An evaluation of the cross-linking model for the interaction of insulin with its receptor.

The cross-linking model for insulin receptor interactions, in which a single insulin molecule may form a cross-link between an insulin receptor's alpha-subunits, has been expressed as a formal compartmental model and subjected to a systematic analysis, examining a number of predictions that have been made for this model. The kinetic parameters for the model were obtained by matching data from insulin receptor equilibrium binding studies and rates of formation of the insulin receptor complex. This analytical study has allowed a clear description of the kinetics of the ligand receptor complexes involved in such a mechanism. We conclude that the cross-linking model accounts for the anomaly of the 10-fold concentration difference in high- and low-affinity binding sites found when insulin binding is analyzed by conventional means. However, the phenomenon of acceleration of dissociation of labeled ligand by unlabeled ligand cannot be accounted for as an intrinsic part of the model. We suggest that this phenomenon arises from the destabilization of cross-link formation when a second insulin molecule binds.

Quantitative study of the control of HIV-1 gene expression.

The biochemical processes that together determine the expression of a human immunodeficiency virus (HIV) provirus integrated into the genome of a host cell are translated into mathematical form to give a dynamic model that can be examined quantitatively. The model includes the contribution of cellular enhancers to transcription of the provirus, the subsequent splicing of the full length transcript, the nuclear export of transcripts and the translation of tat and rev mRNA to produce viral control proteins. The model is completed by the formulation of the feedback effects of Tat protein on transcription and translation and the feedback effect of Rev protein on nuclear export. Initial parameter values are estimated from available experimental data. The model is a formalization of a commonly accepted scheme, but one that has only previously been considered qualitatively. Quantification requires more explicit assumptions, but then allows the precise determination of resultant model behaviour and the stringent comparison of behaviour with experimental observation. Least squares matching of model behaviour to the observed appearance of mRNA in infected H9 cells gives very close agreement and, in particular, supports recent proposals concerning multimerization of the Rev protein. General quantitative characteristics of dynamic and steady-state behaviour of the model are determined and discussed; their possible contribution to the latency of HIV infection is considered.

A model of insulin distribution and uptake in the perfused rat liver.

Indicator dilution curves of 51Cr-EDTA and 125I-insulin injected into perfusate entering the rat liver in vivo are used as a basis for developing a mathematical model of insulin distribution and uptake within the organ. EDTA is not taken up by liver cells and therefore serves as a "volume marker" whose dilution curve reflects the characteristics of perfusate flow through the organ and through the cannulae. These two components are modelled separately but the same approach is used in each case, that is, the minimum number of delayed exponential terms sufficient to reproduce the dilution curves is determined and used as the basis for modelling. This allows the cannula, vascular and sinusoidal volumes to be identified and described as corresponding compartmental configurations. The shape of the insulin dilution curve is additionally influenced by binding to, and uptake by, liver cells. Binding of insulin to receptors on hepatocyte plasma membranes and subsequent internalization of the insulin-receptor complex is modelled by the introduction of additional compartments but this is found to be insufficient unless non-specific binding is also taken into account. The accuracy of determination of the rate constants for insulin-receptor dissociation and for endocytosis is improved by a sudden reduction in the pH of the perfusate about 100 sec after injection of the insulin bolus. This releases any residual receptor bound insulin and is modelled by a sudden shift in the insulin-receptor dissociation rate constant. Matching of the complete model to individual pairs of 51Cr-EDTA and 125I-insulin dilution curves allows vascular and sinusoidal volumes to be determined together with the binding and endocytic rate constants. Use of the model to investigate the effect of substances that modify these rate constants is briefly illustrated in the case where the liver is preperfused with 5 mM indomethacin. The model can also be used to simulate the internal distribution and uptake of insulin with any nominated input function and any set of parameters; this is illustrated by comparing the impulse response in the normal case and that in which indomethacin has been preperfused. Although the present study is confined to insulin, the model and methodology that is developed should be applicable to other ligands for which the hepatocyte carries specific receptors.

Indomethacin inhibits endocytosis and degradation of insulin.

Indomethacin inhibits autophosphorylation of the insulin receptor. The lack of a consensus as to whether phosphorylation of the insulin receptor is necessary for its endocytosis prompted an investigation into the effects of indomethacin on the uptake and subcellular processing of insulin in the perfused rat liver. Indomethacin did not affect total uptake of insulin by the liver, but there was a concentration dependent inhibition of transfer from the plasma membrane to the endosomes (1mM, 32% inhibition; 5mM, 90% inhibition). Compartmental analysis showed the endocytic rate constant to be inhibited by 82% at 5mM indomethacin (0.0084 to 0.0015 sec-1). The similarity between the level of inhibition of autophosphorylation and the inhibition of endocytosis suggest that phosphorylation of the receptor is necessary for endocytosis. Indomethacin at 5mM completely abolished efflux of insulin degradation products from the perfused liver, suggesting that internalisation is an absolute requirement for degradation.

Signal processing technique to extract neuronal activity from noise.

A method of extracting extracellularly recorded action potentials from background electronic noise is described. Segments of traces containing stimulus-induced activity are Fourier transformed and the increase in the total power density over that of control noise segments is used as a measure of stimulus-induced neuronal activity. We show first, with observations from the amphibian visual system and mammalian auditory system, that our technique yields similar quantitative information to that obtained from the conventional spike counting method when the recording arrangement is optimal. Moreover, the size and centre of a visual receptive field can be determined even when the evoked action potentials are buried in the background noise. To investigate the potential of this technique further, we have used it to study the auditory responses in the amphibian midbrain. The power spectral density, we demonstrate here, is proportional to the stimulus intensity over a wide range, and varies systematically with stimulus frequency and the direction of sound source. Other possible applications of this technique, together with the theoretical basis for it, are discussed.

A freeze fracture study of the developing tegumental outer membrane of Schistosoma mansoni.

The freeze fracture technique has been used to quantify changes in the integral components of the double outer membrane of Schistosoma mansoni during the 6-week period of development within the mouse. The intramembraneous particle (IMP) density on the P1 face begins to rise within 6 h of host penetration, reaches a maximum at day 4 and then falls rapidly after day 9, so that it is at a low level between 3 and 6 weeks. The E1 face IMP density follows the same course as that of the P1 face except that maximum particle density is recorded on day 1 and the counts begin to fall on day 5. The IMP density on the P2 face remains at a consistently low level throughout development. The E2 face IMP density rises gradually to a peak at day 4, when the parasites have migrated to the lungs, and remains thereafter at a similar level, so that by 6 weeks the E2 face has a higher IMP density than the other three fracture faces. The E2 face IMP show a marked increase in size on day 4. Morphological studies indicate that a different type of inclusion body makes a transient appearance in the tegument of the lung worms, and immunocytochemical techniques show the lung worms to be nonimmunogenic. It is suggested, therefore, that the E2 face IMP may represent complexes of parasite antigens and acquired host antigens. The tegumental membranes of cultured specimens have also been examined by freeze fracturing and the IMP densities compared with those obtained from in vivo parasites; the cultured schistosomula have a lower E2 face particle density than the in vivo specimens.

A computer simulation study of optimal thyroid radiation protection during investigations involving the administration of radioiodine-labelled pharmaceuticals.

The administration of iodide for thyroid blocking is now known to carry its own risks, at least in certain categories of patients. We have therefore made a theoretical study by computer simulation of the efficacy of various thyroid blocking regimes. In the case of injected 125I- or 131I-iodide, substantial thyroid protection may theoretically be achieved by a single oral dose of inorganic iodide, for example a 90% reduction in radiation dose is produced by only 20 mg iodide. Repeating the initial blocking dose is of little value. A single blocking dose, however, affords poor protection against radioiodine released from labelled plasma proteins. Both for short-lived proteins such as fibrinogen, and for the longer-lived proteins such as albumin, the optimum dosage schedule appears to be stable iodide given daily for two to three weeks. For instance, 10 mg daily for a fortnight will reduce thyroid irradiation by a factor of ten following injection of 125I-fibrinogen.

Theory of hydrokinetic clearance of bacteria from the urinary bladder. I. Effect of variations in bacterial growth rate.

If the bladder is regularly emptied in appropriate circumstances the concentration of bacteria in successively voided samples progressively falls. By making a number of assumptions about conditions of bacterial growth in the bladder the way in which this washout of bacteria will occur can be predicted. Such predictions give a form of washout curve which differs significantly from that commonly encountered in patients. The shape of the predicted washout curve is affected by the form of the bacterial growth curve but this influence is not sufficient to account for the observed difference between patients and predictions.

A compartmental analysis of circulatory lymphocytes in the spleen.

A tentative model describing the passage of circulatory lymphocytes through the spleen is formulated in accord with known anatomical features. In order to preserve isomorphism between the model and the splenic system, the model is formulated in compartmental form and its design allows alternative routes and modes of lymphocyte transit to be considered. The simultaneous differential equations arising from the model are solved using an analogue computer which also provides the means whereby the performance of the model may be compared with suitable dynamic data drawn from literature. This not only allows the selection of a particular configuration of the model in preference to its alternatives, but also allows the numerical determination of certain unknown parameters. In the case of the rat spleen, best agreement between model and experimental data is obtained when between 10 and 25% of the total lymphocyte flux in the model spleen passes through the marginal zone where the average dwell time of the lymphocytes is about 50 min. The white pulp receives a lymphocyte flux from the marginal zone amounting to about 10% of the total splenic flux and the white pulp lymphocytes are sequestered for a period of 4-6 hr before release to the venous circulation. The red pulp receives 90% of the total splenic flux but the majority of lymphocytes find transit through the red pulp in less than 5 min. The remaining flux of lymphocytes, amounting to 10% of the splenic input, is delayed in transit through the red pulp by 2-3 hr before release to the venous circulation.

A mathematical model of common-cold epidemics on Tristan da Cunha.

Records of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

Mathematical approaches to the evaluation of the flux of gamma-aminobutyrate in brain tissue in vitro.

In the preceding paper (Balázs, Machiyama, Hammond, Julian & Richter, 1970) the flux of gamma-aminobutyrate (GABA) was found, in guinea-pig brain-cortex slices incubated in glucose-saline medium, to represent about 10% of the total tricarboxylic acid cycle flux, as opposed to other estimates, which are as high as 40%. However, the latter value was deduced from experimental results by methods that made no allowance for the metabolic compartmentation of glutamate: a mathematical investigation was therefore undertaken to show that this omission necessarily leads to an overestimation of GABA flux. The magnitude of this over-estimation was shown by computer simulation methods to be of such an order as to bring the corrected value into agreement with the lower value. Computer simulation methods were also used to evaluate the GABA flux from the experimental results presented by Balázs et al. (1970) and a value of 0.0315mumol/min per g wet wt. was obtained. This value was also shown to be consistent, in the simulated system, with the experimentally observed time-courses for the radioactivity and quantity of aspartate. Since there is now evidence that GABA is itself a metabolically compartmented intermediate this possibility was considered mathematically, but it was found that in this case the assumption of compartmentation had little effect upon the value of GABA flux deduced on the basis of GABA homogeneity.

The operation of the gamma-aminobutyrate bypath of the tricarboxylic acid cycle in brain tissue in vitro.

1. Cerebral-cortex slices prelabelled with gamma-amino[1-(14)C]butyrate (GABA) were incubated in a glucose-saline medium. After the initial rapid uptake there was no appreciable re-entry of (14)C into the GABA pool, either from the medium or from labelled metabolites formed in the tissue. The kinetic constants of GABA metabolism were determined by computer simulation of the experimental results by using mathematical procedures. The GABA flux was estimated to be 0.03mumol per min/g, or about 8% of the total flux through the tricarboxylic acid cycle. It was found that the assumption of compartmentation did not greatly affect the estimates of the GABA flux. 2. The time-course of incorporation of (14)C into amino acids associated with the tricarboxylic acid cycle was followed with [1-(14)C]GABA and [U-(14)C]-glucose as labelled substrates. The results were consistent with the utilization of GABA via succinate. This was confirmed by determining the position of (14)C in the carbon skeletons of aspartate and glutamate formed after the oxidation of [1-(14)C]GABA. These results also indicated that under the experimental conditions the reversal of reactions catalysed by alpha-oxoglutarate dehydrogenase and glutamate decarboxylase respectively was negligible. The conversion of [(14)C]GABA into gamma-hydroxybutyrate was probably also of minor importance, but decarboxylation of oxaloacetate did occur at a relatively slow rate. 3. When [1-(14)C]GABA was the labelled substrate there was evidence of a metabolic compartmentation of glutamate since, even before the peak of the incorporation of (14)C into glutamate had been reached, the glutamine/glutamate specific-radioactivity ratio was greater than unity. When [U-(14)C]glucose was oxidized this ratio was less than unity. The heterogeneity of the glutamate pool was indicated also by the relatively high specific radioactivity of GABA, which was comparable with that of aspartate during the whole incubation time (40min). The rates of equilibration of labelled amino acids between slice and medium gave evidence that the permeability properties of the glutamate compartments labelled as a result of oxidation of [1-(14)C]GABA were different from those labelled by the metabolism of [(14)C]glucose. The results showed therefore that in brain tissue incubated under the conditions used, the organization underlying metabolic compartmentation was preserved. The observed concentration ratios of amino acids between tissue and medium were also similar to those obtaining in vivo. These ratios decreased in the order: GABA>acidic acids>neutral amino acids>glutamine. 4. The approximate pool sizes of the amino acids in the different metabolic compartments were calculated. The glutamate content of the pool responsible for most of the labelling of glutamine during oxidation of [1-(14)C]GABA was estimated to be not more than 30% of the total tissue glutamate. The GABA content of the ;transmitter pool' was estimated to be 25-30% of the total GABA in the tissue. The structural correlates of metabolic compartmentation were considered.

The metabolism of gamma-aminobutyrate and glucose in potassium ion-stimulated brain tissue in vitro.

1. The metabolism of gamma-aminobutyrate (GABA) was investigated in cerebral-cortex slices incubated in glucose-saline medium with [1-(14)C]GABA and [U-(14)C]-glucose as labelled substrates. 2. A rapid release of GABA from the tissue, amounting to 25-30% of the total, was observed on addition of 66m-equiv. of K(+)/1 to the medium; the liberation of other amino acids was relatively small. The effect was apparently specific for K(+); GABA was not released on addition of equivalent amounts of Na(+) or on increasing the respiration rate with 10mm-ammonium chloride. The results show that GABA behaves like the transmitter compounds (acetylcholine, catecholamines) on K(+) stimulation, and therefore now satisfies certain of the criteria required for a transmitter in mammalian brain. 3. The release of GABA from the tissue on addition of K(+) was followed by a slow re-uptake. The rate of uptake of GABA in a medium containing 5.9m-equiv. of K(+)/1 was more than four times that in a medium containing 66m-equiv. of K(+)/1. 4. The concentration of GABA in brain tissue incubated for 1h in a medium containing 66m-equiv. of K(+)/1 was about 50% higher than that observed under normal conditions. 5. There was evidence that exogenous [(14)C]GABA mixed with the endogenous pool(s), since the proportion of the total GABA released on K(+) stimulation was the same, and the specific radioactivity of the liberated GABA was close to that remaining in the tissue, whether the GABA was labelled by [1-(14)C]GABA from the medium or generated in the tissue from [(14)C]glucose. 6. On the basis of these findings and the observations outlined in the preceding papers it was possible to calculate the kinetic constants of GABA metabolism by computer simulation of the results. K(+) stimulation led to a 2.5-fold increase in the flux through the tricarboxylic acid cycle, whereas the flux in the GABA bypath was little affected; as a result the flux through the GABA bypath, which under normal conditions was 8% of that through the tricarboxylic acid cycle, decreased to 3-5%. 7. The metabolism of glutamine was greatly affected by K(+)-stimulation. The ratio of the concentration of glutamine in the slices to that in the medium, which under normal conditions was the smallest among the amino acids investigated, increased from about 17 to 63 in 1h. This effect was attributable partly to an uptake of glutamine from the medium (1.8mumol/h per g) and partly to a net increase in the total amount of glutamine (2.6mumol/h per g). At 1h after the addition of K(+) the net gain of glutamine could be accounted for by the decrease of glutamate. 8. Metabolic compartmentation was evident when brain-cortex slices were incubated in glucose-saline medium and the labelled substrate was [(14)C]GABA, since the specific radioactivity of glutamine exceeded that of glutamate. On addition of K(+) the signs of metabolic compartmentation promptly disappeared: this effect was apparently associated with an increase in the permeability of the compartments containing labelled metabolites derived from [(14)C]GABA. The change in the permeability, however, did not affect all the compartments; when the labelled substrate was [(14)C]glucose the equilibration of labelled amino acids between tissue and medium was similar under normal conditions and in the presence of high concentrations of K(+). 9. The metabolism of [(14)C]glucose was followed by measuring oxygen uptake, respiratory (14)CO(2), and incorporation of (14)C into amino acids. The results showed that K(+) stimulation increased the flux of glucose carbon, both in the glycolytic pathway and in the tricarboxylic acid cycle.