Improved radial model of nonlinear dynamics of microtubular

Slobodan Zdravkovic

Vinča Institute of Nuclear Sciences, University of Belgrade, Serbia

A new model describing nonlinear dynamics of microtubules (MTs) is explained. The model assumes one radial degree of freedom per each dimer like in -model [S. Zdravković, M.V. Satarić, A. Maluckov and A. Balaž, Appl. Math. Comput. 225 (2014) 227-237], introduced recently. Hence, the model explained here represents its extension and can be called as improved -model (I M). A new term, representing chemical interaction of a dimer with all other dimers, is introduced in Hamiltonian. This term is taken from the previously introduced -model [S. Zdravković, L. Kavitha, M.V. Satarić, S. Zeković, J. Petrović, Chaos Solitons Fract. 45 (2012) 1378-1386], which provides a general feature of the model. Two solutions of the crucial partial differential equation are discussed. Using continuum approximation one obtains kink solitons moving along MT. In case of the -model the wave amplitude turned out to be very big. The I M has solved this problem. Semi discrete approximation was also applied, which brings about localized modulated waves called breathers.