Ab Initio Free Energy Calculations at Multiple Electronic Structure Levels Made Affordable: An Effective Combination of Perturbation Theory and Machine Learning

2020 ◽  
Author(s):  
Tomas Bucko ◽  
Monika Gešvandtnerová ◽  
Dario Rocca
Keyword(s):  
Machine Learning ◽  
Free Energy ◽  
Perturbation Theory ◽  
Ab Initio ◽  
Single Point ◽  
Free Energy Calculations ◽  
Thermodynamic Quantities ◽  
Free Energies ◽  
Energy Calculations ◽  
Ab Initio Theory

<div>While free energies are fundamental thermodynamic quantities to characterize chemical reactions, their calculation based on ab initio theory is usually limited by the high computational cost. This is particularly true if multiple levels of theory have to be tested to establish their relative accuracy, if highly expensive quantum mechanical approximations are of interest, and also if several different temperatures have to be considered. We present an ab initio approach that effectively couples perturbation theory and machine learning to make ab initio free energy calculations more affordable. Starting from results based on a certain production ab initio theory, perturbation theory is applied to obtain free energies. The large number of single point calculations required by a brute force application of this approach are here significantly decreased by applying machine learning techniques. Importantly, the </div><div>training of the machine learning model requires only a small amount of data and does not need to be </div><div>performed again when the temperature is decreased.</div><div>The accuracy and efficiency of this method is demonstrated by computing the free energy of activation of the </div><div>proton exchange reaction in the zeolite chabazite. Starting from an ab initio calculation based on a semilocal</div><div>approximation of density functional theory, free energies based on significantly </div><div>more expensive non-local van der Waals and hybrid functionals are obtained with only a few tens</div><div>of additional single point calculations. In this way this work paves the route to</div><div>quick free energy calculations using different levels of theory or approximations that would be</div><div>too computationally expensive to be directly employed in molecular dynamics or Monte Carlo simulations.</div>

scholarly journals Ab initio calculations of free energy of activation at multiple electronic structure levels made affordable: An effective combination of perturbation theory and machine learning

2020 ◽  
Author(s):  
Tomas Bucko ◽  
Monika Gešvandtnerová ◽  
Dario Rocca
Keyword(s):  
Machine Learning ◽  
Free Energy ◽  
Perturbation Theory ◽  
Ab Initio ◽  
Single Point ◽  
Free Energy Calculations ◽  
Free Energies ◽  
Energy Calculations ◽  
Free Energy Of Activation ◽  
Ab Initio Theory

<div>While free energies are fundamental thermodynamic quantities to characterize chemical reactions, their calculation based on ab initio theory is usually limited by the high computational cost. This is particularly true if multiple levels of theory have to be tested to establish their relative accuracy, if highly expensive quantum mechanical approximations are of interest, and also if several different temperatures have to be considered. We present an ab initio approach that effectively couples perturbation theory and machine learning to make ab initio free energy calculations more affordable. Starting from results based on a certain production ab initio theory, perturbation theory is applied to obtain free energies. The large number of single point calculations required by a brute force application of this approach are here significantly decreased by applying machine learning techniques. Importantly, the training of the machine learning model requires only a small amount of data and does not need to be performed again when the temperature is decreased. The accuracy and efficiency of this method is demonstrated by computing the free energy of activation of the proton exchange reaction in the zeolite chabazite. Starting from an ab initio calculation based on a semilocal approximation of density functional theory, free energies based on significantly more expensive non-local van der Waals and hybrid functionals are obtained with only a few tens of additional single point calculations. In this way this work paves the route to quick free energy calculations using different levels of theory or approximations that would be too computationally expensive to be directly employed in molecular dynamics or Monte Carlo simulations.</div>

scholarly journals Ab initio calculations of free energy of activation at multiple electronic structure levels made affordable: An effective combination of perturbation theory and machine learning

2020 ◽  
Author(s):  
Tomas Bucko ◽  
Monika Gešvandtnerová ◽  
Dario Rocca
Keyword(s):  
Machine Learning ◽  
Free Energy ◽  
Perturbation Theory ◽  
Ab Initio ◽  
Single Point ◽  
Free Energy Calculations ◽  
Free Energies ◽  
Energy Calculations ◽  
Free Energy Of Activation ◽  
Ab Initio Theory

<div>While free energies are fundamental thermodynamic quantities to characterize chemical reactions, their calculation based on ab initio theory is usually limited by the high computational cost. This is particularly true if multiple levels of theory have to be tested to establish their relative accuracy, if highly expensive quantum mechanical approximations are of interest, and also if several different temperatures have to be considered. We present an ab initio approach that effectively couples perturbation theory and machine learning to make ab initio free energy calculations more affordable. Starting from results based on a certain production ab initio theory, perturbation theory is applied to obtain free energies. The large number of single point calculations required by a brute force application of this approach are here significantly decreased by applying machine learning techniques. Importantly, the training of the machine learning model requires only a small amount of data and does not need to be performed again when the temperature is decreased. The accuracy and efficiency of this method is demonstrated by computing the free energy of activation of the proton exchange reaction in the zeolite chabazite. Starting from an ab initio calculation based on a semilocal approximation of density functional theory, free energies based on significantly more expensive non-local van der Waals and hybrid functionals are obtained with only a few tens of additional single point calculations. In this way this work paves the route to quick free energy calculations using different levels of theory or approximations that would be too computationally expensive to be directly employed in molecular dynamics or Monte Carlo simulations.</div>

scholarly journals Teaching free energy calculations to learn from experimental data

2021 ◽  
Author(s):  
Marcus Wieder ◽  
Josh Fass ◽  
John D. Chodera
Keyword(s):  
Machine Learning ◽  
Experimental Data ◽  
Free Energy ◽  
Quantum Chemical ◽  
Free Energy Calculations ◽  
Chemical Bonds ◽  
Free Energies ◽  
Energy Calculations ◽  
Alchemical Free Energy ◽  
Alchemical Free Energy Calculations

AbstractAlchemical free energy calculations are an important tool in the computational chemistry tool-box, enabling the efficient calculation of quantities critical for drug discovery such as ligand binding affinities, selectivities, and partition coefficients. However, modern alchemical free energy calculations suffer from three significant limitations: (1) modern molecular mechanics force fields are limited in their ability to model complex molecular interactions, (2) classical force fields are unable to treat phenomena that involve rearrangements of chemical bonds, and (3) these calculations are unable to easily learn to improve their performance if readily-available experimental data is available. Here, we show how all three limitations can be overcome through the use of quantum machine learning (QML) potentials capable of accurately modeling quantum chemical energetics even when chemical bonds are made and broken. Because these potentials are based on mathematically convenient deep learning architectures instead of traditional quantum chemical formulations, QML simulations can be run at a fraction of the cost of quantum chemical simulations using modern graphics processing units (GPUs) and machine learning frameworks. We demonstrate that alchemical free energy calculations in explicit solvent are especially simple to implement using QML potentials because these potentials lack singularities and other pathologies typical of molecular mechanics potentials, and that alchemical free energy calculations are highly effective even when bonds are broken or made. Finally, we show how a limited number of experimental free energy measurements can be used to significantly improve the accuracy of computed free energies for unrelated compounds with no significant generalization gap. We illustrate these concepts on the prediction of aqueous tautomer free energies (related to tautomer ratios), which are highly relevant to drug discovery in that more than a quarter of all approved drugs exist as a mixture of tautomers.

scholarly journals Towards chemical accuracy for alchemical free energy calculations with hybrid physics-based machine learning / molecular mechanics potentials

2020 ◽  
Author(s):  
Dominic A. Rufa ◽  
Hannah E. Bruce Macdonald ◽  
Josh Fass ◽  
Marcus Wieder ◽  
Patrick B. Grinaway ◽  
...  
Keyword(s):  
Machine Learning ◽  
Free Energy ◽  
Molecular Mechanics ◽  
Force Fields ◽  
Free Energy Calculations ◽  
Binding Affinities ◽  
Free Energies ◽  
Energy Calculations ◽  
Alchemical Free Energy ◽  
Binding Free Energies

AbstractAlchemical free energy methods with molecular mechanics (MM) force fields are now widely used in the prioritization of small molecules for synthesis in structure-enabled drug discovery projects because of their ability to deliver 1–2 kcal mol−1 accuracy in well-behaved protein-ligand systems. Surpassing this accuracy limit would significantly reduce the number of compounds that must be synthesized to achieve desired potencies and selectivities in drug design campaigns. However, MM force fields pose a challenge to achieving higher accuracy due to their inability to capture the intricate atomic interactions of the physical systems they model. A major limitation is the accuracy with which ligand intramolecular energetics—especially torsions—can be modeled, as poor modeling of torsional profiles and coupling with other valence degrees of freedom can have a significant impact on binding free energies. Here, we demonstrate how a new generation of hybrid machine learning / molecular mechanics (ML/MM) potentials can deliver significant accuracy improvements in modeling protein-ligand binding affinities. Using a nonequilibrium perturbation approach, we can correct a standard, GPU-accelerated MM alchemical free energy calculation in a simple post-processing step to efficiently recover ML/MM free energies and deliver a significant accuracy improvement with small additional computational effort. To demonstrate the utility of ML/MM free energy calculations, we apply this approach to a benchmark system for predicting kinase:inhibitor binding affinities—a congeneric ligand series for non-receptor tyrosine kinase TYK2 (Tyk2)—wherein state-of-the-art MM free energy calculations (with OPLS2.1) achieve inaccuracies of 0.93±0.12 kcal mol−1 in predicting absolute binding free energies. Applying an ML/MM hybrid potential based on the ANI2x ML model and AMBER14SB/TIP3P with the OpenFF 1.0.0 (“Parsley”) small molecule force field as an MM model, we show that it is possible to significantly reduce the error in absolute binding free energies from 0.97 [95% CI: 0.68, 1.21] kcal mol−1 (MM) to 0.47 [95% CI: 0.31, 0.63] kcal mol−1 (ML/MM).

SAMPL6 Octanol-Water Partition Coefficients from Alchemical Free Energy Calculations with MBIS Atomic Charges

2019 ◽  
Author(s):  
Maximiliano Riquelme ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Free Energy ◽  
Electron Density ◽  
Free Energy Calculations ◽  
Basis Set ◽  
Energetic Cost ◽  
Atomic Charges ◽  
Free Energies ◽  
Energy Calculations ◽  
Alchemical Free Energy ◽  
Alchemical Free Energy Calculations

In molecular modeling the description of the interactions between molecules forms the basis for a correct prediction of macroscopic observables. Here, we derive atomic charges from the implicitly polarized electron density of eleven molecules in the SAMPL6 challenge using the Hirshfeld-I and Minimal Basis Set Iterative Stockholder(MBIS) partitioning method. These atomic charges combined with other parameters in the GAFF force field and different water/octanol models were then used in alchemical free energy calculations to obtain hydration and solvation free energies, which after correction for the polarization cost, result in the blind prediction of the partition coefficient. From the tested partitioning methods and water models the S-MBIS atomic charges with the TIP3P water model presented the smallest deviation from the experiment. Conformational dependence of the free energies and the energetic cost associated with the polarization of the electron density are discussed.

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 A Hybrid Alchemical Free Energy and Machine Learning Methodology for the Calculation of Absolute Hydration Free Energies of Small Molecules

2020 ◽  
Author(s):  
Jenke Scheen ◽  
Wilson Wu ◽  
Antonia S. J. S. Mey ◽  
Paolo Tosco ◽  
Mark Mackey ◽  
...  
Keyword(s):  
Machine Learning ◽  
Free Energy ◽  
Free Energy Calculations ◽  
Learning Approaches ◽  
Free Energies ◽  
Training Set ◽  
Set Size ◽  
Correction Terms ◽  
Alchemical Free Energy ◽  
Alchemical Free Energy Calculations

A methodology that combines alchemical free energy calculations (FEP) with machine learning (ML) has been developed to compute accurate absolute hydration free energies. The hybrid FEP/ML methodology was trained on a subset of the FreeSolv database, and retrospectively shown to outperform most submissions from the SAMPL4 competition. Compared to pure machine-learning approaches, FEP/ML yields more precise estimates of free energies of hydration, and requires a fraction of the training set size to outperform standalone FEP calculations. The ML-derived correction terms are further shown to be transferable to a range of related FEP simulation protocols. The approach may be used to inexpensively improve the accuracy of FEP calculations, and to flag molecules which will benefit the most from bespoke forcefield parameterisation efforts.

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...

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