Chirped modulated wave excitations in an electrical model of microtubules

Inspired by standard electrophysiological models of microtubules (MTs), we consider a relatively large one-dimensional spatial array of nonlinear electrical transmission network with a negative nonlinear resistance. Employing the reductive perturbation approach in the semi-discrete approximation, we show that the evolution of ionic waves in this electrical circuit model of microtubules is described by a nonlinear Schrödinger (NLS) equation with a dissipative/amplification term in the presence of an external linear potential. The modulational instability analysis of the amplitude equation shows that the derived NLS equation suitably describes the dynamics of our lattice of biochemical units as an excitable medium. Based on exact and approximate solutions of the amplitude equation, we investigate analytically the existence of modulated chirped solitonic waves along microtubules. We suggest possible biological implications of these nonlinear modulated waves. Our system is found to amplify significantly the amplitude of the input signal, confirming thus known experimental results on MTs. Nevertheless, a proper choice of various parameters of the negative nonlinear resistance is required for further validation of our theoretical results. •A nonlinear microtubule RLC transmission network is considered.•Based on a nonlinear equation of Schrödinger type, the modulational instability of Stokes waves in investigated.•Exact and approximate chirped bright and kink soliton solutions are obtained.•Dynamics of modulated wave are investigated analytically.