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A study of synchrony and phaselocking through excitatory/inhibitory coupling

University of British Columbia

This paper is an investigation of the possible behaviours that can arise when oscillators are coupled by excitatory / inhibitory coupling. In the case of two oscillators, this means that the action of the first oscillator inhibits the second oscillator, while the action of the second oscillator activates the first oscillator. Here the first oscillator would be called Vi while the second oscillator would be denoted Ve. This investigation is to clarify the interaction of two oscillators found to operate in a pituitary cell. Within the pituitary cell there is a voltage oscillator that is determined by the flow of currents across the plasma membrane, and a calcium oscillator which measures the change in calcium concentration due to the release of calcium from internal stores. Experimental work has demonstrated that these oscillators are coupled and the voltage oscillator activates the calcium oscillator while the calcium oscillator inhibits the action of the voltage oscillator. Realistic models of pituitary cells are quite complicated and difficult to understand. In order to study this coupling in more detail we can make use of simplified models coupled with excitatory / inhibitory synaptic currents. For this investigation, we will be using the simple models given by the Connor model for type I oscillators and the Morris-Lecar model for type II oscillators. The oscillators are coupled by synaptic currents which can be either excitatory or inhibitory. The synaptic currents have many parameters that influence how the oscillators interact with each other. By varying these parameters, we will gain insight into how oscillators coupled in this manner behave. This will be accomplished by using computer simulations and data analysis. In general we find that oscillators that interact through excitatory / inhibitory coupling can exhibit many different and interesting behaviours including harmonic and asynchronous phase-locking, suppression of one or both oscillators and drifting. Of particular interest is the case of drifting, where the oscillators fire at the same time only after a long period of time and the time between action potentials can vary in both oscillators. This drifting behaviour could help to explain why voltage and calcium oscillators operate on a time scale of milliseconds and seconds respectively, while hormone release occurs on a time scale of minutes to hours.

Thesis/Dissertation

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2009-07-06

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http://hdl.handle.net/2429/10207

Mathematics

University of British Columbia

UBCV

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