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PubMed2003

Level spacing statistics of classically integrable systems: investigation along the lines of the Berry-Robnik approach.

By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single monotonically increasing function mu(S) of the level spacing S. Three cases are distinguished: (1) Poissonian if mu(+ infinity)=0, (2) Poissonian for large S, but possibly not for small S if 0<mu(+infinity)<1, and (3) sub-Poissonian if mu(+infinity)=1. This implies that, even when energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.

Journal Article↗
PubMed1999

Lactate metabolism during exercise: analysis by an integrative systems model.

To provide a framework for quantitative analysis of metabolic and transport processes associated with ATP production during exercise, we adapted a recently developed model that links cellular metabolism and its control to whole body responses at rest. The enhanced model is based on dynamic mass balances for glycogen, glucose, pyruvate (PY), lactate (LA), O(2), and CO(2) and is solved numerically to simulate responses to acute (<20 min), moderate exercise (i.e., below the LA threshold, less than approximately 60% maximal rate of O(2) uptake). Simulations of responses to a step change in muscle ATP turnover predict substrate changes in muscle, splanchnic, and other tissues compartments, as well as changes in other metabolites (e.g., NADH, ADP) whose reactions are coupled to the main reactions. Even a significant (64%) decrease in muscle O(2) concentration (C(m, O(2))) did not affect muscle O(2) consumption. Model simulations of moderate exercise show that 1) muscle oxygenation is sufficient (C(m, O(2)) >2 mM) even during the transient state; 2) transient increases in concentration of muscle LA and arterial concentration of LA are associated with increases in glycolysis from increases in ADP/ATP and in LA production associated with a rise in NADH/NAD; 3) muscle ADP/ATP reaches a higher steady state that stimulates glycolysis, glycogenolysis, and oxidative phosphorylation to match the ATP demand; and 4) muscle NADH/NAD reaches a lower steady state that stimulates LA oxidation. It is suggested that the continuous stimulation of ATP synthesis processes during moderate exercise is mainly due to a higher ADP/ATP, not to a higher NADH/NAD. Critical measurements needed to quantify metabolic control mechanisms are identified.

Adenosine Triphosphate↗