Free Energy Analysis of Protein–DNA Binding: The EcoRI Endonuclease–DNA Complex

A detailed theoretical analysis of the thermodynamics and functional energetics of protein–DNA binding in the EcoRI endonuclease–DNA complex is presented. The standard free energy of complexation is considered in terms of a thermodynamic cycle of seven distinct steps decomposed into a total of 24 well-defined components. The model we employ involves explicit all-atom accounts of the energetics of structural adaptation of the protein and the DNA upon complex formation; the van der Waals and electrostatic interactions between the protein and the DNA; and the electrostatic polarization and screening effects, van der Waals components, and cavitation effects of solvation. The ion atmosphere of the DNA is described in terms of a counterion condensation model combined with a Debye–Huckel treatment of added salt effects. Estimates of entropy loss due to decreased translational and rotational degrees of freedom in the complex relative to the unbound species based on classical statistical mechanics are included, as well as corresponding changes in the vibrational and configurational entropy. The magnitudes and signs of the various components are estimated from the AMBER parm94 force field, generalized Born theory, solvent accessibility measures, and empirical estimates of quantities related to ion release. The calculated standard free energy of formation, −11.5 kcal/mol, agrees with experiment to within 5 kcal/mol. This net binding free energy is discerned to be the resultant of a balance of several competing contributions associated with chemical forces as conventionally defined, with 10 out of 24 terms favoring complexation. Contributions to binding compounded from subsets of the 24 components provide a basis for advancing a molecular perspective of binding in terms of structural adaptation, electrostatics, van der Waals interactions, hydrophobic effects, and small ion reorganization and release upon complexation. The van der Waals interactions and water release favor complexation, while electrostatic interactions, considering both intramolecular and solvation effects, prove unfavorable. Analysis of individual contributions to the standard free energy of complexation at the nucleotide and amino acid residue level highlights the role of contact interactions as well as context effects. Some patterns in compensation effects among the various terms are identified and discussed.