Computational models of single neurons that realistically reflect intrinsic membrane properties can be extremely complex, and hence building large-scale realistic models of neuronal networks is computationally intense. A typical neuron may make 10,000 synaptic contacts with other neurons, and receive a similar number of inputs. Each neuron expresses a large number of channels that contribute to its membrane excitability - including several different classes of Ca2+, K+ and Na+ channels, and each neuronal phenotype differs in its exact composition of membrane channels. Neurons also differ from each other morphologically, in the distribution of channel types in different cellular compartments, and in intracellular properties that influence channel function. A model of a single neuron incorporating all these factors will have a very large number of parameters that must be estimated with reasonable precision from experimental observations, but many of which must be guessed for particular cell types, as the detailed information is not available. Moreover, experimental observations of biophysical parameters are typically made in vitro in conditions that are different from in vivo conditions. The relative scarcity of afferent input in in vitro preparations must always be taken into account, but beyond this, biophysical measurements often require interventions that fundamentally disturb cell properties. For example, measurements of membrane potential often derive from patch-clamp recordings, which may involve dialysis of the neuronal cytoplasm, altering the composition of the intracellular fluid, changing ion gradients and diluting second messenger systems. Measurements of intracellular Ca2+ involve introducing fluorophores into the cell that effectively function as additional Ca2+ buffers. Thus measurements of many variables require consideration of the context in which they are measured.
How many neurons must be included in a realistic network model is far from clear. The human brain is commonly estimated to contain about 2 x 1010 neurons, but a rat gets by with perhaps 107 neurons; the major source of this discrepancy is of course in the size of the neocortex. The neocortex, however, is one of the parts of the brain about which we understand least, substantially because the functions that we think it is principally involved in are, in general, not very amenable to reductionist experimental testing at the single cell level. In the rat brain, prob ably around 106 neurons are in the hypothalamus, and this region controls a wide diversity of clearly definable functions that are much more amenable to experimental investigation. Different neuronal groups in the hypothalamus control the release of different hormones from the pituitary gland - oxytocin; vasopressin; prolactin; growth hormone; the gonadotrophic hormones; adrenocorticotrophic hormone (that in turn controls steroid secretion from the adrenal glands); thyroid stimulating hormone (that controls the functions of the thyroid gland); and melanocyte-stimulating hormone. The hypothalamus also controls thirst, feeding behavior (including specific appetites such as sodium appetite), body composition, blood pressure, thermoregulation, and much instinctive or reflex behavior including male and female sexual behavior and maternal behavior. These functions involve highly specialised cells with specific properties; cells for instance that have receptors or intrinsic properties that enable them to respond to glucose concentration, or the osmotic pressure of extracellular fluid, or to detect specific blood-borne signals released from peripheral tissues, such as leptin from fat cells, angiotensin from the kidney, and ghrelin from the stomach. Many of these cells in turn signal to other neurons using distinct chemical messengers: neurotransmitters, neuromodulators and neurohormones but also other types of signalling molecule, that are transduced by specific receptors that can occur in multiple forms even for one given signalling molecule.
Estimating the number of distinguishable neuronal phenotypes in the rat hypothalamus is imprecise, but there seem likely to be up to 1,000, each of which may be represented by about 1,000 to 10,000 individual neurons. This may seem a high estimate of diversity, but let us consider. The ventro-rostral extent of the hypothalamus is bounded by the organum vasculosum of the lamina terminalis (OVLT). This region is highly specialised in lacking a blood-brain barrier; how many cell types it contains we do not know for sure, but they include a highly specialised population of osmoreceptive neurons . Another area lacking a blood-brain barrier marks the dorso-rostral extent of the hypothalamus - this is the subfornical organ and it contains amongst its neurons (there seem to be at least six types) a population of specialised angiotensin- processing neurons. Between these, the preoptic region of the hypothalamus contains several identified nuclei and many different neuronal populations; one small but interesting population comprises about 700 luteinising-hormone releasing hormone (LHRH) neurons; these are remarkable cells, they are born in the nasal placode and migrate into the brain late in development, and are essential for controlling pituitary gonadotrophic secretion and thereby are essential for sper-matogenesis in males and ovarian function in females . Though very scattered throughout the preoptic area they nonetheless discharge bursts of electrical activity in synchrony to elicit pulsatile secretion of gonadotrophic hormones from the pituitary. Most of these project to the median eminence, the site of blood vessels that enter the pituitary, but some LHRH neurons project to the OVLT - why, we do not know. The preoptic region also includes a sexually dimorphic nucleus larger in males than in females. In the midline periventricular nucleus are neurosecretory somatostatin neurons that provide inhibitory regulation of growth hormone secretion, alongside growth-hormone releasing-hormone neurons of the arcuate nucleus. Caudal to the periventricular nucleus is the paraventricular nucleus; this contains thyrotropin-releasing hormone neurons that indirectly regulate the thyroid gland; corticotrophin-releasing hormone neurons that indirectly control the adrenal gland, magnocellular vasopressin neurons that control the kidney and magnocellular oxytocin neurons that are responsible for controlling parturition and lactation; in addition, smaller, centrally projecting oxytocin neurons regulate gastric function, and centrally projecting vasopressin neurons that regulate body temperature and blood pressure, some of which project into the spinal cord (as do some oxytocin neurons, a subpopulation that seems to be involved in penile erection). Below this, the suprachiasmatic nucleus is the body's principal circadian pacemaker; one population of neurons here makes vasoactive intestinal peptide, another makes vasopressin; these cells are governed by clock genes that confer 24-h cyclicity on their behavior. Behind the suprachiasmatic nucleus is the arcuate nucleus, that in addition to growth-hormone releasing-hormone neurons contains leptin-sensitive neuropeptide Y neurons that regulate feeding, dopamine neurons that regulate the secretion of prolactin, opioid (j3-endorphin) neurons that impact on many neuronal systems through extensive central projections, and a large population of centrally projecting somato-statin neurons of unknown function. Above this, the ventromedial nucleus contains specialised glucoreceptive neurons, and alongside it the lateral hypothalamus contains orexin neurons; orexin is linked to sleep and wakefulness, and orexin knock-out results in narcolepsy.
We have not gone far in the hypothalamus yet, and we have described only some of the best-known populations, and neglected subpopulations of interneurons and many distinctive subnuclei. In addition, the individual cells vary even within a given population: these homogeneous populations are far from clones. Moreover, individuals in one population interact to differing extents with individuals of many other populations, and these interactions differ from cell to cell even within a population.
The populations are not fully interconnected but neither are they as separable as we would like. Take for instance the magnocellular oxytocin neurons of the hypothalamus-and we probably know as much or more about these as about any cells in the brain (see ). These are simple neurons in many respects; there are about 3,000 of them in the rat brain, and each has a single axon that projects to the neural lobe of the pituitary gland. Oxytocin, released from the nerve endings in the pituitary, controls milk let-down in response to suckling, and it controls the progress of parturition by its actions on the uterus. But in the rat, oxytocin also controls the excretion of sodium at the kidney. Moreover, centrally released oxytocin is involved in maternal behavior, sexual behavior, and affiliative behaviors generally, and stress responsiveness, and the magnocellular oxytocin system is involved in these behaviors through secretion of oxytocin from its dendrites rather than from classical nerve endings. Dendritic secretion unfortunately does not parallel secretion from axonal endings - the mechanisms underlying dendritic secretion differ in important ways from those that govern axonal secretion. The diversity of roles played by oxytocin shows both that the oxytocin neurons receive very functionally diverse inputs, and also that they influence many other neuronal populations, including some to which they are not synaptically connected, even indirectly. It would be dangerous to think that oxytocin neurons are exceptionally complicated, just because we know more about them than other neurons; in fact, from what we do know of other neurons, oxytocin neurons are, if anything, rather simple.
Thus models of any function or part of the brain must take due account of the diversity of neuronal phenotypes. In particular, models that seek to understand information processing must take account of the diversity of electrophysiological phenotypes exhibited within interconnected populations. The number of distinct electrophysio-logical phenotypes may be less than the number of chemically definable phenotypes alluded to, but the degree of difference between phenotypes can be striking. For example, magnocellular vasopressin neurons discharge spikes in a distinctive phasic pattern, alternating between periods of silence and periods of stable spike discharge, and these cells function as true bistable oscillators. Other cells, such as those in the suprachiasmatic nucleus, exhibit highly regular discharge activity, whereas the spontaneous activity of oxytocin neurons appears quasi-random. Other cells display intrinsically oscillatory discharge activity, or display a propensity to discharge in brief rapidly adapting bursts. Each of these radically different electrophysiolog-ical phenotypes has significant consequences for information processing within the networks of which they are a part (see ).
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