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. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011

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