The Effects of Temperature on the Stability of a Neuronal Oscillator

Anatoly Rinberg, Adam L Taylor and Eve Marder

PLOS Computational Biology, 2013, vol. 9, issue 1, 1-12

Abstract: The crab Cancer borealis undergoes large daily fluctuations in environmental temperature (8–24°C) and must maintain appropriate neural function in the face of this perturbation. In the pyloric circuit of the crab stomatogastric ganglion, we pharmacologically isolated the pacemaker kernel (the AB and PD neurons) and characterized its behavior in response to temperature ramps from 7°C to 31°C. For moderate temperatures, the pacemaker displayed a frequency-temperature curve statistically indistinguishable from that of the intact circuit, and like the intact circuit maintained a constant duty cycle. At high temperatures (above 23°C), a variety of different behaviors were seen: in some preparations the pacemaker increased in frequency, in some it slowed, and in many preparations the pacemaker stopped oscillating (“crashed”). Furthermore, these crashes seemed to fall into two qualitatively different classes. Additionally, the animal-to-animal variability in frequency increased at high temperatures. We used a series of Morris-Lecar mathematical models to gain insight into these phenomena. The biophysical components of the final model have temperature sensitivities similar to those found in nature, and can crash via two qualitatively different mechanisms that resemble those observed experimentally. The crash type is determined by the precise parameters of the model at the reference temperature, 11°C, which could explain why some preparations seem to crash in one way and some in another. Furthermore, even models with very similar behavior at the reference temperature diverge greatly at high temperatures, resembling the experimental observations. Author Summary: The nervous systems of cold-blooded animals must maintain essential function despite fluctuations in environmental temperature. We studied the pyloric rhythm of the crab, Cancer borealis. The pyloric rhythm is important for the animal's feeding behavior, and previous work has shown that relative timing, or phase, of the neurons in the pyloric circuit is temperature invariant over a range of physiologically realistic temperatures (7 to 23°C), although the frequency of the rhythm increases. At higher temperatures, the rhythm often becomes disorganized or stops. In this paper we present experimental work on the isolated pacemaker of the pyloric rhythm together with a computational model that explores the loss of stability of the pacemaker as a function of temperature. Experimentally, we found that the isolated pacemaker responds to temperature similarly to the intact network, and maintains constant duty cycle over large temperature ranges. At high temperatures, about half of the pacemakers stop oscillating, reminiscent of certain mathematical bifurcations. We varied the temperature dependence and conductance densities of a simple model oscillator, and characterized its bifurcations as a function of temperature. We found that particular temperature-dependent relationships must be maintained to provide robust temperature performance of oscillators with variable underlying conductances.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcbi00:1002857

DOI: 10.1371/journal.pcbi.1002857

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