Measuring Rates of Appearance in Systems Which are not in Steady State

1973 ◽  
Vol 51 (2) ◽  
pp. 91-101 ◽  
Author(s):  
Kenneth H. Norwich
Keyword(s):  
Steady State ◽  
Specific Activity ◽  
General System ◽  
Chemical Substance ◽  
Physiological System ◽  
Mathematical Basis ◽  
Endogenous Production ◽  
General Method

A general method is advanced for measuring the rate of appearance (production) of a chemical substance in an intact physiological system when this rate is changing with respect to time. The method involves infusing an isotope of this substance at such a rate that specific activity remains constant in space and in time. The means of achieving this constancy are discussed, and the mathematical basis of the method is developed for a fairly general system. An. experiment is described in some detail to show how the rate of endogenous production of glucose in a dog may be calculated when this rate is changing quite rapidly.

Theory of production rate calculations in steady and non-steady states and its application to glucose metabolism

1992 ◽  
Vol 262 (6) ◽  
pp. E779-E790 ◽  
Author(s):  
J. A. Jacquez
Keyword(s):  
Steady State ◽  
Experimental Design ◽  
Specific Activity ◽  
Glucose Production ◽  
Central Compartment ◽  
Correct Equation ◽  
Endogenous Production ◽  
Correction Terms ◽  
Theory Of Production ◽  
Constant Specific Activity

I present a review and synthesis of the basic theory, steady state, and non-steady state for the calculation of metabolite production rates for systems that have a central well-mixed compartment that is the site of tracer input and sampling. The theory is then applied to the calculation of glucose production. If the only inputs are into the central compartment, an experimental design that involves varying tracer infusion rates to maintain constant specific activity in the central compartment and the same constant specific activity in the peripheral compartments allows calculation of the endogenous production. That holds even if the models are unidentifiable. The correct equation and Steele's pool fraction approximation reduce to the same result for this experimental design. However, that does not justify the use of Steele's equation when there are deviations from the exact experimental design. When the specific activity in the central compartment is not constant, model-dependent correction terms to Steele's equation are needed.

THE FATE OF 1,2-3H CORTEXOLONE IN MAN

1964 ◽  
Vol 47 (1) ◽  
pp. 165-176 ◽  
Author(s):  
R. De Hertogh ◽  
J. J. Hoet ◽  
F. Materazzi ◽  
E. Ekka
Keyword(s):  
Steady State ◽  
Production Rate ◽  
Open System ◽  
Specific Activity ◽  
Normal Subjects ◽  
Apparent Volume ◽  
Endogenous Production ◽  
Disappearance Curve ◽  
The Mean ◽  
Life Values

ABSTRACT 1,2-3H cortexolone was injected into normal subjects and the disappearance curve of the radioactive hormone in the plasma was determined. This follows a biexponential function, according to a digital computer analysis. The half-life values calculated for the first and the second components of the experimental curves are 4 and 24 min respectively. On the basis of a two compartment open system, in which the second compartment is assumed to be metabolically inactive, cortexolone spreads rapidly into an apparent volume of 19 l and more slowly into a total volume of 37 l. Endogenous production rate of cortexolone was estimated from the isotope dilution of the injected hormone as determined by measurement of the specific activity of urinary tetrahydrocortexolone. The mean production rate for 4 normal subjects was calculated to be 1100 μg per day. From these data the size of the endogenous pool of cortexolone was calculated. This averages 9.3 and 9.2 μg for the first and second compartments respectively. The experiments are discussed with regard to a possible disturbance in the steady state by the amount of cortexolone injected.

scholarly journals Calculation of the Albumin Catabolic Rate in the Non-Steady State

1963 ◽  
Vol 46 (3) ◽  
pp. 405-413 ◽  
Author(s):  
J. J. Franks
Keyword(s):  
Steady State ◽  
Specific Activity ◽  
Steady States ◽  
Breakdown Rate ◽  
Catabolic Rate ◽  
General Method

Methods which are in current use for the calculation of the albumin breakdown rate apply only to the steady state animal. In this paper a simple but more general method based on analyses of I131-albumin tracer data is presented. It utilizes easily measured plasma specific activity and excretory data and is equally applicable to the steady and non-steady states.

Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds

1978 ◽  
Vol 10 (04) ◽  
pp. 836-851 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Steady State ◽  
General System ◽  
State Distribution ◽  
Lifetime Distributions ◽  
State Dependent ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
Infinite State ◽  
State Case ◽  
Residual Lifetimes

A generalized semi-Markov process with speeds describes the fluctuation, in time, of the state of a certain general system involving, at any given time, one or more living components, whose residual lifetimes are being reduced at state-dependent speeds. Conditions are given for the stationary state distribution, when it exists, to depend only on the means of some of the lifetime distributions, not their exact shapes. This generalizes results of König and Jansen, particularly to the infinite-state case.

scholarly journals Triosephosphate isomerase deficiency: consequences of an inherited mutation at mRNA, protein and metabolic levels

2005 ◽  
Vol 392 (3) ◽  
pp. 675-683 ◽  
Author(s):  
Judit Oláh ◽  
Ferenc Orosz ◽  
László G. Puskás ◽  
László Hackler ◽  
Margit Horányi ◽  
...  
Keyword(s):  
Steady State ◽  
Triosephosphate Isomerase ◽  
Specific Activity ◽  
Energy State ◽  
Dihydroxyacetone Phosphate ◽  
Peptidase Activity ◽  
Mrna Levels ◽  
Regulatory Enzymes ◽  
Computational Data ◽  
Fructose 1,6 Bisphosphate

Triosephosphate isomerase (TPI) deficiency is a unique glycolytic enzymopathy coupled with neurodegeneration. Two Hungarian compound heterozygote brothers inherited the same TPI mutations (F240L and E145Stop), but only the younger one suffers from neurodegeneration. In the present study, we determined the kinetic parameters of key glycolytic enzymes including the mutant TPI for rational modelling of erythrocyte glycolysis. We found that a low TPI activity in the mutant cells (lower than predicted from the protein level and specific activity of the purified recombinant enzyme) is coupled with an increase in the activities of glycolytic kinases. The modelling rendered it possible to establish the steady-state flux of the glycolysis and metabolite concentrations, which was not possible experimentally due to the inactivation of the mutant TPI and other enzymes during the pre-steady state. Our results showed that the flux was 2.5-fold higher and the concentration of DHAP (dihydroxyacetone phosphate) and fructose 1,6-bisphosphate increased 40- and 5-fold respectively in the erythrocytes of the patient compared with the control. Although the rapid equilibration of triosephosphates is not achieved, the energy state of the cells is not ‘sick’ due to the activation of key regulatory enzymes. In lymphocytes of the two brothers, the TPI activity was also lower (20%) than that of controls; however, the remaining activity was high enough to maintain the rapid equilibration of triosephosphates; consequently, no accumulation of DHAP occurs, as judged by our experimental and computational data. Interestingly, we found significant differences in the mRNA levels of the brothers for TPI and some other, apparently unrelated, proteins. One of them is the prolyl oligopeptidase, the activity decrease of which has been reported in well-characterized neurodegenerative diseases. We found that the peptidase activity of the affected brother was reduced by 30% compared with that of his neurologically intact brother.

Endurance training enhances lactate clearance during hyperlactatemia

1989 ◽  
Vol 257 (5) ◽  
pp. E782-E789 ◽  
Author(s):  
C. M. Donovan ◽  
M. J. Pagliassotti
Keyword(s):  
Steady State ◽  
Endurance Training ◽  
Specific Activity ◽  
Lactate Production ◽  
Lactate Clearance ◽  
Lactate Removal ◽  
Lactate Levels ◽  
Infusion Period ◽  
Mixed Venous ◽  
Blood Lactate Levels

Constant infusions of cold molar lactate (178.0 +/- 1.6 mumol.kg-1.min-1), [U-14C]lactate (0.50 muCi/min), and [6-3H]glucose (0.5 muCi/min) were employed to study the effects of endurance training (running 1 h/day, at 38 m/min, 10% grade) on lactate clearance in resting, hyperlactatemic rats. Before infusion, resting blood lactate levels were not significantly different between controls, 1.10 +/- 0.04 mM, and trained animals, 1.16 +/- 0.04 mM. Lactate levels increased significantly during the infusion period, attaining steady-state mixed venous concentrations of 11.32 +/- 0.24 mM and 5.44 +/- 0.09 mM, respectively, for controls and trained animals. Lactate clearance rates, based on net lactate removal (i.e., not tracer-estimated lactate removal), were twofold greater in trained animals vs. controls, 33.0 +/- 0.7 and 15.4 +/- 0.4 ml.kg-1. min-1, respectively. Lactate specific activity values during the infusion period were not significantly different between controls, 22,243 +/- 236 dpm/mumol, and trained animals, 21,270 +/- 374 dpm/mumol, indicating similar endogenous dilution of the pyruvate-lactate pool. For both control and trained animals, essentially 100% of the 14C infused as lactate was recovered as either glucose or CO2; however, trained animals demonstrated a 25% greater rate of gluconeogenesis. At a given lactate production rate, trained animals maintain lower lactate levels through enhanced clearance via gluconeogenesis and oxidation.

Estimation of the rate of appearance in the non-steady state with a two-compartment model

1992 ◽  
Vol 263 (2) ◽  
pp. E400-E415 ◽  
Author(s):  
A. Mari
Keyword(s):  
Steady State ◽  
Time Course ◽  
Specific Activity ◽  
Glucose Production ◽  
Compartment Model ◽  
New Method ◽  
Two Compartment Model ◽  
Glucose Clamp Technique ◽  
Glucose Output ◽  
The Relationship

A simple tracer-based method for calculating the rate of appearance of endogenous substances in the non-steady state, free from the inconsistencies of Steele's equation, is still lacking. This paper presents a method based on a two-compartment model by which the rate of appearance can be calculated with only a modest increase in complexity over Steele's approach. An equation is developed where the rate of appearance is expressed as a sum of three terms: a steady-state term, a term for the first compartment, and a term for the second compartment. The formula employs three parameters and makes the relationship between rate of appearance and specific activity changes explicit. An equation is also provided for estimating the error of the method in each individual run. The algorithm can be implemented with a spreadsheet on a personal computer. Simulated and experimental data obtained by the hyperinsulinemic euglycemic glucose clamp technique were used as a test. The accuracy with which the time course of glucose production could be reconstructed was clearly better than that using Steele's equation. Marked negative values for endogenous glucose output were calculated with Steele's equation but not with the new method. The characteristics of generality, simplicity, and accuracy and the availability of an error estimate make this new method suitable for routine application to non-steady-state tracer analysis.

Role of glucose in corneal metabolism

1985 ◽  
Vol 249 (5) ◽  
pp. C409-C416 ◽  
Author(s):  
R. S. Thies ◽  
L. J. Mandel
Keyword(s):  
Oxygen Consumption ◽  
Steady State ◽  
Specific Activity ◽  
Krebs Cycle ◽  
Lactate Production ◽  
Minor Component ◽  
Acid Oxidation ◽  
Endogenous Fatty Acid ◽  
Nonsteady State ◽  
A Minor

Glucose catabolism by glycolysis and the Krebs cycle was examined in the isolated rabbit cornea incubated with [6-14C]glucose. The production of [14C]lactate and 14CO2 from this substrate provided minimal values for the fluxes through these pathways since the tissue was in metabolic steady state but not isotopic steady state during the 40-min incubation. The specific activity of lactate under these conditions was one-third of that for [6-14C]glucose, and label dilution by exchange with unlabeled alanine was minimal, suggesting that glycogen degradation was primarily responsible for this dilution of label in the Embden-Meyerhof pathway. In addition, considerable label accumulation was found in glutamate and aspartate. Calculations revealed that these endogenous amino acid pools were not isotopically equilibrated after the incubation period, suggesting that they were responsible for the isotopic nonsteady state by exchange dilution through transaminase reactions with labeled intermediates. An estimate of glucose oxidation by the Krebs cycle, which was corrected for label dilution by exchange, indicated that glucose could account for most of the measured corneal oxygen consumption that was coupled to oxidative phosphorylation. A minor component of this respiration could not be accounted for by glucose or glycogen oxidation. Additional experiments suggested that endogenous fatty acid oxidation was probably also active under these conditions. Finally, reciprocal changes in plasma membrane Na+-K+-ATPase activity induced by ouabain and nystatin were found to concomitantly alter oxygen consumption rates and [14C]lactate production from [6-14C]glucose. These results demonstrated the capacity for regulating glycolysis and the Krebs cycle in response to changing energy demands in the cornea.

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