Approximating the phase response curves of square wave bursting neurons
© Agbanusi et al; licensee BioMed Central Ltd. 2008
Published: 11 July 2008
The phase response curve (PRC) measures the response of an oscillator to the timing of stimulus and here we construct and study the PRC of the bursting PD neuron of the STG in the crab, Cancer borealis. For bursting neurons whose oscillation is composed of an active phase of fast spiking activity and a silent phase, the response is determined by the change in timing of the start of the active phase after the stimulus. PRCs prove useful, when trying to predict the output of neural networks. We compare experimental results with numerical simulations of a Morris-Lecar type bursting model. We see, for instance, that in both cases, the PRCs saturate with large amplitude perturbations. Our new method is to reconstruct the PRC of the active phase by measuring the changes in the timings of the spikes in the active phase when the stimulus occurs while ignoring the effect of the stimulus in the silent phase. This approach should prove insightful in describing more intricate synchronization patterns in coupled bursting cells. We also use ideas from geometric singular perturbation theory to shed some light on the saturation phenomenon.
To a first order approximation, we have shown that one can predict the PRC by assuming linear spike shifting in the active phase. We also show the importance of phenomena such as spike addition, deletion and burst truncation in determining the phase response properties of the oscillator.
This research was supported by a UBM grant.
This article is published under license to BioMed Central Ltd.