Overcoming dissipation in the calculation of standard binding free energies by ligand extraction

• Published in: Journal of computational chemistry 2013-10, Vol.34 (27), p.2360-2371
• Main Authors: Velez-Vega, Camilo, Gilson, Michael K.
• Format: Article
• Language: English
• Subjects: binding free energy; Binding sites; Biochemistry; Bioenergetics; Bridged Bicyclo Compounds - chemistry; Bridged-Ring Compounds - chemistry; cucurbituril; Extraction processes; Imidazoles - chemistry; ligand; Ligands; Molecular chemistry; Molecular Dynamics Simulation; molecular mechanics; Octanes - chemistry; Simulation; Spermine - chemistry; statistical mechanics; steered molecular dynamics; Thermodynamics; umbrella sampling
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.23398

This article addresses calculations of the standard free energy of binding from molecular simulations in which a bound ligand is extracted from its binding site by steered molecular dynamics (MD) simulations or equilibrium umbrella sampling (US). Host–guest systems are used as test beds to examine the requirements for obtaining the reversible work of ligand extraction. We find that, for both steered MD and US, marked irreversibilities can occur when the guest molecule crosses an energy barrier and suddenly jumps to a new position, causing dissipation of energy stored in the stretched molecule(s). For flexible molecules, this occurs even when a stiff pulling spring is used, and it is difficult to suppress in calculations where the spring is attached to the molecules by single, fixed attachment points. We, therefore, introduce and test a method, fluctuation‐guided pulling, which adaptively adjusts the spring's attachment points based on the guest's atomic fluctuations relative to the host. This adaptive approach is found to substantially improve the reversibility of both steered MD and US calculations for the present systems. The results are then used to estimate standard binding free energies within a comprehensive framework, termed attach‐pull‐release, which recognizes that the standard free energy of binding must include not only the pulling work itself, but also the work of attaching and then releasing the spring, where the release work includes an accounting of the standard concentration to which the ligand is discharged. © 2013 Wiley Periodicals, Inc. The challenge of computing the reversible ΔGbind 0 from steered molecular dynamics and umbrella sampling/Bennett acceptance ratio (BAR) simulations is examined for two host–guest complexes. For both methods, the choice of artificial pulling/restraining points strongly influences the degree of irreversibility in the computed work. The fluctuation‐guided pulling (FGP) scheme is proposed and tested, efficiently identifying low‐dissipation pathways from which greatly improved values of the reversible work can be obtained, either by direct calculation of the potential of mean force (PMF) or through the use of these FGP pathways as guiding routes for equilibrium umbrella sampling/BAR simulations.