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NJIT Mathematical Biology Seminar

Wednesday, December 10, 2008, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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Identifying resonance in the PY neurons of the stomatogastric ganglion of cancer borealis

Joseph Hanna & Karina Aliaga

Department of Mathematical Sciences, NJIT

The property that describes the neuron.s preferred response to inputs of injected current is called resonance. To produce resonance, a cell must have two requirements: a low-pass filter (attenuates high frequencies) and a high-pass filter (attenuates low frequencies). The neuron whose resonance frequency we wish to determine is the PY neuron of the STNS (stomatogastric nervous system) of Cancer borealis. The STNS consists of rhythmic neural networks that control the movement of a crustacean.s foregut. Noting that all neurons exhibit a low-pass filter, we investigate the high-pass filter of the PY neuron, and its properties.

The PY neuron has an Ih (hyperpolarizing activating current) channel as its high-pass filter. Thus, for the PY neuron to exhibit resonance, it must have an Ih channel (or any other high-pass filter) in addition to the inherit low-pass filter property. To inspect if PY has resonance we used the current clamp method and injected a sinusoidal current that sweeps through several frequencies. This current, also called ZAP, produced a voltage response that we can analyze via an impedance versus frequency graph. Resonance was not seen in the preliminary experiments so we decided to use 10 mM CsCl to block Ih, to verify that Ih did not cause an unnoticeable resonant peak. However, resonance was still not seen, so we injected an artificial Ih current via dynamic clamp. Under this method, resonance was produced by increasing the conductance of Ih.

To model these results we used the Hodgkin-Huxley equation and created the same scenario. Under low conductance, resonance was not evident, but when conductance increased the PY neuron had frequency preference. This leads us to believe that while the PY neuron has an Ih current, its conductance is too low to produce resonance. The probable cause for this, is that PY cells are small in size relative to the other STG cells, resulting in less Ih channels per unit membrane.

Predicting Plant Succession

David Hamoui & Catherine Morrison

Department of Mathematical Sciences, NJIT

Plant community succession is the at least somewhat predictable sequence of species compositions that follows a landscape disturbance (for example, clear-cutting). We assisted with the planning process for a proposed experiment to test whether this successional process is amenable to manipulation. First, we tested the magnitude of the influence of two kinds of stochasticity on the prediction of community composition from estimated Markov models of the successional process. The first kind of stochasticity comes from the probabilistic nature of the Markov process, although this is only a factor if individual plant species transitions are modeled (rather than proportions of species in an infinitely large population). The second kind of stochasticity comes from uncertainty about the true underlying Markov model, which can be incorporated if separate estimated transition matrices are available from different experimental plots, for example by the use of an interval, or "set" matrix. We drew conclusions about the appropriate number of plots relative to their size. Second, we examined the relationship between the history length of a successional process available to estimate its transition matrix, and the accuracy of predictions of community composition immediately following the estimation interval. We show how this relationship will differ for homogenous and non-homogenous Markov processes, and present some real-world examples.