Electrostatic potential of a charged ring: Applications to elliptic integral identities

2017 ◽  
Vol 71 (1) ◽  
pp. 37-41 ◽  
Author(s):  
Heung-Ryoul Noh
Keyword(s):  
Electrostatic Potential ◽  
Elliptic Integral ◽  
Charged Ring ◽  
Integral Identities

scholarly journals Conotoxins as Sensors of Local pH and Electrostatic Potential in the Outer Vestibule of the Sodium Channel

2003 ◽  
Vol 122 (1) ◽  
pp. 63-79 ◽  
Author(s):  
Kwokyin Hui ◽  
Deane McIntyre ◽  
Robert J. French
Keyword(s):  
Lipid Bilayers ◽  
Sodium Channels ◽  
Electrostatic Potential ◽  
Single Channel ◽  
Local Environment ◽  
Bound State ◽  
Channel Changes ◽  
Voltage Dependent ◽  
Charged Ring ◽  
Derivatives Of

We examined the block of voltage-dependent rat skeletal muscle sodium channels by derivatives of μ-conotoxin GIIIA (μCTX) having either histidine, glutamate, or alanine residues substituted for arginine-13. Toxin binding and dissociation were observed as current fluctuations from single, batrachotoxin-treated sodium channels in planar lipid bilayers. R13X derivatives of μCTX only partially block the single-channel current, enabling us to directly monitor properties of both μCTX-bound and -unbound states under different conditions. The fractional residual current through the bound channel changes with pH according to a single-site titration curve for toxin derivatives R13E and R13H, reflecting the effect of changing the charge on residue 13, in the bound state. Experiments with R13A provided a control reflecting the effects of titration of all residues on toxin and channel other than toxin residue 13. The apparent pKs for the titration of residual conductance are shifted 2–3 pH units positive from the nominal pK values for histidine and glutamate, respectively, and from the values for these specific residues, determined in the toxin molecule in free solution by NMR measurements. Toxin affinity also changes dramatically as a function of pH, almost entirely due to changes in the association rate constant, kon. Interpreted electrostatically, our results suggest that, even in the presence of the bound cationic toxin, the channel vestibule strongly favors cation entry with an equivalent local electrostatic potential more negative than −100 mV at the level of the “outer charged ring” formed by channel residues E403, E758, D1241, and D1532. Association rates are apparently limited at a transition state where the pK of toxin residue 13 is closer to the solution value than in the bound state. The action of these unique peptides can thus be used to sense the local environment in the ligand-–receptor complex during individual molecular transitions and defined conformational states.

“cases? for φ also” a question raised by Ramanujan

2019 ◽  
Vol 15 (01) ◽  
pp. 183-188 ◽  
Author(s):  
K. R. Vasuki ◽  
E. N. Bhuvan
Keyword(s):  
Elliptic Integral ◽  
Lost Notebook ◽  
Integral Identities

On pages 51–53 of his lost notebook, S. Ramanujan has recorded several incomplete elliptic integral identities of the first kind. In the process, he raises a question “cases? for [Formula: see text] also”, where he intends to obtain identities involving the [Formula: see text] function. Motivated by this, we obtain two new identities involving the [Formula: see text] function.

scholarly journals Determination of the electrostatic potential produced by a uniformly charged ring

2019 ◽  
Vol 1403 ◽  
pp. 012004
Author(s):  
Fernando Mesa ◽  
Edwin Orrego ◽  
Guillermo Villa
Keyword(s):  
Electrostatic Potential ◽  
Charged Ring

The electrostatic potential of a uniformly charged ring

2009 ◽  
Vol 30 (3) ◽  
pp. 623-627 ◽  
Author(s):  
Orion Ciftja ◽  
Arica Babineaux ◽  
Nadia Hafeez
Keyword(s):  
Electrostatic Potential ◽  
Charged Ring

Measurement System of Surface Electrostatic Potential on Insulation Board in Vacuum and its Application

2012 ◽  
Vol 132 (1) ◽  
pp. 95-100
Author(s):  
Hiroshi Morita ◽  
Ayumu Hatanaka ◽  
Toshiyuki Yokosuka ◽  
Yoshitaka Seki ◽  
Yoshiaki Tsumuraya ◽  
...  
Keyword(s):  
Electrostatic Potential ◽  
Measurement System ◽  
Surface Electrostatic Potential

VISUAL DESIGN TOOL FOR ELECTROSTATIC LELSES

2014 ◽  
Vol 5 (2) ◽  
pp. 778-789
Author(s):  
Hassan Nouri Al-Obaidi ◽  
Ali A. Rashead Al-Azawy
Keyword(s):  
Programming Languages ◽  
Electrostatic Potential ◽  
Electric Energy ◽  
Visual Basic ◽  
Visual Programming ◽  
Design Tool ◽  
Mesh Point ◽  
Visual Design ◽  
Computational Tool ◽  
Electrostatic Lenses

Current research presents a visual-computational tool to design and investigate round electrostatic lenses in sense of analysis procedure. The finite elements methods is adopted to find the electrostatic potential in the lens region. Laplace’s equation is first replaced by a certain functional which physically represent the electric energy stored in the electric field. This functional is then minimized at each mesh point with respect to the nearest eight ones. This minimization process is proved to be entirely equivalent to solving Laplace’s equation. The requirement that the functional being minimized is then yields a set of nine point equations which inter relate the potentials at adjacent mesh points. Finally this set of equations is solved to find the electrostatic potential at each mesh point in the region of the lens under consideration. The procedure steps mention above are coded to program written in visual basic. Hence an interface tool for analyzing and designing electrostatic lenses has been built up. Designing results proved that the introduced tools has an excellent outputs in comparison with the others written in not visual programming languages. Furthermore it easier for researchers and designer to use such a tool over their counterpart ones.

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