Quantitative model of NMR chemical shifts of 23Na+ induced by TmDOTP: applications in studies of Na+ transport in human erythrocytes.

The change in the NMR chemical shift of (23)Na(+) induced by the shift reagent TmDOTP was examined under various experimental conditions typical of cells, including changed Na(+), K(+), PO(4)(3-), and Ca(2+) concentrations, pH and temperature. A mathematical model was developed relating these factors to the observed chemical shift change relative to a capillary-sphere reference. This enabled cation concentrations to be deduced quantitatively from experimental chemical shifts, including those observed during biological time courses with cell suspensions containing TmDOTP DOTP, 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrakis (methylenephosphonate) [corrected]. The model was applied to a (23)Na NMR time course in which monensin, a sodium ionophore, was introduced to human erythrocytes, changing the concentration of cations which may bind TmDOTP, and also resulting in cell volume changes. Using the model with experimentally determined conditions, the chemical shift was predicted and closely followed the experimental values over time. In addition to the model, parameter fitting was achieved by calculating the likelihood distribution of parameters, and seeking the maximum likelihood with a Bayesian type of analysis.

Quantitative modelling of sleep dynamics.

Arousal is largely controlled by the ascending arousal system of the hypothalamus and brainstem, which projects to the corticothalamic system responsible for electroencephalographic (EEG) signatures of sleep. Quantitative physiologically based modelling of brainstem dynamics theory is described here, using realistic parameters, and links to EEG are outlined. Verification against a wide range of experimental data is described, including arousal dynamics under normal conditions, sleep deprivation, stimuli, stimulants and jetlag, plus key features of wake and sleep EEGs.

Incorporation of caffeine into a quantitative model of fatigue and sleep.

A recent physiologically based model of human sleep is extended to incorporate the effects of caffeine on sleep-wake timing and fatigue. The model includes the sleep-active neurons of the hypothalamic ventrolateral preoptic area (VLPO), the wake-active monoaminergic brainstem populations (MA), their interactions with cholinergic/orexinergic (ACh/Orx) input to MA, and circadian and homeostatic drives. We model two effects of caffeine on the brain due to competitive antagonism of adenosine (Ad): (i) a reduction in the homeostatic drive and (ii) an increase in cholinergic activity. By comparing the model output to experimental data, constraints are determined on the parameters that describe the action of caffeine on the brain. In accord with experiment, the ranges of these parameters imply significant variability in caffeine sensitivity between individuals, with caffeine's effectiveness in reducing fatigue being highly dependent on an individual's tolerance, and past caffeine and sleep history. Although there are wide individual differences in caffeine sensitivity and thus in parameter values, once the model is calibrated for an individual it can be used to make quantitative predictions for that individual. A number of applications of the model are examined, using exemplar parameter values, including: (i) quantitative estimation of the sleep loss and the delay to sleep onset after taking caffeine for various doses and times; (ii) an analysis of the system's stable states showing that the wake state during sleep deprivation is stabilized after taking caffeine; and (iii) comparing model output successfully to experimental values of subjective fatigue reported in a total sleep deprivation study examining the reduction of fatigue with caffeine. This model provides a framework for quantitatively assessing optimal strategies for using caffeine, on an individual basis, to maintain performance during sleep deprivation.