Discrete surface charge

Beard, D.A. and Schlick, T. (2001) Modeling salt-mediated electrostatics of macromolecules the discrete surface charge optimization algorithm and its application to the nucleosome. Biopolymers 58, 106-115. 

The nature of the solid surface involved in the adsorption process is a major factor in determining the mode and extent of solute adsorption. When one considers the possible nature of an adsorbent surface, three principal groups readily come to mind (1) surfaces that are essentially nonpolar and hydrophobic, such as polyethylene (2) those that are polar but do not possess significant discrete surface charges, such as polyesters and natural fibers such as cotton and (3) those that possess strongly charged surface sites. Each of these surface types will be discussed, beginning with what is probably the simplest, type 1. 

Lately, mean forces and pmfs have been simulated for models containing discrete surface charges inhomogeneously distributed with a spherical hard-sphere potential [99-101] and protein models with a more irregular hard-core potential [102]. 

D. A. Beard and T. Schlick, Biopolymers, 58, 106 (2001). Modeling Salt-Mediated Electrostatics of Macromolecules The Discrete Surface Charge Optimization Algorithm and Its Application to the Nucleosome. 

Fluoride (small and well hydrated) binds exclusively to the discrete surface charges. 

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

Figure 18-82 illustrates the relationship between solids concentration, iuterparticle cohesiveuess, and the type of sedimentation that may exist. Totally discrete particles include many mineral particles (usually greater in diameter than 20 Im), salt crystals, and similar substances that have httle tendency to cohere. Floccnleut particles generally will include those smaller than 20 [Lm (unless present in a dispersed state owing to surface charges), metal hydroxides, many chemical precipitates, and most organic substances other than true colloids. 

The current theory of chemisorption on semiconductors as developed by Hauffe 14) assumes that charge is transferred either from or to the solid, so that the chemisorbed species exists on the surface as an ion. The resulting surface charge is balanced by a charge in the solid associated with the discrete electron levels which are responsible for the semiconducting properties of the solid. It would appear at first sight that the existence of localized states for the combined system, foreign atom plus crystal, is required... 

Vectors whose components have continuous values correspond to the more traditional types of vectors found in the physical sciences. They are of identical form to the discrete-valued vectors (see Eq. 2.16) except that the components, vA(xk), are continuous valued. In chemoinformatics, however, the nature of the components is considerably different from those typically found in physics. For example, physiochemical properties, such as logP, solubility, melting point, molecular volume, Hammett ap parameters, and surface charge, as well as other descriptors derived explicitly for the purpose, such as BCUTs... 

The dispersion contribution to the interaction energy in small molecular clusters has been extensively studied in the past decades. The expression used in PCM is based on the formulation of the theory expressed in terms of dynamical polarizabilities. The Qdis(r, r ) operator is reworked as the sum of two operators, mono- and bielectronic, both based on the solvent electronic charge distribution averaged over the whole body of the solvent. For the two-electron term there is the need for two properties of the solvent (its refractive index ns, and the first ionization potential) and for a property of the solute, the average transition energy toM. The two operators are inserted in the Hamiltonian (1.2) in the form of a discretized surface integral, with a finite number of elements [15]. 

Let us remark incidentally that the van der Waals, solvent-accessible and solvent-excluded molecular surfaces commonly used in apparent surface charge calculations, can be discretized without resorting to a polyhedral approximation. Indeed, these surfaces are made of pieces of spheres and tori and it is therefore possible to mesh and compute integrals on the molecular surfaces since analytical local maps are available [19],... 

For practical calculations, the integral over Y has to be discretized, which introduces an additional numerical error. An alternative consists in applying the Galerkin approximation to system (1.38), which is equivalent to Equation (1.37). The discretized apparent surface charge [cr] is obtained by solving successively the linear systems... 

Despite the simple form of Equation (1.83), the detailed formulation of an extended Lagrangian for CPCM is not a straightforward matter and its implementation remains challenging from the technical point of view. Nevertheless, is has been attempted with some success by Senn and co-workers [31] for the COSMO-ASC model in the framework of the Car-Parrinello ab initio MD method. They were able to ensure the continuity of the cavity discretization with respect to the atomic positions, but they stopped short of providing a truly continuous description of the polarization surface charge as suggested,... 

In the previous contributions to this book, it has been shown that by adopting a polarizable continuum description of the solvent, the solute-solvent electrostatic interactions can be described in terms of a solvent reaction potential, Va expressed as the electrostatic interaction between an apparent surface charge (ASC) density a on the cavity surface which describes the solvent polarization in the presence of the solute nuclei and electrons. In the computational practice a boundary-element method (BEM) is applied by partitioning the cavity surface into Nts discrete elements and by replacing the apparent surface charge density cr by a collection of point charges qk, placed at the centre of each element sk. We thus obtain ... 

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