scholarly journals Diagrammatic expansion of non-perturbative little string free energies

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Stefan Hohenegger
Keyword(s):  
Free Energy ◽  
A Priori ◽  
Jacobi Form ◽  
Leading Order ◽  
Free Energies ◽  
Effective Coupling ◽  
Free Scalar ◽  
Expansion Coefficients ◽  
Disconnected Graphs ◽  
Simple Combination

Abstract In [1] we have studied the single-particle free energy of a class of Little String Theories of A-type, which are engineered by N parallel M5-branes on a circle. To leading instanton order (from the perspective of the low energy U(N) gauge theory) and partially also to higher order, a decomposition was observed, which resembles a Feynman diagrammatic expansion: external states are given by expansion coefficients of the N = 1 BPS free energy and a quasi-Jacobi form that governs the BPS-counting of an M5-brane coupling to two M2-branes. The effective coupling functions were written as infinite series and similarities to modular graph functions were remarked. In the current work we continue and extend this study: working with the full non-perturbative BPS free energy, we analyse in detail the cases N = 2, 3 and 4. We argue that in these cases to leading instanton order all coupling functions can be written as a simple combination of two-point functions of a single free scalar field on the torus. We provide closed form expressions, which we conjecture to hold for generic N. To higher instanton order, we observe that a decomposition of the free energy in terms of higher point functions with the same external states is still possible but a priori not unique. We nevertheless provide evidence that tentative coupling functions are still combinations of scalar Greens functions, which are decorated with derivatives or multiplied with holomorphic Eisenstein series. We interpret these decorations as corrections of the leading order effective couplings and in particular link the latter to dihedral graph functions with bivalent vertices, which suggests an interpretation in terms of disconnected graphs.

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.

Molecular orientation of liquid aliphatic hydrocarbons on the surface and at the interface with water

1989 ◽  
Vol 54 (12) ◽  
pp. 3171-3186 ◽  
Author(s):  
Jan Kloubek
Keyword(s):  
Free Energy ◽  
Surface Free Energy ◽  
Molecular Orientation ◽  
Phase Changes ◽  
Aliphatic Hydrocarbons ◽  
Water Molecules ◽  
Free Energies ◽  
Dispersion Component ◽  
System Water ◽  
Orientation Of Molecules

The validity of the Fowkes theory for the interaction of dispersion forces at interfaces was inspected for the system water-aliphatic hydrocarbons with 5 to 16 C atoms. The obtained results lead to the conclusion that the hydrocarbon molecules cannot lie in a parallel position or be randomly arranged on the surface but that orientation of molecules increases there the ration of CH3 to CH2 groups with respect to that in the bulk. This ratio is changed at the interface with water so that the surface free energy of the hydrocarbon, γH, rises to a higher value, γ’H, which is effective in the interaction with water molecules. Not only the orientation of molecules depends on the adjoining phase and on the temperature but also the density of hydrocarbons on the surface of the liquid phase changes. It is lower than in the bulk and at the interface with water. Moreover, the volume occupied by the CH3 group increases on the surface more than that of the CH2 group. The dispersion component of the surface free energy of water, γdW = 19.09 mJ/m2, the non-dispersion component, γnW = 53.66 mJ/m2, and the surface free energies of the CH2 and CH3 groups, γ(CH2) = 32.94 mJ/m2 and γ(CH3) = 15.87 mJ/m2, were determined at 20 °C. The dependence of these values on the temperature in the range 15-40 °C was also evaluated.

Chemical equilibrium and chemical kinetics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Free Energy ◽  
Equilibrium Constant ◽  
Gibbs Free Energy ◽  
Chemical Kinetics ◽  
Chemical Equilibrium ◽  
First Principles ◽  
Effect Of Temperature ◽  
Total System ◽  
Free Energies

Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, expressing the total Gibbs free energy of a reaction mixture at any time as the sum of the instantaneous Gibbs free energies of each component, as expressed in terms of the extent-of-reaction. The equilibrium reaction mixture is then defined as the point at which the total system Gibbs free energy is a minimum, from which concepts such as the equilibrium constant emerge. The chapter also explores the temperature dependence of equilibrium, this being one example of Le Chatelier’s principle. Finally, the chapter links thermodynamics to chemical kinetics by showing how the equilibrium constant is the ratio of the forward and backward rate constants. We also introduce the Arrhenius equation, closing with a discussion of the overall effect of temperature on chemical equilibrium.

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 Antiviral Resistance against Viral Mutation: Praxis and Policy for SARS-CoV-2

2021 ◽  
Vol 9 (1) ◽  
pp. 81-89
Author(s):  
Robert Penner
Keyword(s):  
Free Energy ◽  
Vaccine Development ◽  
A Priori ◽  
Structural Data ◽  
Medical Sciences ◽  
Spike Glycoprotein ◽  
Mutagenic Potential ◽  
Viral Mutation ◽  
Novel Method ◽  
Antiviral Targets

Abstract Tools developed by Moderna, BioNTech/Pfizer, and Oxford/Astrazeneca, among others, provide universal solutions to previously problematic aspects of drug or vaccine delivery, uptake and toxicity, portending new tools across the medical sciences. A novel method is presented based on estimating protein backbone free energy via geometry to predict effective antiviral targets, antigens and vaccine cargos that are resistant to viral mutation. This method is reviewed and reformulated in light of the recent proliferation of structural data on the SARS-CoV-2 spike glycoprotein and its mutations in multiple lineages. Key findings include: collections of mutagenic residues reoccur across strains, suggesting cooperative convergent evolution; most mutagenic residues do not participate in backbone hydrogen bonds; metastability of the glyco-protein limits the change of free energy through mutation thereby constraining selective pressure; and there are mRNA or virus-vector cargos targeting low free energy peptides proximal to conserved high free energy peptides providing specific recipes for vaccines with greater specificity than the full-spike approach. These results serve to limit peptides in the spike glycoprotein with high mutagenic potential and thereby provide a priori constraints on viral and attendant vaccine evolution. Scientific and regulatory challenges to nucleic acid therapeutic and vaccine development and deployment are finally discussed.

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

scholarly journals Use of scaled-particle theory in the assessment of the Ph4As+/Ph4B− assumption for single ions

1979 ◽  
Vol 57 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Michael H. Abraham ◽  
Asadollah Nasehzadeh
Keyword(s):  
Free Energy ◽  
Recent Work ◽  
Scaled Particle Theory ◽  
Cavity Formation ◽  
Energy Term ◽  
Free Energies ◽  
Particle Theory ◽  
Novel Method ◽  
Energy Of Interaction ◽  
Solvent Molecules

A novel method for the assessment of the Ph4As+/Ph4B− assumption for free energies of transfer of single ions has recently been suggested by Treiner, and used by him to deduce that the assumption is not valid for transfers between water, propylene carbonate, sulpholane, dimethylsulphoxide, N-methyl-2-pyrrolidone, and perhaps also dimethylformamide. The basis of the method is the estimation of the free energy of cavity formation by scaled-particle theory, together with the hypothesis that the free energy of interaction of Ph4As+ (or Ph4B−) with solvent molecules is the same in all solvents, ΔGt0(int) = 0. It is shown in the present paper that (a) whether or not the Ph4As+/Ph4B− assumption applies to transfer to a given solvent depends on which other solvent is taken as the reference solvent in Treiner's method, (b) the calculation of the cavity free energy term by scaled-particle theory and by the theory of Sinanoglu – Reisse – Moura Ramos (SRMR) yields values so different that the method cannot be considered reliable, (c) the calculation of cavity enthalpies and entropies for Ph4As+ or Ph4B− by scaled-particle theory yields results that are chemically not reasonable, (d) the hypothesis that ΔGt0(int) = 0 conflicts with SRMR theory, and (e) the conclusions reached by Treiner are not in accord with recent work that in general supports the Ph4As+/Ph4B− assumption for solvents that are rejected by Treiner.

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