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Title: 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 » 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.« less

Authors:
 [1]; ;  [2];  [3];  [4];  [5]
  1. Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Jiangsu, Suzhou 215006 (China)
  2. Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112 (United States)
  3. Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany and Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin (Germany)
  4. Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, La Jolla, California 92093-0112 (United States)
  5. 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}
}
  • A coupled level set method for the motion of multiple junctions (of, e.g., solid, liquid, and grain boundaries), which follows the gradient flow for an energy functional consisting of surface tension (proportional to length) and bulk energies (proportional to area), is developed. The approach combines the level set method of S. Osher and J. A. Sethian with a theoretical variational formulation of the motion by F. Reitich and H. M. Sonar. The resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions. The gradient projectionmore » method leads to a coupled system of perturbed (by curvature terms) Hamilton-Jacobi equations. The coupling is enforced using a single Lagrange multiplier associated with a constraint which essentially prevents (a) regions from overlapping and (b) the development of a vacuum. The numerical implementation is relatively simple and the results agree with (and go beyond) the theory as given in. Other applications of this methodology, including the decomposition of a domain into subregions with minimal interface length, are discussed. Finally, some new techniques and results in level set methodology are presented. 18 refs., 10 figs.« less
  • A hybrid of the Front-Tracking (FT) and the Level-Set (LS) methods is introduced, combining advantages and removing drawbacks of both methods. The kinematics of the interface is treated in a Lagrangian (FT) manner, by tracking markers placed at the interface. The markers are not connected – instead, the interface topology is resolved in an Eulerian (LS) framework, by wrapping a signed distance function around Lagrangian markers each time the markers move. For accuracy and efficiency, we have developed a high-order “anchoring” algorithm and an implicit PDE-based re-distancing. We have demonstrated that the method is 3rd-order accurate in space, near themore » markers, and therefore 1st-order convergent in curvature; in contrast to traditional PDE-based re-initialization algorithms, which tend to slightly relocate the zero Level Set and can be shown to be non-convergent in curvature. The implicit pseudo-time discretization of the re-distancing equation is implemented within the Jacobian-Free Newton Krylov (JFNK) framework combined with ILU(k) preconditioning. We have demonstrated that the steady-state solutions in pseudo-time can be achieved very efficiently, with iterations (CFL ), in contrast to the explicit re-distancing which requires 100s of iterations with CFL . The most cost-effective algorithm is found to be a hybrid of explicit and implicit discretizations, in which we apply first 10-15 iterations with explicit discretization (to bring the initial guess to the ball of convergence for the Newton’s method) and then finishing with 2-3 implicit steps, bringing the re-distancing equation to a complete steady-state. The eigenscopy of the JFNK-ILU(k) demonstrates the efficiency of the ILU(k) preconditioner, which effectively cluster eigenvalues of the otherwise extremely ill-conditioned Jacobian matrices, thereby enabling the Krylov (GMRES) method to converge with iterations, with only a few levels of ILU fill-ins. Importantly, due to the Level Set localization, the bandwidth of the Jacobian matrix is nearly constant, and the ILU preconditioning scales as , which implies efficiency and good scalability of the overall algorithm. The numerical examples include the well-established tests for interface kinematics under translational, rotational and tearing/stretching motion. We have shown that the mass conservation is not an issue anymore, as demonstrated using the Rider&Kothe’s time-reversed tests with extreme deformation. We are able to stretch interface structures to the under-resolved/subgrid (on the chosen Eulerian mesh) scales, and recover them back without any change in shape/loss of mass.« less
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  • The dynamics of solid-liquid interfaces controlled by solute precipitation and/or dissolution due to the chemical reaction at the interface were computed in two dimensions using a phase field models. Sharp-interface asymptotic analysis demonstrated that the phase field solutions should converge to the proper sharp-interface precipitation/dissolution limit. For the purpose of comparison, the numerical solution of the sharp-interface model for solute precipitation/dissolution was directly solved using a level set method. In general, the phase field results are found in good agreement with the level set results for all reaction rates and geometry configurations investigated. Present study supports the applications of bothmore » methods to more complicated and realistic reactive systems, including the nuclear waste release and mineral precipitation and dissolution« less
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