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NJIT Mathematical Biology Seminar

Tuesday, February 8, 2011, 2:30pm
Cullimore Hall 611
New Jersey Institute of Technology

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Subthreshold resonance in a stellate cell model. Part I

Horacio G. Rotstein

Department of Mathematical Sciences, NJIT

In this work we focus on the biophysical and dynamic mechanisms of generation of membrane potential (subthreshold) resonance in a biophysical (conductance-based) neuron model that includes an h-current (Ih) and a persistent sodium current (INap). This model is based on measurements for stellate cells in layer II of the medial entorhinal cortex which have been shown to exhibit resonance.

We extend previous work on the mechanism of generation of subthreshold oscillations and the onset of spikes in single cells to account for the effect of oscillatory current inputs on the cell's voltage response. The former two phenomena depend critically on the so called canard structure, a combination of parabolic-like nonlinearities associated to the voltage dynamics and the time-scale separation between voltage and the hcurrent gating variables. A salient feature of this type of models is the ability of phase-space trajectories to evolve in a close vicinity of the unstable branch of the parabolic nullcline (or nullsurface) for a significant amount of time. This results in an amplification of the subthreshold oscillations amplitude that is not observed in the corresponding linearized models. Since canard structures contain information about the biophysical properties of neurons, they are useful geometric/dynamic tools to connect between biophysics and dynamics.

We extend this approach to explain (i) the mechanisms of frequency preference selection and voltage response amplification to sinusoidal inputs at the resonant frequency band in the Ih/INap model, (ii) the mechanisms of voltage response attenuation at lower and higher frequencies (high- and low- pass filters respectively), and (iii) how the resonant frequency and other resonance properties depend on the model,F"(Bs biophysical parameters. In contrast to the behavior of the corresponding linearized models, as the amplitude of the oscillatory input increases, the subthreshold voltage responses are amplified, the resonant frequency decreases, the cells become more selective to incoming signal frequencies, and the subthreshold resonant frequency of the cell decreases with increasing levels of hyperpolarization. In contrast to previous claims, we find that both Ih and INap (and not only Ih) are involved in determining the cell,F"(Bs resonant frequency. We discuss the implications of our results for super-threshold (firing frequency) resonance and network dynamics