Max Puckeridge

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 caffeines effectiveness in reducing fatigue being highly dependent on an individuals 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 systems 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.

Transmembrane exchange of hyperpolarized 13C-urea in human erythrocytes: subminute timescale kinetic analysis.

The rate of exchange of urea across the membranes of human erythrocytes (red blood cells) was quantified on the 1-s to 2-min timescale. (13)C-urea was hyperpolarized and subjected to rapid dissolution and the previously reported (partial) resolution of (13)C NMR resonances from the molecules inside and outside red blood cells in suspensions was observed. This enabled a stopped-flow type of experiment to measure the (initially) zero-trans transport of urea with sequential single-pulse (13)C NMR spectra, every second for up to ~2 min. Data were analyzed using Bayesian reasoning and a Markov chain Monte Carlo method with a set of simultaneous nonlinear differential equations that described nuclear magnetic relaxation combined with transmembrane exchange. Our results contribute to quantitative understanding of urea-exchange kinetics in the whole body; and the methodological approach is likely to be applicable to other cellular systems and tissues in vivo.

Stoichiometric Relationship between Na+ Ions Transported and Glucose Consumed in Human Erythrocytes: Bayesian Analysis of 23Na and 13C NMR Time Course Data

We examined the response of Na(+),K(+)-ATPase (NKA) to monensin, a Na(+) ionophore, with and without ouabain, an NKA inhibitor, in suspensions of human erythrocytes (red blood cells). A combination of (13)C and (23)Na NMR methods allowed the recording of intra- and extracellular Na(+), and (13)C-labeled glucose time courses. The net influx of Na(+) and the consumption of glucose were measured with and without NKA inhibited by ouabain. A Bayesian analysis was used to determine probability distributions of the parameter values of a minimalist mathematical model of the kinetics involved, and then used to infer the rates of Na(+) transported and glucose consumed. It was estimated that the numerical relationship between the number of Na(+) ions transported by NKA per molecule of glucose consumed by a red blood cell was close to the ratio 6.0:1.0, agreeing with theoretical prediction.

Simultaneous estimation of T1 and the flip angle in hyperpolarized NMR experiments using acquisition at non-regular time intervals

In NMR spectroscopy of the liquid state T(1) is typically measured using an inversion recovery pulse sequence; but with hyperpolarized spins use is made of a sequence of multiple small radiofrequency (RF) induced nutations, α. Depending on the values of α and τ, the time interval between the pulses, the estimate of T(1) can be artifactually smaller than the real value; so without knowing the value of α the estimate of T(1) can be incorrect. Thus, we propose a method that involves a series of pulses with timing governed by a geometric sequence (or in general, any mathematically specified non-uniformly spaced sequence). This approach enables the simultaneous estimation of both the intrinsic T(1) value and α. The method was successfully applied to obtain T(1)=(44.9 ± 0.3)s and α=(4.0 ± 0.2)° (n=3) for a sample of hyperpolarized (13)C-urea in solution, matching with the inversion recovery pulse sequence estimate of T(1)=44 ± 2s using non-hyperpolarized (13)C-urea in solution.

Quantum confinement effects in gallium nitride nanostructures: ab initio investigations

We present ab initio density functional investigations of the atomic and electronic structure of gallium nitride nanodots and nanowires. With increasing diameter, the average Ga-N bond length in the nanostructures increases, as does the relative stability (heat of formation), approaching the values for bulk GaN. As the diameter decreases, the band gap increases, with the variation for the nanodots greater than that for the nanowires, in qualitative accordance with expectations based on simple geometrical quantum confinement considerations. Interestingly, in contrast to nanowires, the lowest unoccupied states of the nanodots exhibit an extended delocalized (Ga-derived) character, weighted in the centre of the nanodot.

NMR of (133)Cs(+) in stretched hydrogels: One-dimensional, z- and NOESY spectra, and probing the ion's environment in erythrocytes.

(133)Cs nuclear magnetic resonance (NMR) spectroscopy was conducted on (133)Cs(+) in gelatin hydrogels that were either relaxed or stretched. Stretching generated a septet from this spin-7/2 nucleus, and its nuclear magnetic relaxation was studied via z-spectra, and two-dimensional nuclear Overhauser (NOESY) spectroscopy. Various spectral features were well simulated by using Mathematica and the software package SpinDynamica. Spectra of CsCl in suspensions of human erythrocytes embedded in gelatin gel showed separation of the resonances from the cation inside and outside the cells. Upon stretching the sample, the extracellular (133)Cs(+) signal split into a septet, while the intracellular peak was unchanged, revealing different alignment/ordering properties of the environment inside and around the cells. Differential interference contrast light microscopy confirmed that the cells were stretched when the overall sample was elongated. Analysis of the various spectral features of (133)Cs(+) reported here opens up applications of this K(+) congener for studies of cation-handling by metabolically-active cells and tissues in aligned states.

Membrane flickering of the human erythrocyte: physical and chemical effectors

Recent studies suggest a link between adenosine triphosphate (ATP) concentration and the amplitude of cell membrane flickering (CMF) in the human erythrocyte (red blood cell; RBC). Potentially, the origin of this phenomenon and the unique discocyte shape could be active processes that account for some of the ATP turnover in the RBC. Active flickering could depend on several factors, including pH, osmolality, enzymatic rates and metabolic fluxes. In the present work, we applied the data analysis described in the previous article to study time courses of flickering RBCs acquired using differential interference contrast light microscopy in the presence of selected effectors. We also recorded images of air bubbles in aqueous detergent solutions and oil droplets in water, both of which showed rapid fluctuations in image intensity, the former showing the same type of spectral envelope (relative frequency composition) to RBCs. We conclude that CMF is not directly an active process, but that ATP affects the elastic properties of the membrane that flickers in response to molecular bombardment in a manner that is described mathematically by a constrained random walk.

7Li+ NMR quadrupolar splitting in stretched hydrogels: developments in relaxation time estimation from z-spectra

7Li NMR z‐spectra were recorded from the cation constituted in gelatin gels that were held stretched. The system has been studied previously, but we revisited the disparity that was noted between estimates of some of the relaxation times of spin‐states of various ranks and orders made using a global data‐fitting strategy and estimates made from data acquired by using multiple‐quantum‐filter pulse sequences. The global data fitting was performed with a probability approach along with the Markov chain Monte Carlo (MCMC) method applied to z‐spectra from 7Li+ dissolved in 1H2O using more refined experimental methods than hitherto. We also present a more extensive explanation of the MCMC method as it applies in the present NMR context. We achieved much closer agreement between the estimates of relaxation times made by using the two methods of analysis and attribute the previous discrepancies to spectral drift and z‐spectrum asymmetry. Copyright

Membrane flickering of the human erythrocyte: constrained random walk used with Bayesian analysis

The involvement of adenosine triphosphate (ATP) in erythrocyte (red blood cell; RBC) membrane flickering is of particular interest, because ATP turnover in the cell as a whole is not yet fully accounted for. We sought the origins of flickering by deriving a mathematical model of it, on the basis of the idea of thermally driven collisions of small molecules with the membrane, which responds like an over-damped spring. The model gave simulated responses that were similar to a constrained random walk and had the same frequency–spectral characteristics of membrane displacement as those recorded from RBCs by use of differential interference contrast light microscopy. Bayesian analysis was used as the basis for determination, from experimental results, of the values of the parameters in the model. The analysis was used in the accompanying article in which we investigated the response of membrane flickering to different effector molecules and physicochemical conditions. The results implied ATP was involved only indirectly in membrane flickering.