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1. A re-investigation of the kinetics of yeast phosphoglycerate kinase in the direction of 1,3-bisphosphoglycerate formation has been carried out, covering a 1000-fold range in substrate concentrations. A variety of improved spectrophotometric and fluorimetric assay procedures have been used. 2. Kinetic plots proved to be non-linear for each variable substrate. A variety of checks have been carried out to show that this is not due to artifacts in the assay procedures or heterogeneity of the enzyme preparation. 3. The effects of a variety of salts on the activity of the enzyme have been examined. Most salts, especially those with multivalent anions, can cause activation of the enzyme, but inhibit at high concentration. 4. The salt effect is shown to be principally due to anions rather than cations, and not to ionic strength changes. Sulphate, as one of the most effective anions has been used in most comparisons. 5. Salt activation is steepest when the substrate concentrations are low; maximum activation has been about 5-fold with 0.2 mM MgATP and 0.2 mM 3-phosphoglycerate. Inhibition at the higher salt concentrations is strongest at the same substrate concentrations as when activation is steepest, indicating a link between the two effects. 6. The presence of 20 mM or more Na2SO4 converted non-linear kinetic plots to linear ones. A study of the kinetics in the presence of 40 mM Na2SO4 was interpreted in terms of a random sequential binding mechanism, with sulphate acting as a competitive inhibitor. 7. Possible explanations for these anomalous results are discussed in terms of several mechanisms which have been shown to apply in other systems.
An integrated mathematic computer-based model of the pharmacokinetics, intracellular enzyme kinetics, and cell kinetics of the treatment of L1210 leukemia by cytosine arabinoside (ara-C) is described. The compartment model of Bischoff and Dedrick is extended to the intracellular level by inclusion of equations describing the phosphorylation, dephosphorylation, and deamination of ara-C with enzymatic feedback control. The activities of kinase, deaminase, and phosphatase are explicitly included in the models and are estimated from relevant data. Cell proliferation is described by a continuous-flow mathematic model in which cellular maturation and cell-to-cell variability in maturation rates are key variables. Cell proliferation is related to intracellular biochemistry through mathematic expressions which relate cell lethality and progression delay to the time course of intracellular ara-CTP. In vitro and in vivo experiments performed in a number of laboratories are compared by simulation. The most sensitive parameters in dose-response and cell-survival simulations are deoxycytidine kinase activity, ara-CTP half-life, renal clearance of ara-C, and cell-kinetic parameters for proliferation and cell killing. Progression delay is vital to the realistic simulation of divided-dose schedules. By comparative simulation we have identified areas of uncertainty which can be classified by a few additional measurements. The applications of simulations combining pharmacokinetic, biochemical, and cell-kinetic data in vitro and in vivo are discussed, exploring consistency among different measurements, and relating experimental protocols to clinical treatment.
The kinetic parameters of the submitochondrial particles cytochrome chain obtained from steady-state kinetics were studied for pH dependence. The life-times of the activated states (tau) for cytochrome pairs b leads to c1 and a leads to a3 are shown to bear dissimilar dependence on pH of the medium, while for cytochrome pairs c1 leads to c and c leads to a they display practically no pH dependence at all. The rate constants of the non-activated state (alphai-kiCo) decreased for the pair b leads to c1 and increased for a leads to a3 with the increase of pH from 6.5 to 8.5. The apparent pK values obtained therefrom were 7.2 and 8.9, respectively. A kinetic model is proposed suggesting that local pH in the mitochondrial membrane, dependent on the rate of electron transfer, may be a controlling factor for the ratio of activated and non-activated carrier states. The model is in good consistence with the experimental dependences of k'i on V and the pH dependences of alpha2 for b leads to c1 and a leads to a3. It also gives a qualitative prediction for the pH dependences of the ordinate intercepts of the straight lines in l/(k'i--alphai) vs. l/V plots. The rate constants for the diffusion of hydrogen and hydroxyl ions in the membrane are estimated on the basis of our kinetic data to be 10(4)--10(5) s-1 and 10(2)--10(3) s-i, respectively.
Kinetic aspects of reactions in homogeneous multienzyme systems under nonsteady state conditions were investigated. An analysis of formal-kinetic relationships, describing the time course of system was conducted with a bienzyme system. Presteady state kinetics of processes in lineal multienzyme systems was investigated. Relax-kinetics methods were applied for the analysis of processes in lineal sequences. Methods of determination of number of stages initial substrate transformations and of number of enzymes were developed as well as methods for the analysis of sequences of intermediates in reaction pathway. Methods of determination of Vmax and Kmax for each individual enzyme are considered.
pH Dependences of steady-state kinetic parameters of cytochrome chains of submitochondrial particles have been studies. It has been shown that the lifetimes of activated states (tau) of the pairs of cytochromes b leads to c1 and a leads to a3 have different pH dependences; those for the c1 leads to c and c leads to a cytochrome pairs being similar. The rate constants for the non-activated state of the respiratory chains decreased for the b leads to c1 pair and increased for the a leads to a3 pair when the pH value was increased. The values of pK calculated from these dependences for the pairs b leads to c1 and a leads to a3 were 7.2 and 8.9, respectively. It has been supposed that the ratio of activated to non-activated electron carriers may be controlled by the local pH value in the mitochondrial membrane, the latter being dependent upon the rate of electron transfer. The kinetic model based on this assumption allows one to explain the experimental dependences on pH of the rate constants for cytochromes b leads to c, and a leads to a3. The values of the diffusion rate constants for H+ and OH- ions in the mitochondrial membrane estimated from these kinetic data obtained in this study were 10(4)--10(5) s-1 and 10(2)--10(3) s-1, respectively.
Isotope exchange kinetics at chemical equilibrium have been used to investigate the kinetic mechanism of homoserine dehydrogenase (EC 1.1.1.3) of the (Thr-sensitive) aspartokinase/homoserine dehydrogenase-I multifunctional enzyme from E. coli. For the reaction (L-ASA + NADPH + H+ = L-Hse + NADP+), at pH 9.0, 37 degrees C, Keq = 100 (+/- 20). Under these conditions, the rate for exchange of [14C]-L-homoserine (Hse) in equilibrium L-aspartate-beta-semialdehyde (ASA) is nearly twice that for the [3H]-NADP+ in equilibrium NADPH exchange. This indicates that covalent interconversion between reactants and products bound in the active site cannot be rate-limiting. Upon variation of the concentrations of all four substrates in constant ratio at equilibrium (to minimize dead-end complex formation), the Hse in equilibrium ASA exchange increased smoothly toward a maximum. In contrast, the NADP+ in equilibrium NADPH exchange rate increased to a maximum value at partial saturation, then decreased to approximately half the maximum rate. These data are consistent with a preferred-order random kinetic mechanism in which the dominant pathway involves association of NADPH prior to L-ASA and dissociation of L-Hse prior to NADP+.
Although much is known about fibrin polymerization, because it is complex, the effects of various modifications are not intuitively obvious and many experimental observations remain unexplained. A kinetic model presented here that is based on information about mechanisms of assembly accounts for most experimental observations and allows hypotheses about the effects of various factors to be tested. Differential equations describing the kinetics of polymerization were written and then solved numerically. The results have been related to turbidity profiles and electron microscope observations. The concentrations of intermediates in fibrin polymerization, and fiber diameters, fiber and protofibril lengths have been calculated from these models. The simplest model considered has three steps; fibrinopeptide A cleavage, protofibril formation, and lateral aggregation of protofibrils to form fibers. The average number of protofibrils per fiber, which is directly related to turbidity, can be calculated and plotted as a function of time. The lag period observed in turbidity profiles cannot be accurately simulated by such a model, but can be simulated by modifying the model such that oligomers must reach a minimum length before they aggregate. Many observations, reported here and elsewhere, can be accounted for by this model; the basic model may be modified to account for other experimental observations. Modeling predicts effects of changes in the rate of fibrinopeptide cleavage consistent with electron microscope and turbidity observations. Changes only in the rate constants for initiation of fiber growth or for addition of protofibrils to fibers are sufficient to account for a wide variety of other observations, e.g., the effects of ionic strength or fibrinopeptide B removal or thrombospondin. The effects of lateral aggregation of fibers has also been modeled: such behavior has been observed in turbidity curves and electron micrographs of clots formed in the presence of platelet factor 4. Thus, many aspects of clot structure and factors that influence structure are directly related to the rates of these steps of polymerization, even though these effects are often not obvious. Thus, to a large extent, clot structure is kinetically determined.
The underlying principles of the kinetics and equilibrium of a solitary sodium channel in the steady state are examined. Both the open and closed kinetics are postulated to result from round-trip excursions from a transition region that separates the openable and closed forms. Exponential behavior of the kinetics can have origins different from small-molecule systems. These differences suggest that the probability density functions (PDFs) that describe the time dependences of the open and closed forms arise from a distribution of rate constants. The distribution is likely to arise from a thermal modulation of the channel structure, and this provides a physical basis for the following three-variable equation: [formula; see text] Here, A0 is a scaling term, k is the mean rate constant, and sigma quantifies the Gaussian spread for the contributions of a range of effective rate constants. The maximum contribution is made by k, with rates faster and slower contributing less. (When sigma, the standard deviation of the spread, goes to zero, then p(f) = A0 e-kt.) The equation is applied to the single-channel steady-state probability density functions for batrachotoxin-treated sodium channels (1986. Keller et al. J. Gen. Physiol. 88: 1-23). The following characteristics are found: (a) The data for both open and closed forms of the channel are fit well with the above equation, which represents a Gaussian distribution of first-order rate processes. (b) The simple relationship [formula; see text] holds for the mean effective rat constants. Or, equivalently stated, the values of P open calculated from the k values closely agree with the P open values found directly from the PDF data. (c) In agreement with the known behavior of voltage-dependent rate constants, the voltage dependences of the mean effective rate constants for the opening and closing of the channel are equal and opposite over the voltage range studied. That is, [formula; see text] "Bursts" are related to the well-known cage effect of solution chemistry.
The influence of the saddle curvature on abutment tooth kinetics and abutment tooth stress was studied with unilateral rigid and movable free-end saddle dentures. The results showed that, independent of the length of the saddle and/or of the saddle curvature, considerable horizontal and vertical extrusive abutment tooth stress is present in addition to vertical intrusive abutment tooth stress. The saddle kinetics are basically influenced by the form of the saddle. The kinetics cannot be altered appreciably because of the mechanical characteristics of the connecting elements; it can only be surpressed at the cost of increased pier stress.
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.
Steady-state kinetics of electron transfer through the cytochrome chain of uncoupled ultrasonic submitochondrial particles at different pH values has been studied. Rate constants calculated from the Pring equation (ki' = V/PirPi+1ox) increased with the increase of the rate of the process. As in the previous work (Saks, V. A., Kupriyanov, V. V. and Luzikov, V. N. (1972) Biochim. Biophys. Acta 283, 42-53) this dependence was linear, but only at comparatively low rates of electron transfer. To explain the experimental data several kinetic models, based on the assumption that respiratory chains are activated when functioning, have been proposed and analysed. The best agreement with the experimental data was obtained for the model suggesting that the rate of activation of the carriers is directly proportional to the overall rate of electron transfer and to the proportion of non-activated respiratory chains in the system. Hence it appeared that electron transfer through already activated chains entailed activation of adjacent non-activated chains. This model allowed rate constants for non-activated (ki) and activated (ki) states of the carriers, as well as the life-time of the activated carriers (tau) to be determined.
The pharmaco-kinetics of angiographic contrast media in the extra-vascular space, which are largely unknown, were investigated experimentally in dogs. As part of a basic study, using radio-active contrast media, it was possible to determine the concentration and rate of elimination in practically all organs and tissues. Measurements were carried out first after prolonged infusion of the contrast under conditions of balanced flow, and secondly six hours after the end of the infusion. It was therefore possible to determine the inflow and loss of contrast medium in various organs, or organs systems. The most commonly used angiographic contrast media in Germany were investigated. Their kinetic behaviour is largely identical, their pattern of distribution and elimination depended principally on the organ or tissue. A comprehensive discussion of the results of all the experiments will be given in the third article.
The perturbed cellular kinetics of the duodenal crypt following a single injection of hydroxyurea (HU) have been simulated using matrix algebra. Following the direct effects of HU (S-phase cytotoxicity and a G1/S block) the crypt cell kinetics undergo several alterations. Previously documented alterations include: (1) a temporary partial synchronization of the surviving cells, (2) a shortening of the cell-cycle transit time, and (3) recruitment of normally non-proliferating cells into active proliferation. These conclusions have been extended by constructing several different complex but theoretically possible recovery models and the validity of each of these models has been evaluated by simulating the following biological data: the number of cells in the S and M-phase of the cell cycle, total viable cells per crypt, and the per cent labeled mitosis and the number of labeled cells following 3H-TdR injections at 9 and 21 hr after HU treatment. The model which showed visually the best overall agreement with all sets of the data was chosen as "most probable' and leads to the following interpretations. Immediately after the end of the HU block (i.e. 5 hr after HU injection) the modal cell-cycle transit time is reduced to 8 hr. By 17 hr after HU, the modal transit time is increased to 10 hr. Repopulation of the proliferating compartment, i.e. restoration of the proliferating compartment back to the control value, occurs between 12 and 17 hr after HU injection and probably consists of both recycling of the proliferating cells (i.e. they do not progress up into the non-proliferating compartment) and recruitment of the non-proliferating cells into active proliferation. Also, the rate at which the non-proliferating cells move onto the villi is reduced temporarily. The overall recovery process results in a crypt which temporarily is larger than control and produces villi cells at a rate which is faster than the control. The time when the crypt size and villus cell production rate return to normal cannot be established using the available data.
The kinetic mechanism of action of octopine dehydrogenase was investigated. This enzyme catalyses the reversible dehydrogenation of D-octopine to L-arginine and pyruvate, in the presence of nicotinamide-adenine dinucleotide. Initial velocity and product inhibition studies were carried out in both directions. Most of the results are consistent with a bi-ter sequential mechanism where NAD+ binds first to the enzyme followed by D-octopine, and the products are released in the order L-arginine, pyruvate and NADH. Various kinetic parameters were determined for each reactant at 33 degrees C, at pH 9.6 for NAD reduction, at pH 6.6 for NADH oxidation.
Steady-state kinetics of electron transfer through the cytochrome chain of uncoupled ultrasonic submitochondrial particles at different pH values were studied. The rate constants calculated according to Pring's equation (k1=V/Prpoxt i+1) were found to increase linearly with the increase in the rate of electron transfer. Linearity was observed, however, only at relatively low rates of electron transfer. Several kinetic models were developed and analysed to fit the experimental data on the basis of the suggested activation of respiratory chains induced by their functioning. The best agreement with the experimental data was obtained with the model implying that the rate of activation of the electron carriers is directly proportional to the overall rate of electron transfer and the portion of non-activated respiratory chains in the system. It followed therefrom that electron transfer through already activated chains induced activation of adjacent non-activated chains. This model made it possiple to determine the rate constants for non-activated (ki) and activated (k) carrier states and the life-times of activated carriers (tau).
Solvolysis of N-diallylacetylurea and 5.5-diallylmalonuric acid was investigated in the pH range ca. 8--12 by means of spectrophotometric and t.l.c. methods. Their log k--pH profiles were constructed from the experimental results obtained by degradation at 70 degrees C. Therefore, specific catalytic rate constants and pKa's were derived. The kinetic mechanism of N-diallylacetylurea solvolysis, resulting among other things from the so-called kinetic salt effect, depends on hydroxyl-ion attack on its undissociated and monoanionic forms. However, the degradation of alpha.alpha-diallylmalonuric acid in the pH range 10--12 is an example of specific base catalysis which can be explained by hydroxyl-ion attack on its monoanionic species. The degradation of alpha.alpha-diallylmalonuric acid below pH=10 does not follow a theoretical equation postulated, because the spectrophotometric method does not allow monitoring the formation of N-diallylacetylurea in the presence of the above acid. Thin-layer chromatography was used to check different pathways of transformations of the intermediate studies.
Kinetic parameters for carboxypeptidase Y [EC 3.4.12.1], characterized as a nonspecific enzyme, are given for the hydrolysis of a series of acylated peptides, acylated amino acid esters, and amides. We confirmed that the enzyme released COOH-terminal proline and beta-alanine at an appreciable rate, as well as neutral amino acids with aromatic and aliphatic side chains at a very high speed. The rates of hydrolysis of ester and amide substrates were compatible with those produced by chymotrypsin [EC 3.4.21.1]. Stereospecificity was also demonstrated by the failure to hydrolyze peptide, ester, amide, and anilide substrates containing a D-amino acid. The effects of pH, solvents, and salt concentrations on the kinetic parameters of hydrolysis of peptide and ester substrates are also described.