Gordon L. Atkins

Arachidonic acid binds to apolipoprotein D: implications for the protein's function

The lipocalin apolipoprotein D (ApoD) is associated in human plasma with lecithin‐cholesterol acyl transferase. It has also been found in high concentration in the fluid of gross cystic disease of the mammary gland. Using protein fluorescence quenching, it is shown that ApoD binds arachidonic acid (K aof 1.6 × 108M−1) and as previously known progesterone (K aof 2.5 × 106M−1), but neither cholesterol nor any of the other prostanoid molecules examined had measurable affinity. This specific binding of arachidonate, also observable directly, suggests a role for ApoD in the mobilisation of Arachidonic acid, and hence prostaglandin synthesis.

A versatile digital computer program for non-linear regression analysis

Abstract 1. 1. A general purpose digital computer program is described for application to biological experiments that require a non-linear regression analysis. The mathematical function, or model, to be fitted to a given set of experimental data is written as a section within the program. Given initial estimates for the parameters of the function, the program uses an iterative procedure to adjust the parameters until the sum of squares of residuals has converged to a minimum. 2. 2. The iteration procedure used in this program possesses two important advantages over those currently used, namely that second partial derivatives need not be calculated and convergence is guaranteed. 3. 3. The program is depicted in a series of flow diagrams so that it can be written in any language. 4. 4. It can be easily adapted to a wide range of non-linear functions. Three such applications are described and reference is made to several others.

Investigation of some theoretical models relating the concentrations of glucose and insulin in plasma.

Abstract In this survey 24 possible theoretical models for the regulation of plasma glucose concentration by plasma insulin concentration have been proposed and tested. A set of data, consisting of plasma glucose concentrations at various times after an intravenous injection of glucose, was selected from the literature. An attempt was made to fit each model to the chosen data using a digital computer program and ten of these were successful. The behaviour of these ten models under different experimental conditions was compared, using a simulation technique, with further published data. At this stage six models were consistent with a steady state at the start or the end of an experiment, but only three were reasonably good at predicting all aspects of the chosen experiments. One was particularly good. Two other sets of data were taken from the literature and the six best models were fitted in order to calculate replicate values of the physiological parameters.

Some applications of a digital computer program to estimate biological parameters by non-linear regression analysis.

Abstract 1. 1. A digital computer proram for non-linear regression analysis has been used to fit a wide range of biological functions directly to experimental data. 2. 2. The applications included a sine curve, the Michaelis-Menten equation, oxygen binding to haemoglobin, the kinetics of allosteric enzymes and power functions. 3. 3. A sine curve has also been fitted to data in a histogram form by minimising the sum of squares of areas. 4. 4. Where a comparison can be made, the goodness of fit was as good as, or better than, that using other methods.

A comparison of methods for estimating the kinetic parameters of two simple types of transport process.

Sets of experimental data, with known characteristics and error structures, have been simulated for the Michaelis-Menten equation plus a second term, either for linear transport or for competitive inhibition. The Michaelis-Menten equation plus linear term was fitted by several methods and the accuracy and the precision of the parameter estimates from the several methods were compared. The model-fitting methods were: three for least-squares non-linear regression, computer versions of two graphical methods and of two non-parametric methods. The most precise and accurate method was that of D.W. Marquardt (J. Soc. Ind. Appl. Math. 11 (1963) 431--441). The Michaelis-Menten equation with competitive inhibition was also fitted by several methods, viz., two for least-squared non-linear regression, non-parametric method and four variants of the Preston-Schaeffer-Curran plot (Preston, R.L. et al. (1974) J. Gen. Physiol. 64, 443--467). The most precise and accurate of these was the non-linear regression method of W.W. Cleland (Adv. Enzymol. 29 (1967) 1--32). For both these models, the various graphical methods and non-parametric methods gave poor results and are not recommended.

Fitting biological equations to data using non-parametric methods

Simulated experimental data were generated for these equations: a straight line, the integrated Michaelis--Menten equation, plus a linear term, the Hill equation, a two-exponential function and a double Michaelis--Menten equation. The equations were fitted to the data using (i) least-squares and (ii) non-parametric methods. The precision and accuracy of the parameter estimates obtained by each method were compared and the methods assessed. For several of the equations, non-parametric methods provided robust techniques for parameter estimation. For the remainder, the results were poor. The reasons for this are discussed.

WHOLE BODY METABOLISM

This chapter illustrates various hormones concerned with the control of whole body energy metabolism. The major control that maintains this pattern of flow is insulin. Low concentration of insulin allows a high rate for the release of free fatty acids and ensures a low rate for glucose uptake by the peripheral tissues. The two important controls are the increasing concentrations of adrenaline and glucagon. Adrenaline causes the release of free fatty acids and the release of glucose from glycogen if available. On the other hand, glucagon stimulates the release of glucose. During digestion, three important fuels, namely, glucose, trilacylglycerols, and amino acids, are being absorbed from the intestines. Glucose is absorbed and its high blood concentration causes insulin release from the pancreas. Triacylglycerols, after absorption, are converted by the gut mainly into chylomicra but also partly into lipoproteins. The high insulin concentration will activate lipoprotein lipase and accelerate the removal of lipoproteins. On the other hand, amino acids are partly used to replace degraded protein, the synthesis being stimulated by the elevated insulin concentration.

Alternate models for shared carriers or a single maturing carrier in hexose uptake into rabbit jejunum in vitro

The uptake (tissue accumulation) of three hexoses into rabbit jejunum was measured in a flux chamber in conditions of effective stirring. Glucose uptake was inhibited by galactose or 3-O-methylglucose: 1-40 mM galactose caused a progressive decline in glucose uptake; 1-5 mM 3-O-methylglucose inhibited glucose uptake but higher concentrations of 3-O-methylglucose had no further effect. When 1-40 mM 3-O-methylglucose was added to glucose plus galactose there was a further decrease in the uptake of glucose; adding 1-40 mM galactose to glucose plus 3-O-methylglucose also produced a decrease in glucose uptake. Both glucose and 3-O-methylglucose inhibited uptake of galactose but the pattern of inhibition varied between the two sugars. The uptake of 3-O-methylglucose was also inhibited by glucose and by galactose, but the uptake of 3-O-methylglucose in the presence of either galactose or glucose was no further reduced by adding the third hexose. Graphical analysis and analysis by non-linear regression both showed that neither the single Michaelis-Menten function, nor the single Michaelis-Menten-plus-competitive-inhibition function was appropriate for any of these data. The results are consistent with the hypothesis that either there are multiple (at least three) intestinal carriers for hexoses; alternatively that there is a single carrier whose transport properties for the three hexoses change differentially during cell maturation and migration up the villus.

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.

Mean solute concentration for use with the Michaelis-Menten equation applied to the analysis of data from intestinal perfusion experiments.

A number of algebraic expressions for the solute concentration for use with the Michaelis-Menten equation during the analysis of data from intestinal perfusion experiments have been investigated. It is concluded that the most suitable, especially if water absorption is occurring, is of the form: S = (S initial--S effluent)/ln(S initial/S effluent).