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PubMed2002

Quantification of beta-adrenoceptor density in the human heart with (S)-[11C]CGP 12388 and a tracer kinetic model.

The aim of this study was to determine whether the beta-adrenoceptor receptor density (Bmax) and the ligand affinity (KD) of (S)-[11C]CGP 12388 for the beta-adrenoceptor receptor could be determined using full tracer kinetic modelling of the transport of the ligand and its interaction with the receptor. This approach minimises the a priori assumptions and may thus serve as a gold standard to validate other simplified methods. Dynamic positron emission tomography (PET) data were acquired in six healthy subjects during 60 min. Three different injection protocols were applied, each consisting of three injections with varying SAs: high specific activity (SA), low SA or unlabelled ligand only. Arterial blood samples were collected via a cannula in the radial artery. Time-activity data in myocardial tissue were obtained using regions of interest (ROIs) on short-axis planes. All data were analysed with a two-tissue compartment, six-parameter (K1, k2, k(on), k(off), Bmax, F(bv)) model that relies on explicit compartments for describing the kinetics of both labelled and unlabelled radioligand. Time-activity curves showed that unlabelled ligand could displace the radioligand from the receptor. This resulted in increased radioactivity levels in plasma. Modelling results yielded Bmax values of 9.74+/-1.80 nM and a KD of 0.58+/-0.22 nM, assuming a reaction volume of 0.15. In addition, parametric polar images of Bmax could be calculated. The protocol with injections of high SA, low SA, and unlabelled ligand, respectively, was found to be the most sensitive to parameter changes. We conclude that with tracer kinetic modelling of (S)-[11C]CGP 12388, the beta-adrenoceptor density in the human heart can accurately be obtained in vivo. This approach may thus serve as a gold standard.

Adult↗
PubMed2001

Catalytic acid-base groups in yeast pyruvate decarboxylase. 3. A steady-state kinetic model consistent with the behavior of both wild-type and variant enzymes at all relevant pH values.

The widely quoted kinetic model for the mechanism of yeast pyruvate decarboxylase (YPDC, EC 4.1.1.1), an enzyme subject to substrate activation, is based on data for the wild-type enzyme under optimal experimental conditions. The major feature of the model is the obligatory binding of substrate in the regulatory site prior to substrate binding at the catalytic site. The activated monomer would complete the cycle by irreversible decarboxylation of the substrate and product (acetaldehyde) release. Our recent kinetic studies of YPDC variants substituted at positions D28 and E477 at the active center necessitate some modification of the mechanism. It was found that enzyme without substrate activation apparently is still catalytically competent. Further, substrate-dependent inhibition of D28-substituted variants leads to an enzyme form with nonzero activity at full saturation, requiring a second major branch point in the mechanism. Kinetic data for the E477Q variant suggest that three consecutive substrate binding steps may be needed to release product acetaldehyde, unlikely if YPDC monomer is the minimal catalytic unit with only two binding sites for substrate. A model to account for all kinetic observations involves a functional dimer operating through alternation of active sites. In the context of this mechanism, roles are suggested for the active center acid-base groups D28, E477, H114, and H115. The results underline once more the enormous importance that both aromatic rings of the thiamin diphosphate, rather than only the thiazolium ring, have in catalysis, a fact little appreciated prior to the availability of the 3-dimensional structure of these enzymes.

Acetaldehyde↗
PubMed1983

[Kinetic model of the gating system of the sodium channel in a Ranvier node membrane].

A kinetic model of the sodium channel gating system consisting of four subunits with three states--closed (X), open (Y) and inactivated (Z)--is proposed. For the channel to conduct, all the four subunits must be in the open state. The transitions between states X and Y are independent, while those between states X and Z are coupled, so that for the particle considered transition of one of two neighbouring particles into state Z increases the activation energy of the step by kT. The model fits rather well to the experimental data.

Animals↗
PubMed1988

Metabolic studies with L-[1-14C]tyrosine for the investigation of a kinetic model to measure protein synthesis rates with PET.

To evaluate a kinetic model for measuring protein synthesis rates by positron emission tomography (PET) in neoplastic and normal tissue, metabolic studies with L-[1-14C]tyrosine were carried out. As an animal model, rats bearing Walker 256 carcinosarcoma were used. Within 60 min after injection, several metabolic parameters were measured. The highest radioactivity uptake, expressed as the differential absorption ratio, was found in pancreas, followed by liver, tumor, and brain. A rapid decarboxylation was observed during the first 15 min. After 60 min, 7.4% of the total injected 14C was expired as 14CO2. In plasma a significant amount of [14C]bicarbonate was detected, but in tissue the amount was negligible. Protein incorporation increased with time. The incorporation rate was the highest in the liver followed by pancreas, tumor, and brain tissues. At 60 min after injection, more than approximately 80% of the 14C in tissue was protein bound. In plasma after a rapid clearance during the first 15 min, the total 14C level increased rapidly and paralleled the increase of protein-bound 14C. As nonprotein [14C]metabolites, in plasma, tumor and brain tissues, p-hydroxyphenylpyruvic acid, p-hydroxyphenyllactic acid, and unidentified metabolites were observed by high performance liquid chromatography. The formation of 14C-labeled 3,4-dihydroxyphenylalanine was found to be negligible. The total amount of these nonprotein metabolites increased with time. At 60 min after injection the percentages of the total nonprotein metabolites and [14C]bicarbonate were only 5.0%, 1.9%, and 3.7% in plasma, tumor and brain tissue, respectively. From our data it is concluded that [11C]carboxylic-labeled tyrosine would be a suitable radiopharmaceutical for measuring protein synthesis rates in neoplastic and normal tissue by PET.

Animals↗
PubMed1998

A putative kinetic model for substrate metabolisation by Drosophila acetylcholinesterase.

Insect acetylcholinesterase, an enzyme whose catalytic site is located at the bottom of a gorge, can metabolise its substrate in a wide range of concentrations (from 1 microM to 200 mM) since it is activated at low substrate concentrations. It also presents inhibition at high substrate concentrations. Among the various rival kinetic models tested to analyse the kinetic behaviour of the enzyme, the simplest able to explain all the experimental data suggests that there are two sites for substrate molecules on the protein. Binding on the catalytic site located at the bottom of the gorge seems to be irreversible, suggesting that each molecule of substrate which enters the active site gorge is metabolised. Reversible binding at the peripheral site of the free enzyme has high affinity (2 microM), suggesting that this binding increases the probability of the substrate entering the active site gorge. Peripheral site occupation decreases the entrance rate constant of the second substrate molecule to the catalytic site and strongly affects the catalytic activity of the enzyme. On the other hand, catalytic site occupation lowers the affinity of the peripheral site for the substrate (34 mM). These effects between the two sites result both in apparent activation at low substrate concentration and in general inhibition at high substrate concentration.

Acetylcholine↗
PubMed2005

Kinetic modeling of 3'-deoxy-3'-fluorothymidine in somatic tumors: mathematical studies.

UNLABELLED: We present a method to measure the regional rate of cellular proliferation using a positron-emitting analog of thymidine (TdR) for human imaging studies. The method is based on the use of 3'-deoxy-3'-(18)F-fluorothymidine (FLT) to estimate the flux of TdR through the exogenous pathway. The model reflects the retention of FLT-monophosphate (FLTMP), which is generated by the phosphorylation of FLT by thymidine kinase 1 (TK1), the initial step in the exogenous pathway. METHODS: A model of FLT kinetics has been designed based on the assumptions of a steady-state synthesis and incorporation of nucleotides into DNA, an equilibration of the free nucleoside in tissue with the plasma level, and the relative rates of FLT and TdR phosphorylation from prior data using direct analysis with in vitro assays. A 2-compartment model with 4 rate constants adequately describes the kinetics of FLT uptake and retention over 120 min and leads to an estimation of the rate of cellular proliferation using the measured FLT blood clearance and the dynamic FLT uptake curve. RESULTS: Noise characteristics of kinetic parameter estimates for 3 tissues were assessed under a range of conditions representative of human cancer patient imaging. The FLT flux in these tissues can be measured with a SE of <5%, and FLT transport can be estimated with a SE of <15%. Abbreviating the data collection to 60 min or neglecting k(4), giving a 3-parameter model, results in an unsatisfactory loss of accuracy in the flux constant in tumor simulations. CONCLUSION: These analyses depict model behavior and provide expected values for the accuracy of parameter estimates from FLT imaging in human patients. Our companion paper describes the performance of the model for human data in patients with lung cancer. Further studies are necessary to determine the fidelity of K(FLT) (FLT flux) as a proxy for K(TDR) (thymidine flux), the gold standard for imaging cellular proliferation.

Algorithms↗
PubMedDate not supplied

Intracellular activation of cytotoxic agents: kinetic models for methylnitrosoureas and N-methyl-N'-nitro-N-nitrosoguanidine in cell culture.

The cytotoxic activity of N-methyl-N-nitrosourea (MNU), streptozotocin, and N-methyl-N'-nitro-N-nitrosoguanidine (MNNG) was determined in cell culture by using a P388 cell growth rate inhibition assay. These agents appear to have very different activities when inhibition is related to the agent concentration in the culture medium: ED50(C0) = 40 microM for MNNG to 875 microM for streptozotocin. The mechanism of action of these three agents involves conversion to the active methanediazonium ion and subsequent methylation of cellular macromolecules. As a consequence, the rates of conversion of the parent agent to the methylating species in the medium and within the cell are important parameters that also need to be considered to reach a more detailed understanding of the mechanism of action. In order to do this, a kinetic model has been developed to calculate the concentration of drug that is converted to active methylating species within the cell during the assay incubation period. The use of cell culture kinetic models was extended from simple compounds activated through solvolytic reactions (nitrosoureas) to an agent that undergoes selective intracellular activation (MNNG). By use of measured values for initial drug concentration, incubation time, and cell volume, as well as extracellular and intracellular chemical activation rate constants, the intracellular concentration, [P4], which represents the cumulative intracellular reaction products formed during the incubation period, was calculated and related to cytotoxicity. All three agents showed an ED50[P4] between 140 and 180 microM, and for MNNG, this ED50 was independent of extracellular sulfhydryl concentration.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1998

The general kinetic model of electron transfer in photosynthetic reaction centers activated by multiple flashes.

A new general kinetic model for the functioning of photosynthetic reaction centers (RC) of purple bacteria, under multiple flash activation, has been developed. The model includes the primary electron donor (P870) as well as the primary (QA) and secondary (QB) acceptor quinones. The new features of this general model include: (1) consideration of four different states of the QB binding site (vacant, occupied by QB, by QB- and by QBH2), (2) incorporation of the dark relaxation of the RC between flashes, (3) the assumption of fast exchange of quinones between the RC and quinone pool in detergent micelles or chromatophore membrane, (4) description of the kinetics of electron transfer in both oxidized (no donor for P870+) and reduced (in the presence of donor for P870+) conditions simultaneously, (5) the consideration of both single and multiple flash activation of the RC of purple bacteria and (6) consideration of the cumulative effects of all previous flashes of the series in the response induced by the current flash. This model is used to calculate and predict (1) flash-induced binary oscillations of the secondary acceptor semiquinone (QB-), (2) flash-induced behavior of P870+ in the presence and absence of electron donor and (3) the apparent equilibrium constant of electron transfer between QA and QB and others. Different characteristics of RC are analyzed as a function of flash intensity, time between flashes, concentration of electron donor, redox-potential of the medium, concentration of pool quinone and quinol, association and dissociation equilibrium constants for quinone and quinol at the QB binding site, equilibrium constants of electron transfer between QA- and QB and between QA- and QB-, as well as the rate constants of oxidation of QA- and QB- by redox mediators. The proposed model can be used as a basis for assays of kinetic behavior of native and mutant RC of purple bacteria and for determination of the factors influencing the release of QH2 from RC. The latter is needed for analysis of factors controlling light-activated electron transport in the cytochrome bc1 complexes of purple bacteria by quinol molecules released from RC. The developed general approach for parallel consideration of flash-induced transitions of RC and its following dark relaxation between flashes can also be used for kinetic description of photosynthetic RC of oxygenic photosynthesis.

Electron Transport↗
PubMed1986

A kinetic model for the Ca2+ + Mg2+-activated ATPase of sarcoplasmic reticulum.

The Ca2+ + Mg2+-activated ATPase of sarcoplasmic reticulum exhibits complex kinetics of activation with respect to ATP. ATPase activity is pH-dependent, with similar pH-activity profiles at high and low concentrations of ATP. Low concentrations of Ca2+ in the micromolar range activate the ATPase, whereas activity is inhibited by Ca2+ at millimolar concentrations. The pH-dependence of this Ca2+ inhibition and the effect of the detergent C12E8 (dodecyl octaethylene glycol monoether) on Ca2+ inhibition are similar to those observed on activation by low concentrations of Ca2+. On the basis of these and other studies we present a kinetic model for the ATPase. The ATPase is postulated to exist in one of two conformations: a conformation (E1) of high affinity for Ca2+ and MgATP and a conformation (E2) of low affinity for Ca2+ and MgATP. Ca2+ binding to E2 and to the phosphorylated form E2P are equal. Proton binding at the Ca2+-binding sites in the E1 and E2 conformations explains the pH-dependence of Ca2+ effects. Binding of MgATP to the phosphorylated intermediate E1'PCa2 and to E2 modulate the rates of the transport step E1'PCa-E2'PCa2 and the return of the empty Ca2+ sites to the outside surface of the sarcoplasmic reticulum, as well as the rate of dephosphorylation of E2P. Only a single binding site for MgATP is postulated.

Adenosine Triphosphate↗
PubMed1974

Derivation of a quantitative kinetic model for a visual pigment from observations of early receptor potential.

A "complete" and quantitative kinetic model for the states and transitions of the barnacle visual pigment in situ has been constructed from intracellular recordings of the early receptor potential responses to long light pulses. The model involves two stable and four thermolabile states and 10 photochemical, thermal, and metabolic transitions among them. The existence of each state and transition is demonstrated by qualitative examination of the response resulting from a carefully chosen experimental paradigm (combination of intensity, duration, and wavelength of adaptation and stimulation). Quantitative examination of the same responses determines all of the model transition rates, but only puts constraints on the state dipole moments. The latter are determined, and the former refined, by quantitative comparison of the predictions of the complete model with the responses to a set of paradigms chosen to involve as many states and transitions as possible. The fact that good fits can be obtained to these responses without further modification of the model supports its completeness.

Animals↗
PubMed1998

A physiologically based kinetic model for lead in children and adults.

A physiologically based model of lead kinetics in children and adults has been developed and tested. The premises on which the physiologically based model is founded are reviewed in this paper. Because 95% or more of the body burden of lead in adults is found in the bone, bone metabolism is central to the model. Bone volumes are expressed as functions of body weight. Bone formation and resorption rates are estimated from human studies of stable labeled calcium kinetics. Cortical and trabecular bone are modeled separately, with their surface-to-volume ratios taken into account. Standardized growth curves are used to relate body weight to age. Other model features such as organ volumes and physiologic functions are related to body weight based on measurements made in human subjects over a range of ages. Calibrations of the model to two human data sets are shown, and two applications to specific research questions are illustrated. A brief comparison of the structure of this model with that of the Leggett model, and a comparison of the output of this model with that of the integrated exposure uptake biokinetic model of the U.S. Environmental Protection Agency, are also included.

Adult↗
PubMed1992

Studies on kinetic model of vitamin C two-step fermentation process.

This paper aims at analyzing the bioconversion process from L-sorbose to 2-Keto-L-gulonic acid with the aid of the growth factor assumption. Fermentation mechanism is discussed after making necessary simplifications. A model is established for this second step fermentation process. Nonlinear optimization together with Runge-Kutta method, are used to obtain model parameters. Results of computer simulation agree with experimental data to show the reliability of the kinetic model.

Ascorbic Acid↗
PubMed1999

Kinetic model for the co-action of beta-amylase and debranching enzymes in the production of maltose.

The kinetics of the hydrolysis of starch with beta-amylase and debranching enzymes was studied. The hydrolysis of the alpha-1, 6-glycoside bonds of the substrate by debranching enzymes does not create any new nonreducing ends, so debranching enzyme promotes the action of beta-amylase not by increasing the concentration of the substrate of beta-amylase but by increasing the linear linkage portion of the substrate. The introduction of an effective chain length function was used to formulate a kinetic model.

Biotechnology↗
PubMed2001

Duplication and extension of the Thorneley and Lowe kinetic model for Klebsiella pneumoniae nitrogenase catalysis using a MATHEMATICA software platform.

The Thorneley and Lowe kinetic model for nitrogenase catalysis was developed in the early to mid 1980s, and has been of value in accounting for many aspects of nitrogenase catalysis. It has also been of value by providing a model for predicting new catalytic behavior. Since its original publication, new results have been obtained and have been successfully incorporated into the model. However, the computer program used for nitrogenase simulations has not been generally available. Using kinetic schemes and assumptions previously outlined by Thorneley and Lowe, we report attempts to duplicate the original T&L kinetic simulation for Klebsiella pneumoniae nitrogenase catalysis using an updated simulation based on the MATHEMATICA programming format, which makes it more user-friendly and more readily available. Comparisons of our simulations with the original T&L simulations are generally in agreement, but in some cases serious discrepancy is observed. Possible reasons for the differences are discussed. In addition to duplicating the original T&L model, we report effects of updating it by including information that has come to light subsequent to its original publication.

Adenosine Triphosphate↗
PubMed1987

Tracer-kinetic models for measuring cerebral blood flow using externally detected radiotracers.

All tracer-kinetic models currently employed with positron-emission tomography (PET) are based on compartmental assumptions. Our first indication that a compartmental model might suffer from severe limitations in certain circumstances when used with PET occurred when we implemented the Kety tissue-autoradiography technique for measuring CBF and observed that the resulting CBF estimates, rather than remaining constant (to within predictable statistical uncertainty) as expected, fell with increasing scan duration T when T greater than 1 min. After ruling out other explanations, we concluded that a one-compartment model does not possess sufficient realism for adequately describing the movement of labeled water in brain. This article recounts our search for more realistic substitute models. We give our derivations and results for the residue-detection impulse responses for unit capillary-tissue systems of our two candidate distributed-parameter models. In a sequence of trials beginning with the simplest, we tested four progressively more detailed candidate models against data from appropriate residue-detection experiments. In these, we generated high-temporal-resolution counting-rate data reflecting the history of radiolabeled-water uptake and washout in the brains of rhesus monkeys. We describe our treatment of the data to yield model-independent empirical values of CBF and of other parameters. By substituting these into our trial-model functions, we were able to make direct comparisons of the model predictions with the experimental dynamic counting-rate histories, confirming that our reservations concerning the one-compartment model were well founded and obliging us to reject two others. We conclude that a two-barrier distributed-parameter model has the potential of serving as a substitute for the Kety model in PET measurements of CBF in patients, especially when scan durations for T greater than 1 min are desired.

Animals↗
PubMed2004

Discrimination among eight modified michaelis-menten kinetics models of cellulose hydrolysis with a large range of substrate/enzyme ratios: inhibition by cellobiose.

The kinetics of exoglucanase (Cel7A) from Trichoderma reesei was investigated in the presence of cellobiose and 24 different enzyme/Avicel ratios for 47 h, in order to establish which of the eight available kinetic models best explained the factors involved. The heterogeneous catalysis was studied and the kinetic parameters were estimated employing integrated forms of Michaelis-Menten equations through the use of nonlinear least squares. It was found that cellulose hydrolysis follows a model that takes into account competitive inhibition by cellobiose (final product) with the following parameters: Km = 3.8 mM, Kic = 0.041 mM, kcat = 2 h-1 (5.6 x 10-4 s-1). Other models, such as mixed type inhibition and those incorporating improvements concerning inhibition by substrate and parabolic inhibition, increased the modulation performance very slightly. The results support the hypothesis that nonproductive enzyme substrate complexes, parabolic inhibition, and enzyme inactivation (Selwyn test) are not the principal constraints in enzymatic cellulose hydrolysis. Under our conditions, the increment in hydrolysis was not significant for substrate/enzyme ratios <6.5.

Algorithms↗
PubMed1991

Lipid-dependent membrane enzymes. Kinetic modelling of the activation of protein kinase C by phosphatidylserine.

A previously developed kinetic theory for lipid-dependent membrane enzymes (Sandermann, H. (1982) Eur. J. Biochem. 127, 123-128) is used to examine the activation of protein kinase C by phosphatidylserine. Hill-coefficients ranging up to 11 have been reported for activation in mixed micelles with Triton X-100. On the basis of this uniquely high degree of cooperativity, protein kinase C has been postulated to represent a new class of lipid-dependent membrane enzymes (Newton, A. and Koshland, D.E., Jr. (1989) J. Biol. Chem. 264, 14909-14915). In contrast, activation in the absence of Triton X-100 has led to Hill-coefficients of only less than or equal to 2.6. In order to resolve the apparent discrepancy, activation is now considered to involve binding of PS monomers to interacting sites on the enzyme, a non-activating PS trapping process also occurring in the presence of Triton X-100. Estimates for trapping are made for several sets of published data for micellar activation. The kinetic model developed here successfully fits each data set using a Hill-coefficient of only 3.0. An influence of Ca2+/ions or of a two-step mechanism of lipid-protein interaction are considered as possible molecular explanations. It is concluded (i) that lipid activation of protein kinase C may proceed without unique cooperativity and (ii) that ligand trapping could provide another means for 'threshold-type' kinetic regulation of membrane enzyme and receptor systems.

Calcium↗