Using the fast fourier transform in binding free energy calculations

Abstract

According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the ligand apo ensemble and a rigid receptor. Here, we use the Fast Fourier Transform (FFT) to efficiently estimate BPMFs by calculating interaction energies as rigid ligand configurations from the apo ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex (R ≈ 0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations (R ≈ 0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. Keywords:Noncovalent We demonstrate the feasibility of using the fast Fourier transform to calculate how tightly proteins and small molecules bind to each other. The algorithm is used to calculate the interaction energy as the small molecule is translated across the binding site. With the appropriate averages over the interaction energies and over multiple protein conformations, the standard binding free energy is recapitulated.2

Estimating the ligand‐binding affinity via λ‐dependent umbrella sampling simulations

“…[16] In particular, a rapid protocol is generally engaged to rank the ligand-binding affinity of several thousand to million compounds. [17][18][19][20][21][22] A more CPU time consumption method was then employed to refine the results. [23][24][25][26][27][28][29][30] Finally, a high accuracy method will be employed to confirm the observation before an in vitro and/or in vivo studies would be achieved.…”

CBSF: A New Empirical Scoring Function for Docking Parameterized by Weights of Neural Network

“…Remarkable progress in the eld of arti cial intelligence and increasing availability of high-quality reference data have resulted in a rapid development of protein-ligand interaction scoring functions (Huang, Grinter, & Zou, 2010;Nguyen, Zhou, & Minh, 2018;Yadava, 2018) using machine learning algorithms (Chen, Engkvist, Wang, Olivecrona, & Blaschke, 2018) such as vector support machines or neural networks. Neural networks designed for the prediction of binding energies between receptors and ligands are typically based on the pattern recognition and computer vision ideas and have deep architecture utilizing 2D-or 3Dconvolution (Gomes, Ramsundar, Feinberg, & Pande, 2017;Gonczarek et al, 2018;Ragoza, Hochuli, Idrobo, Sunseri, & Koes, 2017;Stepniewska-Dziubinska, Zielenkiewicz, & Siedlecki, 2018;Sunseri, King, Francoeur, & Koes, 2019) or graph-convolution (Feinberg et al, 2018;Lim, Ryu, Park, Choe, & Ham, 2019;Torng & Altman, 2018) approaches.…”

Implicit ligand theory for relative binding free energies

“…In practice, however, the computation of these integrals is different. While solvation free energies are usually based on a continuum dielectric model that ignore positions of solvent molecules, BPMFs have hitherto been based on Monte Carlo simulations 20 or fast Fourier transform operations 21 that explicitly consider the position of the ligand.…”