Powered by OpenAIRE graph
Found an issue? Give us feedback
addClaim

Entropy-preserving transformation method

Authors: Hennig, Marcus;

Entropy-preserving transformation method

Abstract

Numerous biological effects may strongly be influenced by solvent entropy, such as the hydrophobic effect or the formation of lipid bilayers. To explain such effects we need to compute thermodynamic quantities as the entropy and the free energy. Calculation of both quantities requires knowledge of the density of all possible spatial configurations of solvent molecules. The density, however, is not directly accessible by simple numerical methods. Thus, we need easily manageable analytical estimation methods for the solvent density. For proteins many established estimation methods are available, such as the Principle Component Analysis [1], which require a condensed distribution of configurations in the vicinity of a single stable configuration. However, the density estimation was originally tailored for proteins, thus, the solvent cannot easily be incorporated. Two major problems occur when treating solvents. First, the diffusive motion of the solvent leads to a large configurational space that has to be sampled. Second, the motion of the solvent molecules is governed by a very shallow energy landscape. Hence, the configurational density has a complex topology excluding it from a straightforward analytical estimation. Friedemann Reinhard et al. developed a transformation, exploiting the permutation symmetry of the solvent [2]. Their approach rendered established estimation methods applicable. Whereas this permutation algorithm provides a promising method to locally condense the configurational density, the topology stays complex. Thus, the transformed configurational density cannot be optimally fitted by a Gaussian distribution allowing a simple entropy estimation. Here, we present a new method to improve Reinhard's permutation reduction by deforming the density in an entropy-preserving fashion such that we can make use of established entropy estimations. In order to deform the density we solve the convection equation in an incompressible flow, which we construct by means of divergence-free wavelets. With this method we want to contribute to the understanding of biological processes such as protein folding. We have developed a method that lays the ground for solvent entropy calculations and likewise enables to estimate entropies from highly unharmonic systems.

Keywords

530

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!