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Showing 1 to 20 of 52 for “"Poisson-Boltzmann"”.
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Multilevel Methods for the Poisson-Boltzmann Equation
We consider the numerical solution of the Poisson-Boltzmann equation (PBE), a three-dimensional second order nonlinear elliptic partial differential equation arising in biophysics. This problem has several interesting features impacting numerical algorithms, including discontinuous coefficients …
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Consistent approach for calculating protein pKa's using Poisson-Boltzmann Model
… the accuracy of pKa prediction using the Poisson-Boltzmann electrostatic model remains an active area of research. The major challenge is to determine the appropriate dielectric constant that best describes the heterogeneous protein environment. The common use of a single large dielectric …
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Beyond Poisson-Boltzmann : strong correlations and extreme confinement in ionic fluids
… in physics for over a century since the "Poisson-Boltzmann" theory was first introduced. In this thesis, we study the bulk properties of ionic fluids in two important cases where the "Poisson-Boltzmann" theory fails: extreme confinement and strong ion-ion interactions. We first ask how …
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Regularization methods on solving Poisson’s equation and Poisson Boltzmann equation with singular charge sources and diffuse interfaces
… singular charges is a grand challenge in solving Poisson-Boltzmann (PB) equation for analyzing electrostatic interactions between the solute biomolecules and the surrounding solvent with ions. For diffuse interface models in which solute and solvent are separated by a smooth boundary, no effective …
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Studies on Electrolytes: A. The Effect of Pressure on The Transference Numbers of Simple Electrolytes. B. Numerical Solution to the Poisson-Boltzmann Equation for Spherical Polyelectrolyte Molecules
Made available in DSpace on 2014-12-05T19:36:15Z (GMT). No. of bitstreams: 1 0015187.pdf: 6174274 bytes, checksum: b48419f94ed3a0aff12b81fd390a4af6 (MD5) Previous issue date: 1955
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Finite element methods for implicit solvent models
… and are thus computationally efficient. The Poisson-Boltzmann equation (PBE) is one important example. We design a FEM for the linear PBE by directly exposing the flux through a first-order system. We propose a system that yields a tractable least-squares finite element formulation and …
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Numerical Methods for Computing the Free Energy of Coarse-Grained Molecular Systems
… a partial differential equation known as the Poisson-Boltzmann equation. We develop algorithms that accurately compute the solvation free energy by using goal-oriented mesh refinement. Results indicating the benefits of goal-oriented refinement are presented.
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Model and analysis of MoS2 nanopore biomolecule detection via membrane current
… transverse current biosensor is built based on Boltzmann transport formalism. The model employs a self-consistent Poisson-Boltzmann scheme for the interaction among ions, charge carriers around the pore rim, and biomolecules. In combination with experimental study and molecular dynamics (MD) …
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Surface Charge Regulation Effects on Fluidic Nanoscale Systems
… studies of uidic nanoscale systems using the Poisson{Boltzmann equation which treats the uid as a continuum, and density functional theory of uids which uses a statistical mechanical treatment of the uid that includes nite-size e ects. Chemical equilibria at the interface is accounted for by …
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A meshless, high-order integral equation method for smooth surfaces, with application to biomolecular electrostatics
… of biomolecular electrostatics based on Poisson-Boltzmann equation. Current techniques using finite-difference solution of differential formulation have many drawbacks. We present an integral formulation that resolves these difficulties and enables an efficient implementation using a …
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Mathematical Modeling of Microscale Biology in Polyelectrolyte Brushes
… brushes using both steady state modified Poisson-Boltzmann models and transient modified Poisson-Nernst-Planck models that incorporate important ion-specific (Hofmeister) effects. The transient model enables observation of the relative physical effects as an initial non-equilibrium state …
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A new computationally facile approximation of electrostatic potential suitable for macromolecules
… analytical solution to the (linearized) Poisson-Boltzmann equation is proposed that is suitable for realistic biomolecules of virtually any size. A comparison with accepted numerical approaches on a large test set of biomolecular structures shows that the proposed method is considerably …
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Predicting Articular Cartilage Constituent Material Properties Following In Vitro Growth Using a Proteoglycan-Collagen Mixture Model
… based on the continuum electromechanical Poisson-Boltzmann unit cell model for proteoglycan interactions. The resulting proteoglycan model was combined with a novel collagen fibril model and a ground substance matrix material to create a polyconvex constitutive finite element model of …
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Continuum and Atomistic Simulation of Electrically-Mediated Flow Through Nanometer Channels
… As the continuum theories based on the Poisson-Boltzmann and the Navier-Stokes equations account for the various intermolecular interactions in a mean-field fashion, they fail to predict the fluid/ion characteristics accurately. In addition, fluids or electrolytes confined in …
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THEORETICAL PREDICTIONS OF POTENTIALS FOR INTERMEDIATE STEPS IN METHANOL AND ETHANOL ELECTROCHEMICAL OXIDATION ON Pt(111)
… functional theory (DFT) code uses modified Poisson-Boltzmann theory (MPB) and the dielectric continuum model to model the solvent, and allows adding or subtracting electronic charge to the solute or the surface with considering electrolyte response. Adsorption energies for reaction …
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Conservation of Electrostatically Mediated Function Across Protein Families and Superfamilies
… Continuum electrostatics methods (based on the Poisson-Boltzmann equation) provide a cornputationally efficient method for calculating electrostatic properties of biological molecules. The insights from these methods show that the electrostatically mediated function within a variety of enzyme …
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Counterion Behavior in Biopolymers
… to describing counterion behavior, such as the Poisson-Boltzmann formalism and Manning condensation theory, predict that charged surfaces are renormalized by a surrounding counterion cloud or condensed counterion layer, but such mean field approaches never predict an attraction. However, a large …
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Molecular mechanics of cartilage : quantification of GAG electrostatic interactions via high-resolution force spectroscopy
… electrical double layer repulsion based on the Poisson-Boltzmann formulation. The CS-GAG brush layer was approximated as either a flat surface charge density or a smoothed volume of known fixed charge density and the probe tip was modeled as a smooth hemisphere of constant surface charge density.
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Protein design with hierarchical treatment of solvation and electrostatics
… to finite-difference solution of the linearized Poisson-Boltzmann equation. Parameter sets optimized on a "testing" biomolecular binding system yield reduced average errors for related biomolecular systems. Finally, a protein design method is developed which uses the dead-end elimination and A* …
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Counterion Distribution around a Macroion in Polyelectrolytes Probed by Anomalous Small-Angle X-ray Scattering
… are compared with the predictions of the Poisson-Boltzmann Cell Model. The results suggest that the counterions are strongly correlated with the macroion. Osmotic coefficient measurements on rod-like polyelectrolytes show that approximately 20 percent of the counterions are osmotically …
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