Ion channels are transmembrane proteins in neurons that allow the flow of specific ions that produce an electrical charge responsible for fluctuations in the membrane voltage across the cell’s plasma membrane. A sufficiently large fluctuation produces an all-or-none response called an action potential. Analyses of single-neuron electrical activity models often focus on the long-term behavior of the system. However, most single-cell biological experiments look at the short-term, transient dynamics. These short-term dynamics are more physiologically relevant and can be quite different from the asymptotic behavior of the system. Thus, there is a mismatch between biologically relevant neuronal activity and the classical methods used for analysis of mathematical models. Our collaborators recently conducted pioneering studies on neuronal electrical activity in response to a novel experimental protocol wherein current applied to the individual neurons was continuously ramped to mimic how neurons would actually receive input biologically. They used fast applied current ramps to stimulate the neurons and varied the slope of the ramp over a range of values. They found that it was the weaker currents applied with smaller slopes that produced the most spikes in the neurons. Further, the neurons receiving this input produced multiple action potentials in response to the stimuli. This protocol is a novel advancement from the standard protocol, where current is applied to the neuron in steps but produced behaviors that are hard to interpret without some theoretical foundation. In this project, we have developed an integrated experimental-mathematical methodology to study transient dynamics in the electrical activity of single neurons by studying the response to the novel ramped current protocol.

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Work performed in collaboration with Dr. Kirill Korshunov, Dr. Paul Trombley, and Dr. Richard Bertram.