Equilibrium binding of insulin to rat white fat cells at 15 degrees C

Analysis of steady-state carbon tracer experiments using akaike information criteria

INTRODUCTION

Carbon isotope tracers have been used to determine relative rates of tricarboxylic acid cycle (TCA) cycle pathways since the 1950s. Steady-state experimental data are typically fit to a single mathematical model of metabolism to determine metabolic fluxes. Whether the chosen model is appropriate for the biological system has generally not been evaluated systematically. An overly-simple model omits known pathways while an overly-complex model may produce incorrect results due to overfitting.

OBJECTIVES

The objectives were to develop and study a method that systematically evaluates multiple TCA cycle mathematical models as part of the fitting process.

METHODS

The problem of choosing overly-simple or overly-complex models was approached by developing software that automatically explores all possible combinations of flux through pyruvate dehydrogenase, pyruvate kinase, pyruvate carboxylase and anaplerosis at propionyl-CoA carboxylase, and equivalent pathways, all relative to TCA cycle flux. Typical TCA cycle metabolic tracer experiments that use ¹³C nuclear magnetic resonance for detection and quantification of ¹³C-enriched glutamate products were simulated and analyzed. By evaluating the multiple model fits with both the conventional sum-of-squares residual error (SSRE) and the Akaike Information Criterion (AIC), the software helps the investigator understand the interaction between model complexity and goodness of fit.

RESULTS

When fitting alternative models of the TCA cycle metabolism, the SSRE may identify more than one model that fits the data well. Among those models, the AIC provides guidance as to which is the simplest of the candidate models is sufficient to describe the observed data. However under some conditions, AIC used alone inappropriately discriminates against necessary metabolic complexity.

CONCLUSION

In combination, the SSRE and AIC help the investigator identify the model that best describes the metabolism of a biological system.

Insulin receptor binding kinetics: modeling and simulation studies

Biological actions of insulin regulate glucose metabolism and other essential physiological functions. Binding of insulin to its cell surface receptor initiates signal transduction pathways that mediate cellular responses. Thus, it is of great interest to understand the mechanisms underlying insulin receptor binding kinetics. Interestingly, negative cooperative interactions are observed at high insulin concentrations while positive cooperativity may be present at low insulin concentrations. Clearly, insulin receptor binding kinetics cannot be simply explained by a classical bimolecular reaction. Mature insulin receptors have a dimeric structure capable of binding two molecules of insulin. The binding affinity of the receptor for the second insulin molecule is significantly lower than for the first bound insulin molecule. In addition, insulin receptor aggregation occurs in response to ligand binding and aggregation may also influence binding kinetics. In this study, we develop a mathematical model for insulin receptor binding kinetics that explicitly represents the divalent nature of the insulin receptor and incorporates receptor aggregation into the kinetic model. Model parameters are based upon published data where available. Computer simulations with our model are capable of reproducing both negative and positive cooperativity at the appropriate insulin concentrations. This model may be a useful tool for helping to understand the mechanisms underlying insulin receptor binding and the coupling of receptor binding to downstream signaling events.

Comparison of IL-1 alpha effectiveness in activating murine pre-B and T cell lines

Interleukin-1 (IL-1) is a potent agent that induces a wide range of biological effects. The action of IL-1 is mediated by surface IL-1 receptors (IL-1R). Two types of IL-1 receptors have been identified in lymphocytes. In this study we examined activity of IL-1 alpha in two murine lymphocyte lines that express different types of IL-1 receptors. The T lymphoid cell line EL-4 6.1 C10 expresses type I IL-1R that mediates IL-1 alpha-induced IL-2 gene expression and secretion of IL-2. The pre-B lymphoid cell line 70Z/3 was previously shown to express type II IL-1R and responds to IL-1 alpha by expressing immunoglobulin kappa light chain mRNA and increased levels of surface IgM. We found that IL-1 alpha was as potent in inducing IgM expression in 70Z/3 cells as it was in inducing IL-2 secretion in EL-4 6.1 C10 cells. Likewise, the IL-1 alpha concentration sufficient to trigger kappa light chain gene expression in 70Z/3 cells was similar to the concentration of IL-1 alpha sufficient to trigger IL-2 gene expression in EL-4 6.1 C10. In both cell lines, IL-1 alpha activated NF-kappa B-like DNA-binding activity but in EL-4 6.1 C10 cells the IL-1 alpha concentration sufficient to induce NF-kappa B response was 1000-fold lower than in 70Z/3 cells. Monoclonal antibody, mAb M15, to the type I IL-1R blocked IL-1-induced responses in EL-4 6.1 C10 cells. Surprisingly mAb M15 also blocked IL-1 action in 70Z/3 cells, even though these cells predominantly express type II IL-1R. 15% of the total IL-1 binding sites in 70Z/3 cells were recognized by mAb M15. Human IL-1 receptor antagonist (IL-1ra), which binds to the natural murine type I but not the type II IL-1R, blocked IL-1 alpha responses in EL-4 6.1 C10 and 70Z/3 cells. Although at low levels, Northern blot analysis confirmed that 70Z/3 cells express low levels of type I IL-1R mRNA. Taken together, these results suggest that type I IL-1R are expressed and transduce IL-1 signals in both 70Z/3 and El-4 6.1 C10 cells.

Characterization of diadenosine tetraphosphate (Ap4A) binding sites in cultured chromaffin cells: evidence for a P2y site

1. Diadenosine tetraphosphate (Ap4A) a dinucleotide, which is stored in secretory granules, presents two types of high affinity binding sites in chromaffin cells. A Kd value of 8 +/- 0.65 x 10(-11) M and Bmax value of 5420 +/- 450 sites per cell were obtained for the high affinity binding site. A Kd value of 5.6 +/- 0.53 x 10(-9) M and a Bmax value close to 70,000 sites per cell were obtained for the second binding site with high affinity. 2. The diadenosine polyphosphates, Ap3A, Ap4A, Ap5A and Ap6A, displaced [3H]-Ap4A from the two binding sites, the Ki values being 1.0 nM, 0.013 nM, 0.013 nM and 0.013 nM for the very high affinity binding site and 0.5 microM, 0.13 microM, 0.062 microM and 0.75 microM for the second binding site. 3. The ATP analogues displaced [3H]-Ap4A with the potency order of the P2y receptors, adenosine 5'-O-(2 thiodiphosphate) (ADP-beta-S) greater than 5'-adenylyl imidodiphosphate (AMP-PNP) greater than alpha, beta-methylene ATP (alpha, beta-MeATP), in both binding sites. The Ki values were respectively 0.075 nM, 0.2 nM and 0.75 nM for the very high affinity binding site and 0.125 microM, 0.5 microM and 0.9 microM for the second binding site.

Insulin binding to individual rat skeletal muscles

Studies of insulin binding to skeletal muscle, performed using sarcolemmal membrane preparations or whole muscle incubations of mixed muscle or typical red (soleus, psoas) or white [extensor digitorum longus (EDL), gastrocnemius] muscle, have suggested that red muscle binds more insulin than white muscle. We have evaluated this hypothesis using cryostat sections of unfixed tissue to measure insulin binding in a broad range of skeletal muscles; many were of similar fiber-type profiles. Insulin binding per square millimeter of skeletal muscle slice was measured by autoradiography and computer-assisted densitometry. We found a 4.5-fold range in specific insulin tracer binding, with heart and predominantly slow-twitch oxidative muscles (SO) at the high end and the predominantly fast-twitch glycolytic (FG) muscles at the low end of the range. This pattern reflects insulin sensitivity. Evaluation of displacement curves for insulin binding yielded linear Scatchard plots. The dissociation constants varied over a ninefold range (0.26-2.06 nM). Binding capacity varied from 12.2 to 82.7 fmol/mm2. Neither binding parameter was correlated with fiber type or insulin sensitivity; e.g., among three muscles of similar fiber-type profile, the EDL had high numbers of low-affinity binding sites, whereas the quadriceps had low numbers of high-affinity sites. In summary, considerable heterogeneity in insulin binding was found among hindlimb muscles of the rat, which can be attributed to heterogeneity in binding affinities and the numbers of binding sites. It can be concluded that a given fiber type is not uniquely associated with a set of insulin binding parameters that result in high or low binding.

A modified theta-toxin produced by limited proteolysis and methylation: a probe for the functional study of membrane cholesterol

A derivative of cytolytic theta-toxin from Clostridium perfringens was prepared by limited proteolytic digestion of the native toxin followed by methylation. Among the chloroform/methanol-extractable, lipid components of sheep and human erythrocytes, the proteinase-nicked and methylated derivative (MC theta) specifically binds to cholesterol. While MC theta retains binding affinity comparable to that of intact toxin, it causes no obvious membrane damage, resulting in no hemolysis at temperatures of 37 degrees C or lower. Using MC theta, we demonstrated the possible existence of high- and low-affinity sites for theta-toxin on sheep erythrocytes at both 37 degrees C and 10 degrees C. The number of high-affinity sites on sheep erythrocytes was estimated to be approximately 3-times larger at 37 degrees C than that at 10 degrees C. In addition, high- and low-affinity sites were demonstrated in human erythrocytes and a lymphoma B cell line, BALL-1 cells. Both binding sites disappear upon simultaneous treatment of cells with sublytic doses of digitonin, suggesting that cholesterol is an essential component of both the high- and low-affinity sites and that the mode of cholesterol existence in plasma membranes is heterogeneous in these cells. Because of its high affinity for membrane cholesterol without causing any obvious membrane changes at physiological temperatures, MC theta may provide a probe for use in the functional study of membrane cholesterol.

The insulin-receptor interaction: is the kinetic approach for inferring negative-cooperative site-site interactions valid?

The dissociation of insulin from its receptor is reportedly enhanced when the dissociation is induced by dilution in the presence of insulin. This experiment is frequently conducted when curvilinear Scatchard plots of insulin binding are observed in order to infer negative cooperative site-site interactions amongst insulin receptors. However, when insulin binding to purified liver plasma membranes was measured at 15 degrees C in 50 mM Tris, pH 7.5 containing 0.1% bovine serum albumin and 100 U/ml bacitracin, the insulin binding data was characterised by a linear Scatchard plot and a Hill plot with a slope equal to unity. Thus, under the conditions of this binding assay, insulin apparently bound to a single non-interacting class of homogeneous binding sites. But, despite the apparent absence of cooperative interactions under these specific conditions, the dissociation of receptor-bound insulin was still enhanced when the dissociation of insulin from its receptor was induced by dilution in the presence of insulin. This result cast serious doubt on the validity of inferring negative-cooperative site-site interactions amongst insulin receptors based solely on the observation that the dissociation of receptor-bound insulin is enhanced by dilution in the presence of insulin.

Testing models of insulin binding in rat adipocytes using network thermodynamic computer simulations

Many different models have been proposed to explain the complex binding behavior of insulin to its receptor, but a systematic comparison of models with experimental results is lacking. We have used network thermodynamic computer simulations to compare models of insulin binding against the results of several experimental tests designed to differentiate between the models. Six models of insulin binding were tested (simple, diffusion-reaction, conversion, dissociation, heterogeneous site, and two-step intramembrane) against results reported in the literature for isolated rat adipocytes. Although still a matter of experimental controversy, the criteria selected for modeling were curvilinear Scatchard plots, bi-or multi-exponential dissociation, insulin-accelerated dissociation, lack of dependence of the overall dissociation constant on receptor number, and receptor reserve. Using a given set of parameter values most appropriate for each model, none was able to account for all of the observed experimental results. This indicates both the complexity of the binding reaction and the need for further model development. The approach of using computer simulations to systematically test models against experimental results affords not only insight into the critical features of a model enabling it to pass a test, but also indicates potential experiments which might differentiate between models.