We present the first fully quantum chemical estimates of ligand-binding affinities, performed at a reasonable level of theory (MP2/cc-pVTZ) and at the same time including all physically important effects, such as solvation, entropy, and sampling. We have studied the binding of seven biotin analogues to the avidin tetramer. The calculations have been performed by the recently developed PMISP approach (polarisable multipole interactions with supermolecular pairs), which treats electrostatic interactions by multipoles up to quadrupoles, induction by anisotropic polarisabilities, and non-classical interactions (dispersion, exchange repulsion, etc.) by explicit quantum chemical calculations, using a fragmentation approach, except for long-range interactions, which are treated by standard molecular mechanics LennardJones terms. In order to include effects of sampling, ten snapshots from a molecular dynamics simulation are studied for each complex. Solvation energies are estimated by a polarised continuum model (PCM), coupled to the multipole-polarisability model. Entropy effects are estimated from vibrational frequencies, calculated at the molecular mechanics level. We encounter several problems, not previously discussed, illustrating that we are first to apply such a method. For example, the PCM model is questionable for large molecules, owing to the use of a surface definition that gives numerous small cavities in a protein.
IntroductionA major goal of theoretical chemistry is to accurately predict the free energy for the binding of a ligand to a macromolecule. If such binding affinities could be accurately predicted, large parts of the drug development could be performed by computer simulations rather than by costly experiments, because essentially all drugs evoke their action by binding to a target macromolecule. Likewise, many interesting questions in biochemistry can be formulated as the differential binding affinities of a substrate, product, or transition-state to a protein or enzyme.