Abstract
Microtubules (MTs) are important cytoskeletal polymers engaged in a number of specific cellular activities including the traffic of organelles using motor proteins, cellular architecture and motility, cell division and a possible participation in information processing within neuronal functioning. How MTs operate and process electrical information is still largely unknown. In this paper we investigate the conditions enabling MTs to act as electrical transmission lines for ion flows along their lengths. We introduce a model in which each tubulin dimer is viewed as an electric element with a capacitive, inductive and resistive characteristics arising due to polyelectrolyte nature of MTs. Based on Kirchhoff’s laws taken in the continuum limit, a nonlinear partial differential equation is derived and analyzed. We demonstrate that it can be used to describe the electrostatic potential coupled to the propagating localized ionic waves.
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References
Albriton NL, Meyer T, Stryer L (1992) Range of messenger activation of calcium ions and IP3. Science 258:1812–1815
Braun D, Libchaber A (2004) Thermal force approach to molecular evolution. Phys Biol 1:P1–P8
Chrétien D, Fuller SD, Karsenti E (1995) Structure of growing microtubule ends: two-dimensional sheets close into tubes at variable rates. JCB 129(5):1311–1328
Del Giudice, Preparata G, Vitiello G (1988) Water as a free electric dipole laser. Phys Rev Lett 61:1085–1088
Jimenez MA, Evangelio JA, Aranda C, Lopez-Brauet A et al (1999) Helicity of alpha (404–451) and beta (394–445) tubulin C-terminal recombinant peptides. Protein Sci 8:788–799
Lin EC, Cantiello HF (1993) A novel method to study the electrodynamic behavior of actin filaments. Evidence for cable-like properties of actin. Biophys J 65(4):1371–1378
Luchko L, Huzil JT, Stepanova M, Tuszynski JA (2008) Conformational analysis of the carboxy-terminal tails of human beta tubulin isotypes. Biophys J 94:1971–1982
Manning GS (1969) Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties. J Chem Phys 51:924–933
Minoura I, Muto E (2006) Dielectric measurement of individual microtubules using the electroorientation method. Biophys J 90:3739–3748
Pokorný J, Hašek J, Jelínek F (2005) Electromagnetic field of microtubules: effects of transfer of mass particles and electrons. J Biol Phys 31:501–514
Priel A, Ramos AJ, Tuszynski JA, Cantiello HF (2006) A biopolymer transistor: electrical amplification by microtubules. Biophys J 90:4639–4643
Satarić MV, Tuszynski JA (2003) Relationship between the nonlinear ferroelectric and liquid crystal models for microtubules. Phys Rev E 67:011901–011912
Satarić MV, Tuszynski JA (2005) Nonlinear dynamics of microtubules and its biophysical implications. J Biol Phys 31:487–496
Satarić MV, Tuszynski JA, Žakula RB (1993) Kinklike excitations as an energy-transfer mechanism in microtubules. Phys Rev E 48:589–597
Satarić MV, Budinski-Petković Lj, Lončarević I (2007) Microtubules as active tracks for bi-directional cellular traffic of motor proteins. IJMPB 21(32):5387–5398
Strogatz SH (1994) Nonlinear dynamics and chaos. Addison-Wesley, Reading
Tuszynski JA, Portet S, Dixon JM, Luxford C, Cantiello HF (2004) Ionic wave propagation along actin filaments. Biophys J 86:1890–1903
Tuszynski JA, Brown JA, Crawford E, Carpenter EJ, Nip MLA, Dixon JM, Satarić MV (2005) Molecular dynamics simulations of tubulin structure and calculations of electrostatic properties of microtubules. Math Comput Model 41:1055–1070
Wang BG, Zhao XA, Wang J, Guo H (1999) Nonlinear quantum capacitance. Appl Phys Lett 74:2887–2999
Wang K, Rappel W-J, Levine H (2004) Cooperativity can reduce stochasticity in intracellular calcium dynamics. Phys Biol 1:27–34
Acknowledgments
The authors from Faculty of Technical Sciences are grateful for grants 141018A and 23036 provided by the Government of Serbia. JAT gratefully acknowledges funding for this project from NSERC, Alberta Cancer Foundation, the Allard Foundation and Alberta's Advanced Education and Technology.
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An erratum to this article can be found at http://dx.doi.org/10.1007/s00249-009-0540-z
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Satarić, M.V., Ilić, D.I., Ralević, N. et al. A nonlinear model of ionic wave propagation along microtubules. Eur Biophys J 38, 637–647 (2009). https://doi.org/10.1007/s00249-009-0421-5
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DOI: https://doi.org/10.1007/s00249-009-0421-5