Alchemical Hydration Free Energy Calculations Using Molecular Dynamics with Explicit Polarization and Induced Polarity Decoupling: An OTFP Approach

2019 ◽  
Author(s):  
Braden Kelly ◽  
William Smith
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Force Field ◽  
Energy Difference ◽  
Free Energy Calculations ◽  
Experimental Uncertainty ◽  
Test Set ◽  
Fixed Charges ◽  
Partial Charges ◽  
The Difference

We present an algorithm to calculate hydration free energies in explicit solvent that incorporates polarization of the solute molecule in conjunction with the use of a classical fixed--charge force field. The goal is to improve the accuracy over the alternative approach of developing a polarizable force field with adjustable parameters. We incorporate polarization by implementing on--the--fly periodic updating of the solute's partial charges during a standard molecular dynamics (MD) alchemical change simulation by the use of mixed QM/MM calculations. We decouple the polarizing solvent's electric field along with the normal MD solute Coulomb decoupling to calculate the free energy difference between an unpolarized solute in vacuum and a fully polarized solute in solution. This approach is in contrast to the common approach of GAFF, which calculates the difference between a solute in vacuum that is over--polarized by the use of fixed charges calculated using HF/6-31G*, and correspondingly under--polarized by the same partial charge set in the solution phase. We apply our methodology to a test set of 31 molecules, ranging from small polar to large drug--like molecules. We find that results using our method with Minimum Basis Iterative Stockholder (MBIS) charges and using RESP charges with B3LYP/cc-pVTZ are superior to results calculated using the current ``gold standard" AM1--BCC method. We show results using MBIS partial charges using B3LYP/cc-pVTZ and MP2/cc-pVTZ, RESP partial charges using B3LYP/cc-pVTZ and HF/6-31G*, and AM1-BCC partial charges. Our method using MBIS in conjunction with MP2/cc-pVTZ yields an AAD that is 2.91 kJ$\cdot$mol$^{-1}$ (0.70 kcal$\cdot$mol$^{-1}$) lower than that of AM1--BCC for our test set. AM1-BCC was within experimental uncertainty on 13 \% of the data, while our method using MP2 was within experimental uncertainty on 43 \% of the data. We conjecture that results can be further improved by using Lennard--Jones and torsional parameters that are fitted to the MBIS charge method and that using RESP with our method can be improved by using a higher level of theory than B3LYP, for instance MP2 or $\omega$B97X-D.

scholarly journals A Simple Method for Including Polarization Effects in Solvation Free Energy Calculations When Using Fixed-Charge Force Fields: Alchemically Polarized Charges.

2020 ◽  
Author(s):  
Braden Kelly ◽  
William Smith
Keyword(s):  
Free Energy ◽  
Electronic Structure ◽  
Force Fields ◽  
Free Energy Calculations ◽  
Fixed Charge ◽  
Basis Sets ◽  
Hydration Free Energy ◽  
Simple Method ◽  
Test Set ◽  
Partial Charges

<div><div>The incorporation of polarizability in classical force-field molecular simulations is an ongoing area of research. We focus here on its application to hydration free energy simulations of organic molecules. In contrast to computationally complex approaches involving the development of explicitly polarizable force fields, we present herein a simple methodology for incorporating polarization into such simulations using standard fixed-charge force-fields, which we call the Alchemically Polarized Charges (APolQ) method. APolQ employs a standard classical alchemical free energy change simulation to calculate the free energy difference between a fully polarized solute particle in a condensed phase and its unpolarized state in a vacuum. One electronic structure (ES) calculation to of the electron densities is required for each state: for the former, we use a Polarizable Continuum Model (PCM), and for the latter we use vacuum-phase electronic structure calculations.</div><div><br></div><div>We applied APolQ to hydration free energy data for a test set of 45 neutral solute molecules in the FreeSolv database, and compared results obtained using three different water models (SPC/E, TIP3P, OPC3) and using MBIS and RESP partial charge methodologies. ES calculations were carried out at the MP2 level of theory and with cc-pVTZ and aug-cc-pVTZ basis sets. In comparison with AM1-BCC, we found that APolQ outperforms it for the test set. Despite our method using default GAFF parameters, the MBIS partial charges yield Absolute Average Deviations (AAD) 1.5 to 1.9 kJ·mol<sup>−1</sup> lower than AM1-BCC.</div><div><br></div><div>We conjecture that this method can be further improved by fitting the Lennard-Jones and torsional parameters to partial charges derived using MBIS or RESP methodologies. </div></div>

scholarly journals Perturbation Free-Energy Toolkit: Automated Alchemical Topology Builder and Optimized Simulation Update Scheme

2021 ◽  
Author(s):  
Drazen Petrov
Keyword(s):  
Free Energy ◽  
Graph Matching ◽  
Linear Interpolation ◽  
Energy Difference ◽  
Free Energy Calculations ◽  
Rational Drug Design ◽  
True Error ◽  
Energy Calculations ◽  
Common Substructure ◽  
The Difference

Free-energy calculations play an important role in the application of computational chemistry to a range of fields, including protein biochemistry, rational drug design or material science. Importantly, the free energy difference is directly related to experimentally measurable quantities such as partition and adsorption coefficients, water activity and binding affinities. Among several techniques aimed at predicting the free-energy differences, perturbation approaches, involving alchemical transformation of one molecule into another through intermediate states, stand out as rigorous methods based on statistical mechanics. However, despite the importance of efficient and accurate free energy predictions, applicability of the perturbation approaches is still largely impeded by a number of challenges. This study aims at addressing two of them: 1) the definition of the perturbation path, i.e., alchemical changes leading to the transformation of one molecule to the other, and 2) determining the amount of sampling along the path to reach desired convergence. In particular, an automatic perturbation builder based on a graph matching algorithm is developed, that is able to identify the maximum common substructure of two molecules and provide the perturbation topologies suitable for free-energy calculations using GROMOS and GROMACS simulation packages. Moreover, it was used to calculate the changes in free energy of a set of post-translational modifications and analyze their convergence behavior. Different methods were tested, which showed that MBAR and extended thermodynamic integration (TI) in combination with MBAR show better performance as compared to BAR, extended TI with linear interpolation and plain TI. Also, a number of error estimators were explored and how they relate to the true error, estimated as the difference in free energy from an extensive set of simulation data. This analysis shows that most of the estimators provide only a qualitative agreement to the true error, with little quantitative predictive power. This notwithstanding, the preformed analyses provided insight into the convergence of free-energy calculations, which allowed for development of an iterative update scheme for perturbation simulations that aims at minimizing the simulation time to reach the convergence, i.e., optimizing the efficiency. Importantly, this toolkit is made available online as an open-source python package (https://github.com/drazen-petrov/SMArt).

scholarly journals A Simple Method for Including Polarization Effects in Solvation Free Energy Calculations When Using Fixed-Charge Force Fields: Alchemically Polarized Charges.

2020 ◽  
Author(s):  
Braden Kelly ◽  
William Smith
Keyword(s):  
Free Energy ◽  
Electronic Structure ◽  
Force Fields ◽  
Free Energy Calculations ◽  
Fixed Charge ◽  
Basis Sets ◽  
Hydration Free Energy ◽  
Simple Method ◽  
Test Set ◽  
Partial Charges

<div><div>The incorporation of polarizability in classical force-field molecular simulations is an ongoing area of research. We focus here on its application to hydration free energy simulations of organic molecules. In contrast to computationally complex approaches involving the development of explicitly polarizable force fields, we present herein a simple methodology for incorporating polarization into such simulations using standard fixed-charge force-fields, which we call the Alchemically Polarized Charges (APolQ) method. APolQ employs a standard classical alchemical free energy change simulation to calculate the free energy difference between a fully polarized solute particle in a condensed phase and its unpolarized state in a vacuum. One electronic structure (ES) calculation to of the electron densities is required for each state: for the former, we use a Polarizable Continuum Model (PCM), and for the latter we use vacuum-phase electronic structure calculations.</div><div><br></div><div>We applied APolQ to hydration free energy data for a test set of 45 neutral solute molecules in the FreeSolv database, and compared results obtained using three different water models (SPC/E, TIP3P, OPC3) and using MBIS and RESP partial charge methodologies. ES calculations were carried out at the MP2 level of theory and with cc-pVTZ and aug-cc-pVTZ basis sets. In comparison with AM1-BCC, we found that APolQ outperforms it for the test set. Despite our method using default GAFF parameters, the MBIS partial charges yield Absolute Average Deviations (AAD) 1.5 to 1.9 kJ·mol<sup>−1</sup> lower than AM1-BCC.</div><div><br></div><div>We conjecture that this method can be further improved by fitting the Lennard-Jones and torsional parameters to partial charges derived using MBIS or RESP methodologies. </div></div>

Alchemical Hydration Free Energy Calculations Using Molecular Dynamics with Explicit Polarization and Induced Polarity Decoupling: An OTFP Approach

2019 ◽  
Author(s):  
Braden Kelly ◽  
William Smith
Keyword(s):  
Free Energy ◽  
Gas Phase ◽  
Free Energy Calculations ◽  
Partial Charge ◽  
Experimental Uncertainty ◽  
Hydration Free Energy ◽  
Energy Calculations ◽  
Lennard Jones ◽  
Partial Charges ◽  
The Cost

We present a methodology using fixed charge force–fields for alchemical solvation free energy calculations which accounts for the change in polarity that the solute experiences as it transfers from the gas-phase to the condensed phase. We update partial charges use QM/MM snapshots, decoupling the electric field appropriately when updating the partial charges. We also show how to account for the cost of self-polarization. We test our methodology on 30 molecules ranging from small polar to large drug–like molecules.We use Minimum Basis Iterative Stockholder (MBIS), Restrained Electrostatic Potential(RESP) and AM1-BCC partial charge methodologies. Using our method with MP2/cc-pVTZ and MBIS partial charges yields an AAD that is 2.98 kJ·mol−1(0.71 kcal·mol−1) lower than AM1–BCC. AM1–BCC is within experimental uncertainty on 10% of thedata compared to 40% with our method. We conjecture that results can be further improved by using Lennard–Jones and torsional parameters refitted to MBIS and RESP partial charge methods that use high levels of theory.<br>

scholarly journals Perturbation Free-Energy Toolkit: Automated Alchemical Topology Builder and Optimized Simulation Update Scheme

2021 ◽  
Author(s):  
Drazen Petrov
Keyword(s):  
Free Energy ◽  
Graph Matching ◽  
Linear Interpolation ◽  
Energy Difference ◽  
Free Energy Calculations ◽  
Rational Drug Design ◽  
True Error ◽  
Energy Calculations ◽  
Common Substructure ◽  
The Difference

Free-energy calculations play an important role in the application of computational chemistry to a range of fields, including protein biochemistry, rational drug design or material science. Importantly, the free energy difference is directly related to experimentally measurable quantities such as partition and adsorption coefficients, water activity and binding affinities. Among several techniques aimed at predicting the free-energy differences, perturbation approaches, involving alchemical transformation of one molecule into another through intermediate states, stand out as rigorous methods based on statistical mechanics. However, despite the importance of efficient and accurate free energy predictions, applicability of the perturbation approaches is still largely impeded by a number of challenges. This study aims at addressing two of them: 1) the definition of the perturbation path, i.e., alchemical changes leading to the transformation of one molecule to the other, and 2) determining the amount of sampling along the path to reach desired convergence. In particular, an automatic perturbation builder based on a graph matching algorithm is developed, that is able to identify the maximum common substructure of two molecules and provide the perturbation topologies suitable for free-energy calculations using GROMOS and GROMACS simulation packages. Moreover, it was used to calculate the changes in free energy of a set of post-translational modifications and analyze their convergence behavior. Different methods were tested, which showed that MBAR and extended thermodynamic integration (TI) in combination with MBAR show better performance as compared to BAR, extended TI with linear interpolation and plain TI. Also, a number of error estimators were explored and how they relate to the true error, estimated as the difference in free energy from an extensive set of simulation data. This analysis shows that most of the estimators provide only a qualitative agreement to the true error, with little quantitative predictive power. This notwithstanding, the preformed analyses provided insight into the convergence of free-energy calculations, which allowed for development of an iterative update scheme for perturbation simulations that aims at minimizing the simulation time to reach the convergence, i.e., optimizing the efficiency. Importantly, this toolkit is made available online as an open-source python package (https://github.com/drazen-petrov/SMArt).

A Simple Method for Incorporating Polarization Effects in Solvation Free Energy Calculations Using Fixed-Charge Force Fields

2020 ◽  
Author(s):  
Braden Kelly ◽  
William Smith
Keyword(s):  
Free Energy ◽  
Electronic Structure ◽  
Force Fields ◽  
Free Energy Calculations ◽  
Fixed Charge ◽  
Basis Sets ◽  
Hydration Free Energy ◽  
Simple Method ◽  
Test Set ◽  
Partial Charges

<div><div>The incorporation of polarizability in classical force-field molecular simulations is an ongoing area of research. We focus here on its application to hydration free energy simulations of organic molecules. In contrast to computationally complex approaches involving the development of explicitly polarizable force fields, we present herein a simple methodology for incorporating polarization into such simulations using standard fixed--charge force-fields, which we call the Alchemically Polarized Charges (APolQ) method. APolQ employs a standard classical alchemical free energy change simulation to calculate the free energy difference between a fully polarized solute particle in a condensed phase and its unpolarized state in a vacuum. One electronic structure (ES) calculation to of the electron densities is required for each state: for the former, we use a Polarizable Continuum Model (PCM), and for the latter we use vacuum-phase electronic structure calculations.</div><div><br></div><div>We applied APolQ to hydration free energy data for a test set of 45 neutral solute molecules in the FreeSolv database, and compared results obtained using three different water models (SPC/E, TIP3P, OPC3) and using MBIS and RESP partial charge methodologies. ES calculations were carried out at the MP2 level of theory and with cc-pVTZ and aug-cc-pVTZ basis sets. In comparison with AM1-BCC, we found that APolQ outperforms it for the test set. Despite our method using default GAFF parameters, the MBIS partial charges yield Absolute Average Deviations (AAD) 1.5 to 1.9 kJ·mol<sup>−1</sup> lower than AM1-BCC.</div><div><br></div><div>We conjecture that this method can be further improved by fitting the Lennard-Jones and torsional parameters to partial charges derived using MBIS or RESP methodologies. We note that APolQ can in principle be applied to any pure or mixed solvent.</div></div>

Assessing the ligand selectivity of sphingosine kinases using molecular dynamics and MM-PBSA binding free energy calculations

2016 ◽  
Vol 12 (4) ◽  
pp. 1174-1182 ◽  
Author(s):  
Liang Fang ◽  
Xiaojian Wang ◽  
Meiyang Xi ◽  
Tianqi Liu ◽  
Dali Yin
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Model Building ◽  
Binding Free Energy ◽  
Homology Model ◽  
Free Energy Calculations ◽  
Dynamics Simulation ◽  
Ligand Selectivity ◽  
Sphingosine Kinases ◽  
Binding Free Energy Calculations

Three residues of SK1 were identified important for selective SK1 inhibitory activity via SK2 homology model building, molecular dynamics simulation, and MM-PBSA studies.

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