Absolute Binding Free Energies: A Quantitative Approach for Their Calculation
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, Δ A r, 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 Δ A r 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 Δ A r 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 Δ A r and the loss of translational and rotational entropy during a binding process is analyzed.
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Boresch restraints were proposed by Boresch et al. in the context of small molecule-protein binding free energy calculations.
“An alternative set of orientational and positional restraints has been proposed by Boresch et al.77 in the context of small molecule-protein binding free energy calculations.”
From Assessment of the Topology and Oligomerisation States of Coiled Coils Using Metadynamics with Conformational Restraints (2025) · cites this paper as [77]
Boresch restraints are constructed by selecting three anchor points on the receptor and three on the ligand, and correspond to the external degrees of freedom of the ligand: a distance r, two angles θA, θB and three dihedrals φA, φB, φC.
“Boresch restraints are constructed by selecting three anchor points (atoms or groups of atoms) on the receptor and three on the ligand. The restraints correspond to the external degrees of freedom of the ligand, and consist of a distance r, two angles θA, θB and three dihedrals ϕA, ϕB, ϕC.”
From Assessment of the Topology and Oligomerisation States of Coiled Coils Using Metadynamics with Conformational Restraints (2025) · cites this paper as [77]
In principle, the binding free energy should be independent of the type of restraints, the atom centers selected for the construction of the restraints, or the values of the force constants, provided stable restraints that have been appropriately selected.
“In principle, the binding free energy should be independent of the type of restraints, the atom centers selected for the construction of the restraints, or the values of the force constants,64,77,86 provided stable restraints that have been appropriately selected.87”
From Assessment of the Topology and Oligomerisation States of Coiled Coils Using Metadynamics with Conformational Restraints (2025) · cites this paper as [77]
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- Authors
- Boresch, S., Tettinger, F., Leitgeb, M., & Karplus, M.
- Affiliations
- University of Vienna (AT)
- Harvard University (US)
- Venue
- The Journal of Physical Chemistry B
- Publisher
- American Chemical Society (ACS)
- Published
- 2003-08-13
- Volume
- 107
- Issue
- 35
- Pages
- 9535-9551
- ISSN
- 1520-5207 (ISSN-L)
- 1520-6106
- OpenAlex
- W2072604508
- Cited by
- 569
- References
- 2
- Citations by year
- 2026: 29 · 2025: 40 · 2024: 45 · 2023: 34 · 2022: 47 · 2021: 49 · 2020: 38 · 2019: 17 · 2018: 34 · 2017: 21 · 2016: 31 · 2015: 15 · 2014: 16 · 2013: 17 · 2012: 21
- FWCI
- 9.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Journal of Physical Chemistry B (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Keywords
- absolute binding free energy, alchemical free energy calculations, harmonic restraint, translational entropy, rotational entropy, solute-solvent interactions
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