Quantum mechanical binding free energy calculation for phosphopeptide inhibitors of the Lck SH2 domain

The accurate and efficient calculation of binding free energies is essential in computational biophysics. We present a linear-scaling quantum mechanical (QM)-based end-point method termed MM/QM-COSMO to calculate binding free energies in biomolecular systems, with an improved description of entropic changes. Molecular dynamics trajectories are re-evaluated using a semiempirical Hamiltonian and a continuum solvent model; translational and rotational entropies are calculated using configurational integrals, and internal entropy is calculated using the harmonic oscillator approximation. As an application, we studied the binding of a series of phosphotyrosine tetrapeptides to the human Lck SH2 domain, a key component in intracellular signal transduction, modulation of which can have therapeutic relevance in the treatment of cancer, osteoporosis, and autoimmune diseases. Calculations with molecular mechanics Poisson-Boltzmann, and generalized Born surface area methods showed large discrepancies with experimental data stemming from the enthalpic component, in agreement with an earlier report. The empirical force field-based solvent interaction energy scoring function yielded improved results, with average unsigned error of 3.6 kcal/mol, and a better ligand ranking. The MM/QM-COSMO method exhibited the best agreement both for absolute (average unsigned error = 0.7 kcal/mol) and relative binding free energy calculations. These results show the feasibility and promise of a full QM-based end-point method with an adequate balance of accuracy and computational efficiency.