scholarly journals Energy–entropy method using multiscale cell correlation to calculate binding free energies in the SAMPL8 host–guest challenge

2021 ◽  
Author(s):  
Hafiz Saqib Ali ◽  
Arghya Chakravorty ◽  
Jas Kalayan ◽  
Samuel P. de Visser ◽  
Richard H. Henchman
Keyword(s):  
Free Energy ◽  
Drugs Of Abuse ◽  
Binding Free Energy ◽  
Average Error ◽  
Scoring Functions ◽  
Vibrational Entropy ◽  
Free Energies ◽  
Energy Entropy ◽  
Wide Range ◽  
Binding Free Energies

AbstractFree energy drives a wide range of molecular processes such as solvation, binding, chemical reactions and conformational change. Given the central importance of binding, a wide range of methods exist to calculate it, whether based on scoring functions, machine-learning, classical or electronic structure methods, alchemy, or explicit evaluation of energy and entropy. Here we present a new energy–entropy (EE) method to calculate the host–guest binding free energy directly from molecular dynamics (MD) simulation. Entropy is evaluated using Multiscale Cell Correlation (MCC) which uses force and torque covariance and contacts at two different length scales. The method is tested on a series of seven host–guest complexes in the SAMPL8 (Statistical Assessment of the Modeling of Proteins and Ligands) “Drugs of Abuse” Blind Challenge. The EE-MCC binding free energies are found to agree with experiment with an average error of 0.9 kcal mol−1. MCC makes clear the origin of the entropy changes, showing that the large loss of positional, orientational, and to a lesser extent conformational entropy of each binding guest is compensated for by a gain in orientational entropy of water released to bulk, combined with smaller decreases in vibrational entropy of the host, guest and contacting water.

scholarly journals Automation of absolute protein-ligand binding free energy calculations for docking refinement and compound evaluation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Germano Heinzelmann ◽  
Michael K. Gilson
Keyword(s):  
Free Energy ◽  
Early Stage ◽  
Binding Free Energy ◽  
Low Cost ◽  
Free Energy Calculations ◽  
Free Energies ◽  
Energy Calculations ◽  
Drug Candidates ◽  
Binding Free Energy Calculations ◽  
Binding Free Energies

AbstractAbsolute binding free energy calculations with explicit solvent molecular simulations can provide estimates of protein-ligand affinities, and thus reduce the time and costs needed to find new drug candidates. However, these calculations can be complex to implement and perform. Here, we introduce the software BAT.py, a Python tool that invokes the AMBER simulation package to automate the calculation of binding free energies for a protein with a series of ligands. The software supports the attach-pull-release (APR) and double decoupling (DD) binding free energy methods, as well as the simultaneous decoupling-recoupling (SDR) method, a variant of double decoupling that avoids numerical artifacts associated with charged ligands. We report encouraging initial test applications of this software both to re-rank docked poses and to estimate overall binding free energies. We also show that it is practical to carry out these calculations cheaply by using graphical processing units in common machines that can be built for this purpose. The combination of automation and low cost positions this procedure to be applied in a relatively high-throughput mode and thus stands to enable new applications in early-stage drug discovery.

scholarly journals Alchemical Absolute Protein-Ligand Binding Free Energies for Drug Design

2021 ◽  
Author(s):  
Yuriy Khalak ◽  
Gary Tresdern ◽  
Matteo Aldeghi ◽  
Hannah Magdalena Baumann ◽  
David L. Mobley ◽  
...  
Keyword(s):  
Free Energy ◽  
Drug Discovery ◽  
Drug Design ◽  
Ligand Binding ◽  
Binding Free Energy ◽  
Free Energy Calculations ◽  
Free Energies ◽  
Energy Calculations ◽  
Binding Free Energy Calculations ◽  
Binding Free Energies

The recent advances in relative protein-ligand binding free energy calculations have shown the value of alchemical methods in drug discovery. Accurately assessing absolute binding free energies, although highly desired, remains...

scholarly journals Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision and Reproducibility

2021 ◽  
Author(s):  
Alexander Wade ◽  
Agastya Bhati ◽  
Shunzhou Wan ◽  
Peter Coveney
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Binding Free Energy ◽  
Thermodynamic Integration ◽  
Free Energy Perturbation ◽  
Free Energies ◽  
Ensemble Averaging ◽  
Relative Binding ◽  
Energy Perturbation ◽  
Binding Free Energies

The binding free energy between a ligand and its target protein is an essential quantity to know at all stages of the drug discovery pipeline. Assessing this value computationally can offer insight into where efforts should be focused in the pursuit of effective therapeutics to treat myriad diseases. In this work we examine the computation of alchemical relative binding free energies with an eye to assessing reproducibility across popular molecular dynamics packages and free energy estimators. The focus of this work is on 54 ligand transformations from a diverse set of protein targets: MCL1, PTP1B, TYK2, CDK2 and thrombin. These targets are studied with three popular molecular dynamics packages: OpenMM, NAMD2 and NAMD3. Trajectories collected with these packages are used to compare relative binding free energies calculated with thermodynamic integration and free energy perturbation methods. The resulting binding free energies show good agreement between molecular dynamics packages with an average mean unsigned error between packages of 0.5 $kcal/mol$ The correlation between packages is very good with the lowest Spearman's, Pearson's and Kendall's tau correlation coefficient between two packages being 0.91, 0.89 and 0.74 respectively. Agreement between thermodynamic integration and free energy perturbation is shown to be very good when using ensemble averaging.

scholarly journals A replica exchange umbrella sampling (REUS) approach to predict host–guest binding free energies in SAMPL8 challenge

2021 ◽  
Author(s):  
Mahdi Ghorbani ◽  
Phillip S. Hudson ◽  
Michael R. Jones ◽  
Félix Aviat ◽  
Rubén Meana-Pañeda ◽  
...  
Keyword(s):  
Free Energy ◽  
Binding Free Energy ◽  
Umbrella Sampling ◽  
Free Energy Calculations ◽  
Replica Exchange ◽  
Free Energies ◽  
Guest Binding ◽  
Binding Free Energy Calculations ◽  
Force Field Parameters ◽  
Binding Free Energies

AbstractIn this study, we report binding free energy calculations of various drugs-of-abuse to Cucurbit-[8]-uril as part of the SAMPL8 blind challenge. Force-field parameters were obtained from force-matching with different quantum mechanical levels of theory. The Replica Exchange Umbrella Sampling (REUS) approach was used with a cylindrical restraint to enhance the sampling of host–guest binding. Binding free energy was calculated by pulling the guest molecule from one side of the symmetric and cylindrical host, then into and through the host, and out the other side (bidirectional) as compared to pulling only to the bound pose inside the cylindrical host (unidirectional). The initial results with force-matched MP2 parameter set led to RMSE of 4.68 $${\text{kcal}}/{\text{mol}}$$ kcal / mol from experimental values. However, the follow-up study with CHARMM generalized force field parameters and force-matched PM6-D3H4 parameters resulted in RMSEs from experiment of $$2.65$$ 2.65 and $$1.72 {\text{kcal}}/{\text{mol}}$$ 1.72 kcal / mol , respectively, which demonstrates the potential of REUS for accurate binding free energy calculation given a more suitable description of energetics. Moreover, we compared the free energies for the so called bidirectional and unidirectional free energy approach and found that the binding free energies were highly similar. However, one issue in the bidirectional approach is the asymmetry of profile on the two sides of the host. This is mainly due to the insufficient sampling for these larger systems and can be avoided by longer sampling simulations. Overall REUS shows great promise for binding free energy calculations.

scholarly journals Accurate absolute free energies for ligand–protein binding based on non-equilibrium approaches

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Vytautas Gapsys ◽  
Ahmet Yildirim ◽  
Matteo Aldeghi ◽  
Yuriy Khalak ◽  
David van der Spoel ◽  
...  
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Binding Free Energy ◽  
Free Energy Perturbation ◽  
Free Energies ◽  
Hamiltonian Replica Exchange ◽  
Current State ◽  
Energy Perturbation ◽  
Binding Free Energies ◽  
Non Equilibrium

AbstractThe accurate calculation of the binding free energy for arbitrary ligand–protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art molecular dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equilibrium sampling of the phase space. In the current work we demonstrate that accurate absolute binding free energies (ABFE) can also be obtained via theoretically rigorous non-equilibrium approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equilibrium and non-equilibrium approaches converge to the same results. The non-equilibrium approach achieves the same level of accuracy and convergence as an equilibrium free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equilibrium approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equilibrium ABFE calculations are shown to yield reliable and well-converged estimates of protein–ligand binding affinity.

scholarly journals Evaluating the use of absolute binding free energy in the fragment optimization process.

2022 ◽  
Author(s):  
Irfan Alibay ◽  
Aniket Mangakar ◽  
Daniel Seeliger ◽  
Philip Biggin
Keyword(s):  
Free Energy ◽  
Computational Methods ◽  
Binding Free Energy ◽  
Optimization Process ◽  
Energy Estimates ◽  
Free Energies ◽  
Chemical Modifications ◽  
The Right ◽  
Absolute Binding Free Energy ◽  
Binding Free Energies

Key to the fragment optimization process is the need to accurately capture the changes in affinity that are associated with a given set of chemical modifications. Due to the weakly binding nature of fragments, this has proven to be a challenging task, despite recent advancements in leveraging experimental and computational methods. In this work, we evaluate the use of Absolute Binding Free Energy (ABFE) calculations in guiding fragment optimization decisions, retrospectively calculating binding free energies for 59 ligands across 4 fragment elaboration campaigns. We first demonstrate that ABFEs can be used to accurately rank fragment-sized binders with an overall Spearman’s r of 0.89 and a Kendall τ of 0.67, although often deviating from experiment in absolute free energy values with an RMSE of 2.75 kcal/mol. We then also show that in several cases, retrospective fragment optimization decisions can be supported by the ABFE calculations. Cases that were not supported were often limited by large uncertainties in the free energy estimates, however generally the right direction in ΔΔG is still observed. Comparing against cheaper endpoint methods, namely Nwat-MM/GBSA, we find that ABFEs offer better outcomes in ranking binders, improving correlation metrics, although a similar confidence in retrospective synthetic decisions is achieved. Our results indicate that ABFE calculations are currently at the level of accuracy that can be usefully employed to gauge which fragment elaborations are likely to offer the best gains in affinity.

scholarly journals A simple model for predicting the free energy of binding between anthracycline antibiotics and DNA.

2000 ◽  
Vol 47 (1) ◽  
pp. 1-9 ◽  
Author(s):  
W R Rudnicki ◽  
M Kurzepa ◽  
T Szczepanik ◽  
W Priebe ◽  
B Lesyng
Keyword(s):  
Free Energy ◽  
Theoretical Model ◽  
Density Functional ◽  
Binding Free Energy ◽  
Binding Energies ◽  
Free Energies ◽  
Anthracycline Antibiotics ◽  
Free Energy Of Binding ◽  
Derivatives Of ◽  
Binding Free Energies

A theoretical model for predicting the free energy of binding between anthracycline antibiotics and DNA was developed using the electron density functional (DFT) and molecular mechanics (MM) methods. Partial DFT-ESP charges were used in calculating the MM binding energies for complexes formed between anthracycline antibiotics and oligodeoxynucleotides. These energies were then compared with experimental binding free energies. The good correlation between the experimental and theoretical energies allowed us to propose a model for predicting the binding free energy for derivatives of anthracycline antibiotics and for quickly screening new anthracycline derivatives.

scholarly journals Alchemical Absolute Protein-Ligand Binding Free Energies for Drug Design

2021 ◽  
Author(s):  
Yuriy Khalak ◽  
Gary Tresadern ◽  
Matteo Aldeghi ◽  
Hannah Magdalena Baumann ◽  
David L. Mobley ◽  
...  
Keyword(s):  
Free Energy ◽  
Drug Discovery ◽  
Ligand Binding ◽  
Binding Free Energy ◽  
Free Energy Calculations ◽  
Free Energies ◽  
Energy Calculations ◽  
Binding Free Energy Calculations ◽  
Binding Free Energies ◽  
Apo State

The recent advances in relative protein-ligand binding free energy calculations have shown the value of alchemical methods in drug discovery. Accurately assessing absolute binding free energies, although highly desired, remains a challenging endeavour, mostly limited to small model cases. Here, we demonstrate accurate first principles based absolute binding free energy estimates for 128 pharmaceutically relevant targets. We use a novel rigorous method to generate protein-ligand ensembles for the ligand in its decoupled state. Not only do the calculations deliver accurate protein-ligand binding affinity estimates, but they also provide detailed physical insight into the structural determinants of binding. We identify subtle rotamer rearrangements between apo and holo states of a protein that are crucial for binding. When compared to relative binding free energy calculations, obtaining absolute binding free energies is considerably more challenging in large part due to the need to explicitly account for the protein in its apo state. In this work we present several approaches to obtain apo state ensembles for accurate absolute ΔG calculations, thus outlining protocols for prospective application of the methods for drug discovery.

scholarly journals Comparing alchemical and physical pathway methods for computing the absolute binding free energy of charged ligands

2018 ◽  
Vol 20 (25) ◽  
pp. 17081-17092 ◽  
Author(s):  
Nanjie Deng ◽  
Di Cui ◽  
Bin W. Zhang ◽  
Junchao Xia ◽  
Jeffrey Cruz ◽  
...  
Keyword(s):  
Free Energy ◽  
Binding Free Energy ◽  
Potential Of Mean Force ◽  
Free Energies ◽  
Decoupling Method ◽  
The Absolute ◽  
Absolute Binding Free Energy ◽  
Binding Free Energies ◽  
Charged Ligands

We compare the performance of the potential of mean force (PMF) method and double decoupling method (DDM) for computing absolute binding free energies for charged ligands.

scholarly journals Correction Terms for Calculating Binding Free Energy Using Rates from Nonequilibrium Simulations

2020 ◽  
Author(s):  
Robert Hall ◽  
Tom Dixon ◽  
Alex Dickson
Keyword(s):  
Free Energy ◽  
Electrostatic Interactions ◽  
Binding Free Energy ◽  
Molecular Simulations ◽  
Binding Kinetics ◽  
Drug Candidate ◽  
Free Energies ◽  
Unbound States ◽  
Correction Terms ◽  
Binding Free Energies

<div>The free energy of a process is the fundamental quantity that determines its spontaneity or propensity at a given temperature. Binding free energy of a drug candidate to its biomolecular target is used as an objective quantity in drug design. Binding kinetics -- rates of association (k<sub>on</sub>) and dissociation (k<sub>off</sub>) -- have also demonstrated utility for their ability to predict efficacy and in some cases have been shown to be more predictive than the binding free energy alone. Although challenging, some methods exist to calculate binding kinetics from molecular simulations. While the kinetics of the binding process are related to the free energy by the log of their ratio, it is not straightforward to account for common, practical details pertaining to the calculation of rates in molecular simulations, such as the finite simulation volume or the particular definition of the ``bound" and ``unbound" states. Here we derive a set of correction terms that can be applied to calculations of binding free energies using rates observed in simulations. One term accounts for the particular definitions of the bound and unbound states. The second term accounts for residual electrostatic interactions that might still be present between the molecules, which is especially useful if one or both of the molecules carry an explicit charge. The third term accounts for the volume of the unbound state in the simulation box, which is useful to keep the simulated volume as small as possible during rate calculations. We apply these correction terms to revisit the calculation of binding free energies from rate constants for a host-guest system that was part of a blind prediction challenge, where significant deviations were observed between free energies calculated with rate ratios and those calculated from alchemical perturbation. The correction terms combine to significantly decrease the error with respect to computational benchmarks, from 3.4 to 0.76 kcal/mol.</div>

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