Abstract of Time Dependent Solutions For A Cable Model Of An Olfactory Receptor Neuron

Research Report SRR95-008

Time Dependent Solutions For A Cable Model Of An Olfactory Receptor Neuron

Henry C. Tuckwell, Jean-Pierre Rospars, Arthur Vermeulen, and Petr Lansky

Abstract: A mathematical model for an olfactory receptor neuron is investigated. The model, which has been described previously, has three components, including one on which are found the receptor proteins themselves, and others consisting of a passive cable leading to a trigger zone and axon. We pursue here an analytical approach in the important case of weak stimulation, where the input current increases to its asymptotic value. This latter condition means that we can use a Green's function approach in order to obtain accurate representations for the solution for the entire length of the nerve cell. In the case of finite cables the solution is obtained as an infinite series which is shown to converge and can be easily used to find the depolarization at all space and time points of interest. A steady state result is obtained directly by solving the relevant ordinary differential equation. For a semi-infinite cable an explicit expression is found for the voltage as a function of time and space variables involving a single integral. However, the exact expression follows from this for the steady state result. The analytical results obtained are employed to investigate various aspects of olfactory coding at the receptor level.

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