A model of magnesium metabolism in young sheep: transactions between plasma, cerebrospinal fluid and bone.

An extension of the previously proposed model of Mg metabolism (Robson et al. 1997) has been developed to consider the transactions of Mg that are associated with cerebrospinal fluid (CSF) and bone. The representation of the CSF as a single MG compartment with uptake from the plasma described by Michaelis-Menten kinetics gives very good agreement with published experiments. Analysis of the available information on resorption of Mg from adult bone indicated that this process makes a negligible contribution to Mg homeostasis and can be omitted from the model.

CRH-induced electrical activity and calcium signalling in pituitary corticotrophs.

Pituitary corticotroph cells generate repetitive action potentials and associated Ca2+ transients in response to the agonist corticotropin releasing hormone (CRH). There is indirect evidence suggesting that the agonist, by way of complex intracellular mechanisms, modulates the voltage sensitivity of the L-type Ca2+ channels embedded in the plasma membrane. We have previously constructed a Hodgkin-Huxley-type model of this process, which indicated that an increase in the L-type Ca2+ current is sufficient to generate repetitive action potentials (LeBeau et al. (1997). Biophys. J.73, 1263-1275). CRH is also believed to inhibit an inwardly rectifying K+ current. In this paper, we have found that a CRH-induced inhibition of the inwardly rectifying K+ current increases the model action potential firing frequency, [Ca2+]i transients and membrane excitability. This dual modulatory action of CRH on inward rectifier and voltage-gated Ca2+ channels better describes the observed CRH-induced effects. This structural alteration to the model along with parameter changes bring the model firing frequency in line with experimental data. We also show that the model exhibits experimentally observed bursting behaviour, where the depolarization spike is followed by small oscillations in the membrane potential.

Analysis of a reduced model of corticotroph action potentials.

We have previously described a model for corticotroph plasma membrane electrophysiology [LeBeau et al. (1997). Biophysical Journal 73, 1263-1275]. The model is a Hodgkin-Huxley-like formalism consisting of six coupled ordinary differential equations. Analysis of this model showed that Ca2+ action potentials could be induced by an increase in the L-type voltage-sensitive Ca2+ current. Thus we have demonstrated a putative causal link between an increase in the corticotroph Ca2+ current and action potential generation. We report here the reduction of the model to one with three equations, the behaviour of which was found to correspond well with that of the full model. The reduced model was then subjected to fast-slow subsystem analysis, which revealed the mechanistic interaction between the membrane potential and intracellular Ca2+ concentration that underlies action potential generation. Insights obtained from this analysis were used to investigate experimentally observed aspects of corticotroph electrophysiology such as spontaneous electrical activity, bursting action potentials, and observations from anode break excitation experiments.

A simulation model for the spread of bovine tuberculosis within New Zealand cattle herds.

Bovine tuberculosis, caused by Mycobacterium bovis, presents a major problem to New Zealand agriculture because of the risk that it poses to export-market access. New Zealand research has focused largely on the epidemiology of the disease in wildlife reservoirs, and relatively little is known about the dynamics of the disease in cattle. This study, therefore, investigates bovine tuberculosis (Tb) dynamics within cattle herds, by construction and application of a simple simulation model of disease transmission. The model was designed firstly to estimate rates of disease transmission within herds, and secondly to identify likely consequences of changes in herd Tb-testing policies. Both deterministic and stochastic versions of the model were used to achieve these aims. The model suggests that within-herd Tb transmission does occur and contributes to the reactor rates observed under annual herd testing regimens. The mass-action disease transmission coefficient (proportion of susceptible animals infected per unit time per infectious animal, i.e. not per diseased animal or per reactor), appears to be in the order of 2.7 x 10(-5) per cow per day for a typical herd of around 200 animals, resulting in a contact rate (number of potentially infectious contacts made per infectious cow per day) of about 0.0073. These are average estimates for both beef and dairy herds. Model results suggest that improving the sensitivity of the test used to diagnose bovine Tb would improve control in areas where wildlife reservoirs are absent but have little effect where they are present. Reducing the time between tests of herds on Tb-induced movement control from the current 6 months to 2 or 3 months reduces the average time a herd spends on movement control and hence national Tb prevalence. In the presence of wildlife reservoirs of infection, both the total number of tests and total reactors per unit time increase, but the extent depends on the level of external infection. In all scenarios examined, involving thousands of model runs in total, infection was invariably absent from the modelled herd by the time it was considered clear of Tb based on testing results. This suggests that the caudal fold test is a realistic measure of herd Tb status and that Tb is unlikely to persist in herds under current testing practices in the absence of anergic cattle or an external source of infection. Specificity of the caudal-fold test as used in practice was estimated to be greater than 99%.

Generation of action potentials in a mathematical model of corticotrophs.

Corticotropin-releasing hormone (CRH) is an important regulator of adrenocorticotropin (ACTH) secretion from pituitary corticotroph cells. The intracellular signaling system that underlies this process involves modulation of voltage-sensitive Ca2+ channel activity, which leads to the generation of Ca2+ action potentials and influx of Ca2+. However, the mechanisms by which Ca2+ channel activity is modulated in corticotrophs are not currently known. We investigated this process in a Hodgkin-Huxley-type mathematical model of corticotroph plasma membrane electrical responses. We found that an increase in the L-type Ca2+ current was sufficient to generate action potentials from a previously resting state of the model. The increase in the L-type current could be elicited by either a shift in the voltage dependence of the current toward more negative potentials, or by an increase in the conductance of the current. Although either of these mechanisms is potentially responsible for the generation of action potentials, previous experimental evidence favors the former mechanism, with the magnitude of the shift required being consistent with the experimental findings. The model also shows that the T-type Ca2+ current plays a role in setting the excitability of the plasma membrane, but does not appear to contribute in a dynamic manner to action potential generation. Inhibition of a K+ conductance that is active at rest also affects the excitability of the plasma membrane.

A model of magnesium metabolism in young sheep. Magnesium absorption and excretion.

A model of Mg metabolism in sheep is proposed. It is based on standard Michaelis-Menten enzyme kinetics to describe the transport of Mg across the rumen wall and passive diffusion to describe the absorption of Mg in the hindgut. Factors known to have an effect on Mg metabolism in farm animals, namely the concentrations of K and Mg in the diet, and the physico-chemical conditions within the rumen as determined by the type of diet, are incorporated into the model. Consideration of the rumen as the only site of Mg absorption provided an inadequate mechanistic description of Mg metabolism in sheep. To ensure compatibility between predicted Mg absorption and recent independent data sets for Mg balances, it was necessary to include in the model aspects of Mg absorption that operate in the hindgut. The results from this model suggest that there is a need for a series of experiments to determine the important aspects of Mg transport in the hindgut of sheep. Mechanisms of homeostasis are discussed.

Effect of ileal infusion of volatile fatty acids on feed intake and urinary magnesium excretion in sheep.

Five 2-year-old female sheep fitted with cannulae in the terminal ileum and proximal colon were infused, intra-ilealy during a 24 h period, with volatile fatty acids (VFA) (ratio of acetic:propionic:butyric acid, 0.80:0.15:0.05) at rate of 0, 220, 440, 660 or 880 mmol/day in 21 deionized water. Daily feed intake was progressively depressed by VFA and reached 87 +/- 4.7% (S.E.M.) at the highest rate of infusion. Colonic digesta pH decreased by 2.1 +/- 0.48 units and Mg solubility increased from 21 +/- 2.6 to 52 +/- 1.2% 16 h after the start at the highest rate of VFA infusion. Urinary Mg excretion increased during the first 4 h of infusion on all treatments but the increase was not sustained. The results are discussed in the context of limited knowledge of the importance of the large intestine in intake regulation and Mg absorption.