Johan Klint: Firing patterns and multistability in a neuron model

Neuron cells are the basic unit of neural systems, and a prerequisite for all animal behavior and human cognition. The complexity of a neural structure, such as the human brain, is truly remarkable and any deeper aspects of its function may therefore appear difficult to grasp. Understanding a single neuron’s function, with complex dendrite structure with up to 150 000 branches, connections to up to 10 000 other neurons and axon extensions more than a meter long, is a great challenge for the scientific community. However, with the use of modern computer technology, the electrophysical and mathematical mechanisms behind neuron signal generation can be visualized. In this work, the leech heart interneuron is modelled, and parameter ranges producing autonomous action potentials with different firing patterns were explored. A Java program was developed as a working tool for investigating this Hodgkin-Huxley type of model. The outcome from five explicit, including Euler and Runge-Kutta fourth order, and one semi-implicit numerical method was compared and their stability properties were discussed. The parameter space was explored with respect to the maximum membrane conductance of sodium, calcium and leak ions, with the parameters denoted gNa, gCaS and gleak, respectively. One intriguing feature of this neuron model is the appearance of multistability, where the same parameter settings may generate different signal output from the neuron model depending on the initial conditions of the state variables. This was visualized by simulations and phase portraits.