The purpose of this project is to investigate the potentials of neuronal cell membrane ion channels being memristors. Neurons biologically exhibit the behavior of circuits, and we will study the components of neurological activity in terms of classical and modern circuit elements. Moreover, the recently characterized ‘memristor’ is a new circuit element that completes mathematical symmetry of electrical variables. They have been found to express ‘memory’, by retaining a physical conformation and particular resistance after current has passed through it.
Memristors have eluded discovery until the emergence of nanotechnology; we are interested in that neurons are vital, naturally occurring analogues for microscopic circuits. Neurons generate electrical potential via membrane channels, which maintain an ionic gradient. We are investigating the dynamics of ion channel structure and resistance in terms of current. We hope to show these relationships as memristive, and therefore contribute to biophysical uses of neurons in nanotechnology.
To do this, we will continue to investigate the Hodgkin-Huxley models for neurons, and expand the ordinary differential equations to describe the cell’s electrical activity in terms of memristance. Hopefully, this will give a new perspective on circuit activity. Wolfram Mathematica is mathematical computation software that will provide solutions to nonlinear differential equations. Memristors are known to have nonlinear trends; while the relationship between resistance, current and channel shape are related, their change is not proportional to each other. Therefore, we will also have to employ more advanced mathematical tools to describe it, specifically differential calculus.