A multi-scale method for dynamics simulation in continuum solvent models. I: Finite-difference algorithm for Navier–Stokes equation

Xiao, Li; Cai, Qiong; Li, Zhilin; Zhao, Hongkai; Luo, Ray

doi:10.1016/j.cplett.2014.10.033

Cited by 12 publications

(13 citation statements)

References 47 publications

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“…Thus Rational numbers are compatible with explicit methods, but not when adaptive timestepping is enabled. Some of the stiff solvers require the ability to be used in autodifferentiation via ForwardDiff.jl 30 if the user does not provide a function for calculating the Jocobian. However, ForwardDiff.jl currently does not include compatibility with complex numbers.…”

Section: Limitations and Future Development Plansmentioning

confidence: 99%

“…Differential equations are fundamental components of many scientific models; they are used to describe large-scale physical phenomena like planetary systems [10] and the Earth's climate [12,18], all the way to smaller scale biological phenomena like biochemical reactions [30] and developmental processes [27,7]. Because of the ubiquity of these equations, standard sets of solvers have been developed, including Shampine's ODE suite for MATLAB [25], Hairer's Fortran codes [8], and the Sundials CVODE solvers [11].…”

Section: Introductionmentioning

confidence: 99%

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DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia

Rackauckas

Nie

2017

JORS

1,252

877

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DifferentialEquations.jl is a package for solving differential equations in Julia. It covers discrete equations (function maps, discrete stochastic (Gillespie/Markov) simulations), ordinary differential equations, stochastic differential equations, algebraic differential equations, delay differential equations, hybrid differential equations, jump diffusions, and (stochastic) partial differential equations. Through extensive use of multiple dispatch, metaprogramming, plot recipes, foreign function interfaces (FFI), and call-overloading, DifferentialEquations.jl offers a unified user interface to solve and analyze various forms of differential equations while not sacrificing features or performance. Many modern features are integrated into the solvers, such as allowing arbitrary user-defined number systems for high-precision and arithmetic with physical units, built-in multithreading and parallelism, and symbolic calculation of Jacobians. Integrated into the package is an algorithm testing and benchmarking suite to both ensure accuracy and serve as an easy way for researchers to develop and distribute their own methods. Together, these features build a highly extendable suite which is feature-rich and highly performant.

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Section: Limitations and Future Development Plansmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia

Rackauckas

Nie

2017

JORS

1,252

877

View full text Add to dashboard Cite

show abstract

“…The Poisson-Boltzmann equation (PBE) has been established as a fundamental equation to model continuum electrostatic interactions 29-47 . The solvent molecules are modeled as a continuum with a high dielectric constant, and the solute atoms are modeled as a continuum with a low dielectric constant and buried atomic charges.…”

Section: Introductionmentioning

confidence: 99%

A Continuum Poisson–Boltzmann Model for Membrane Channel Proteins

Xiao¹,

Diao²,

Greene³

et al. 2017

J. Chem. Theory Comput.

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Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows:1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. 2) The highly different accessibility in the membrane and water regions are addressed with a two-step, two-probe grid labeling procedure, and 3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions that we focus on. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe a good agreement with experiment results.

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“…Our model is adapted from that proposed in our previous work [43] (cf. also [44]), and consists of the following main elements:…”

Section: Introductionmentioning

confidence: 99%

Stability of a Cylindrical Solute-Solvent Interface: Effect of Geometry, Electrostatics, and Hydrodynamics

Sun

Zhou

2015

SIAM J. Appl. Math.

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The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson’s equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.

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A multi-scale method for dynamics simulation in continuum solvent models. I: Finite-difference algorithm for Navier–Stokes equation

Cited by 12 publications

References 47 publications

DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia

DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia

A Continuum Poisson–Boltzmann Model for Membrane Channel Proteins

Stability of a Cylindrical Solute-Solvent Interface: Effect of Geometry, Electrostatics, and Hydrodynamics

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