Date Published: July 6, 2017
Publisher: Public Library of Science
Author(s): Trystan Leng, Gareth Leng, Duncan J. MacGregor, William W Lytton.
Integrate-and-fire (IF) models can provide close matches to the discharge activity of neurons, but do they oversimplify the biophysical properties of the neurons? A single compartment Hodgkin-Huxley (HH) model of the oxytocin neuron has previously been developed, incorporating biophysical measurements of channel properties obtained in vitro. A simpler modified integrate-and-fire model has also been developed, which can match well the characteristic spike patterning of oxytocin neurons as observed in vivo. Here, we extended the HH model to incorporate synaptic input, to enable us to compare spike activity in the model with experimental data obtained in vivo. We refined the HH model parameters to closely match the data, and then matched the same experimental data with a modified IF model, using an evolutionary algorithm to optimise parameter matching. Finally we compared the properties of the modified HH model with those of the IF model to seek an explanation for differences between spike patterning in vitro and in vivo. We show that, with slight modifications, the original HH model, like the IF model, is able to closely match both the interspike interval (ISI) distributions of oxytocin neurons and the observed variability of spike firing rates in vivo and in vitro. This close match of both models to data depends on the presence of a slow activity-dependent hyperpolarisation (AHP); this is represented in both models and the parameters used in the HH model representation match well with optimal parameters of the IF model found by an evolutionary algorithm. The ability of both models to fit data closely also depends on a shorter hyperpolarising after potential (HAP); this is explicitly represented in the IF model, but in the HH model, it emerges from a combination of several components. The critical elements of this combination are identified.
The supraoptic nucleus of the hypothalamus has been a rich source of insight into how the intrinsic properties of neurons are adapted to meet physiological requirements. It contains only neuroendocrine neurons that secrete their peptide products into the circulation from nerve terminals in the posterior pituitary gland. Some of these neurons make vasopressin, which acts at the kidneys and the peripheral vasculature to mediate antidiuresis and to control plasma volume, the rest make oxytocin, which promotes uterine contractions during parturition and mediates milk let-down in response to suckling. However, both oxytocin and vasopressin have additional roles, some mediated by release of oxytocin and vasopressin within the brain, and some by actions at other peripheral targets [1,2]. These two populations display very different discharge characteristics, and extensive studies in vitro have characterised their intrinsic membrane properties [3–7], while studies in vivo have characterised their responses to physiological challenges [1,8]. During suckling in lactating rats, oxytocin neurons discharge in intermittent bursts that give rise to pulses of oxytocin secretion. The same neurons, in response to increases in plasma osmotic pressure, show graded increases in electrical activity  that result in increases in plasma oxytocin that modulate sodium excretion by actions at the heart and kidneys. Oxytocin neurons are osmosensitive: the increases in osmotic pressure result in a graded depolarisation of membrane potential, and, in addition, they receive synaptic input from other osmosensitive neurons in anterior brain regions [10,11].
Supraoptic oxytocin neurons in virgin rats in vitro have a mean (SD) resting potential of −62 (7.2) mV , and spikes are triggered when depolarising current drives the membrane above a threshold of ∼ -50 mV. The spikes (measured from within 5 mV of spike threshold) have a mean (SD) amplitude of 73.2 (7.6) mV and a width at half-maximal amplitude of 1.5 (0.4) ms. The repolarization phase overshoots rest and merges into an HAP, which lasts for up to ∼ 100 ms  with a maximum magnitude of 8.6 (5.7) mV . Trains of spikes evoke an AHP with a peak amplitude of 0.9 (0.3) mV per spike, which decays with a time constant of 520 (567) ms . The AHP is abolished by removing extracellular Ca2+, and is attenuated by exposure to apamin [24–26], which selectively blocks SK-type small conductance K+ channels.
The common advantage of HH models and IF models is their ‘observability’, the ability to relate their parameters to measurable physiological values . This study has shown that a HH model of oxytocin neurons, based on current dynamics and spike waveforms derived from in vitro experiments, with minor modifications and the addition of a simulated random synaptic input, can fit the ISI distribution of spike times and other statistical features of spike patterning recorded in vivo. This allows a direct comparison with an IF model in terms of how well they match functionally relevant data, and enables a better understanding of how the simplified HAP and AHP in the IF model relate to detailed current-based mechanisms.