Equation For Steel Research Articles

1377-P: Pramlintide Lowers Postprandial Glucagon Concentrations by Inhibiting Glucagon Secretion without Altering Clearance in Type 1 Diabetes: A [13C15N]-Glucagon Study

To determine the underlying mechanism of pramlintide effects on postprandial (PP) glucagon concentrations, we studied thirteen C-peptide negative T1D subjects (Age 35±yrs, BMI 27.6±2.2 kg/m2, fasting plasma glucose 9.4±4 mM, HbA1c 7.1±1%) on two occasions in random order, with and without 30 μg of sc pramlintide at the onset of a mixed meal (75 gm carb, 15% fat and 35% protein; 8 kcal/kg) . Subjects administered insulin bolus at meal onset. 13C15N glucagon tracer was infused intravenously to estimate PP glucagon turnover. Arterialized venous samples were drawn periodically for measurements of glucose (YSI) , 13C15N-glucagon (LC-MS/MS) and glucagon (Mercodia) concentrations. Systemic glucagon turnover was calculated using non-steady state Steele's equation after determining glucagon volume of distribution. Integrated PP glucagon concentrations were lower (p<0.01) in pramlintide (Pram) than without pramlintide (No Pram) . Integrated rates of glucagon appearance and glucagon disappearance were lower (p<0.01) in Pram vs. No Pram. When adjusted for plasma glucagon concentrations, glucagon clearance was not different (p=0.7) between Pram vs. No Pram. These data demonstrate that pramlintide lowers postprandial glucagon concentrations by lowering glucagon secretion without altering clearance in subjects with T1D. Disclosure F.Ruchi: None. D.Romeres: None. M.Schiavon: None. S.Renuse: None. A.Pandey: None. C.Dalla man: Research Support; Becton, Dickinson and Company, Sanofi-Aventis Deutschland GmbH. C.Cobelli: None. R.Basu: Consultant; Sparrow Pharmaceuticals Inc, Research Support; Abbott Diabetes, AstraZeneca. A.Basu: Speaker's Bureau; Zealand Pharma A/S. Funding National Institute of Health (DK 085516, DK 029953)

Whole Body Deletion of AMP-activated Protein Kinase β2 Reduces Muscle AMPK Activity and Exercise Capacity

AMP-activated protein kinase (AMPK) β subunits (β1 and β2) provide scaffolds for binding α and γ subunits and contain a carbohydrate-binding module important for regulating enzyme activity. We generated C57Bl/6 mice with germline deletion of AMPK β2 (β2 KO) and examined AMPK expression and activity, exercise capacity, metabolic control during muscle contractions, aminoimidazole carboxamide ribonucleotide (AICAR) sensitivity, and susceptibility to obesity-induced insulin resistance. We find that β2 KO mice are viable and breed normally. β2 KO mice had a reduction in skeletal muscle AMPK α1 and α2 expression despite up-regulation of the β1 isoform. Heart AMPK α2 expression was also reduced but this did not affect resting AMPK α1 or α2 activities. AMPK α1 and α2 activities were not changed in liver, fat, or hypothalamus. AICAR-stimulated glucose uptake but not fatty acid oxidation was impaired in β2 KO mice. During treadmill running β2 KO mice had reduced maximal and endurance exercise capacity, which was associated with lower muscle and heart AMPK activity and reduced levels of muscle and liver glycogen. Reductions in exercise capacity of β2 KO mice were not due to lower muscle mitochondrial content or defects in contraction-stimulated glucose uptake or fatty acid oxidation. When challenged with a high-fat diet β2 KO mice gained more weight and were more susceptible to the development of hyperinsulinemia and glucose intolerance. In summary these data show that deletion of AMPK β2 reduces AMPK activity in skeletal muscle resulting in impaired exercise capacity and the worsening of diet-induced obesity and glucose intolerance.

Indices of insulin action calculated from fasting glucose and insulin reflect hepatic, not peripheral, insulin sensitivity in African-American and Caucasian adolescents.

Insulin stimulates muscle glucose uptake and inhibits hepatic glucose production. Measures of insulin sensitivity or insulin resistance must take both of these actions into account. Homeostatic model assessment of insulin resistance (HOMA(IR)) and quantitative insulin sensitivity check index (QUICKI) are two simple measures of insulin resistance and insulin sensitivity that are derived from fasting glucose and insulin levels as such it is likely that they reflect primary hepatic insulin action and not muscular effects. To prove this hypothesis, the relationships of HOMA(IR) and QUICKI to peripheral insulin sensitivity (S(I)(*)) and hepatic insulin resistance (HIR) were assessed in 34 adolescents (age 13.5 +/- 2.9 yr, body mass index 23.0 +/- 5.7, mean +/- SD; 16 Caucasian and 14 African-American). S(I)(*) and HIR were determined using the stable-labeled, frequently sampled intravenous glucose tolerance test (250 mg total glucose/kg, 13% [6,6]-D(2)-glucose). The former was calculated using the one-compartment minimal model and stable glucose concentration (S(I)(*)), and the latter was determined over the last hour of the study by multiplying hepatic glucose production (Steele's equation) by mean plasma insulin concentration. As expected, HOMA(IR) and QUICKI were significantly related to HIR (log HOMA(IR) and log HIR, r = 0.73, p < 0.001; QUICKI and log HIR, r = -0.69, p < 0.001) but not S(I)(*). When both S(I)(*) and HIR were included in the equations, only the relationships to log HIR were significant (log HOMA(IR), p < 0.001; QUICKI, p < 0.001). The relationships were similar in African-American and Caucasian subjects. These results demonstrate that in adolescents, HOMA(IR) and QUICKI assess hepatic but not peripheral insulin action.

The development of a mechanistic model to investigate the impacts of the light dynamics on algal productivity in a Hydraulically Integrated Serial Turbidostat Algal Reactor (HISTAR)

A deterministic model was developed to predict microalgal productivity within the Hydraulically Integrated Serial Turbidostat Algal Reactor (HISTAR). HISTAR consists of two turbidostats, which concomitantly inoculate the first of a series of CFSTRs. The CFSTRs function as a biomass amplifier of the inoculated culture. The model included an analysis of the internal light dynamics within each CFSTR and the effect of the instantaneous average irradiance (Ian(PAR)) on the instantaneous growth rate (μn) within CFSTRn. The latter effect was accomplished using Steele's equation. The instantaneous average irradiance was determined by integrating the Lambert–Beer Law over the depth of the culture within the CFSTRs. Fourier series analysis was used to model the biorhythms of the microalgae. The model was calibrated for biomass using four data sets collected at system dilution rates (Ds) of 0.265day−1, 0.385day−1, 0.641day−1 and 1.127day−1. The ability of the calibrated model to simulate daily volumetric productivity (Pv) within HISTAR was determined through calculation of the percent standard error of prediction. The overall mean for the four data sets was 24.8%. The average predicted productivity for the data sets was 24.2gm−3day−1 (16.2gm−2day−1) and the average actual productivity of the data sets were 25.5gm−3day−1 (19.9gm−2day−1), resulting in only a 5.1% error. Simulations produced by the calibrated model were used to estimate the optimum Ds (between 0.641day−1 and 0.884day−1). The model predicted a Pv of 70.2gm−3day−1 (Pa=46.8gm−2day−1) at optimum Ds. The maximum Pa observed in the model simulations was 39.9gm−2day−1.

Modeling the influence of growth hormone on lipolysis.

Lipolysis (the breakdown of fat) is generally estimated using stable isotopes, where the rate of appearance (Ra) of glycerol is calculated using Steele's equations. These equations are based on single-compartment differential equations for tracer and tracee where rate of change is approximated by the change in concentration from one time point to the next. We demonstrate an alternative approach to estimate metabolic processes, and to determine relationships between hormones and their actions. Growth hormone (GH) or saline was administered in a double-blind randomized crossover design to eight normal weight (NW) and eight obese (OB) subjects, and differences in the effects of GH on lipolysis were investigated. The relationship between the plasma GH concentration and glycerol Ra (as an index of lipolysis) was described using PK/PD modeling. The model incorporated the plasma GH, glycerol and D5-glycerol concentration profiles, and two sequential effect compartments to account for the delay in response. The estimated time-profile of glycerol Ra was compared with estimates obtained using Steele's equations. NONMEM (Version V) FOCE was used for parameter estimation, four differential equations were used, and glycerol and D5-glycerol were estimated simultaneously. The model adequately described both primary variables (glycerol) and derived variables (glycerol Ra as obtained using Steele's equations). Modeling allowed the assessment of potential differences in GH sensitivity in the two groups, and indicated the importance of GH in lipolysis.

The dual tracer time-varying volume method for measuring hepatic glucose release on nonsteady state: theoretical and simulation results

Measurement of hepatic glucose release in nonsteady state is difficult and experimental approaches have been developed in order to circumvent Steele's model inadequacy. Recently, a resurgence of interest in the time-varying volume method developed by Issekutz has taken place. Issekutz's approach assumes that the volume of Steele's model is not constant but time-varying and that its time course can be measured by infusing two tracers with different patterns. The time-varying volume is then substituted into Steele's equation and hepatic glucose release is estimated. The aim of this study was to analyze some basic aspects of Issekutz's method and to determine the accuracy of its estimate of hepatic glucose release. A theoretical analysis showed that the time-varying volume measured by Issekutz's approach is not unique but depends on the format of administration of the two tracers. In addition, such a volume allows an accurate estimate of hepatic glucose release if one of the two tracers is infused in such a way that its specific activity is maintained perfectly constant during the experiment. Since it is impossible to achieve a perfect clamp of specific activity, we also evaluated the performance of Issekutz's approach in more realistic experimental conditions which were reproduced by resorting to computer simulation. We simulated a euglycaemic clamp with insulin rising from basal to a plateau of approximately 40 μU/ml and then returning to basal. Nonsteady-state glucose kinetics were described by a previously validated two-compartment model while the time course of hepatic glucose release was derived from the literature. Both noise-free and noisy experimental conditions were simulated. We showed that the degree of accuracy of Issekutz's approach is very good and better than the one associated with the hot-ginf method. On the other hand, the major problem with Issekutz's approach is the sensitivity of the volume estimate tot he measurement noise, which may limit its applicability in practice. In conclusion, we elucidated the theoretical grounds of Issekutz's approach and assessed its performance during nonsteady state in a realistic scenario using computer simulation.

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

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.

On the determination of basal glucose production rate in patients with Type 2 (non-insulin-dependent) diabetes mellitus using primed-continuous 3-3H-glucose infusion

Using primed-continuous 3-3H-glucose infusion, basal glucose production rate has been reported to be 140% higher than normal or almost normal in hyperglycaemic patients with Type 2 (non-insulin-dependent) diabetes mellitus. To determine whether these markedly different results could be due to the mode of priming: fixed or adjusted, or the mode of calculation: steady state or non-steady state equations, we studied 11 patients with Type 2 diabetes (fasting plasma glucose 8-20 mmol/l). For 6 h 3-3H-glucose (0.40 microCi/min) was infused preceded by a priming dose of 40 microCi (fixed priming), or 40 microCi.plasma glucose (mmol/l).5(-1) (adjusted priming). In diabetic patients the plasma glucose concentration was not constant but declined 0.52 +/- 0.07 mmol.l-1.h-1. Furthermore, the rate of fall was correlated to the fasting plasma glucose concentration (r = 0.90, p less than 0.01). Thus, the fasting state was not a steady state condition. Using adjusted priming a constant tracer steady state level was obtained within 60 min. In contrast, using fixed priming tracer steady state was not reached within 6 h. The initial tracer level was far below, and increased in time towards the steady state level observed after adjusted priming. Consequently, using Steele's equations after fixed priming, glucose production rates calculated after 90-120 min were overestimated in proportion to fasting hyperglycaemia. The fasting state in patients with Type 2 diabetes is not a steady state condition. Adjusted priming seems most appropriate in Type 2 diabetes.(ABSTRACT TRUNCATED AT 250 WORDS)

Experimental validation of a glucose-insulin control model to simulate patterns in glucose turnover

To verify a structured model of the glucose-insulin system, metabolic measurements were compared with model-based simulations in insulin-dependent diabetic dogs which had been previously identified in terms of model parameters. Glycaemia, glucosuria, plasma insulin, and the rates of appearance R a and disappearance R d of glucose (kinetics of double-labelled glucose, evaluated according to Steele's equation in its non-steady-state version) were observed under the following conditions, starting from normoglycaemia during glucose-controlled insulin infusion (GCII): (I) insulin withdrawal, (II) insulin withdrawal and glucose infusion, (III) constant i.v. infusion of glucose and insulin, (IV) glucose infusion during GCII. After fitting the patterns of glycaemia, simulations of the other state variables were accomplished, employing the individual model parameters, the preset experimental inputs, and the GCII control constants (test IV only). Under nearly all conditions, correspondence was excellent between measured and simulated data. There were, however, the following exceptions: incomplete representation by the model of kinetics in glucose utilisation after interruption of insulin supply, overestimation of glucosuria by the model in the presence of insulin. It is concluded that the model provides a reasonable representation of metabolic processes which are of importance in the treatment of insulin-dependent diabetes mellitus and that it might thus appropriately simulate the outcome of metabolic regimens.

Effects of fasting on plasma glucose and prolonged tracer measurement of hepatic glucose output in NIDDM.

We studied the measurement of hepatic glucose output (HGO) with prolonged [3-3H]glucose infusion in 14 patients with non-insulin-dependent diabetes mellitus (NIDDM). Over the course of 10.5 h, plasma glucose concentration fell with fasting by one-third, from 234 +/- 21 to 152 +/- 12 mg/dl, and HGO fell from 2.35 +/- 0.18 to 1.36 +/- 0.07 mg . kg-1 . min-1 (P less than .001). In the basal state, HGO and glucose were significantly correlated (r = 0.68, P = .03), and in individual patients, HGO and glucose were closely correlated as both fell with fasting (mean r = 0.79, P less than .01). Plasma [3-3H]glucose radioactivity approached a steady state only 5-6 h after initiation of the primed continuous infusion, and a 20% overestimate of HGO was demonstrated by not allowing sufficient time for tracer labeling of the glucose pool. Assumption of steady-state instead of non-steady-state kinetics in using Steele's equations to calculate glucose turnover resulted in a 9-24% overestimate of HGO. Stimulation of glycogenolysis by glucagon injection demonstrated no incorporation of [3-3H]glucose in hepatic glycogen during the prolonged tracer infusion. In a separate study, plasma glucose was maintained at fasting levels (207 +/- 17 mg/dl) for 8 h with the glucose-clamp technique. Total glucose turnover rates remained constant during this prolonged tracer infusion. However, HGO fell to 30% of the basal value simply by maintaining fasting hyperglycemia in the presence of basal insulin levels.(ABSTRACT TRUNCATED AT 250 WORDS)

Non-steady state: error analysis of Steele's model and developments for glucose kinetics.

The model proposed by Steele (Ann. NY Acad. Sci. 82: 420-430, 1959) to compute rates of appearance and disappearance in non-steady state is subjected to theoretical analysis. It is shown that this model introduces an error with two components, one dependent on the volume of the compartment, the other related to the complex configuration of the system. The errors depend on the time course of specific activity, change differently with time, and may take the opposite sign but they do not, in general, cancel each other. Corollaries of this analysis are the following: there is no single pool-fraction value satisfactory under all non-steady-state situations; keeping tracer specific activity as constant as possible during the experiment minimizes both errors; and non-steady-state analysis demands proper modeling of the system. Tracer experiments were carried out in five normal volunteers. Plasma [3-3H]glucose concentration was first brought to equilibrium by means of a primed constant 2-h infusion, and then the steady state was perturbed by a 2-h euglycemic insulin (1 mU X min-1 X kg-1) clamp, realizing a transition between a basal and a euglycemic hyperinsulinemic steady state. These data were analyzed with Steele's equation, the two compartment models of Radziuk et al. [Am. J. Physiol. 234 (Endocrinol. Metab. Gastrointest. Physiol. 3): E84-E93, 1978], and a new model based on a study on glucose kinetics carried out in the two steady states separately. Steele's equation yielded negative values for hepatic glucose production already 40 min into the clamp and throughout the study. The average value of glucose production during the 2nd h was -0.88 mg X min-1 X kg-1; the suppression of basal release over the 2-h period was 115%. In contrast, the new model calculated a mean glucose production of 0.37 mg X min-1 X kg-1 during the 2nd h and an overall suppression of 62%; no negative values were obtained.

Interactions between light and temperature on the physiological ecology ofGracilaria tikvahiae (Gigartinales: Rhodophyta)

Main effects and interactions of light and temperature on rates of growth (μ), net photosynthesis (Ps), and dark respiration (R) of the red seaweedGracilaria tikvahiae were investigated in outdoor, nutrient-replete continuous-flow seawater culture chambers. Below 15°C,G. tikvahiae did not grow and between 15° and 30°C, both main effects and interactions of light and temperature on μ and Ps were significant, which explains the occurrence of this alga as a summer annual in its northern range. Temperature interacted with light (I) through its influence on the μ vs I and Ps vs I curves. The initial slope of the μ vs I curve, α, the light saturation intensity, Is, and maximum growth rate, μmax, were all significantly lowerat 15°C compared to 20°, 25°, or 30°C. Maximum values of μmax, the Ps:R ratio and the net photosynthesis:gross photosynthesis ratio (Ps:Pg) all occurred at 25°C, suggesting that this is the best temperature for growth ofG. tikvahiae. Values for Pmax increased up to 30°C, indicating that the temperature for maximum growth and net photosynthesis are not the same forG. tikvahiae. Significant photoinhibition of growth and photosynthesis at full incident sunlight (I0) occurred at 15°C but not at 20°, 25°, or 30°C. Steele's equation fit the 15°C μ vs I data best, whereas the hyperbolic tangent function fit the 20°, 25°, and 30°C data best. Main effects and interactionof light intensity and temperature on rates of R were also significant (P<0.001). R was highly intercorrelated with μ and Ps (0.86≦r≦0.94), indicating that R inG. tikvahiae is primarily regulated by growth rate and not temperatureper se. Environmental factors that regulate growth, such as light intensity, exert a great influence on R inG. tikvahiae.

Optimal segments: a method for smoothing tracer data to calculate metabolic fluxes.

Metabolic fluxes (Ra and Rd) are calculated in the nonsteady state using Steele's equations. These calculations require estimates of the values and rates of change of glucose and specific activity at discrete sampling times. Data smoothing minimizes the effect of measurement error that confounds the Ra and Rd calculations. We compared three smoothing methods: a) moving average, b) polynomial fitting, and c) optimal segments, a new technique that utilizes optimization methods. Experimental designs were simulated: 1) constant infusion of glucagon in depancreatized dogs, and 2) glucose oscillations generated by constant high-level glucose infusion. Measurement error was added to raw data. After smoothing, fluxes were calculated and compared to the "actual" Ra and Rd. Ra calculated from unsmoothed noisy data were in error by an average 39%. Error was reduced by smoothing to: 23%, moving average; 18%, polynomial fitting; 15%, optimal segments. Optimal segments was best for calculating Ra (P less than 0.01) and was better than or equal to other methods for Rd. Distortion in flux patterns was greatest for polynomial fitting (P less than 0.01) and least for optimal segments (P less than 0.001). Optimal segments is the method of choice for smoothing tracer data; it improves calculations of Ra and Rd with minimal distortion.