Estimation of parameters in a two-pool urea kinetic model for hemodialysis.
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We have tested whether our previous finding in normal subjects that the disappearance of insulin from plasma obeys saturation kinetics alone also applies to type I diabetic patients. In six long-term diabetic patients steady state plasma insulin concentrations resulting from constant insulin infusion at different rates were compared with the predictions of three models for the kinetics of insulin in plasma. The models allowed the existence of non-saturable (first order equation) or saturable (Michaëlis-Menten equation) mechanisms, or both. The minimal acceptable model included saturation kinetics alone in four subjects and first order kinetics alone in two subjects. The clearance of insulin in diabetic patients, calculated from the best fitting model, was 18.0 (median, range 10.0-23.7) ml X kg-1 X min.-1 versus 25.0 (18.6-47.1) ml X kg-1 X min.-1 in six normal subjects (2p = 0.008). Insulin thus disappears from plasma at a lower rate in diabetic patients than in normal subjects at physiological plasma concentrations.
A five-step model for the reaction catalyzed by beef heart lactate dehydrogenase (EC 1.1.1.27) reconciles differences observed in the four-step model if pre-steady-state data in the forward direction are compared with similar data in the reverse direction. The relationship between the four-and five-step models indicates what problems can develop when an incomplete model is proposed. Nevertheless, there are advantages to using the less complicated four-step model when comparing the molecular kinetics of enzymes catalyzing the same reaction but obtained from different sources.
A combined first and second-order model was developed to describe the bulk decay of chlorine in water distribution systems. The parameters of model were determined by deriving the best fit with a lot of experimental data. The complex relationships between bulk decay and the temperature, the initial chlorine concentration and TOC were quantificationally described in the model. Except for the initial stages the combined model can be simplified into the first-order model and these relationships can be simplified into a linear increase with TOC, a linear decrease with initial chlorine concentration and an exponential relationship with the temperature. The model also explained why chlorine decays more rapidly in the initial stages. The accuracy of model was verified by using the experimental data. The results showed that the combined model has better agreement with the experimental data than the conventional first-order model.
A theoretical model is presented that explains slow copper-induced oxidation of low-density lipoprotein in the systems free of seeded hydroperoxydes. The model is based on the probabilistic kinetic theory, modified to take into account different radical generation rates by oxidized and reduced forms of the metal ions. It is shown that the initiation and progression of the LDL oxidation can take place in any LDL dispersion by metal-induced oxidation of alpha-tocopherol, one of the constituents of LDL, and formation of slowly reacting alpha-tocopheroxyl radical. Selected values of several adjustable parameters define actual temporal profiles of the quantities defining the oxidation process.
A quantitative model is developed that describes the kinetics of the early phases of zinc metabolism in humans. The model is based on averaged data obtained over 5 days from 17 atients with smell and/or taste dysfunction who were given 69mZn in trace amounts orally and intravenously. A function describing the rate of entry of 69mZn into systemic plasma following ingestion of the isotope is derived showing that about 37% of the ingested zinc enters plasma. Gastrointestinal absorption is essentially completed by 4 h. Sixty-seven percent of the absorbed zinc in the portal circulation is extracted by the liver before being released into the systemic circulation and agrees with the calculated extraction efficiency from the systemic circulation. There are both rapid and slow exchnage phases between plasma and liver and between plasma and red cells. The calculated steady-state zinc values for plasma, red cells, and liver agree with previously reported measured values implying there are no additional zinc pools in these tissues. The tracer data, however, account for only 10% of total body zinc, the remaining 90% in tissues whose kinetics are too slow to be resolved from a 5-day study.
A kinetic scheme of the prostacyclin-thromboxane system has been evolved on the basis of the authors experimental data and the results described elsewhere. The kinetic behavior of the model has been analysed with the aid of computer technology by varying the following parameters: phospholipase activities, free arachidonic acid exchange rates between platelets and endothelium, PGH-synthetase biosynthesis rates, velocities of arachidonic acid pathways other than the cyclooxygenase ones. It has been demonstrated that the biological system is capable of sustaining prostacyclin and thromboxane concentrations at steady fixed levels within a wide range of kinetic parameters.
A major obstacle in gene delivery is the transport of intact plasmid DNA (pDNA) to target sites. We sought to investigate the kinetic processes underlying the degradation of pDNA in a rat plasma model, as this is one of the main components responsible for the clearance of pDNA after intravenous administration. We further sought to construct a complete kinetic model to describe the degradation of all three topoforms (supercoiled, open circular, and linear) of pDNA in a rat plasma model. Supercoiled pDNA was incubated in isolated rat plasma at 37 degrees C in vitro. At various time points, the plasma was assayed by electrophoresis for the amounts of supercoiled, open circular, and full-length linear pDNA remaining. The calculated amounts remaining were fit to linear differential equations describing this process. In this model, pDNA degradation is considered to be a unidirectional process, with supercoiled degrading to open circular and then to the linear topoform. The calculated kinetic parameters suggested that supercoiled pDNA degrades in rat plasma with a half-life of 1.2 minutes, open circular pDNA degrades with a half-life of 21 minutes, and linear pDNA degrades with a half-life of 11 minutes. Complexation of pDNA with liposomes resulted in a portion of the supercoiled plasmid remaining detectable through 5.5 hours.
The dependence of integral membrane enzymes on lipid activators in analyzed in terms of multiple binding site kinetics. Rate equations for an enzyme with n independent and indentical lipid binding sites are derived for the case that enzyme activity is proportional to the total amount of lipid bound, or that only fully substituted enzyme is active. A third equation applies to the case that lipids bind with infinite cooperativity to give fully substituted and active enzyme. None of the three models was entirely consistent with existing experimental data. The following kinetic model is shown to accommodate the degree of cooperativity observed in lipid activation experiments as well as the number of independent lipid-binding sites determined by electron-spin resonance measurements. The membrane enzyme is assumed to have n non-interacting and identical lipid-binding sites. Only fully substituted enzyme (ELn) and the next most highly substituted forms such as ELn-1 and ELn-2 may possess enzyme activity. These assumptions lead to cooperativity in activation. Cooperativity reaches a maximum when enzyme activity starts to appear with about 80% of the full lipid substitution. The increase in cooperativity is accompanied by a decrease in the lipid concentration required for half-maximal activation. Further kinetic aspects of a dynamic boundary lipid layer around integral membrane enzymes are discussed.
Clones of Trypanosoma congolense which express resistance to the widely used trypanocide isometamidium chloride accumulate less of the drug than clones which are sensitive to drug treatment. A mathematical model has been developed which was able to predict theoretical lines representing the uptake kinetics in trypanosomes which were sensitive to isometamidium, as well as for resistant trypanosomes in which reduced accumulation was a result of either reduced uptake or enhanced efflux of the drug. Data from drug uptake experiments were then fitted to these theoretical lines. While the value for drug efflux could not be separated from the dissociation constant of the trypanosomes for isometamidium, it was demonstrated that reduced accumulation is not a result of reduced uptake of isometamidium by drug-resistant trypanosomes.
Kinetic studies on the oxidative reaction of glutathione by hydrogen peroxide were performed using soluble and membrane-bound ox erythrocyte glutathione peroxidase of various types. The effects of organic and inorganic selenium on the glutathione peroxidase activity were also examined. The kinetic behaviour of the enzyme was investigated using a coupled reaction within a relatively large range of hydrogen peroxide and glutathione concentrations. Non-parallel double-reciprocal plots were obtained which suggested that a sequential ordered rather than a ping-pong mechanism was involved. Similar results were obtained with soluble and membrane-bound enzyme, whatever the type of crosslinking used. Crosslinking was performed on a nylon support using various alkylating agents and bifunctional molecules. With all three types of immobilized enzyme thus obtained, a slight but significant increase in the Km was observed. The effects of selenium were then studied. Using soluble enzyme, a slight increase in the activity was observed in the presence of inorganic selenium (sodium selenite) but not with organic selenium (seleno-L-methionine). Inorganic selenium alone was also found to have a slight effect on the membrane-bound enzyme. An increase in the catalytic efficiency was observed when glutathione peroxidase was bound using lysine as the bifunctional agent and either glutaraldehyde or triethyloxonium tetrafluoroborate as the reticulation agent, after a three-month period of incubation.
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