# The Weighted Mean Curvature Derivative of a Space-Filling Diagram

@article{Akopyan2020TheWM, title={The Weighted Mean Curvature Derivative of a Space-Filling Diagram}, author={Arseniy V. Akopyan and Herbert Edelsbrunner}, journal={Computational and Mathematical Biophysics}, year={2020}, volume={8}, pages={51 - 67} }

Abstract Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the…

## 2 Citations

The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram

- Computer Science, PhysicsComputational and Mathematical Biophysics
- 2020

The morphometric approach to solvation free energy is rewritten as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram and a formula is given for the derivative of the weighted GaRussian curvature.

On M-theory on real toric fibrations

- Physics, Mathematics
- 2021

Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory…

## References

SHOWING 1-10 OF 28 REFERENCES

The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram

- Computer Science, PhysicsComputational and Mathematical Biophysics
- 2020

The morphometric approach to solvation free energy is rewritten as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram and a formula is given for the derivative of the weighted GaRussian curvature.

The weighted-volume derivative of a space-filling diagram

- Chemistry, MedicineProceedings of the National Academy of Sciences of the United States of America
- 2003

A formula is given for the volume derivative of a molecule modeled as a space-filling diagram made up of balls in motion in terms of the weights, radii, and distances between the centers as well as the sizes of the facets of the power diagram restricted to the space- filling diagram.

The Area Derivative of a Space-Filling Diagram

- Computer Science, MathematicsDiscret. Comput. Geom.
- 2004

Formulas are given for the weighted and unweighted area derivatives of a molecule modeled as a space-filling diagram made up of balls in motion that contribute to the force that drives the motion.

Morphological thermodynamics of fluids: shape dependence of free energies.

- Physics, MedicinePhysical review letters
- 2004

If motion invariance, continuity, and additivity of the potential are satisfied, only four morphometric measures are needed to describe fully the influence of an arbitrarily shaped container on the fluid and this can be understood as a more precise definition for the conventional term extensive.

Morphometric approach to the solvation free energy of complex molecules.

- Physics, MedicinePhysical review letters
- 2006

The new approach provides a practical and efficient way for calculating the solvation free energy which can be employed when this quantity has to be calculated for a large number of structures, as in a simulation study of protein folding.

A morphometric approach for the accurate solvation thermodynamics of proteins and ligands

- Chemistry, MedicineJ. Comput. Chem.
- 2013

A versatile method for calculating solvation thermodynamic quantities for molecules, starting from their atomic coordinates, that can readily be applied to macromolecules in an all‐atom molecular model, allowing the stability of these molecules' structures in solution to be evaluated.

A morphological model for complex fluids

- Physics
- 1996

A new model is proposed for the study of porous media and complex fluids using morphological measures to describe homogeneous spatial domains of the constituents. Under rather natural assumptions a…

Solvation of proteins: linking thermodynamics to geometry.

- MedicinePhysical review letters
- 2007

This work calculates the solvation free energy of proteins in the tube model of Banavar and Maritan using morphological thermodynamics which is based on Hadwiger's theorem of integral geometry and extends recent results to hard-sphere solvents at finite packing fractions.

The interpretation of protein structures: estimation of static accessibility.

- Chemistry, MedicineJournal of molecular biology
- 1971

The accessibility of atoms in the twenty common amino acids in model tripeptides of the type Ala-X-Ala are given for defined conformation and the larger non-polar amino acids tend to be more “buried” in the native form of all three proteins.

Solvation Free Energies Estimated from Macroscopic Continuum Theory: An Accuracy Assessment

- Chemistry
- 1994

The solvation thermodynamics of a set of small organic molecules is studied using a simple continuum model. Transfer from vapor or cyclohexane to water is decomposed into three steps: first the…