Approximation of delays in biochemical systems.

In the past metabolic pathway analyses have mostly ignored the effects of time delays that may be due to processes that are slower than biochemical reactions, such as transcription, translation, translocation, and transport. We show within the framework of biochemical systems theory (BST) that delay processes can be approximated accurately by augmenting the original variables and non-linear differential equations with auxiliary variables that are defined through a system of linear ordinary differential equations. These equations are naturally embedded in the structure of S-systems and generalized mass action systems within BST and can be interpreted as linear signaling pathways or cascades. We demonstrate the approximation method with the simplest generic modules, namely single delayed steps with and without feedback inhibition. These steps are representative though, because they are easily incorporated into larger systems. We show that the dynamics of the approximated systems reflects that of the original delay systems well, as long as the systems do not operate in very close vicinity of threshold values where the systems lose stability. The accuracy of approximation furthermore depends on the selected number of auxiliary variables. In the most relevant situations where the systems operate at states away from their critical thresholds, even a few auxiliary variables lead to satisfactory approximations.

Kinetics of growth process controlled by convective fluctuations.

A model of the spherical (compact) growth process controlled by a fluctuating local convective velocity field of the fluid particles is introduced. It is assumed that the particle velocity fluctuations are purely noisy, Gaussian, of zero mean, and of various correlations: Dirac delta, exponential, and algebraic (power law). It is shown that for a large class of the velocity fluctuations, the long-time asymptotics of the growth kinetics is universal (i.e., it does not depend on the details of the statistics of fluctuations) and displays the power-law time dependence with the classical exponent 1/2 resembling the diffusion limited growth. For very slow decay of algebraic correlations of fluctuations asymptotically like t(-gamma), gamma in (0,1]), kinetics is anomalous and depends strongly on the exponent gamma. For the averaged radius of the crystal approximately t(1-gamma/2) for 0 approximately (t ln t)1/2 for gamma=1.

Studies on abscisic acid in apple seeds.

Abscisic acid (AbA) was found to be present in non-stratified apple seeds. The evidence is based on chromatographic behaviour, fluorescence, UV-spectrum and growth inhibition in a wheat-coleoptile straight-growth test.The AbA level, as measured by this bioassay, falls considerably with progressing stratification; after 3 weeks of after-ripening no AbA could be detected in the seeds.The longer the period of stratification, the higher was the concentration of synthetic AbA necessary to inhibit germination.

Global stability in a delayed partial differential equation describing cellular replication.

Here we consider the dynamics of a population of cells that are capable of simultaneous proliferation and maturation. The equations describing the cellular population numbers are first order partial differential equations (transport equations) in which there is an explicit temporal retardation as well as a nonlocal dependence in the maturation variable due to cell replication. The behavior of this system may be considered along the characteristics, and a global stability condition is proved.

Abscisic acid in Penicillium italicum.

Abscisic acid (ABA) was found in Penicillium italicum Wehmer collected from the surface of infected oranges. After growth and subculturing 6 times on Czapek's medium, the fungus did not contain any detectable ABA.

The efficacy of antimalarials in systemic lupus erythematosus.

Of 209 patients who fulfilled the A.R.A. criteria for the diagnosis of systemic lupus erythematosus, 43 were selected for study because each had been treated for at least two years with antimalarials, but had not received antimalarials for at least one subsequent year. In each instance, the antimalarial was discontinued solely because of the development of retinopathy. Each year on antimalarials was matched with a subsequent year off antimalarials for each patient. The year immediately following diagnosis and years of pregnancy were excluded. Paired-t test analysis of matched years revealed that general symptoms (fever, fatigue, weight loss) were less common during years on 500 mg chloroquine daily than during years off the drug (p less than 0.05). Skin manifestations were also less frequent during the years on 500 mg chloroquine daily than during the years off (p less than 0.05). No significant steroid sparing effect was found. However, a greater incidence of flare-ups during the matched years off the drug was statistically significant.

Modeling complex neutrophil dynamics in the grey collie.

We have developed a mathematical model for the peripheral regulation of neutrophil production mediated by granulocyte colony-stimulating factor. We have used that model to show that the pattern of neutrophil oscillations in nine grey collies is consistent with the hypothesis that cyclical neutropenia is due to an oscillatory stem cell input to the neutrophil regulatory system, and not due to autonomous oscillations in the peripheral neutrophil regulatory system. In the process of interfacing our model with the laboratory data, we have estimated parameters for the peripheral neutrophil control system consistent with higher than normal apoptotic cell loss within the recognizable neutrophil precursors. This is in agreement with other experimental data. Our estimated model parameters also predict that the peripheral neutrophil production system is globally stable in the grey collies we studied. This further supports our hypothesis that the origin of the oscillatory behavior in cyclical neutropenia is in the stem cell population, consistent with other clinical and experimental evidence.