A new method of spike modelling and interval analysis.

Here we develop a new model of spike firing, based on the leaky integrate and fire model, modified to simulate afterpotentials. We also develop new analysis techniques, applying these to recorded and model generated data in order to make a comparative analysis and develop the model as a hypothesis for the functional components of the neuron. The model is based in this first instance on hypothalamic oxytocin neurons. We demonstrate how model parameters and cell properties relate to features observed in inter-spike intervals histograms, and the limits of these in being able to detect patterning features in spike recordings. A new technique, spike train analysis, is able to detect previously unobserved patterning, showing a dependence of spike intervals on previous firing activity. This effect is reproduced in the model by adding the small amplitude but long lasting after hyper-polarising potential (AHP). A fit measure based on log likelihood is used to compare model generated data to recorded spike intervals, taking account of interval dependence on previous activity. This measure is used with the simplex multiple parameter search algorithm to develop an automated method for fitting the model to recorded data.

Oxytocin Neurones: Intrinsic Mechanisms Governing the Regularity of Spiking Activity.

Oxytocin neurones of the rat supraoptic nucleus are osmoresponsive and, with all other things being equal, they fire at a mean rate that is proportional to the plasma sodium concentration. However, individual spike times are governed by highly stochastic events, namely the random occurrences of excitatory synaptic inputs, the probability of which is increased by increasing extracellular osmotic pressure. Accordingly, interspike intervals (ISIs) are very irregular. In the present study, we show, by statistical analyses of firing patterns in oxytocin neurones, that the mean firing rate as measured in bins of a few seconds is more regular than expected from the variability of ISIs. This is consistent with an intrinsic activity-dependent negative-feedback mechanism. To test this, we compared observed neuronal firing patterns with firing patterns generated by a leaky integrate-and-fire model neurone, modified to exhibit activity-dependent mechanisms known to be present in oxytocin neurones. The presence of a prolonged afterhyperpolarisation (AHP) was critical for the ability to mimic the observed regularisation of mean firing rate, although we also had to add a depolarising afterpotential (DAP; sometimes called an afterdepolarisation) to the model to match the observed ISI distributions. We tested this model by comparing its behaviour with the behaviour of oxytocin neurones exposed to apamin, a blocker of the medium AHP. Good fits indicate that the medium AHP actively contributes to the firing patterns of oxytocin neurones during non-bursting activity, and that oxytocin neurones generally express a DAP, even though this is usually masked by superposition of a larger AHP.

Modelling the hypothalamic control of growth hormone secretion.

Here, we construct a mathematical model of the hypothalamic systems that control the secretion of growth hormone (GH). The work extends a recent model of the pituitary GH system, adding representations of the hypothalamic GH-releasing hormone (GHRH) and somatostatin neurones, each modelled as a single synchronised unit. An unpatterned stochastic input drives the GHRH neurones generating pulses of GHRH release that trigger GH pulses. Delayed feedback from GH results in increased somatostatin release, which inhibits both GH secretion and GHRH release, producing an overall pattern of 3-h pulses of GH secretion that is very similar to the secretory profile observed in male rats. Rather than directly stimulating somatostatin release, GH feedback triggers a priming effect, increasing releasable stores of somatostatin. Varying this priming effect to reduce the effect of GH can reproduce the less pulsatile form of GH release observed in the female rat. The model behaviour is tested by comparison with experimental observations with a range of different experimental protocols involving GHRH injections and somatostatin and GH infusion.

Chemoprevention of colon cancer carcinogenesis by balsalazide: inhibition of azoxymethane-induced aberrant crypt formation in the rat colon and intestinal tumor formation in the B6-Min/+ mouse.

Non-steroidal anti-inflammatory drugs (NSAIDs) including aspirin have been shown to suppress colon carcinogenesis and in some cases reduce the size of colorectal polyps. Balsalazide disodium (BSZ) is a colon-specific prodrug of the salicylate, 5-aminosalicylic acid. The aim of the present study was to test the chemopreventive activity of BSZ in two established animal models of colon tumorigenesis, azoxymethane-induced aberrant crypt formation in the rat and intestinal tumor formation in the B6-Min/+ mouse. Aberrant crypt foci (ACF) were induced in Fischer 344 rats via 2 subcutaneous injections of azoxymethane (20 mg/kg). BSZ was supplied in the drinking water for 8 weeks and ACF quantitated. B6-Min/+ mice were treated from 55 days of age for 90 days and intestinal tumors scored for number, size and location. BSZ treatment of AOM-injected rats reduced ACF formation in a dose-dependent manner by 60% with the greatest effect observed on ACF with 4 or more crypts. In B6-Min/+ mice a dose-dependent reduction of intestinal tumor number was observed which reached 80% in the distal small intestine and colon. A preliminary mechanistic study in cultured human colon cancer cells showed that both BSZ and 5-ASA inhibited colon cancer cell proliferation in vitro. However, 5-ASA but not BSZ produced changes consistent with the induction of apoptosis. BSZ produces a dose-dependent chemopreventive effect on colon carcinogenesis. A possible mechanism is consistent with the inhibition of cellular proliferation and the induction of apoptosis.

Information coding in vasopressin neurons--the role of asynchronous bistable burst firing.

The task of the vasopressin system is homeostasis, a type of process which is fundamental to the brain's regulation of the body, exists in many different systems, and is vital to health and survival. Many illnesses are related to the dysfunction of homeostatic systems, including high blood pressure, obesity and diabetes. Beyond the vasopressin system's own importance, in regulating osmotic pressure, it presents an accessible model where we can learn how the features of homeostatic systems generally relate to their function, and potentially develop treatments. The vasopressin system is an important model system in neuroscience because it presents an accessible system in which to investigate the function and importance of, for example, dendritic release and burst firing, both of which are found in many systems of the brain. We have only recently begun to understand the contribution of dendritic release to neuronal function and information processing. Burst firing has most commonly been associated with rhythm generation; in this system it clearly plays a different role, still to be understood fully.

Mathematical modelling in neuroendocrinology.

In neuroendocrinology, mathematical modelling is about formalising our understanding of the behaviour of the complex biological systems with which we deal. Formulating our explanations mathematically ensures their logical consistency, and makes them open to structured analysis; it is a stringent test of their intellectual coherence. In addition, however, modellers are seeking to extend our understanding in new ways, by seeking novel, simple explanations for complex behaviour. Here we discuss some styles of modelling as they have been applied to neuroendocrine systems, and discuss some of their strengths and limitations.