Noctiluca Miliaris is a single cell, multi-membrane organism that has bioluminescent capabilities. This luminescent ability is closely associated with the flash triggering potential produced by an excitable membrane under active conditions such as the movement of ions through channels against the concentration gradient. External energy in the form of an electrical or mechanical stimulus is required for this type of ionic movement that can result in all-or-none spikes in the transmembrane potential if a certain threshold voltage is exceeded. Further examination of this strong nonlinear relationship between the transmembrane voltage and rate of ion flow due to an applied stimulating source provides valuable insight into the action potential that leads to the luminescence, and it also allows for the development of models of the vacuolar potential of Noctiluca Miliaris due to an applied current.
An electric circuit model based upon a two-membrane, spherical cell consists of the series combination of a parallel R-C circuit representing the non-excitable, passive outer membrane and a parallel R-C-variable source resistor circuit representing the excitable, inner membrane. The variable source resistor represents a series combination of a dependent voltage source with a variable resistor. The dependent voltage source models the ionic gradient, and the variable resistor models the voltage-time dependent conductance of the ion channel of the active membrane. The variable resistor is also known as the active resistance, and a model of this resistance is primarily governed by the active membrane voltage. With knowledge of the values of each circuit element extracted from experimental measurements, the transmembrane potential is simulated using rectangular current pulses as the stimulating source for both sub-threshold and threshold conditions.
A model of a spherical cell model with an external electric field incident on it is evaluated by solving Poisson’s equation. This model requires knowledge of the cell radius, membrane thickness, and the conductivity and permittivity of the bath, membrane, and vacuole. With knowledge of these values from experimental measurements, the transmembrane potential is calculated for a stimulating source of known external electric field intensity under sub-threshold conditions.
