Calculation of the Affinity of the λ Repressor-Operator Complex Based on Free Energy Component Analysis

Abstract

A calculation of the binding free energy of the u repressor-operator complex is described based on free energy component analysis. The calculations are based on a thermodynamic cycle of seven steps decomposed into a total of 24 individual components. The values of these terms are estimated using a combination of empirical potential functions from AMBER, generalized Born - solvent accessibility calculations, elementary statistical mechanics and semiempirical physicochemical properties. Two alternative approaches are compared, one based on the crystal structure of the complex and the other based on the molecular dynamics simulation of the u repressor-operator complex. The calculated affinity is m 19.7 kcal/mol from the crystal structure calculation and m 17.9 kcal/mol from the MD method. The corresponding experimental affinity of the complex is about m 12.6 kcal/mol, indicating reasonable agreement between theory and experiment, considering the approximations involved in the computational methodology. The results are analyzed in terms of contributions from electrostatics, van der Waal interactions, the hydrophobic effect and solvent release. The capabilities and limitations of free energy component methodology are assessed and discussed on the basis of these results.