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General models of hypothalamic MNC's

I work, with William Armstrong, on mathematical models of the electrical activity of hypothalamic magnocellular neurosecretory cells (MNCs) of the supraoptic nucleus. These cells are neurones that project from the hypothalamus to the posterior pituitary (or neurohypophysis), where they secrete one of two hormones: oxytocin (OT) or vasopressin (AVP), into the blood from their axonal terminals. Secretion occursvia exocytosis when the terminal is electrically stimulated by an action potential. These peptides are released to counter several physiological stresses:  dehydration  (AVP and OT); haemorrhage (AVP and OT); or to control the physiological processes of parturition (OT) and lactation (OT). The rate and temporal profile of secretion of each hormone are dictated both by the cell's firing rate and by its discharge pattern. These cells are well known to be archetypes both for smooth and for pulsatile hormonal release, and which pattern arises depends upon the prevailing physiological condition.

Both species of cell are morphologically and electrically very similar and their individual action potentials cannot easily be distinguished. Furthermore, when stress is absent, both exhibit similar background firing patterns, which is typically a Poissonian distributed spike train of mean frequency < 1.5Hz.

We have constructed a model for in vitro electrical activity and calcium dynamics of these cells, which is based on a set of Hodgkin-Huxley differential equations. The model's parameters are drawn from in vitro electrophysiology and calcium imaging data and its behaviour has been verified against both in vitro and in vivo experiments. Our model shows that many of the typically observed modulations of the firing pattern are underpinned by a subtle interplay between several different potassium currents. This model also provides the starting point for much of the work outlined below, and is published in the Journal of Computational Neuroscience.

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Phasic bursting in vasopressin cells

Vasopressin (AVP) controls both the concentration of the blood and the blood pressure. It is released in response to either dehydration or haemorrhage, and it acts both as a vasoconstrictor and also upon the kidney to regulate water excretion. AVP cells in the unstimulated rat fire in a slow, irregular discharge pattern (<1.5Hz). However if the animal becomes dehydrated, these cells start to discharge lengthy (>20s), repeating bursts of spikes which are separated by equally lengthy silences.

Using a combination of electrical recording, calcium fluorescence and mathematical modelling we have proposed that bursts are initiated by the calcium mediated inhibition of a resting potassium current (possibly mediated by TASK-1 channels) and terminate when the channel becomes progressively desensitized to calcium. The model predicts the time course of this desensitization, and we proposed that the opioid dynorphin, which is secreted by dense core granule exocytosis from the cell's dendrites and acts as back on kappa-autoreceptors (see figure above), is the messenger for the process.

Since spikes occur on a timescale of milliseconds, while bursts last for many seconds, we may reduce the model to two subsystems, FAST and SLOW, that oscillate on distinct timescales. Using techniques from dynamical systems we can then show that SLOW is equivalent to a Morris-Lecar oscillator, and hence has both excitable and oscillatory modes.

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Online seminar: Excitable bursting in the rat neurohypophysis

The dynamics of dense-core granule exocytosis

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Bursting in Cold Receptors

Mammalian cold receptors are free nerve endings, found in most layers of the skin, that transduce patterns of heat energy into neuronal signals, and exhibit a highly temperature-dependent discharge pattern. At low temperatures they discharge short bursts (< 10 spikes) of action potentials that repeat periodically. As the temperature increases, these bursts become shorter and shorter, until eventually each burst comprises only a single spike, a mode of discharge that is termed beating. If the temperature is increased yet further, then the cell occasionally fails to fire and cycles of the oscillation are skipped. Thus the neuro-physiological evidence supports a simple model that comprises a slow oscillation of the neuronal membrane potential coupled to some source of noise.

Using Floquet theory and a Fokker-Planck analysis, we analyzed a canonical model for thermally active parabolic neurones which exhibits bursting, skipping and stochastic resonance and so is a good model for the activity of these cells. With this analysis we showed that skipping can either be caused by noise-induced trapping or by noise-induced escape over a barrier. Furthermore we could predict how many spikes occur per burst, and at what temperature the transition from bursting to spiking takes place.

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