Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets...

We apply the adaptive multilevel finite element techniques described in [20] to the nonlinear Poisson-Boltzmann equation (PBE) in the context of biomolecules. Fast and accurate numerical solution of the PBE in this setting is usually difficult to accomplish due to presence of discontinuous coefficients, delta functions, three spatial dimensions, unbounded domains, and rapid (exponential) nonlin...

We show the existing solution of Poisson-Boltzmann equation (PBE) to violate charge conservation principle, and then derive the correct formula for charge density distribution (ρe) in a fluid. We replaced unphysical old boundary conditions with some conditions that have never been used. Our result demonstrates that PBE cannot explain the formation of ‘Electric Double Layer’ (EDL); it follows th...

In this paper, we present a new regularization scheme for the linearized Poisson--Boltzmann equation (PBE) which models electrostatic potential of biomolecules in solvent. This is base...

electrostatic potential as well as the local volume charge density are computed for a macromolecule by solving the poisson-boltzmann equation (pbe) using the finite element method (fem). as a verification, our numerical results for a one dimensional pbe, which corresponds to an infinite-length macromolecule, are compared with the existing analytical solution and good agreement is found. as a ma...

in the present study an alternative model allows the extension of the debye-hückel theory (dht) considering time dependence explicitly. from the electro-quasistatic approach (eqs) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes.this...

SMPBS (Size Modified Poisson-Boltzmann Solvers) is a web server for computing biomolecular electrostatics using finite element solvers of the size modified Poisson-Boltzmann equation (SMPBE). SMPBE not only reflects ionic size effects but also includes the classic Poisson-Boltzmann equation (PBE) as a special case. Thus, its web server is expected to have a broader range of applications than a ...

Electrostatic potential as well as the local volume charge density are computed for a macromolecule by solving the Poisson-Boltzmann equation (PBE) using the finite element method (FEM). As a verification, our numerical results for a one dimensional PBE, which corresponds to an infinite-length macromolecule, are compared with the existing analytical solution and good agreement is found. As a ma...

The finite element methodology has become a standard framework for approximating the solution to the Poisson–Boltzmann equation in many biological applications. In this article, we examine the numerical efficacy of least-squares finite element methods for the linearized form of the equations. In particular, we highlight the utility of a first-order form, noting optimality, control of the flux v...

In the present study an alternative model allows the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly. From the Electro-Quasistatic approach (EQS) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes. Thi...