[Paper Review] Protein-Ligand Binding Potential of Mean Force Calculations with Hamiltonian Replica Exchange on Alchemical Interaction Grids

David D. L Minh|arXiv (Cornell University)|Jul 14, 2015

Protein Structure and Dynamics4 citations

TL;DR

This paper presents a Hamiltonian replica exchange method on alchemical interaction grids to calculate protein-ligand binding potential of mean force (BPMF), using precomputed electrostatic and van der Waals grids and thermodynamic length-based state spacing. The approach achieves robust sampling with ~5 kT convergence in BPMF standard deviation and improved precision via multi-step free energy cycles, though sampling adequacy remains sensitive to initial ligand poses.

ABSTRACT

A binding potential of mean force (BPMF) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid. I have developed a method to calculate BPMFs for protein-ligand systems. The method is based on replica exchange sampling from multiple thermodynamic states at different temperatures and protein-ligand interaction strengths. Protein-ligand interactions are represented by interpolating precomputed electrostatic and van der Waals grids. Using a simple estimator for thermodynamic length, thermodynamic states are initialized at approximately equal intervals. The method is demonstrated on the Astex diverse set, a database of 85 protein-ligand complexes relevant to pharmacy or agriculture. Fifteen independent simulations of each complex were started using poses from crystallography, docking, or the lowest-energy pose observed in the other simulations. Benchmark simulations completed within three days on a single processor. Overall, protocols initialized using the thermodynamic length estimator were system-specific, robust, and led to approximately even replica exchange acceptance probabilities between neighboring states. In most systems, the standard deviation of the BPMF converges to within 5 kT. Even with low variance, however, the mean BPMF was sometimes dependent on starting conditions, implying inadequate sampling. Within the thermodynamic cycle, free energies estimated based on multiple intermediate states were more precise, and those estimated by single-step perturbation were less precise. The results demonstrate that the method is promising, but that ligand pose sampling and phase space overlap can sometimes prevent precise BPMF estimation. The software used to perform these calculations, Alchemical Grid Dock (AlGDock), is available under the open-source MIT license at this https URL

Motivation & Objective

• To develop a robust and efficient method for calculating protein-ligand binding potential of mean force (BPMF) with improved sampling efficiency.
• To address challenges in phase space overlap and ligand pose sampling that hinder accurate free energy estimation in alchemical free energy calculations.
• To enable precise BPMF estimation using thermodynamically spaced alchemical states and precomputed interaction grids.
• To evaluate the impact of initial ligand pose and sampling protocol on BPMF convergence and accuracy.

Proposed method

• Utilizes Hamiltonian replica exchange sampling across multiple thermodynamic states with varying protein-ligand interaction strengths and temperatures.
• Represents protein-ligand interactions via interpolation of precomputed electrostatic and van der Waals grid maps to avoid recalculating interactions at each step.
• Employs a thermodynamic length estimator to initialize thermodynamic states at approximately equal intervals, ensuring balanced replica exchange acceptance rates.
• Applies a multi-step alchemical pathway with intermediate states to improve free energy estimation precision over single-step perturbations.
• Uses a single processor to run benchmark simulations on the Astex diverse set of 85 protein-ligand complexes, with 15 independent runs per complex.
• Employs a consistent free energy cycle to assess convergence and accuracy, comparing single-step and multi-step perturbation protocols.

Experimental results

Research questions

• RQ1 Can thermodynamically spaced alchemical states improve replica exchange efficiency and sampling in protein-ligand binding free energy calculations?
• RQ2 How does the choice of initial ligand pose affect the convergence and accuracy of BPMF estimates?
• RQ3 To what extent does multi-step alchemical free energy cycling improve precision compared to single-step perturbation?
• RQ4 Can precomputed interaction grids enable accurate and efficient BPMF calculations without recalculating nonbonded interactions at each step?
• RQ5 What is the impact of phase space overlap and ligand pose sampling on the reliability of BPMF estimates?

Key findings

• The thermodynamic length-based state initialization led to approximately even replica exchange acceptance probabilities between neighboring states, indicating effective sampling spacing.
• For most systems, the standard deviation of the BPMF converged to within 5 kT, indicating low statistical variance in the estimates.
• Despite low variance, the mean BPMF value sometimes depended on starting conditions, suggesting inadequate sampling due to poor phase space overlap or ligand pose sampling.
• Free energy estimates based on multiple intermediate alchemical states were more precise than those from single-step perturbations, highlighting the benefit of multi-step pathways.
• The method demonstrated system-specific robustness and feasibility, with complete benchmark simulations finishing within three days on a single processor.
• The open-source software AlGDock, used in the study, is available under the MIT license, enabling reproducibility and wider adoption.