title: Waves transmission and amplification in an electrical model of microtubules.
abstract: Inspired by standard electrophysiological models of microtubules, a discrete nonlinear equation for ionic wave propagation that incorporates a negative nonlinear resistance is presented. The conditions for wave propagation in forbidden band gap are analyzed without and with dissipation. The nonlinear response manifold method is used to determine the supratransmission threshold of the case of study without dissipation. This threshold is found to be similar to the value obtained by analytical methods. With the dissipation, the monitoring of the accumulated energy is used to estimate the infratransmission threshold. It appears that the value of the supratransmission threshold can be lower than the value of the infratransmission threshold. The system is found to amplify significantly the amplitude of the input signal, thus confirming known experimental results. Nevertheless, a proper choice of the parameter of the nonlinear resistance is required for further validation of our results. A possible biological implication of the obtained results is presented.
authors.affiliation: icipe-African Insect Science for Food and Health, P.O. Box 30772-00100, Nairobi, Kenya.
authors.forename: Frank T
authors.initials: FT
authors.lastname: Ndjomatchoua
authors.affiliation: Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon.
authors.forename: Clément
authors.initials: C
authors.lastname: Tchawoua
authors.affiliation: icipe-African Insect Science for Food and Health, P.O. Box 30772-00100, Nairobi, Kenya.
authors.forename: Francois M M
authors.initials: FM
authors.lastname: Kakmeni
authors.affiliation: icipe-African Insect Science for Food and Health, P.O. Box 30772-00100, Nairobi, Kenya.
authors.forename: Bruno P
authors.initials: BP
authors.lastname: Le Ru
authors.affiliation: International Maize and Wheat Improvement Center (CIMMYT) ICRAF House, United Nation, Avenue, Gigiri, P. O. Box 1041, Village Market, 00621 Nairobi, Kenya.
authors.forename: Henri E Z
authors.initials: HE
authors.lastname: Tonnang
mesh_terms: D004560:Electricity; D008870:Microtubules / Q000378:metabolism*; D008954:Models, Biological; D017711:Nonlinear Dynamics