PH Dependence of binding reactions from free energy simulations and macroscopic continuum electrostatic calculations: Application to 2′GMP/3′GMP binding to ribonuclease T 1 and implications for catalysis

Abstract

An approach is described for extending free energy calculations to take into account the pH dependence of the relative binding of ligands to an enzyme or other receptor protein. The method is based on the calculation of the free energy difference for a single protonation state via the thermodynamic cycle simulation approach followed by inclusion of all possible protonation states of the enzyme and the inhibitor by use of a macroscopic continuum dielectric (Poisson-Boltzmann) model. A detailed formulation of the combined model is presented. It involves solution of the multiple equilibrium problem and makes use of the calculated pKa values of all titrating groups on both enzyme and ligand. The method is illustrated by calculations of the pH dependence of the differential binding of the inhibitors 2′GMP and 3′GMP to ribonuclease T1. A free energy simulation of the differential binding is made for a given protonation state of the enzyme and inhibitor. Although only qualitative agreement with experiment is obtained, the results provide insights concerning the interactions involved. The pH dependence of the binding is calculated by using the protonation state of the residues from the free energy simulation as the standard state for a Poisson-Boltzmann calculation. Information is obtained concerning the pKa values of the titrating amino acids in the free, 2′GMP and 3′GMP bound enzyme forms of RNase T1 and the difference in the pH dependence of the binding of 2′GMP and 3′GMP to RNase T1. The contributions of different types of interactions (e.g. protein residues versus solvent) to the free energy differences are examined. A free energy simulation of the pKa shift of Glu58 shows that it is important to consider both carboxyl oxygen atoms as possible protonation sites since they may behave very differently in a protein. It is found in the protein that the interactions with the solvent favor the neutral (protonated) state of Glu58. This contrasts sharply with the solution behavior, where the solvent favors the charged state. Analysis of the results shows that the interactions of bound water with other protein residues leads to the observed effect. Comparisons are made with a continuum calculation that uses the charged state employed in the free energy simulation. Implications of the calculations and results for the catalytic mechanism of RNascT1 are outlined. An analysis is given of the stronger binding of 2′GMP, which is more similar to the cyclic phosphate transition state, than 3′GMP. The pKa calculations support the role of His92 as the general acid in donating a proton to the 5′ leaving group and the role of Glu58 as the general base involved in the extraction of a proton from the 2′ hydroxyl of the substrate, a necessary step for the formation of the pentacovalent transition state.