# Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

## Abstract

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describemore »

- Authors:

- Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Jiangsu, Suzhou 215006 (China)
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112 (United States)
- Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany and Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin (Germany)
- Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, La Jolla, California 92093-0112 (United States)
- Department of Chemistry and Biochemistry, Department of Pharmacology, Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093-0365 (United States)

- Publication Date:

- OSTI Identifier:
- 22679024

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COMPUTERIZED SIMULATION; CONFORMATIONAL CHANGES; DIELECTRIC MATERIALS; FLUCTUATIONS; FREE ENERGY; MOLECULAR DYNAMICS METHOD; NUMERICAL DATA; SOLUTES; SOLVENTS

### Citation Formats

```
Zhou, Shenggao, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu, Sun, Hui, Cheng, Li-Tien, Dzubiella, Joachim, Li, Bo, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu, and McCammon, J. Andrew.
```*Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations*. United States: N. p., 2016.
Web. doi:10.1063/1.4959971.

```
Zhou, Shenggao, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu, Sun, Hui, Cheng, Li-Tien, Dzubiella, Joachim, Li, Bo, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu, & McCammon, J. Andrew.
```*Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations*. United States. doi:10.1063/1.4959971.

```
Zhou, Shenggao, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu, Sun, Hui, Cheng, Li-Tien, Dzubiella, Joachim, Li, Bo, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu, and McCammon, J. Andrew. Sun .
"Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations". United States.
doi:10.1063/1.4959971.
```

```
@article{osti_22679024,
```

title = {Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations},

author = {Zhou, Shenggao, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu and Sun, Hui and Cheng, Li-Tien and Dzubiella, Joachim and Li, Bo, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu and McCammon, J. Andrew},

abstractNote = {Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.},

doi = {10.1063/1.4959971},

journal = {Journal of Chemical Physics},

number = 5,

volume = 145,

place = {United States},

year = {Sun Aug 07 00:00:00 EDT 2016},

month = {Sun Aug 07 00:00:00 EDT 2016}

}