Repetitive responses to alternating current stimulation in molluscan neuron

The living cell maintain an electrical potential difference between the interior and the environment and this potential is one of the components of the energy barrier encountered by charged particles leaving or entering the cell. Neurons and muscle fibres may be excited; the cellular electrical potential may change in response to chemical stimuli or in response to current flow. In the nervous cells these electrical changes give the possibility to process and to transmit information also over long distances in the organism. Information processing in the brain is supported by the abundant dynamical behaviours of the neurons and by interactions between the neurons. Neuronal electrical activity is a fondamental point for the development of complex kind of behaviour in living systems. In the excitable tissues electric current may flow either between the intracellular and extracellular fluids by leaving or entering the cells as membrane current or it may flow within the cells as intracellular current. Many nervous cells show, when impaled, different patterns of spontaneous activity (pacemaker or regular discharging, bursting, etc.). Endogenously oscillating neurons are cells that have a range of membrane potential values in which their membrane potentials are instable: within this range the membrane potential oscillates rhythmically between relatively depolarized and hyperpolarized states. If the depolarized phase exceeds the threshold for excitation, a burst or train of action potential each cycle is produced. The different types of oscillators have been reviewed considering the neural events underlying rhythmic behaviours (connectivity and endogenous oscillators), the environmental and synaptic influences and the mechanisms involved in spontaneous bursting activity. Various form of stimulating current may be applied in order to investigate the electrical properties of cells, the way in which the cell responds and to verify the possibility to induce particular discharge pattern. In squid axon stimulated with sinusoidally sub-threshold currents the recorded voltage increases continously with the current amplitude and a sinusoidal current yields a sinusoidal voltage. Action potentials appear when the membrane is excited by the outward-flowing or positive phase of the alternating current. Threshold values of the stimulating current and its amplitude are frequency-dependent. Oscillatory membrane potential changes and bursting activity have been induced in Aplysia neurons, silent at rest, when treated with convulsants (strychnine and pentylenetetrazol) and also reducing concentrations of Ca and Mg in the external medium. In Aplysia and Helix pomatia it has been shown that in response to injected sinusoidal alternating currents the neurons demonstrate a phase-locking behavior consisting of a train of repetitive action potential whose pattern is frequency dependent and, when the frequency of the current is suitably low, these neurons exhibit impulse output patterns qualitatively similar to these of normally bursting neurons. I wish here to analyze a simple mathematical model, utilized to describe adaptation of discharge frequency and generalized to account for the sinusoidal stimulating currents. By means of combined bias and cyclic currents the possibility to induce different patterns of electrical activity in neurons spontaneously discharging or silent at rest has been tested.