evaluating their performance in reproducing pure 1-octanol properties. It is concluded that all-atom force fields can provide good accuracy but at the cost of a higher computational time compared to that of the united-atom force fields. Recent versions of united-atom force fields, such as Gromos and TraPPE, provide satisfactory results and are, thus, useful alternatives to the more expensive all-atom models. In the second part of the paper, the Gibbs free energy of solvation in 1-octanol is calculated for several n-alkanes using three force fields to describe the solutes, namely Gromos, TraPPE, and OPLS-AA. Generally, the results obtained are in excellent agreement with the available experimental data and are of similar accuracy to commonly used QSPR models. Moreover, we have estimated the Gibbs free energy of hydration for the different compounds with the three force fields, reaching average deviations from experimental data of less than 0.2 kcal/mol for the case of the Gromos force field. Finally, we systematically compare different strategies to obtain the 1-octanol/water partition coefficient from the simulations. It is shown that a fully predictive method combining the Gromos force field in the aqueous phase and the OPLS-AA/TraPPE force field for the organic phase can give excellent predictions for n-alkanes up to C8 with an absolute average deviation of 0.1 log P units to the experimental data.

Solubility of KF in water by molecular dynamics using the Kirkwood integration method

We have studied the solubility of potassium fluoride in aqueous solution at near ambient condition, using a simple modeling for the ion and water interactions and computing the values of the chemical potential by molecular dynamics within the framework of Kirkwood generalized thermodynamic integration approach for the evaluation of free energy differences. We report the details of the procedure we used, which is based—at variance with previous attempts—on the individual determination of the chemical potential for the ions in solution. We explore a wide range of salt concentrations up to more than 25 M and determine the solubility. The agreement with the experimental value is reasonable, taking account of the rather crude model used.

Determination of solvation free energy using molecular dynamics with solute Cartesian mapping: An application to the solvation of 18-crown-6

The determination of relative stabilities of conformations of a molecule in solution has received much interest due to its relevance to chemical and biological properties in solution. Free energy perturbation (FEP) methodologies using molecular dynamics simulations have been used for the evaluation of free energy differences between two similar molecular systems. We present here a FEP method for the evaluation of the solvation free energy difference between two conformations. The simulations are carried out by fixing the Cartesian coordinates of a solute molecule. The molecule is switched from one conformer to another through a linear couping of the Cartesian coordinates of the two conformers. The solvation free energy is calculated from the interactions between the solvent and the solute using the standard FEP approach. This method is expected to be particularly useful for molecules with complicated conformational changes involving a large number of dihedral angle rotations. A crown ether, 18-crown-6, a cyclic molecule with 18 rotatable bonds, is used as a test case to demonstrate the method. The solvation free energy differences between four selected conformations of 18-crown-6 have been determined. The results are in agreement with available experiments and consistent with other theoretical calculations.

Treatment of rotational isomers in free energy calculations. II. Molecular dynamics simulation study of 18-crown-6 in aqueous solution as an example of systems with large numbers of rotational isomeric states

The evaluation of free energy differences using the perturbation method or thermodynamic integration method requires special caution if multiple rotational isomeric states may exist in the system under investigation. In this article a recently suggested procedure to properly treat rotational isomeric states is illustrated with a molecular dynamics simulation of an aqueous solution of uncomplexed 18-crown-6 crown ether, as an example of a system in which large numbers of isomeric states may exist. By using very long molecular dynamics simulations, thermodynamic perturbation methods and symmetry arguments, the free energy of host organization into the conformation required to form the complex with K+ is estimated to be 2.6 kJ mol−1. It has also been found that the lowest energy conformations of 18-crown-6 in vacuo do not necessarily correspond to the most populated conformations in aqueous solution.

Treatment of rotational isomers in free energy evaluations. Analysis of the evaluation of free energy differences by molecular dynamics simulations of systems with rotational isomeric states

Using 1,2-dimethoxy ethane in aqueous solution as an example, the applicability of the perturbation method and the thermodynamic integration technique to evaluate free energy differences is considered for systems with multiple rotational isomeric states. It is shown that the naive application of these methods to evaluate free energy differences for such systems, even in a simple case such as the free energy of hydration of 1,2-dimethoxy ethane, may lead to unreasonable results. This problem is due to the fact that, in a conventional simulation, it is unlikely that all isomeric states will be sampled with the appropriate equilibrium probabilities. A procedure is proposed to estimate the contributions of isomeric states in free energy difference calculations.