A NOTE ON THE NEW GEOMETRIC REPRESENTATION FOR THE PARAMETERS IN THE FIBRIL ELONGATION PROCESS

In this note we give new geometric representation for the parameters in the fibril elongation process. We provide more precise estimates for the Haus-dorff approximation of the shifted (interval) step function by sigmoidal Richards function. We propose a modified lag time, elongation rate and appare...

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Published inComptes rendus de l'Academie bulgare des Sciences Vol. 69; no. 8; p. 963
Main Author Kyurkchiev, Nikolay
Format Journal Article
LanguageEnglish
Published Bulgarian Academy of Sciences 01.01.2016
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Summary:In this note we give new geometric representation for the parameters in the fibril elongation process. We provide more precise estimates for the Haus-dorff approximation of the shifted (interval) step function by sigmoidal Richards function. We propose a modified lag time, elongation rate and apparent nucleation rate in terms of Hausdorff distance - d. Numerical examples, illustrating our results are given, too. The differential kinetic (mass action) equations for the fibril elongation mechanism are generated automatically in the module (intellectual property) via programming environment Mathematica. Graphics of the part of solutions - [f.sub.1](t),..., [f.sub.n](t) of the system of differential equations are visualized.Key words: sigmoidal richards function, shifted (interval) step function, Hausdorff distance, upper and lower bounds, elongation rate, lag time, apparent nucleation rate2010 Mathematics Subject Classification: 41A46, 62P10
ISSN:1310-1331