Julia Sets and Complex Singularities of Free Energies

2015 ◽  
Vol 234 (1102) ◽  
pp. 0-0 ◽  
Author(s):  
Jianyong Qiao
Keyword(s):  
Julia Sets ◽  
Free Energies ◽  
Complex Singularities

scholarly journals Julia sets and complex singularities in hierarchical Ising models

1991 ◽  
Vol 141 (3) ◽  
pp. 453-474 ◽  
Author(s):  
P. M. Bleher ◽  
M. Yu. Lyubich
Keyword(s):  
Julia Sets ◽  
Ising Models ◽  
Complex Singularities

Understanding Conformational Entropy in Small Molecules

2020 ◽  
Author(s):  
Lucian Chan ◽  
Garrett Morris ◽  
Geoffrey Hutchison
Keyword(s):  
Small Molecules ◽  
Degrees Of Freedom ◽  
Absolute Error ◽  
Low Energy ◽  
Standard Entropy ◽  
Free Energies ◽  
Conformational Entropy ◽  
Wide Range ◽  
High Degree ◽  
Empirical Corrections

The calculation of the entropy of flexible molecules can be challenging, since the number of possible conformers grows exponentially with molecule size and many low-energy conformers may be thermally accessible. Different methods have been proposed to approximate the contribution of conformational entropy to the molecular standard entropy, including performing thermochemistry calculations with all possible stable conformations, and developing empirical corrections from experimental data. We have performed conformer sampling on over 120,000 small molecules generating some 12 million conformers, to develop models to predict conformational entropy across a wide range of molecules. Using insight into the nature of conformational disorder, our cross-validated physically-motivated statistical model can outperform common machine learning and deep learning methods, with a mean absolute error ≈4.8 J/mol•K, or under 0.4 kcal/mol at 300 K. Beyond predicting molecular entropies and free energies, the model implies a high degree of correlation between torsions in most molecules, often as- sumed to be independent. While individual dihedral rotations may have low energetic barriers, the shape and chemical functionality of most molecules necessarily correlate their torsional degrees of freedom, and hence restrict the number of low-energy conformations immensely. Our simple models capture these correlations, and advance our understanding of small molecule conformational entropy.

Hydration Free Energies of Organic Molecules in the FreeSolv Database Calculated with Polarized Atom In Molecules Atomic Charges and the GAFF Force Field.

2018 ◽  
Author(s):  
Maximiliano Riquelme ◽  
Alejandro Lara ◽  
David L. Mobley ◽  
Toon Vestraelen ◽  
Adelio R Matamala ◽  
...  
Keyword(s):  
Force Field ◽  
Functional Groups ◽  
Electrostatic Interactions ◽  
Organic Molecules ◽  
Force Fields ◽  
Chemical Elements ◽  
Atomic Charges ◽  
Free Energies ◽  
Molecular Systems ◽  
Solvent Model

<div>Computer simulations of bio-molecular systems often use force fields, which are combinations of simple empirical atom-based functions to describe the molecular interactions. Even though polarizable force fields give a more detailed description of intermolecular interactions, nonpolarizable force fields, developed several decades ago, are often still preferred because of their reduced computation cost. Electrostatic interactions play a major role in bio-molecular systems and are therein described by atomic point charges.</div><div>In this work, we address the performance of different atomic charges to reproduce experimental hydration free energies in the FreeSolv database in combination with the GAFF force field. Atomic charges were calculated by two atoms-in-molecules approaches, Hirshfeld-I and Minimal Basis Iterative Stockholder (MBIS). To account for polarization effects, the charges were derived from the solute's electron density computed with an implicit solvent model and the energy required to polarize the solute was added to the free energy cycle. The calculated hydration free energies were analyzed with an error model, revealing systematic errors associated with specific functional groups or chemical elements. The best agreement with the experimental data is observed for the MBIS atomic charge method, including the solvent polarization, with a root mean square error of 2.0 kcal mol<sup>-1</sup> for the 613 organic molecules studied. The largest deviation was observed for phosphor-containing molecules and the molecules with amide, ester and amine functional groups.</div>

Partition Coefficients of Methylated DNA Bases Obtained from Free Energy Calculations with Molecular Electron Density Derived Atomic Charges.

2018 ◽  
Author(s):  
Alejandro Lara ◽  
Maximiliano Riquelme ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Electron Density ◽  
Partition Coefficients ◽  
Dna Bases ◽  
Atomic Charges ◽  
Free Energies ◽  
Solvation Model ◽  
Minimal Basis ◽  
Methylated Dna ◽  
Implicit Solvation Model ◽  
Good Agreement

<div> <div> <div> <p>Partition coefficients serve in various areas as pharmacology and environmental sciences to predict the hydrophobicity of different substances. Recently, they have been also used to address the accuracy of force fields for various organic compounds and specifically the methylated DNA bases. In this study atomic charges were derived by different partitioning methods (Hirshfeld and Minimal Basis Iterative Stockholder) directly from the electron density obtained by electronic structure calculations in vac- uum, with an implicit solvation model or with explicit solvation taking the dynamics of the solute and the solvent into account. To test the ability of these charges to describe electrostatic interactions in force fields for condensed phases the original atomic charges of the AMBER99 force field were replaced with the new atomic charges and combined with different solvent models to obtain the hydration and chloroform solvation free energies by molecular dynamics simulations. Chloroform-water partition coefficients derived from the obtained free energies were compared to experimental and previously reported values obtained with the GAFF or the AMBER-99 force field. The results show that good agreement with experimental data is obtained when the polarization of the electron density by the solvent has been taken into account deriving the atomic charges of polar DNA bases and when the energy needed to polarize the electron den- sity of the solute has been considered in the transfer free energy. These results were further confirmed by hydration free energies of polar and aromatic amino acid side chain analogues. Comparison of the two partitioning methods Hirsheld-I and Minimal Basis Iterative Stockholder (MBIS) revealed some deficiencies in the Hirshfeld-I method related to nonexistent isolated anionic nitrogen pro-atoms used in the method. Hydration free energies and partitioning coefficients obtained with atomic charges from the MBIS partitioning method accounting for polarization by the implicit solvation model are in good agreement with the experimental values. </p> </div> </div> </div>

Molecular Docking Approaches to Suggest the Anti-Mycobacterial Targets of Natural Products

2020 ◽  
Author(s):  
Rafael Baptista ◽  
Sumana Bhowmick ◽  
Shen Jianying ◽  
Luis Mur
Keyword(s):  
Natural Products ◽  
Molecular Docking ◽  
Free Energies ◽  
Antibiotic Resistant ◽  
Drug Lead ◽  
Bisbenzylisoquinoline Alkaloids ◽  
Docking Approach ◽  
Global Threat ◽  
Physicochemical And Structural Properties

Tuberculosis (TB) is a major global threat mostly due to the development of antibiotic resistant forms of Mycobacterium tuberculosis, the causal agent of the disease. Driven by the pressing need for new anti-mycobacterial agents, several natural products (NPs) have been shown to have in vitro activities against M. tuberculosis. The utility of any NP as a drug lead is augmented when the anti-mycobacterial target(s) is unknown. To suggest these, we used a molecular docking approach to predict the interactions of 53 selected anti-mycobacterial NPs against known ‘druggable’ mycobacterial targets ClpP1P2, DprE1, InhA, KasA, PanK, PknB and Pks13. The docking scores / binding free energies were predicted and calculated using AutoDock Vina along with physicochemical and structural properties of the NPs, using PaDEL descriptors. These were compared to the established inhibitor (control) drugs for each mycobacterial target. The specific interactions of the bisbenzylisoquinoline alkaloids 2-nortiliacorinine, tiliacorine and 13’-bromotiliacorinine against the targets PknB and DprE1 (-11.4, -10.9 and -9.8 kcal.mol-1 ; -12.7, -10.9 and -10.3 kcal.mol-1 , respectively) and the lignan αcubebin and Pks13 (-11.0 kcal.mol-1 ) had significantly superior docking scores compared to controls. Our approach can be used to suggest predicted targets for the NP to be validated experimentally but these in silico steps are likely to facilitate drug optimisation.

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.

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