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A model of single muscle contraction is proposed. The kinetics of two reactions have been used: interaction between the excitation mediator and the muscle membrane receptor, and the reaction of enzymatic mediator splitting. The muscle contraction parameters have been correlated with the concentration of the mediator-receptor complex.
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The effects of synergistic binding among co-substrates on the kinetic saturation patterns for equilibrium isotope exchange rates have been derived. Models considered for a two reactant-two product system were those in which one substrate may either decrease the dissociation rate or increase the association rate for its co-substrate. These studies help define limits of this versatile kinetic probe technique. The most sensitive indicator for synergistic substrate binding appears to be the different apparent Km values for different exchange rate curves; e.g,, A in equilibrium P and B in equilibrium Q. Model patterns for mutual synergism effects are also presented; the slowest exchange reactions were found the most sensitive to preferred orders of substrate binding. Conditions that can prevent detection of preferred or even compulsory order binding are discussed.
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The time courses of coagulation and coagulation-lysis were spectrophotometrically monitored after the addition of thrombin or thrombin-streptokinase to plasma, diluted 1:5 with normal saline, obtained from normal and presumably abnormal subjects. The kinetics of clotting, after an initial lag period of 0.5-1.5 min, demonstrated essentially first-order dependence on the amount of fibrinogen available to form the clot, and the asymptotic absorbance was independent of thrombin concentration. The rate of clotting was a function of added thrombin, and the ratios of the rate constants at 2.5 and 1.25 units of thrombin/ml of undiluted plasma were 1.65 +/- 0.03 SEM. At early times, the coagulation-lysis curve with thrombin-streptokinase could be superimposed on the clotting curve with thrombin alone for a given plasma with minor compensation for variable lag times. Subsequently, the curves diverged; lysis was monitored by the decrease in absorbance of the coagulation-lysis system. The rate of fibrinolysis increased with streptokinase concentration and was a function of the extent of lysis, and it permitted the description of the kinetics of lysis by a pseudoautocatalytic mechanism where the bimolecular rate constant appears proportional to streptokinase concentration. Ranges of clotting and lytic parameters for the plasma of normal subjects are given, and their potential use in diagnosing abnormalities is described.
A mathematical model was developed to describe the multiregional flow of intrathecal indium-111 DTPA, and hence indirectly the flow of cerebrospinal fluid, in sequential spinal and cerebral CSF images. The model provides for an arbitrary input function, transport delay between appropriate compartments, transmeningeal and transependymal transport, and for bidirectional flow between most compartments. Two- and eight-compartment models were evaluated. The set of eight nonlinear differential equations was solved using numerical techniques. This model provides a quantitative basis for the interpretation of CSF kinetics.
1. Evolutionary changes in the structure of an enzyme that provide an increase in its K(m) value are considered. Provided that K(m) increases as a result of increases in the forward rate constants of the catalysis relative to the reverse rate constants, the enzyme catalyses the conversion of a fixed concentration of its substrate more rapidly when its structure provides that K(m)>[S] than when K(m)<[S]. 2. Catalytic efficiency of enzymes is discussed in terms of the simplest plausible model, the Haldane [(1930) Enzymes, Longmans, London] reversible three-step model: [Formula: see text] The rate equation for the forward reaction of this model (formation of P) may be written in the simple form: [Formula: see text] K(eq.) is the equilibrium constant (=[P](eq.)/[S](eq.)), and k(cat.)=V/[E](T), where [E](T) is the total enzyme concentration. 3. To assess the effectiveness of an enzyme, it is necessary only to determine the extent to which the constraints of a particular kinetic mechanism permit v(2) (v when K(m)>>[S]) to approach v(d) (the diffusion-limited rate). 4. The value of the optimal rate of catalysis (v(opt.), the maximal value of v(2)) is dictated by the equilibrium constant for the reaction, K(eq.); v(2)=v(d)/a, where [Formula: see text] when k(+1) is assumed equal to k(-3), and v(opt.)=v(d)/a(min.). When K(eq.)>/=1, it is necessary that k(+2)>>k(-1) for a to take its minimum value, a(min.); when K(eq.)<<1, it is necessary only that k(+2)>>K(eq.).k(-1), i.e. a can equal a(min.) even if k(+2) >1, v(opt.)=v(d); when K(eq.)=1, v(opt.)=v(d)/2, and when K(eq.)<<1, v(opt.)=K(eq.).v(d). 5. The analysis, together with predicted effects of evolutionary pressure, suggests that in practice the rates of the fastest enzyme-catalysed freely reversible reactions might be expected to be lower than the value of k(+1)[E](T)[S] by about an order of magnitude, particularly if K(eq.)<1. 6. The existing literature suggests that, in general, appropriate values of K(m) have evolved for the provision of high rates of catalysis but that many values of k(cat.) are not large enough to provide optimal rates of catalysis unless the value of k(+1)in vivo is lower than its value in free solution.
The timecourse of the membrane hyperpolarization evoked by stimulation of postganglionic parasympathetic nerve endings in isolated atria from the guinea-pig heart is mainly governed by two exponentials, one describing most of the rising phase (rate constant k alpha = 2.88+/-1.135 s-1) and one which completely describes the decline of the response (k beta = 0.58+/-0.31 s-1). An exact description of the muscarinic receptor mediated potential change, which also allows for its apparent latency and its s-shaped beginning, is found if two additional faster exponentials are introduced. In agreement with earlier results a model of four consecutive reactions is presented. It is concluded that during muscarinic cholinergic transmission reactions subsequent to binding of the ACh-molecules to the receptor are rate-limiting.
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The method of progress curve analysis for enzyme-catalyzed reactions (Duggleby, R.G. and Morrison, J.F. (1977) Biochim. Biophys. acta 481, 297--312) has been extended to a two substrate, reversible reaction through the use of enzyme-catalyzed recycling of one of the products. The reaction investigated was that catalyzed by aspartate aminotransferase (L-aspartate:2-oxoglutarate aminotransferase, EC 2.6.1.1) and the product, alpha-ketoglutarate was recycled to glutamate using NADH and NH4Cl in the presence of glutamate dehydrogenase. The values determined for the kinetic parameters of the aminotransferase were found to agree well with those obtained from steady-state velocity measurements. The standard errors of the parameters, as calculated by the procedure originally described, were found to underestimate the observed variation between different experiments. Therefore, a procedure of data compression was devised which leads to more realistic values for standard errors. The compressed data obtained with aspartate aminotransferase have been fitted to the integrated rate equations that describe a variety of kinetic mechanisms. The best fit was obtained with the Ping-Pong model which is applicable to the aspartate aminotransferase reaction. Thus, progress curve analysis may be used to determine the kinetic mechanism of, and values of the kinetic parameters associated with, an enyzme-catalyzed reaction.
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Three models of tumor cell loss are described. The effects of cell loss on other cellular kinetic parameters are evaluated, and experiments which may distinguish among the models are discussed. Each model is based on a different cell-loss mechanism, and equations for the cell-cycle, cell-frequency distribution, the growth of both the proliferating and non-proliferating cell population, the growth fraction (GF), and the relative rate of volumetric growth, (dV/dt)/V, are derived. The following types of data are simulated for each model: the pulse labelling index, the mitotic index, and the labeling index as a function of time after a single or a series of 3H-TdR injections. The relative volumetric growth rate has the same mathematical form for each model. The PLM curves predicted by each model for the tumor lines studied (S102F and Slow) are not appreciably different. The predicted initial labeling index and mitotic index may differ significantly among the models depending upon the tumor line. The most striking difference among the models lies in the predictions regarding the labeling index as a function of time after a single or after a series of 3H-TdR injections. These types of labeling experiments should be valuable for distinguishing the different cell-loss mechanisms in solid tumors.
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