Modelling the flow through ion channels at the cell membrane

Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate and teach differential equations. Ion channels on the cell membrane allow the passage of ions from one side of the membrane to the other. The movement of these ions drives crucial processes such as the beating of our hearts. Using a system of two ordinary differential equations it is possible to capture the movement across ion channels that are opening and closing. Then using standard undergraduate techniques, we can predict how these channels behave in the long-term. In this work, we discuss how this example can be used to create tangible links to mathematical equations and motivate the teaching of techniques such as differentiation, integration, algebraic manipulation and equilibrium analysis. Furthermore, we show how a simple reformulation of this model into a stochastic setting using Gillespie's Stochastic Simulation Algorithm can allow us to capture the noise in ion channel flow.