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Dynamics of modulated waves in a nonlinear microtubule RLC transmission line. (English) Zbl 1524.35595

Summary: We study the dynamics of modulated ionic waves in a microtubule modeled by a nonlinear RLC transmission line [J. A. Tuszynski et al., “Ionic wave propagation along actin filaments”, Biophysical J. 86, No. 4, 1890–1903 (2004; doi:10.1016/S0006-3495(04)74255-1); M. V. Sataric et al., “A nonlinear model of ionic wave propagation along microtubules”, Eur. Biophysical J. 38, No. 5, 637–647 (2009; doi:10.1007/s00249-009-0421-5)]. We show through the application of a reductive perturbation technique that the network can be reduced in the continuum limit to the dissipative nonlinear Schrödinger equation. The processes of the modulational instability and the effects of the dissipative elements of the network on wave propagation are investigated. We perform numerical simulations which confirm analytical predictions and give rise to localized modulated wave formation. The results suggest that microtubules can be biological structures where short-duration nonlinear waves called electrical envelope solitons can be created and propagated.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
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