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Quantitative modeling of chloride conductance in yeast TRK potassium transporters.

So-called TRK proteins are responsible for active accumulation of potassium in plants, fungi, and bacteria. A pair of these proteins in the plasma membrane of Saccharomyces cerevisiae, ScTrk1p and ScTrk2p, also admit large, adventitious, chloride currents during patch-recording (Cl- efflux). Resulting steady-state current-voltage curves can be described by two simple kinetic models, most interestingly, voltage-driven channeling of ions through a pair of activation-energy barriers that lie within the membrane dielectric, near the inner (alpha) and outer (beta) surfaces. Two barrier heights (E(alpha) and E(beta)) and two relative distances (a1 and b2) from the surfaces specify the model. Measured current amplitude parallels intracellular chloride concentration and is strongly enhanced by acidic extracellular pH. The former implies an exponential variation of a1, between approximately 0.2 and approximately 0.4 of the membrane thickness, whereas the latter implies a linear variation of E(beta), by 0.69 Kcal mol(-1)/pH. The model requires membrane slope conductance to rise exponentially with increasingly large negative membrane voltage, as verified by data from a few yeast spheroplasts that tolerated voltage clamping at -200 to -300 mV. The behaviors of E(beta) and a1 accord qualitatively with a hypothetical structural model for fungal TRK proteins, suggesting that chloride ions flow through a central pore formed by symmetric aggregation of four TRK monomers.

Cation Transport Proteins↗

Choice, changeover, and travel: A quantitative model.

Six pigeons were trained on concurrent variable-interval schedules in which responding on fixed-interval schedules was required to give access to the alternate schedule. Responding on the concurrent schedules was not allowed, after changing over had commenced, until the changeover schedule had been completed. In Parts 1 to 3 of the experiment, the changeover fixed-interval schedules were equal and were 0 s, 10 s, and 20 s, respectively. In each part, the relative frequency of reinforcement obtained on the concurrent schedules was varied over at least five conditions. In Part 4, the concurrent schedules were equal, and one changeover fixed-interval schedule was twice the other. Under these conditions, the absolute sizes of the changeover schedules were varied. Increasing the changeover requirement from 0 s to 10 s (Parts 1 and 2) resulted in increases in the sensitivity of behavior allocation to reinforcers obtained, but no further increase was obtained when the changeover schedules were increased to 20 s (Part 3). In Part 4, performance was biased towards the concurrent schedule that took less time to enter. These results are consistent with a subtractive punishment model of travel in which the degree of punishment is measured by the number of reinforcers apparently lost from a schedule when the subject changes to that schedule. Absolute times spent on the main keys could be accurately described by a previous model of changeover performance.

Journal Article↗

Equivalence of quantitative models for tumour response to ionizing radiation in treatment field optimisation procedures.

Three cell kinetic models of tumour response to ionising radiation were compared with regard to their prediction of variation in curability when the dose to the tumour varied between 54 and 66 Gy given in 30 fractions. It was found that a simple model emulated the results of the more complex ones when the parameters of the simple model were properly adjusted. A comparison of the simple model and the CRE formula gave a similar result.

Cell Survival↗

A quantitative model for prediction of iron bioavailability from Indian meals: an experimental study.

The major goal of the study was to explore the possibility of developing an updated model that integrates the effect of various enhancers and inhibitors for predicting the potential availability of iron from typical Indian vegetarian meals. The interaction effects of four constituents namely ascorbic acid, citric acid, tannic acid and calcium phosphate was studied using a standard cereal meal (STD meal) providing 3 mg non-heme iron/250 ml homogenate. Based on the data, a regression equation was evolved which was tested for its predictive power as applied to a set of 10 typical Indian meals. Regression analysis of the data revealed that both ascorbate and citrate emerged as equally strong enhancers while tannate and calcium phosphate demonstrated strong inhibitory effect on iron availability in the STD meal. Further, when the prediction equation, generated on the basis of the interaction effect data was applied to the typical Indian meals, it showed a high correlation coefficient (r = 0.76) between the analysed values for iron availability vs the values computed using the enhancer and inhibitor contents of the meals. Comparison with the only other model available in the literature namely that of Monsen & Balintfy (1982) revealed that the present model was far better in predicting iron availability from cereal based Indian meals (r = 0.76) than Monsen's model (r = 0.19). The findings of the present study substantiated the hypothesis that a regression model, evolved from a cereal meal, by integrating the effect of enhancers as well as inhibitors, rather than only enhancers, provides a more precise estimate of iron availability from typical Indian meals. A limitation of the model however, was that phytate could not be incorporated into the equation.

Ascorbic Acid↗

Arthritis in the rabbit knee joint: a quantitated model.

The knee joint in rabbits has been used as an arthritis model for the study of acute immunologic injury. Histologic examination of synovium plus a standardized procedure for irrigating inflammatory exudate from the joint allowed study of damage due to immune complexes, urate crystals, and Arthus type vascular lesions by multiple parameters. With this model Arthus lesions could be abolished with neutrophil depletion and reconstituted with intra-articular injection of neutrophil suspension. The rate and degree of injury could also be diminished by depletion of complement components.

Animals↗

[Quantitative model of human erythrocyte glycolysis. I. Relationship between the stationary rate of glycolysis and the ATP concentration].

A mathematical model is presented of the Embden--Meyerhof pathway in the human red blood cell. The rate of the system stationary flux is determined by the first part of the chain including three enzymatic reactions. The function has been calculated which describes the dependence of the stationary rate of glucose consumption and ATP production on the concentration of ATP. The curve has a bell shape with the physiological normal point situated in the descending segment. The descending segment is a result of the inhibition of the phosphofructokinase by ATP and the strong inhibition of the hexokinase by glucose-6-phosphate.

Adenosine Triphosphate↗

[Quantitative model of human erythrocyte glycolysis. Region of cell viability determined by ATP concentration].

The boundaries of the cell vitality domain in the enzyme activity space are calculated on the basis of a mathematical model of erythrocyte glycolysis. The boundaries are determined by key metabolite concentrations. The results obtained are compared with experimental data related to erythrocytic enzymopathies. It is shown that theoretical boundary enzyme activities coincide with the activities of hexokinase and in some cases phosphofruktokinase in enzyme deficient erythrocytes.

Adenosine Triphosphatases↗

A quantitative model of technetium-99m-DTPA-galactosyl-HSA for the assessment of hepatic blood flow and hepatic binding receptor.

Technetium-99m-diethylenetriaminepentaacetic acid-galactosyl-human serum albumin (99mTc-GSA) was studied in normal volunteers and in patients with impaired liver function. The extrapolation approach originated the absolute dose of 99mTc-GSA in blood and the hepatic blood volume. The heart and liver regression curves were simultaneously fractionated into the three compartments (extrahepatic blood, hepatic blood and hepatocytes). Four differential equations were integrated with the six parameters as variables, and the smallest residual sum of squares was obtained by the damping Gauss-Newton method. The result of hepatic blood flow was 1603 +/- 144 (ml/min) in normal controls, which was compatible with previously reported values. Maximal removal rate (mg/min) showed statistically significant differences between the normal volunteers and patients with chronic hepatitis or liver cirrhosis. Our kinetic model of 99mTc-GSA can be used in the evaluation of liver function.

Adult↗

A quantitative model of DNA fragments generated by ionizing radiation, and possible experimental applications.

We derive an equation for observed frequencies of DNA fragments as a function of size. In this derivation, we consider an experimental system where fragments are generated by random, independent double-strand breaks on chromosomes (or other large DNA molecules) and then separated by size on agarose gels. When visualizing these fragments using Southern hybridization techniques (employing a site-specific probe), we predict an intensity distribution that has unusual properties. In particular, peaks in the fragment size distribution depend not only on standard breakage parameters, but also on the location of the hybridization site. Our model is consistent with experimental and theoretical results reported elsewhere, where measurements of peaks are used for the physical mapping of genes. Further, we propose that similar experiments might be suitable for precise measurements of the parameters of double-strand breakage (as an alternative to neutral filter elutions and neutral sucrose gradients) and for testing the assumption of random, independent breakage for different types of radiation.

Blotting, Southern↗

[Quantitative model of human erythrocyte glycolysis. Relationship between erythrocyte energy metabolism and Na+, K+-ATPase activity].

The influence of the changes of the transport Na+, K+-ATPase activity on the human red blood cell (RBC) glycolysis was studied. Two different types of energetic regulation were found out under the strophanthin inhibition. A decrease of ATP comsumption results in a drop of glucose consumption and lactate production in the first type regulation of RBC. In the second type regulation of RBC the glucose consumption does not change after ATPase inhibition and the excess metabolic flux is directed through the hexosemonophosphate shunt. In both cases the resulting decrease of ATP production leads to the ATP level stabilization. An increase of potassium ions concentration in the external medium does not influence the RBC glycolysis. The valinomycin added increases the glucose consumption and the lactate production. The cell volume decreases under the effect of valinomycin.

Erythrocytes↗

A quantitative model for the kinetics of cAMP-dependent protein kinase (type II) activity. Long-term activation of the kinase and its possible relevance to learning and memory.

Using computer simulation we have modeled the kinetics of cAMP-dependent protein kinase, type II, following transient pulses of cAMP. We show that under the appropriate physiological conditions, the kinase can remain activated 20 min or longer after the cessation of adenylate cyclase activation, in a process we term long-term activation. Long-term activation depends in part on the state of phosphorylation of the regulatory subunit, because phosphorylation of the regulatory subunit regulates the affinity of this subunit for the catalytic subunit. We have used our model to simulate experiments that have been performed on the kinetic and steady state activities of cAMP-dependent protein kinase and have found good agreement between the simulations and the experimental data. The effects of the activity of phosphodiesterase, adenylate cyclase, and protein phosphatase on the kinetics of cAMP-dependent protein kinase have been modeled, as have the effects of different ratios of regulatory subunit to catalytic subunit. We have also simulated the activation of the cAMP-dependent protein kinase in Drosophila learning and memory mutants having primary or secondary defects in the cAMP cascade. We make predictions regarding the behavior of different mutants, which are in line with the experimental data. The model corroborates the assumption that the cAMP cascade may play a role in learning and short-term memory.

Animals↗

Quantitative models for growth inhibition of human leukemia cells by antitumor anthracycline derivatives.

A batch elution method with hydroxylapatite was developed to assay DNA damage by a set of antitumor anthracycline derivatives and was standardized with respect to the kinetics of unwinding, size of the alkaline unwinding unit, and fidelity of selective elution of single and double-stranded DNA. The method was applied to a study of a set of 10 antitumor anthracycline derivatives which inhibit growth of CCRF-CEM human leukemia cells over a range of potencies exceeding four orders of magnitude. The derivatives, including Adriamycin, daunorubicin, and carminomycin, vary in structure at C-4 and C-13, with substitutions at C-14 and N and stereochemical differences at C-4'. In a static model (fixed drug concentrations and incubation times), the potency [1/ID37 (concentration of agent that inhibits cell growth by 37%)] of nine of the ten derivatives may be expressed as functions of DNA damage (n), inhibition of thymidine incorporation (l), and drug retention (r): ID37 = Ka(r/l . n)kb, with a coefficient of correlation of greater than 0.99. A kinetic model with 4-demethoxydaunorubicin (varying concentrations and incubation times) was also described. Following initial uptake and a period of rapid loss after cells are washed free of excess drug, the change in agent concentration in the cells follows first-order kinetics. The cell index (cell number after 50 hr in drug-free growth medium/cell number after initial 2-hr exposure with drug) may be expressed linearly in terms of the kinetics of drug loss (coefficient of correlation, greater than 0.98), or as functions of 1/n (coefficient of correlation, greater than 0.958), 1/l . n (coefficient of correlation, greater than 0.963, or r/l . n (coefficient of correlation, greater than 0.963). These studies may be used to define a class of similarly acting anthracycline agents and to give some insight into the mechanism of action of the agents that fall within the class.

Antibiotics, Antineoplastic↗