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On the Use of Interaction Entropy and Related Methods to Estimate Binding Entropies

Ekberg, Vilhelm LU and Ryde, Ulf LU orcid (2021) In Journal of Chemical Theory and Computation 17(8). p.5379-5391
Abstract

Molecular mechanics combined with Poisson-Boltzmann or generalized Born and solvent-accessible area solvation energies (MM/PBSA and MM/GBSA) are popular methods to estimate the free energy for the binding of small molecules to biomacromolecules. However, the estimation of the entropy has been problematic and time-consuming. Traditionally, normal-mode analysis has been used to estimate the entropy, but more recently, alternative approaches have been suggested. In particular, it has been suggested that exponential averaging of the electrostatic and Lennard-Jones interaction energies may provide much faster and more accurate entropies, the interaction entropy (IE) approach. In this study, we show that this exponential averaging is... (More)

Molecular mechanics combined with Poisson-Boltzmann or generalized Born and solvent-accessible area solvation energies (MM/PBSA and MM/GBSA) are popular methods to estimate the free energy for the binding of small molecules to biomacromolecules. However, the estimation of the entropy has been problematic and time-consuming. Traditionally, normal-mode analysis has been used to estimate the entropy, but more recently, alternative approaches have been suggested. In particular, it has been suggested that exponential averaging of the electrostatic and Lennard-Jones interaction energies may provide much faster and more accurate entropies, the interaction entropy (IE) approach. In this study, we show that this exponential averaging is extremely poorly conditioned. Using stochastic simulations, assuming that the interaction energies follow a Gaussian distribution, we show that if the standard deviation of the interaction energies (σIE) is larger than 15 kJ/mol, it becomes practically impossible to converge the interaction entropies (more than 10 million energies are needed, and the number increases exponentially). A cumulant approximation to the second order of the exponential average shows a better convergence, but for σIE > 25 kJ/mol, it gives entropies that are unrealistically large. Moreover, in practical applications, both methods show a steady increase in the entropy with the number of energies considered.

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type
Contribution to journal
publication status
published
subject
in
Journal of Chemical Theory and Computation
volume
17
issue
8
pages
13 pages
publisher
The American Chemical Society (ACS)
external identifiers
  • pmid:34254810
  • scopus:85111188272
ISSN
1549-9618
DOI
10.1021/acs.jctc.1c00374
language
English
LU publication?
yes
id
a1a7ba90-4ac6-4147-99b3-5053977c8319
date added to LUP
2021-12-27 13:46:14
date last changed
2024-04-20 18:22:25
@article{a1a7ba90-4ac6-4147-99b3-5053977c8319,
  abstract     = {{<p>Molecular mechanics combined with Poisson-Boltzmann or generalized Born and solvent-accessible area solvation energies (MM/PBSA and MM/GBSA) are popular methods to estimate the free energy for the binding of small molecules to biomacromolecules. However, the estimation of the entropy has been problematic and time-consuming. Traditionally, normal-mode analysis has been used to estimate the entropy, but more recently, alternative approaches have been suggested. In particular, it has been suggested that exponential averaging of the electrostatic and Lennard-Jones interaction energies may provide much faster and more accurate entropies, the interaction entropy (IE) approach. In this study, we show that this exponential averaging is extremely poorly conditioned. Using stochastic simulations, assuming that the interaction energies follow a Gaussian distribution, we show that if the standard deviation of the interaction energies (σIE) is larger than 15 kJ/mol, it becomes practically impossible to converge the interaction entropies (more than 10 million energies are needed, and the number increases exponentially). A cumulant approximation to the second order of the exponential average shows a better convergence, but for σIE &gt; 25 kJ/mol, it gives entropies that are unrealistically large. Moreover, in practical applications, both methods show a steady increase in the entropy with the number of energies considered. </p>}},
  author       = {{Ekberg, Vilhelm and Ryde, Ulf}},
  issn         = {{1549-9618}},
  language     = {{eng}},
  number       = {{8}},
  pages        = {{5379--5391}},
  publisher    = {{The American Chemical Society (ACS)}},
  series       = {{Journal of Chemical Theory and Computation}},
  title        = {{On the Use of Interaction Entropy and Related Methods to Estimate Binding Entropies}},
  url          = {{http://dx.doi.org/10.1021/acs.jctc.1c00374}},
  doi          = {{10.1021/acs.jctc.1c00374}},
  volume       = {{17}},
  year         = {{2021}},
}