Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603

Abstract

The study of antibody-antigen interactions should greatly benefit from the development of quantitative models for the evaluation of binding free energies in proteins. The present work addresses this challenge by considering the test case of the binding free energies of phosphorylcholine analogs to the murine myeloma protein McPC603. This includes the evaluation of the differential binding energy as well as the absolute binding energies and their corresponding electrostatic contributions. Four different approaches are examined: the Protein Dipoles Langevin Dipoles (PDLD) method, the semi-microscopic PDLD (PDLD/S) method, a free energy perturbation (FEP) method based on an adiabatic charging procedure and a linear response approximation that accelerates the FEP calculation. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions. The determination of the hydrophobic energy involves an approach which considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. This treatment, which considers the protein as a harmonic system, views the steric forces as the restoring forces for the electrostatic interactions. The FEP method is found to give unreliable results with regular cut-off radii and starts to give quantitative results only in very expensive treatment with very large cut-off radii. The PDLD and PDLD/S methods are much faster than the FEP approach and give reasonable results for both the relative and absolute binding energies. The speed and simplicity of the PDLD/S method make it an effective strategy for interactive docking studies and indeed such an option is incorporated in the program MOLARIS. A component analysis of the different energy contributions of the FEP treatment and a similar PDLD analysis indicate that electrostatic effects provide the largest contribution to the differential binding energy, while the hydrophobic and steric contributions are much smaller. This finding lends further support to the idea that electrostatic interactions play a major role in determining the antigen specificity of McPC603.