Document Type


Date of Award

Summer 8-31-2011

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Horacio G. Rotstein

Second Advisor

Farzan Nadim

Third Advisor

Jorge P. Golowasch

Fourth Advisor

Victor Victorovich Matveev

Fifth Advisor

Vijayalakshmi Santhakumar


Various neuron types exhibit sub-threshold and firing frequency resonance in which the sub-threshold membrane potential or firing frequency responses to periodic inputs peak at a preferred frequency (or frequencies). Previous experimental work has shown that medial entorhinal cortex layer II stellate cells (SCs) exhibit sub-threshold and firing frequency resonance in the theta frequency band (4 - 10 Hz). In this thesis we seek to understand the biophysical and dynamic mechanism underlying these phenomena and how they are related. We studied the effects of sinusoidal current and synaptic conductance inputs at various frequencies, with and without noise, on the supra-threshold dynamics of a SC model. For current inputs, our results show that while the SC model exhibits a single frequency preference peak (in the theta frequency band) for low sinusoidal input levels, it exhibits three preferred frequency peaks for larger input levels. These additional peaks occur at frequencies that are roughly a multiple of the "theta" one. For synaptic conductance inputs, we observe an additional peak in the signal gain which occurs at a much higher frequency (in the high gamma frequency band). These findings depart from the linear prediction. The corresponding linearized model does not exhibit three preferred frequency peaks for current inputs and a much higher frequency for conductance inputs under the same conditions (such as parameters, noise, amplitude of inputs and maximal synaptic conductance) in the nonlinear model.

Previous experimental work has shown high-frequency Poisson-distributed trains of combined excitatory and inhibitory conductance- and current-based synaptic inputs reduce amplitude of subthreshold oscillations of SCs. The second goal of this thesis is to investigate the mechanism underlying these phenomena in the context of the model. More specially, we studied the effects of both conductance- and current-based synaptic inputs at various maximal conductance values on a SC model. Our numerical simulations show that conductance-based synaptic inputs reduce the amplitude of SC's subthreshold oscillations for low enough value of the maximal synaptic conductance value but amplify these oscillations at a higher range. These results are in contrast to the experimental results.

Included in

Mathematics Commons



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