Emergent decision-making behaviour and rhythm generation in a computational model of the ventromedial nucleus of the hypothalamus.

The ventromedial nucleus of the hypothalamus (VMN) has an important role in diverse behaviours. The common involvement in these of sex steroids, nutritionally-related signals, and emotional inputs from other brain areas, suggests that, at any given time, its output is in one of a discrete number of possible states corresponding to discrete motivational drives. Here we explored how networks of VMN neurons might generate such a decision-making architecture. We began with minimalist assumptions about the intrinsic properties of VMN neurons inferred from electrophysiological recordings of these neurons in rats in vivo, using an integrate-and-fire based model modified to simulate activity-dependent post-spike changes in neuronal excitability. We used a genetic algorithm based method to fit model parameters to the statistical features of spike patterning in each cell. The spike patterns in both recorded cells and model cells were assessed by analysis of interspike interval distributions and of the index of dispersion of firing rate over different binwidths. Simpler patterned cells could be closely matched by single neuron models incorporating a hyperpolarising afterpotential and either a slow afterhyperpolarisation or a depolarising afterpotential, but many others could not. We then constructed network models with the challenge of explaining the more complex patterns. We assumed that neurons of a given type (with heterogeneity introduced by independently random patterns of external input) were mutually interconnected at random by excitatory synaptic connections (with a variable delay and a random chance of failure). Simple network models of one or two cell types were able to explain the more complex patterns. We then explored the information processing features of such networks that might be relevant for a decision-making network. We concluded that rhythm generation (in the slow theta range) and bistability arise as emergent properties of networks of heterogeneous VMN neurons.

The spiking and secretory activity of oxytocin neurones in response to osmotic stimulation: a computational model.

KEY POINTS: A quantitative model of oxytocin neurones that combines a spiking model, a model of stimulus-secretion coupling and a model of plasma clearance of oxytocin was tested. To test the model, a variety of sources of published data were used that relate either the electrical activity of oxytocin cells or the secretion of oxytocin to experimentally induced changes in plasma osmotic pressure. To use these data to test the model, the experimental challenges involved were computationally simulated. The model predictions closely matched the reported outcomes of the different experiments. ABSTRACT: Magnocellular vasopressin and oxytocin neurones in the rat hypothalamus project to the posterior pituitary, where they secrete their products into the bloodstream. In rodents, both vasopressin and oxytocin magnocellular neurones are osmoresponsive, and their increased spiking activity is mainly a consequence of an increased synaptic input from osmoresponsive neurons in regions adjacent to the anterior wall of the third ventricle. Osmotically stimulated vasopressin secretion promotes antidiuresis while oxytocin secretion promotes natriuresis. In this work we tested a previously published computational model of the spiking and secretion activity of oxytocin cells against published evidence of changes in spiking activity and plasma oxytocin concentration in response to different osmotic challenges. We show that integrating this oxytocin model with a simple model of the osmoresponsive inputs to oxytocin cells achieves a strikingly close match to diverse sources of data. Comparing model predictions with published data using bicuculline to block inhibitory GABA inputs supports the conclusion that inhibitory inputs and excitatory inputs are co-activated by osmotic stimuli. Finally, we studied how the gain of osmotically stimulated oxytocin release changes in the presence of a hypovolaemic stimulus, showing that this is best explained by an inhibition of an osmotically regulated inhibitory drive to the magnocellular neurones.

Spike triggered hormone secretion in vasopressin cells; a model investigation of mechanism and heterogeneous population function.

Vasopressin neurons generate distinctive phasic patterned spike activity in response to elevated extracellular osmotic pressure. These spikes are generated in the cell body and are conducted down the axon to the axonal terminals where they trigger Ca²âº entry and subsequent exocytosis of hormone-containing vesicles and secretion of vasopressin. This mechanism is highly non-linear, subject to both frequency facilitation and fatigue, such that the rate of secretion depends on both the rate and patterning of the spike activity. Here we used computational modelling to investigate this relationship and how it shapes the overall response of the neuronal population. We generated a concise single compartment model of the secretion mechanism, fitted to experimentally observed profiles of facilitation and fatigue, and based on representations of the hypothesised underlying mechanisms. These mechanisms include spike broadening, Ca²âº channel inactivation, a Ca²âº sensitive K⁺ current, and releasable and reserve pools of vesicles. We coupled the secretion model to an existing integrate-and-fire based spiking model in order to study the secretion response to increasing synaptic input, and compared phasic and non-phasic spiking models to assess the functional value of the phasic spiking pattern. The secretory response of individual phasic cells is very non-linear, but the response of a heterogeneous population of phasic cells shows a much more linear response to increasing input, matching the linear response we observe experimentally, though in this respect, phasic cells have no apparent advantage over non-phasic cells. Another challenge for the cells is maintaining this linear response during chronic stimulation, and we show that the activity-dependent fatigue mechanism has a potentially useful function in helping to maintain secretion despite depletion of stores. Without this mechanism, secretion in response to a steady stimulus declines as the stored content declines.

Phasic firing in vasopressin cells: understanding its functional significance through computational models.

Vasopressin neurons, responding to input generated by osmotic pressure, use an intrinsic mechanism to shift from slow irregular firing to a distinct phasic pattern, consisting of long bursts and silences lasting tens of seconds. With increased input, bursts lengthen, eventually shifting to continuous firing. The phasic activity remains asynchronous across the cells and is not reflected in the population output signal. Here we have used a computational vasopressin neuron model to investigate the functional significance of the phasic firing pattern. We generated a concise model of the synaptic input driven spike firing mechanism that gives a close quantitative match to vasopressin neuron spike activity recorded in vivo, tested against endogenous activity and experimental interventions. The integrate-and-fire based model provides a simple physiological explanation of the phasic firing mechanism involving an activity-dependent slow depolarising afterpotential (DAP) generated by a calcium-inactivated potassium leak current. This is modulated by the slower, opposing, action of activity-dependent dendritic dynorphin release, which inactivates the DAP, the opposing effects generating successive periods of bursting and silence. Model cells are not spontaneously active, but fire when perturbed by random perturbations mimicking synaptic input. We constructed one population of such phasic neurons, and another population of similar cells but which lacked the ability to fire phasically. We then studied how these two populations differed in the way that they encoded changes in afferent inputs. By comparison with the non-phasic population, the phasic population responds linearly to increases in tonic synaptic input. Non-phasic cells respond to transient elevations in synaptic input in a way that strongly depends on background activity levels, phasic cells in a way that is independent of background levels, and show a similar strong linearization of the response. These findings show large differences in information coding between the populations, and apparent functional advantages of asynchronous phasic firing.

Mathematical modelling of the oxytocin and vasopressin secretory system.

Magnocellular oxytocin and vasopressin neurons of the hypothalamus project to the posterior pituitary where they secrete their peptide hormone signals directly into the bloodstream. Their large anatomically distinct secretory mechanisms provide a uniquely accessible system in which to unite experimental and modelling approaches in the investigation of how input signals and electrophysiological properties of neurons relate to physiological function. We describe how the mechanisms have been translated and assembled into a mathematical model representation that can explain and simulate the complex and highly non-linear stimulus-secretion coupling of these neurons, and how this model has been applied to further understand these systems.

Phasic spiking in vasopressin neurons: How and Why.

The plain title might have been an almost retro sounding grumpy retort, but it has inspired a journey of sorts, and something along the way I hope you won't have come across before. An opinionated exploration of the distinctive phasic spiking patterns of magnocellular vasopressin neurons of the supraoptic and paraventricular nuclei of the hypothalamus. A mostly life essential population of neurons that signal the kidneys to regulate water loss in response to signals that encode plasma volume and osmotic pressure, as well as regulating blood pressure, and possibly metabolism and social behaviour. The viewpoint of a modeller shorn of any explicit maths.

A physiological model of a circannual oscillator.

Recent evidence based on studies in hypothalamo-pituitary disconnected Soay sheep suggests that the generation of circannual rhythms may be local to specific tissues or physiological systems. Now, the authors present a physiological model of a circannual rhythm generator centered in the pituitary gland based on the interaction between melatonin-responsive cells in the pars tuberalis that act to decode photoperiod, and lactotroph cells of the adjacent pars distalis that secrete prolactin. The model produces a self-sustained, circannual rhythm in endocrine output that the authors explore by mathematical modeling. The circannual oscillation requires a delayed negative feedback mechanism. The authors highlight specific features of the pituitary dynamics as a guide to future research on circannual rhythms.

Models in neuroendocrinology.

The neuroendocrine systems of the hypothalamus are critical for survival and reproduction, and are highly conserved throughout vertebrate evolution. Their roles in controlling body metabolism, growth and body composition, stress, electrolyte balance and reproduction have been intensively studied, and have yielded a rich crop of original and challenging insights into neuronal function, insights that circumscribe a vision of the brain that is quite different from conventional views. Despite the diverse physiological roles of pituitary hormones, most are secreted in a pulsatile pattern, but arising through a variety of mechanisms. An important exception is vasopressin which uses bursting neural activity, but produces a graded secretion response to osmotic pressure, a sustained robust linear response constructed from noisy, nonlinear components. Neuroendocrine systems have many features such as multiple temporal scales and nonlinearity that make their underlying mechanisms hard to understand without mathematical modelling. The models presented here cover the wide range of temporal scales involved in these systems, including models of single cell electrical activity and calcium dynamics, receptor signalling, gene expression, coordinated activity of neuronal networks, whole-organism hormone dynamics and feedback loops, and the menstrual cycle. Many interesting theoretical approaches have been applied to these systems, but important problems remain, at the core the question of what is the true advantage of pulsatility.

A Predictive, Quantitative Model of Spiking Activity and Stimulus-Secretion Coupling in Oxytocin Neurons.

Oxytocin neurons of the rat hypothalamus project to the posterior pituitary, where they secrete their products into the bloodstream. The pattern and quantity of that release depends on the afferent inputs to the neurons, on their intrinsic membrane properties, and on nonlinear interactions between spiking activity and exocytosis: A given number of spikes will trigger more secretion when they arrive close together. Here we present a quantitative computational model of oxytocin neurons that can replicate the results of a wide variety of published experiments. The spiking model mimics electrophysiological data of oxytocin cells responding to cholecystokinin (CCK), a peptide produced in the gut after food intake. The secretion model matches results from in vitro experiments on stimulus-secretion coupling in the posterior pituitary. We mimic the plasma clearance of oxytocin with a two-compartment model, replicating the dynamics observed experimentally after infusion and injection of oxytocin. Combining these models allows us to infer, from measurements of oxytocin in plasma, the spiking activity of the oxytocin neurons that produced that secretion. We have tested these inferences with experimental data on oxytocin secretion and spiking activity in response to intravenous injections of CCK. We show how intrinsic mechanisms of the oxytocin neurons determine this relationship: In particular, we show that the presence of an afterhyperpolarization (AHP) in oxytocin neurons dramatically reduces the variability of their spiking activity and even more markedly reduces the variability of oxytocin secretion. The AHP thus acts as a filter, protecting the final product of oxytocin cells from noisy fluctuations.

Spike patterning in oxytocin neurons: Capturing physiological behaviour with Hodgkin-Huxley and integrate-and-fire models.

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.