Computer simulation for studying calcium dependent abnormalities in firing mechanism of molluscan neurones

Computer modelling technique is proposed to assist in physiological research on invertebrate neuronal membranes. The firing mechanism of a single patch of invertebrate neuronal membrane has been studied in dependence on maximum Ca++ conductance. The calculations are based on modification of Hodgkin-Huxley's data completed by a straight line approximation between experimental points of the kinetic parameters of Ca++ current and early transient potassium current. The time course of conductance changes is assumed to be proportional to m2h for Ca++ current. Three distinct potassium currents are involved into the model, viz. transient potassium current, delayed potassium current and Ca++-dependent potassium current. The modified Euler method run on a digital computer has been used for numerical integration of kinetic equations. Significant effects of Ca++ conductance on spike broadening, plateau development and spike afterhyperpolarization are represented. In the range of small Ca++ conductance an infinite spontaneous activity can be triggered by a short (suprathreshold) current pulse which may be considered a model of pacemaker activity. Plateau development resulting from potassium blocking or decreasing potassium equilibrium is facilitated by Ca++ conductance in the range of greater Ca++ conductance. The effects of voltage sensitivity of the coupling coefficient describing the current of Ca++-dependent K+ channels were studied and compared to the voltage independent case. The coupling coefficient seems to be a crucial factor in broadening the range of Ca++ conductance responsible for pacemaker activity. For greater values of Ca++ conductance, a decrease of the coupling coefficient leads to a transition from prolonged bursting to interruption of burst activity by burst-afterhyperpolarization. The blocking effect of 4-aminopyridine on fast outward current has been studied by the model which has a practical significance considering that aminopyridine is known as a convulsive agent. We suppose that it is reasonable to study the convulsive effects of aminopyridine by the model based on the kinetics of the isolated neuronal membrane. The model may help in understanding the ionic background underlying abnormal network activity during epileptic discharges of mammalian neurones.