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

doi:10.1088/1674-1056/23/2/020504

Abstract 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 kink-type 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.

Keywords: Jacobian elliptic functions ordinary differential equations microtubules kink soliton

Received: 03 April 2013
Revised: 03 April 2013
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	87.10.Ed	(Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models)
	87.15.-v	(Biomolecules: structure and physical properties)

Fund: Project supported by Serbian Ministry of Education and Sciences (Grant No. Ⅲ45010), UGC, NBHM, India (major research projects), BRNS, India (Young Scientist Research Award), ICTP, Italy (Junior Associateship) and UGC (Rajiv Gandhi National Fellowship).

Corresponding Authors: Slobodan Zdravković
E-mail: szdjidji@vinca.rs

About author: 05.45.Yv; 87.10.Ed; 87.15.-v

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Slobodan Zeković, Annamalai Muniyappan, Slobodan Zdravković, Louis Kavitha Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules 2014 Chin. Phys. B 23 020504

[1]	Cifra M, Pokorný J, Havelka D and Kučera O 2010 BioSystems 100 122
[2]	Dustin P Microtubules 1984 (Springer, Berlin)
[3]	Tuszyńsky J A, Hameroff S, Satarić M V, Trpisová B and Nip M L A 1995 J. Theor. Biol. 174 371
[4]	Satarić M V and Tuszyńsky J A 2005 J. Biol. Phys. 31 487
[5]	Schoutens J E 2005 J. Biol. Phys. 31 35
[6]	Havelka D, Cifra M, Kučera O, Pokorný J and Vrba J 2011 J. Theor. Biol. 286 31
[7]	Zdravković S, Satarić M V and Zeković S 2013 Europhys. Lett. 102 38002
[8]	Drabik P, Gusarov S and Kovalenko A 2007 Biophys. J. 92 394
[9]	Nogales E, Whittaker M, Milligan R A and Downing K H 1999 Cell 96 79
[10]	Satarić M V, J A Tuszyńsky J A and Žakula R B 1993 Phys. Rev. E 48 589
[11]	Collins M A, Blumen A, Currie J F and Ross J 1979 Phys. Rev. B 19 3630
[12]	Gordon A 1987 Physica B 146 373
[13]	Gordon A 1988 Physica B 151 453
[14]	Gordon A 1989 Solid State Commun. 69 1113
[15]	Satarić M V, Koruga Dj, Ivić Z and Žakula R 1990 J. Mol. Electron. 6 63
[16]	Elwakil S A, El-labany S K, Zahran M A and Sabry R 2002 Phys. Lett. A 299 179
[17]	Ali A H A 2007 Phys. Lett. A 363 420
[18]	El-Wakil S A and Abdou M A 2007 Chaos, Solitons and Fractals 31 840
[19]	Kavitha L, Prabhu A and Gopi D 2009 Chaos, Solitons and Fractals 42 2322
[20]	Kavitha L, Srividya B and Gopi D 1010 J. Magn. Magn. Mater. 322 1793
[21]	Kavitha L, Akila N, Prabhu A, Kuzmanovska-Barandovska O and Gopi D 2011 Math. Comput. Modelling 53 1095
[22]	Remoissenet M 1989 Waves Called Solitons (Berlin, Heidelberg: Springer-Verlag)
[23]	Akhiezer N I 1990 Elements of the Theory of Elliptic Functions, Translations of Mathematical Monographs 79 (Providence: American Mathematical Society)
[24]	Lakshmanan M and Rajasekar S 2003 Nonlinear Dynamics (Berlin, Heidelberg: Springer-Verlag)
[25]	Dai C and Zhang J 2006 Chaos, Solitons and Fractals 27 1042
[26]	Scott A 2007 Nonlinear Science Emergence and Dynamics of Coherent Structures (Moscow: Fizmatlit) (in Russian)
[27]	Zdravković S, Kavitha L, Satarić M V, Zeković S and Petrović J 2012 Chaos, Solitons and Fractals 45 1378
[28]	Smirnov V I 1965 Kurs Vishey Matematiki, Tom 1 (Moscow: Nauka) (in Russian)
[29]	Zdravković S, Satarić M V, Maluckov A and Balaž A, A radial model of nonlinear dynamics of microtubules, Submitted to Eur. Phys. J. E.

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

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