A Two-Pathway Mathematical Model of the LH Response to GnRH that Predicts Self-Priming.

An acute response of LH to a stimulatory pulse of GnRH is modelled as a result of a pathway (Pathway I) that consists of two compartments including a single (rate limiting) intermediate. In addition, a second pathway (Pathway II) was added, consisting of an intermediate transcription factor and subsequently a synthesised protein. Pathway II had a delayed effect on LH release due to the time taken to produce the intermediate protein. The model included synergism between these two pathways, which yielded an augmented response. The model accounts for a number of observations, including GnRH self-priming and the biphasic pattern of LH response. The same model was used to fit the data of the LH response when gonadotrophs responded to the addition of oxytocin in the response with a shoulder on the profile. Pathway I is able to be conceptualised as the basic Ca(2+)-mediated pathway. Pathway II contains features characteristic of the cAMP-mediated pathway. Thus, we have provided an explanation for details of the nature of the profile of LH secretion and additionally enabled incorporation of cAMP in an integrating model. The study investigated the possibility of two interacting pathways being at the basis of both the shoulder on the LH surges and self-priming, and the model illustrates that this appears to be highly likely.

The role of endothelial calcium and nitric oxide in the localisation of atherosclerosis.

A mathematical model of endothelial cell calcium signalling and nitric oxide synthesis under flow conditions is presented. The model is coupled to two important environmental stimuli for endothelial cells: the frictional shear stress exerted on the cell membrane by the blood flow; and the binding of adenosine triphosphate in the bloodstream to cell surface receptors. These stimuli are closely linked to haemodynamic flow conditions and are, in general, spatially varying, allowing the cellular response in different regions of the endothelium to be evaluated. This is used to indicate which areas of the artery wall experience reduced bioavailability of nitric oxide, which is a major factor in the onset of atherosclerosis. The model thus directly addresses the key issue of the causative link, and its underlying biochemical mechanisms, between incidence of atherosclerosis and regions of low wall shear stress (WSS). Model results show that intracellular levels of free calcium and endothelial nitric oxide synthase are lower in endothelial cells adjacent to a region of recirculating flow than in cells adjacent to regions of fully developed arterial flow. This will lead to deficient levels of nitric oxide in the recirculation zone and hence a potentially elevated risk of developing atherosclerotic plaque. This is consistent with the observed spatial correlation between atherosclerosis and regions of disturbed blood flow and low WSS, and provides a mechanism for the localisation of the disease to sites such as arterial bifurcations and bends.

Atherosclerosis and calcium signalling in endothelial cells.

The link between atherosclerosis and regions of disturbed flow and low wall shear stress is now firmly established, but the causal mechanisms underlying the link are not yet understood. It is now recognised that the endothelium is not simply a passive barrier between the blood and the vessel wall, but plays an active role in maintaining vascular homeostasis and participates in the onset of atherosclerosis. Calcium signalling is one of the principal intracellular signalling mechanisms by which endothelial cells (EC) respond to external stimuli, such as fluid shear stress and ligand binding. Previous studies have separately modelled mass transport of chemical species in the bloodstream and calcium dynamics in EC via the inositol trisphosphate (IP(3)) signalling pathway. We review existing models of these two phenomena, before going on to integrate the two components to provide an inclusive new model for the calcium response of the endothelium in an arbitrary vessel geometry. This enables the combined effects of fluid flow and biochemical stimulation on EC to be investigated and is the first time spatially varying, physiological fluid flow-related environmental factors have been combined with intracellular signalling in a mathematical model. Model results show that low endothelial calcium levels in the area of disturbed flow at an arterial widening may be one contributing factor to the onset of vascular disease.

On a cell-growth model for plankton.

The frequency distribution of diatoms (microscopic unicellular alga with silicified cell-walls, found as plankton) is shown to evolve in time as a steady-size distribution with constant shape, scaled by time. This distribution is preserved when the division occurs at a fixed size into two daughter cells of half-size. In cases where the parameters for growth, division frequency, dispersion and mortality are constants, the frequency distributions can be found explicitly and thus provide a benchmark for computations in more complex cases.

Changes in mass and energy transfer between the canopy and the atmosphere: model development and testing with a free-air CO2 enrichment (FACE) experiment.

The rationale for this study is found in the probable higher temperatures and changes in rainfall patterns that are expected in the future as a result of increasing levels of CO2 in the atmosphere. In particular, higher air temperatures may cause an increase in evapotranspiration demand while a reduction in rainfall could increase the severity and duration of drought in arid and semi-arid regions. Representation of the water transfer scheme includes water uptake by roots and the interaction between evapotranspiration and CO2 enrichment. The predicted response of a spring wheat (Triticum aestivum L. cv. Yecora rojo) canopy in terms of energy exchange processes to elevated atmospheric CO2 level was tested against measurements collected at the FACE (Free Air Enrichment Experiment) site in 1994. Simulated and measured canopy conductances were reduced by about 30% under elevated [CO2] under optimum conditions of water supply. Reductions in latent heat fluxes under elevated instead of ambient [CO2] caused reductions in both simulated and measured seasonal water use of 6% under optimum and 2% under suboptimum irrigation. The soil-plant-atmosphere water transfer scheme proposed here offers several advances in the simulation of land surface interactions. First, the stomatal resistance model minimizes assumptions in existing land surface schemes about the effects of interactions among environmental conditions (radiation, temperature, CO2) upon stomatal behavior. These interactions are resolved in the calculation of CO2 in which processes are already well understood.

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.

A Hodgkin-Huxley model exhibiting bursting oscillations.

We investigate bursting behaviour generated in an electrophysiological model of pituitary corticotrophs. The active and silent phases of this mode of bursting are generated by moving between two stable oscillatory solutions. The bursting is indirectly driven by slow modulation of the endoplasmic reticulum Ca2+ concentration. The model exhibits different modes of bursting, and we investigate mode transitions and similar modes of bursting in other Hodgkin-Huxley models. Bifurcation analysis and the use of null-surfaces facilitate a geometric interpretation of the model bursting modes and action potential generation, respectively.