Unfolding free energy changes determined by the linear extrapolation method. 2. Incorporation of .DELTA.G.degree.N-U values in a thermodynamic cycle

Biochemistry ◽  
1988 ◽  
Vol 27 (21) ◽  
pp. 8069-8074 ◽  
Author(s):  
D. W. Bolen ◽  
Marcelo M. Santoro
Keyword(s):  
Free Energy ◽  
Thermodynamic Cycle ◽  
Extrapolation Method ◽  
Linear Extrapolation

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.

scholarly journals BAR-based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscapes: Varying the QM Region

2021 ◽  
Author(s):  
Zhaoxi Sun ◽  
Zhirong Liu
Keyword(s):  
Free Energy ◽  
Main Idea ◽  
Thermodynamic Cycle ◽  
Basis Set ◽  
Energy Landscapes ◽  
Computationally Efficient ◽  
Feasible Alternative ◽  
Free Energy Landscapes ◽  
Energy Simulations ◽  
High Level

<div><p>The indirect construction of the free energy landscape at Quantum mechanics (QM)/ molecular mechanics (MM) levels provides a feasible alternative to the direct QM/MM free energy simulations. The main idea under the indirect method is constructing a thermodynamic cycle, exploring the configurational space at a computationally efficient but less accurate low-level Hamiltonian, and performing an alchemical correction to obtain the thermodynamics at an accurate but computationally demanding high-level Hamiltonian. In our previous works, we developed a multi-dimensional nonequilibrium free energy simulation framework to obtain QM/MM free energy landscapes indirectly. Specifically, we considered obtaining semi-empirical QM (SQM) results by combining the MM results and the MM-to-SQM correction and obtaining the QM results by combining the SQM results and the SQM-to-QM correction. In this work, we explore the possibility of changing the region for electronic structure calculations in the multi-scale QM/MM treatment, which could also be considered as a change of the level of theory. More generally, the multi-dimensional nonequilibrium Hamiltonian-variation/perturbation framework could be used to obtain transformations between different Hamiltonians of interest, such as changing the QM theory, the size of the QM region, and the basis set simultaneously. </p> <p> </p></div>

scholarly journals Entropy, Carnot Cycle, and Information Theory

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 3
Author(s):  
Mario Martinelli
Keyword(s):  
Information Theory ◽  
Free Energy ◽  
Internal Conversion ◽  
Thermodynamic Cycle ◽  
Statistical Thermodynamics ◽  
Carnot Cycle ◽  
Isothermal Expansion ◽  
The Cost

The fundamental intuition that Carnot had in analyzing the operation of steam machines is that something remains constant during the reversible thermodynamic cycle. This invariant quantity was later named “entropy” by Clausius. Jaynes proposed a unitary view of thermodynamics and information theory based on statistical thermodynamics. The unitary vision allows us to analyze the Carnot cycle and to study what happens when the entropy between the beginning and end of the isothermal expansion of the cycle is considered. It is shown that, in connection with a non-zero Kullback–Leibler distance, minor free-energy is available from the cycle. Moreover, the analysis of the adiabatic part of the cycle shows that the internal conversion between energy and work is perturbed by the cost introduced by the code conversion. In summary, the information theoretical tools could help to better understand some details of the cycle and the origin of possible asymmetries.

Are thermodynamic cycles necessary for continuum solvent calculation of pKas and reduction potentials?

2015 ◽  
Vol 17 (4) ◽  
pp. 2859-2868 ◽  
Author(s):  
Junming Ho
Keyword(s):  
Free Energy ◽  
Gas Phase ◽  
Thermodynamic Cycle ◽  
Free Energies ◽  
Thermodynamic Cycles ◽  
Reduction Potentials ◽  
Reaction Free Energy

Continuum solvent calculations of pKas and reduction potentials usually entail the use of a thermodynamic cycle to express the reaction free energy in terms of gas phase energies and free energies of solvation.

Extrapolation of Strain and Stress From Holographically Measured Surface Displacement

1979 ◽  
Vol 46 (3) ◽  
pp. 581-586 ◽  
Author(s):  
R. Da¨ndliker
Keyword(s):  
Stress Field ◽  
Boundary Conditions ◽  
Internal Pressure ◽  
Input Data ◽  
Cylindrical Tube ◽  
Surface Displacement ◽  
Volume Element ◽  
Extrapolation Method ◽  
Linear Extrapolation ◽  
Elastic Materials

For isotropic elastic materials, following Hooke’s law, the strain and stress field below the surface is uniquely determined by the knowledge of the displacement of the surface itself. From the holographically measured surface displacement u and the boundary conditions for the surface-stresses one can determine all 9 components of the vector-gradient grad u, which describes the strains as well as the tilt and the rotation of a volume element adjacent to the surface. It is shown that strain and stress can be uniquely calculated in a cone-shaped zone below the observed part of the surface by stepwise linear extrapolation. The depth of this cone depends on the density of the sample points and on the accuracy of the displacement measurement on the surface, as well as on the required accuracy of the extrapolated strain and stress values. The suggested extrapolation method has been tested numerically for a thick-walled cylindrical tube under internal pressure using simulated input data. The limitations and the accuracy are discussed.

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