Modeling Action Potentials of Neurons and Investigating Stochastic Additions

Discections of squid giant axons by Alan Hodgkin and Andrew Huxley in the 1950’s and 60’s revealed through the size of the axons, that the large axon allowed direct measurements of ionic currents, enabling them to model membrane dynamics mathematically and with electrical circuit analogs. This is because a neuron creates action potentials when ion channels are opened, allowing ions to flow across the membrane down their electrochemical gradients.  Because of the predictable oscillations of this system, scientists Richard FitzHugh and Jinichi Nagumo were able to simplify the model to a set of equations that still maintain the biological significance, while allowing for more manipulations. My project has been to use the simplified FitzHugh-Nagumo model to simulate the action potentials of neurons within Python to be further explored in two way: how stochastic noise affects action potentials, and how this affects coupled neuron simulations. A major point of exploration is the effect of stochasticity, or random noise, on action potentials. In biological systems, fluctuations of heat and vibrations from elements like the opening of ion channels can introduce random noise into the system, and my investigation is to see whether certain levels of noise can induce action potentials that otherwise wouldn’t occur.  The second component is to see how this induction of action potentials through noise effects systems of multiple neurons, which are simulated to be coupled (meaning they are simulated to influence each other's activity) to each other in an analogous function to that of connected neurons in the brain which transmit signals to each other.