Measuring the free energy of hard-sphere colloidal glasses

2022 ◽  
Author(s):  
Minh Triet Dang ◽  
Luka Gartner ◽  
Peter Schall ◽  
Edan Lerner
Keyword(s):  
Free Energy ◽  
Glass Transition ◽  
Colloidal Particles ◽  
Dominant Role ◽  
Particle Diameter ◽  
Energy Difference ◽  
Free Energy Calculations ◽  
Average Particle ◽  
Vibrational Entropy ◽  
Colloidal Glasses

Abstract Free energy is a key thermodynamic observable that controls the elusive physics of the glass transition. However, measuring the free energy of colloidal glasses from microscopy images is challenging due to the difficulty of measuring the individual particle size in the slightly polydisperse glassy systems. In this paper, we carry out experiments and numerical simulations of colloidal glasses with the aim to find a practical approach to measure the free energy from colloidal particles at mild polydispersity. We propose a novel method which requires only the particle coordinates from a few confocal microscopy snapshots to estimate the average particle diameter and use it as an input for our experimental free energy measurements. We verify our free energy calculations from Cell Theory with the free energy obtained by Thermodynamic Integration. The excellent agreement between the free energies measured using the two methods close to the glass transition packing fraction highlights the dominant role played by \emph{vibrational} entropy in determining a colloidal glass's free energy. Finally, the noticeable free energy difference calculated from uniform and conjectured particle sizes emphasizes the sensitivity on particle free volumes when measuring free energy in the slightly polydisperse colloidal glass.

Exploring metal-driven stereoselectivity of glycopeptides by free-energy calculations

2012 ◽  
Vol 84 (9) ◽  
pp. 1919-1930 ◽  
Author(s):  
Adriana Pietropaolo
Keyword(s):  
Free Energy ◽  
Bond Distance ◽  
Thermodynamic Cycle ◽  
Energy Difference ◽  
Accurate Estimate ◽  
Free Energy Calculations ◽  
Titration Calorimetry ◽  
Free Energy Difference ◽  
Free Energy Of Binding ◽  
Peptide Core

A formalism to quantify the chemical stereoselectivity, based on free energy of binding calculations, is here discussed. It is used to explain the stereoselectivity of two diastereoisomeric frameworks, comprising the dimer of a copper(II)-peptide core of L- and D-carnosine, respectively, each bound to two chains of D-trehalose, in which copper(II) adopts a type-II coordination geometry. The stereocenter of carnosine is varied both L and D, giving rise to two diastereoisomers. A thermodynamic cycle crossing the formation of the two enantiomeric copper(II) peptide cores was devised. A harmonic restraining potential that depends only on the bond distance was added to ensure reversibility in bond formation and dissociation, for an accurate estimate of the free energy. The calculation of the free energy of binding between D-trehalose and the two enantiomeric copper(II) peptide cores reproduces the free-energy quantities observed from stability constants and isothermal titration calorimetry (ITC) measurements. This is an example of chirality selection based on free-energy difference.

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 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 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 Relative free-energy calculations for scaffold hopping-type transformations with an automated RE-EDS sampling procedure

2022 ◽  
Author(s):  
Benjamin Ries ◽  
Karl Normak ◽  
R. Gregor Weiß ◽  
Salomé Rieder ◽  
Emília P. Barros ◽  
...  
Keyword(s):  
Free Energy ◽  
Computational Cost ◽  
Sampling Strategy ◽  
Energy Difference ◽  
Sampling Procedure ◽  
Free Energy Calculations ◽  
Ease Of Use ◽  
State Graph ◽  
Scaffold Hopping ◽  
Relative Free Energy

AbstractThe calculation of relative free-energy differences between different compounds plays an important role in drug design to identify potent binders for a given protein target. Most rigorous methods based on molecular dynamics simulations estimate the free-energy difference between pairs of ligands. Thus, the comparison of multiple ligands requires the construction of a “state graph”, in which the compounds are connected by alchemical transformations. The computational cost can be optimized by reducing the state graph to a minimal set of transformations. However, this may require individual adaptation of the sampling strategy if a transformation process does not converge in a given simulation time. In contrast, path-free methods like replica-exchange enveloping distribution sampling (RE-EDS) allow the sampling of multiple states within a single simulation without the pre-definition of alchemical transition paths. To optimize sampling and convergence, a set of RE-EDS parameters needs to be estimated in a pre-processing step. Here, we present an automated procedure for this step that determines all required parameters, improving the robustness and ease of use of the methodology. To illustrate the performance, the relative binding free energies are calculated for a series of checkpoint kinase 1 inhibitors containing challenging transformations in ring size, opening/closing, and extension, which reflect changes observed in scaffold hopping. The simulation of such transformations with RE-EDS can be conducted with conventional force fields and, in particular, without soft bond-stretching terms.

Large-Scale Assessment of Binding Free Energy Calculations in Active Drug Discovery Projects

2020 ◽  
Author(s):  
Christina Schindler ◽  
Hannah Baumann ◽  
Andreas Blum ◽  
Dietrich Böse ◽  
Hans-Peter Buchstaller ◽  
...  
Keyword(s):  
Free Energy ◽  
Drug Discovery ◽  
Large Scale ◽  
Active Drug ◽  
Binding Free Energy ◽  
Free Energy Calculations ◽  
Energy Calculation ◽  
Large Scale Assessment ◽  
New Public ◽  
Binding Free Energy Calculations

Here we present an evaluation of the binding affinity prediction accuracy of the free energy calculation method FEP+ on internal active drug discovery projects and on a large new public benchmark set.<br>

Automated Assessment of Binding Affinity via Alchemical Free Energy Calculations

2020 ◽  
Author(s):  
Maximilian Kuhn ◽  
Stuart Firth-Clark ◽  
Paolo Tosco ◽  
Antonia S. J. S. Mey ◽  
Mark Mackey ◽  
...  
Keyword(s):  
Free Energy ◽  
Protein Structures ◽  
Free Energy Calculations ◽  
Distinct Advantage ◽  
Binding Affinities ◽  
Structure Based Drug Design ◽  
Energy Calculations ◽  
Kendall’S Τ ◽  
Experimental Values ◽  
Better Than

Free energy calculations have seen increased usage in structure-based drug design. Despite the rising interest, automation of the complex calculations and subsequent analysis of their results are still hampered by the restricted choice of available tools. In this work, an application for automated setup and processing of free energy calculations is presented. Several sanity checks for assessing the reliability of the calculations were implemented, constituting a distinct advantage over existing open-source tools. The underlying workflow is built on top of the software Sire, SOMD, BioSimSpace and OpenMM and uses the AMBER14SB and GAFF2.1 force fields. It was validated on two datasets originally composed by Schrödinger, consisting of 14 protein structures and 220 ligands. Predicted binding affinities were in good agreement with experimental values. For the larger dataset the average correlation coefficient Rp was 0.70 ± 0.05 and average Kendall’s τ was 0.53 ± 0.05 which is broadly comparable to or better than previously reported results using other methods. <br>

SAMPL7 TrimerTrip Host-Guest Binding Poses and Binding Affinities from Spherical-Coordinates-Biased Simulations

2020 ◽  
Author(s):  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Computational Modelling ◽  
Free Energy Calculations ◽  
Energy Estimates ◽  
Binding Affinities ◽  
Spherical Coordinates ◽  
Collective Variables ◽  
Guest Binding ◽  
Starting Point ◽  
Sampl Challenge

Host-guest binding remains a major challenge in modern computational modelling. The newest 7<sup>th</sup> statistical assessment of the modeling of proteins and ligands (SAMPL) challenge contains a new series of host-guest systems. The TrimerTrip host binds to 16 structurally diverse guests. Previously, we have successfully employed the spherical coordinates as the collective variables coupled with the enhanced sampling technique metadynamics to enhance the sampling of the binding/unbinding event, search for possible binding poses and predict the binding affinities in all three host-guest binding cases of the 6<sup>th</sup> SAMPL challenge. In this work, we employed the same protocol to investigate the TrimerTrip host in the SAMPL7 challenge. As no binding pose is provided by the SAMPL7 host, our simulations initiate from randomly selected configurations and are proceeded long enough to obtain converged free energy estimates and search for possible binding poses. The predicted binding affinities are in good agreement with the experimental reference, and the obtained binding poses serve as a nice starting point for end-point or alchemical free energy calculations.

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