Web Release Date: August 13,
Absolute Binding Free Energies: A Quantitative Approach for Their Calculation
Molecular Dynamics and Biomolecular Simulation Group, Department of Theoretical Chemistry and Molecular Structural Biology, University of Vienna, Währingerstrasse 17, 1090 Vienna, Austria
Laboratoire de Chimie Biophysique, ISIS, Université Louis Pasteur, 67000 Strasbourg, France, and Department of Chemical Biology, 12 Oxford Street, Harvard University, Cambridge, Massachusetts 02138
Received: August 1, 2002
In Final Form: February 21, 2003
Abstract:
The computation of absolute binding affinities by molecular dynamics (MD) based free energy simulations
is analyzed, and an exact method to carry out such a computation is presented. The key to obtaining converged
results is the introduction of suitable, auxiliary restraints to prevent the ligand from leaving the binding site
when the native ligand-receptor interactions are turned off alchemically. We describe a versatile set of restraints
that (i) can be used in MD simulations, that (ii) restricts both the position and the orientation of the ligand,
and that (iii) is defined relative to the receptor rather than relative to a fixed point in space. The free energy
cost, 
Ar, for this set of restraints can be evaluated analytically. Although the techniques were originally
developed for the gas phase, the resulting expression is exact, since all contributions from solute-solvent
interactions cancel from the final result. The value of Ar depends only on the equilibrium values and force
constants of the chosen harmonic restraint terms and, therefore, can be easily calculated. The standard state
dependence of binding free energies is also investigated, and it is shown that the present approach takes this
into account correctly. The analytical expression for Ar is verified numerically by calculations on the complex
formed by benzene with the L99A mutant of T4 lysozyme. The overall approach is illustrated by a complete
binding free energy calculation for a complex based on a simplified model for tyrosine bound to tyrosyl-tRNA-synthetase. The results demonstrate the usefulness of the proposed set of restraints and confirm that
the calculated binding free energy is independent of the details of the restraints. Comparisons are made with
earlier formulations for the calculation of binding free energies, and certain limitations of that work are
described. The relationship between Ar and the loss of translational and rotational entropy during a binding
process is analyzed.
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