Free Energy Perturbation Approach Research Articles

Computer simulation studies of spherands, crowns and porphyrins: application of computer graphics, distance geometry, molecular mechanics and molecular dynamics approaches

Abstract

Evaluation of catalytic free energies in genetically modified proteins

A combination of the empirical valence bond method and a free energy perturbation approach is used to simulate the activity of genetically modified enzymes. The simulations reproduce in a semiquantitative way the observed effects of mutations on the activity and binding free energies of trypsin and subtilisin. This suggests that we are approaching a stage of quantitative structure-function correlation of enzymes. The analysis of the calculations points towards the electrostatic energy of the reacting system as the key factor in enzyme catalysis. The changes in the charges of the reacting system and the corresponding changes in “solvation” free energy (generalized here as the interaction between the charges and the given microenvironment) are emphasized. It is argued that a reliable evaluation of these changes might be sufficient for correlating structure and catalysis. The use of free energy perturbation methods and thermodynamic cycles for evaluation of solvation energies and reactivity is discussed, pointing out our early contributions. The apparent elaborated nature of our treatment is clarified, explaining that such a treatment is essential for consistent calculations of chemical reactions in polar environments. The problems associated with seemingly more rigorous quantum mechanical methods are discussed, emphasizing the inconsistency associated with using gas phase charge distributions. The importance of dynamic aspects is examined by evaluating the autocorrelation of the protein “reaction field” on the reacting substrate. It is found that, at least in the present case, dynamic effects are not important. The nature of the catalytic free energy is considered, arguing that the protein provides preoriented dipoles (polarized to stabilize the transition state charge distribution) and small reorganization energy, thus reducing the activation free energy. The corresponding catalytic free energy is related to the folding free energy, which is being invested in aligning the active site dipoles.

Calculation of free energy changes in ion–water clusters using nonadditive potentials and the Monte Carlo method

A thermodynamic perturbation method, using a Monte Carlo procedure, has been applied to the calculation of the free energy differences between ion–water clusters containing a given number of water molecules (n=1,...,6) and different monovalent ions, i.e., Li+, Na+, K+, F−, and Cl−. To our knowledge, this is the first application of the free energy perturbation approach with a nonadditive intermolecular potential. The results confirm the usefulness of the method and yield free energy differences of hydration which are in generally very good agreement with experiment. Our calculations have also revealed some structural changes which take place within the first hydration shell when one ion is replaced by another in the hexahydrate clusters. For Li+ one obtains a well defined 4+2 mean structure, whereas for a larger ion such as K+ the solvation structure is closer to a 5+1 type. For anions, this tendency is reversed, i.e., for F− one finds a well defined four coordinate structure for a cluster with four water molecules, but for the larger anion Cl− the cluser tends to be a 3+1 structure. In addition, favorable water–water interactions are apparent in anion–water clusters, but not in cation–water clusters.