Coarse-grained potential for interaction with a spherical colloidal particle and planar wall

2010 ◽  
Vol 75 (5) ◽  
pp. 527-545 ◽  
Author(s):  
Milan Předota ◽  
Ivo Nezbeda ◽  
Stanislav Pařez
Keyword(s):  
Colloidal Particle ◽  
Point Interaction ◽  
Point Particle ◽  
Coarse Grained ◽  
Large Sphere ◽  
Interaction Sites ◽  
Inverse Power Law ◽  
Graphite Sphere ◽  
Point To Point ◽  
Spherical Colloidal Particle

An effective coarse-grained interaction potential between a point particle and a spherical colloidal particle with continuously distributed inverse power-law interaction sites is derived. The potential covers all ranges of spherical particle size, from a point particle up to an infinitely large particle forming a planar surface. In the small size limit, the point-to-point interaction is recovered, while in the limit of an infinitely large sphere the potential comes over to the known particle–wall potentials as, e.g., the 9–3 potential in the case of the Lennard–Jones interaction. Correctness and usefulness of the derived potential is exemplified by its application to SPC/E water at a graphite sphere and wall.

scholarly journals Sequence-dependent Three Interaction Site (TIS) Model for Single and Double-stranded DNA

2018 ◽  
Author(s):  
Debayan Chakraborty ◽  
Naoto Hori ◽  
D. Thirumalai
Keyword(s):  
Electrostatic Interactions ◽  
Persistence Length ◽  
Data Bank ◽  
Coarse Grained ◽  
Force Extension ◽  
Sequence Dependence ◽  
Coarse Grained Model ◽  
Interaction Sites ◽  
Double Stranded Dna ◽  
Centers Of Mass

AbstractWe develop a robust coarse-grained model for single and double stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduces the experimentally measured salt and sequence dependence of the size of single stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin, and could be described by a standard polymer model. We also show that the persistence length of double stranded DNA, formed from two complementary ssDNAs with one hundred and thirty base pairs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

Change of Shape and Change of Volume

1993 ◽  
Author(s):  
Brian Bayly
Keyword(s):  
Isotropic Material ◽  
Chemical Potential ◽  
Stress Gradient ◽  
Small Length ◽  
Large Sphere ◽  
Point Of Interest ◽  
Principal Axes ◽  
Principal Directions ◽  
Point To Point ◽  
Spatial Stress

In earlier chapters we first defined a material's chemical potential, and then went on to enquire how the material responds. And similarly with a state of nonhydrostatic stress: having reviewed what it is, we consider how a material might respond. For the sake of simplicity, we imagine an extensive sample, such as a cubic meter, and suppose that the stress state is the same in every cubic centimeter; that is to say, there are no gradients in stress from point to point. Thus we do not enquire yet how a material responds to a spatial stress gradient; that comes later. We first enquire how it responds to a homogeneous but nonhydrostatic stress. Inside the material, close to the point of interest, we define a small length l by means of the material particles at its two ends. If, at a later moment, we find the distance between the particles to be l — δl, then we envisage the limit of the ratio δl/l as l goes to zero, give the limit the symbol ε, and name it the linear strain at the point of interest in the direction of l, positive when δl is positive, i.e., for a shortening and negative for an elongation. Another mental operation that can be performed in the neighborhood of the point of interest is to define a small sphere by means of the material particles that form its surface. At a later moment the particles will form the surface of an ellipsoid. (For a large sphere and an inhomogeneous situation, the new shape can be something more complicated; but as the imagined original sphere approaches zero diameter, the shape of its deformed counter-part can only approach an ellipsoid). The axes of the ellipsoid are principal directions of strain, and the magnitudes of the strains along them are named ε1, ε2, and ε3, with ε1 the largest. In an isotropic material, the principal axes of stress and strain coincide, with ε1 lying along the direction of σ1 and correspondingly; see Figure 7.la. As with stresses, the three values of ε themselves define an ellipsoid if they are all positive—see Figure 7.1b.

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