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Biomedical subjects

G L Atkins

Publications and source records attributed to G L Atkins.

At least 37 records · Page 2Linked to original sources
PubMed1980

Simulation studies on the kinetics of intestinal absorption.

1. A model has been used to simulate the absorption of solutes from perfused intestines. The model makes possible the numerical solution of the differential equations describing absorption processes along the length of the intestine which cannot be solved analytically. It allows for water absorption and the non-linear fall in solute concentration down the intestine. It can be modified easily to include other features, e.g. a change in V (maximum rate of absorption) or K (solute concentration at V/2) along the intestine. 2. 90 perfect data sets have been simulated using the model. The Michaelis-Menten equation was fitted to a quarter of them using different algebraic expressions for the apparent solute concentration. The fit of the equation was very good in every case and it was not possible to explain the poorness-of-fit encountered during an earlier survey (Atkins, G.L. and Gardner, M.L.G. (1977) Biochim, Biophys. Acta 468, 127--145) in terms of the fall in solute concentration described above. 3. The equation was also fitted to all the data sets in order to compare the use of several algebraic expressions for the apparent solute concentration. It has been shown that the current practice of using either the initial concentration or the effluent concentration can lead to estimates of V and K up to amost twice their true value. It has been shown that in one situation (glucose absorption by perfused rat intestine) it is possible to use an empirical expression that will reduce the errors considerably. 4. It is also possible, and perhaps preferable, to use a computer program to fit the model directly to data from the simulated experiments and obtain precise estimates of V and K. 5. In order to show that the model can be easily modified to incorporate other characteristics of perfused intestines, simulations were performed in which V decreased linearly down the intestine. In this example, it was concluded that an inhomogeneity due to non-constancy of V cannot be detected by single-pass perfusions.

Animals↗
PubMed1980

Glucose kinetics in non-steady states.

A two-compartment model has been used to represent glucose tracer kinetics in the rabbit. Simulations were performed in which the model system was not in a steady state. The disturbances from the steady state included: input and output rates constant but not equal, rates varying linearly with time, rates varying sinusoidally with periods of 2 h and 4 min and rates varying at 1-min intervals in a random manner. Plasma glucose concentrations and 'true' mean glucose uptake rates, over the 2-h period, were calculated from the simulated data. Glucose uptake rates were also calculated from the simulated 'experimental' results using compartmental analysis and assuming the model was in a steady state. The errors caused by using compartmental analysis were found, in most cases, to be small. If doubtful experiments were to be discarded then the variation in plasma glucose concentration would be a very good guide.

Animals↗
PubMed1980

A new technique for maintaining and monitoring conscious, stress-free rabbits in a steady state: its use in the determination of glucose kinetics.

1. A new technique is described for maintaining and monitoring conscious rabbits in a steady state. Solutions were infused and blood samples were withdrawn without major surgery and without causing stress. Cannulation, for infusion and blood sampling, was via the ear veins and arteries. 2. The validity of the technique is discussed with special reference to: the amount of blood removed from the animal; the use of a plasma substitute solution; the use of heparin; and assessing whether the animal was in a steady-state with respect to glucose. 3. The technique was used to determine glucose kinetics in the fasted rabbit after an injection of [2-(3)H]glucose with subsequent blood sampling over 2 h. A two compartment model was used to calculate certain physiological values, the two principal ones being the glucose uptake rate (3.30 +/- 0.24 (13) mg.kg-1.min-1) and the initial volume of distribution (74.8 +/- 7.8 (13) ml.kg-1). 4. The accuracy and precision of the results obtained from this study are discussed and shown to be more reliable than other published values.

Animals↗
PubMed1977

The computation of saturable and linear components of intestinal and other transport kinetics.

1. Published data for absorption kinetics have been fitted by non-linear regression to (i) a single Michaelis-Menten function, (ii) a Michaelis-Menten function plus a linear term and (iii) a sum of two Michaelis-Menten functions. A series of criteria have been drawn up to establish the goodness of fit in each case. 2. In 17 out of 35 cases the Michaelis-Menten function was the "best fit". In nine cases the "best-fit" model also included a linear term, but never was the sum of two Michaelis-Menten functions accepted to be the "best-fit" model. 3. Linearity of a Lineweaver-Burk plot was of unreliable diagnostic value in assessing goodness of fit. 4. Since the fit of a Michaelis-Menten function was often poor, simulated data sets with error were used to study the influence of experimental design etc. on Michaelis-Menten parameter estimation. 5. Precision of estimation of Km is increased by increasing the number of data points, reducing their variance, increasing the data range and by straddling Km in the observations. For a given constant number of observations there is no advantage in using replicate observations at few concentrations or single values at relatively many concentrations, or in using single values rather than means. 6. The caution necessary in interpretation of kinetic models is emphasized.

Animals↗
PubMed1977

An evaluation of ways of using equilibrium dialysis to quantify the binding of ligand to macromolecule.

1. The effect of systematic error (loss of ligand, complex or macromolecule) on three of the experimental designs by which equilibrium dialysis may be used to quantify the interaction of ligand and macromolecule is examined theoretically, and the design that is least sensitive to systematic error is identified. 2. Thirteen methods for fitting the binding isotherm to experimental data are compared by using them to analyse simulated data containing random error, and the most reliable method is identified.

Dialysis↗
PubMed1976

Methods for fitting equations with two or more non-linear parameters.

1. Descriptions are given of two ways for fitting non-linear equations by least-squares criteria to experimental data. One depends on solving a set of non-linear simultaneous equations, and the other on Taylor's theorem. 2. It is shown that better parameter estimates result when an equation with two or more non-linear parameters is fitted to all the sets of data simultaneously than when it is fitted to each set in turn.

Enzymes↗
PubMed1975

A comparison of seven methods for fitting the Michaelis-Menten equation.

The Michaelis-Menten equation was fitted to simulated data containing different sorts of error by using the three linear transformations, and the methods of S. R. Cohen [Anal. Biochem. (1968) 22, 549-552], R. Eisenthal & A. Cornish-Bowden [Biochem. J. (1974) 139, 715-120], F. de M. Merino [Biochem. J. 143, 93-95] and G. N. Wilkinson [Biochem. J. (1961) 808 324-332). The best methods were those of Eisenthal & Cornish-Bowden (1974) and Wilkinson (1961).

Kinetics↗
PubMed1974

Weighting functions and data truncation in the fitting of multi-exponential functions.

Artificial data were simulated by using two-exponential functions and normally distributed pseudo-random numbers. The variation corresponded to either constant or relative variance for the data error. These data were used to test (i) three different weighting functions and (ii) the effect of data truncation on the precision of estimating the parameters of two-exponential functions.

Analysis of Variance↗
PubMed1974

A comparison of two methods for fitting the integrated Michaelis-Menten equation.

The methods of Atkins & Nimmo (1973) and Fernley (1974) for fitting the integrated Michaelis-Menten equation were compared by using the same sets of simulated experimental data. The method of Fernley (1974) is to be preferred because it gives precise and unbiased estimates of the Michaelis-Menten parameters over a wide range of substrate concentrations. However, the estimates may not be symmetrically distributed, especially at low substrate concentrations.

Catalysis↗
PubMed1974

The effect of systematic error on the accuracy of Michaelis constants and maximum velocities estimated by using the integrated Michaelis-Menten equation.

Systematic errors in initial substrate concentration (s(0)), product concentration and reaction time give much larger errors in the Michaelis-Menten parameters unless s(0) is treated as an unknown parameter. These errors are difficult to detect because the fitted curve deviates little from the data. The effect of non-enzymic reaction is also examined.

Enzymes↗