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Propagation of kink–antikink pair along microtubules as a control mechanism for polymerization and depolymerization processes

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Chinese Physics B 2014年第9期23卷 556-570页

作者： L.Kavitha a.muniyappan S.Zdravkovi M.V.Satari A.Marlewski S.Dhamayanthi D.Gopi Department of Physics School of Basic and Applied SciencesCentral University of Tamilnadu (CUTN) The Abdus Salam International Center for Theoretical Physics Department of Physics Periyar University Institut za nuklearne nauke Vinca Laboratorija za atomsku fiziku 040Univerzitet u Beogradu Fakultet tehnickih nauka Univerzitet u Novom Sadu Institute of Mathematics Poznan University of Technology Center for Nanoscience and Nanotechnology Periyar University Department of Chemistry Periyar University

Among many types of proteinaceous filaments, microtubules （MTs） constitute the most rigid components of the cellular cytoskeleton. Microtubule dynamics is essential for many vital cellular processes such as intracellular transport, metabolism, and cell division. We investigate the nonlinear dynamics of inhomogeneous microtubulin systems and the MT dynamics is found to be governed by a perturbed sine-Gordon equation. In the presence of various competing nonlinear inhomogeneities, it is shown that this nonlinear model can lead to the existence of kink and antikink solitons moving along MTs. We demonstrate kink-antikink pair collision in the framework of Hirota＇s bilinearization method. We conjecture that the collisions of the quanta of energy propagating in the form of kinks and antikinks may offer a new view of the mechanism of the retrograde and anterograde transport direction regulation of motor proteins in microtubulin systems.

关键词： microtubules solitons solitary solutions partial differential equations

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Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules

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Chinese Physics B 2014年第2期23卷 178-182页

作者： Slobodan Zekovi Annamalai muniyappan Slobodan Zdravkovi Louis Kavitha Institut za nuklearne nauke Vina Laboratorija za atomsku fiziku 040Univerzitet u Beogradu Department of Physics Periyar University Center for Nanoscience and Nanotechnology Periyar University

We show how Jacobian elliptic functions （JEFs） can be used to solve ordinary differential equations （ODEs） describing the nonlinear dynamics of microtubules （MTs）. We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kinkbtype soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.

关键词： Jacobian elliptic functions ordinary differential equations microtubules kink soliton

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