Resonances in the voltage statistics and upcrossing rate of a minimal dendritic neuron model with a passive membrane

• Published in: Physical review. E Vol. 111; no. 5-1; p. 054406
• Main Authors: Gowers, Robert P, Richardson, Magnus J E
• Format: Journal Article
• Language: English
• Published: United States 01.05.2025
• Subjects: Action Potentials - physiology; Animals; Cell Membrane - metabolism; Cell Membrane - physiology; Dendrites - physiology; Models, Neurological; Neurons - cytology; Neurons - physiology
• ISSN: 2470-0053
• DOI: 10.1103/PhysRevE.111.054406

A dendritic neuron model subject to spatiotemporal fluctuating synaptic drive and a pointlike oscillating current stimulation is considered. Unlike for dendritic models that are statistically homogeneous in space, this experimentally plausible scenario allows for the electrotonic length constant to feature in quantities like the modulated firing rate as a function of the distance to current stimulation. The cable equation for the voltage is solved to find the modulated first- and second-order moments featuring the voltage and its rate of change. These are then used to calculate the frequency dependence of the firing-rate response in the upcrossing approximation as a function of the distance between a nominal soma and current stimulation. With an isopotential model as a reference, this minimal dendritic model exhibits some surprising features such as modulated first-order moments that grow with frequency. In addition, despite the model's passive membrane, the voltage moments and upcrossing rate exhibit frequency preferences in the form of resonances and troughs. These features are in the same class of morphological resonance phenomena previously seen in Purkinje cells and in models of cells driven by external electrical fields.