Continuous signaling pathways instability in an electromechanical coupled model for biomembranes and nerves

Information processing is a basic part of life and, presumably, the nervous system’s primary purpose. Neurons perform a variety of tasks that collect useful information from the organism’s periphery sensor receptor arrays and transfer it into action, imagery, and memory. Brain communication, also known as neural signaling, is now assumed to be electromechanical, based on a large body of observational and experimental evidence acquired over the last two centuries. In this paper, modulational instability is investigated as a mechanism of wave trains and soliton formation in neurons using a nonlinearly coupled complex Ginzburg–Landau equation derived from the Morris–Lecar neural model for nerve electrical activity and the Heimburg–Jackson model for longitudinal density pulses. Using standard linear stability analysis, the growth rate of modulation instability is studied analytically and numerically as a function of perturbation frequency and system parameters. In particular, it is shown that the gain depends strongly on the coupling parameters. We also investigated the effect of coupling parameters on the gain of modulation instability, thus confirming the continuous signaling instability. This is highly significant from a theoretical point of view and could be a plus to explain the process of generation of action potential as the consequences of instability between coupled electrical and mechanical weakly continuous wave in nerve. Graphical abstract