AJP - Endo AJP: Heart and Circulatory Physiology
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Am J Physiol Endocrinol Metab 292: E1890-E1898, 2007. First published March 6, 2007; doi:10.1152/ajpendo.00563.2006
0193-1849/07 $8.00
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
292/6/E1890    most recent
00563.2006v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Salinari, S.
Right arrow Articles by Mingrone, G.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Salinari, S.
Right arrow Articles by Mingrone, G.

NEFA-glucose comodulation model of beta-cell insulin secretion in 24-h multiple-meal test

Serenella Salinari,1 Alessandro Bertuzzi,2 Melania Manco,3 and Geltrude Mingrone4

1Department of Systems Analysis and Informatics, University of Rome "La Sapienza"; 2Institute of Systems Analysis and Computer Science-Italian National Research Council; 3Liver Unit, Bambino Gesù Hospital and Research Institute; and 4Institute of Internal Medicine, Catholic University, School of Medicine, Rome, Italy

Submitted 17 October 2006 ; accepted in final form 26 February 2007


   ABSTRACT
TOP
 ABSTRACT
RESEARCH DESIGN AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
There is experimental evidence that a source of fatty acids (FAs) that is either exogenous or endogenous is necessary to support normal insulin secretion. Therefore, FAs comodulate the glucose-induced pancreatic insulin secretion. To assess the role of FAs, 16 morbidly obese nondiabetic patients and 6 healthy volunteers were studied. The controls and the obese subjects, before and after diet-induced weight loss, spent 24 h in a calorimetric chamber, where they consumed standardized meals. Hourly blood samples were drawn from a central venous catheter for the measurement of glucose, C-peptide, and nonesterified fatty acid (NEFA) concentrations. Insulin sensitivity was measured (as the M value) by euglycemic hyperinsulinemic clamp. In the present study, we propose a mathematical model in which insulin secretion rate (ISR) is expressed as a function of both plasma glucose and NEFA concentrations. Model parameters, obtained by fitting the individual experimental data of plasma C-peptide concentration, gave an estimated ISR comparable with that obtained by the deconvolution method. To evaluate the performance of the model in an experimental condition in which incretin effect was minimized, previous data on insulin secretion following a butter load and subsequent hyperglycemic clamp were reanalyzed. This model of nutrient-stimulated insulin secretion is the first attempt to represent in a simple way the interaction between glucose and NEFA in the regulation of insulin secretion in the beta-cell and explains, at least in part, the "potentiation factor" used in previous models to account for other control factors different from glucose after either an intravenous infusion of glucose or a mixed meal.

nonesterified fatty acid; mathematical model

FATTY ACIDS (FAs) act as effector molecules in insulin stimulus-secretion coupling. Glucose increases cytosolic long-chain acyl-CoA (LC-CoA) through the rise of malonyl-CoA, which is the starter of FA synthesis and inhibits mitochondrial beta-oxidation, thus realizing a shift from FA to glucose oxidation. The role of FAs in controlling insulin secretion (IS) has recently been reviewed by Yaney and Corkey (32), who underlined that 1) a source of FA that is either exogenous or endogenous is necessary to support normal IS, and 2) a rapid increase of FAs potentiates glucose-stimulated secretion by increasing the concentration of fatty acyl-CoA or complex lipids that act indirectly by modulating key enzymes, such as protein kinase C, or directly by modulating the exocytotic machinery.

In recent papers (15, 16), the glucose-stimulated IS (GSIS) in 24-h multiple-meal tests was represented by three components: 1) a static component that relates IS rate (ISR) to plasma glucose concentration, 2) a potentiation factor that modulates the static component in time by taking into account the influence of a variety of hormonal stimuli on the beta-cell, and 3) a dynamic component that represents the rapid pancreatic response to glucose rise. The time course of the potentiation factor, together with the parameters of the static response and the amplitude of the dynamic component, were estimated by the deconvolution technique from the C-peptide and glucose concentration data (15, 16). Another model proposed by Toffolo et al. (26) allows calculation of the ISR by using a dynamic model where ISR depends on the plasma glucose concentration as well as on its time derivative.

Recently, it has been proposed (3) that incretins enhance IS by increasing both static and dynamic response to orally administered glucose. In fact, glucagon-like peptide-1 (GLP-1) and, to a lesser extent, glucose-dependent insulinotropic polypeptide (GIP) are potent stimulators of IS in either in vitro or in vivo models (28).

However, none of the above-mentioned models takes into account the emerging evidence that cytosolic LC-CoAs cover a key role as coupling factors for IS and that both glucose and nonesterified free fatty acids (NEFAs) are signaling through LC-CoAs (19, 31). It has been hypothesized (32) that nutrients stimulate IS through the simultaneous activation of two pathways. One pathway involves accelerated ATP production and increase in intracellular Ca2+. The other pathway is dependent on the generation and accumulation of excess citrate in the cytosol and increase in cytosolic malonyl-CoA, which in turn blocks LC-CoA transport into mitochondria. GSIS is in fact associated with decreased NEFA oxidation.

In the present study, we report a new mathematical model that describes the dual control of insulin release by glucose and NEFA. Based on this model, data of multiple-meal experiments were analyzed. Parameters of beta-cell function were estimated in control subjects compared with obese patients before and after diet. Twenty-four-hour insulin release, calculated using the present model, is very close to the values obtained by the C-peptide deconvolution method. To better evaluate the effect of NEFA vs. incretin effect, we also applied the model analysis to an experimental situation in which the role of incretins that are maximally stimulated by carbohydrate ingestion was minimized. Thus we reanalyzed data from a previously published study (14) where IS was measured in lean subjects during a hyperglycemic clamp after ingestion of saturated fat (butter) or water.


   RESEARCH DESIGN AND METHODS
TOP
 ABSTRACT
 RESEARCH DESIGN AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Subjects. Sixteen morbidly obese [body mass index (BMI) >40 kg/m2], nondiabetic patients and six sex- and age-matched healthy, untrained volunteers (BMI <25 kg/m2) were studied. None of the obese patients had the metabolic syndrome by either the National Cholesterol Education Program Adult Treatment Panel III (9) or the World Health Organization (30) definition. At the time of the baseline study, all subjects were on a diet with the following average composition: 60% carbohydrates, 30% fat, and 10% protein (≥1 g/kg body wt). This dietary regimen was maintained for 1 wk before the study. The study protocol was approved by the Institutional Ethics Committee of the Catholic University of Rome. The nature and purpose of the study were carefully explained to all subjects before they provided their written consent to participate.

Study protocol. All subjects underwent the metabolic study at baseline and 6 mo after a balanced, low-calorie diet (1,400 kcal). For the basal study, each subject spent 24 h (starting at 8:00 AM) on the metabolic ward. During this period, four meals were administered for a total caloric intake of 25 kcal (104.5 kJ) per kg of fat-free mass (FFM): 20% breakfast at 9:00 AM, 40% lunch at 1:00 PM, 10% afternoon snack at 4:00 PM, and 30% dinner at 8:00 PM. Diet composition was 10% protein, 30% fat, and 60% carbohydrates. Hourly blood samples were drawn from a central venous catheter for the measurement of glucose, C-peptide, and NEFA concentrations. Body composition was evaluated, on a separate day, by the determination of total body water (TBW) using 0.19 Bq 3H2O in 5 ml of saline administered as an intravenous bolus injection (23). Blood samples were drawn before and 3 h after the injection. Radioactivity was determined in duplicate on 0.5 ml of plasma in a beta-scintillation counter (Model 1600TR; Canberra-Packard, Meriden, CT). Corrections were made for nonaqueous hydrogen exchange (5). Water density at body temperature was assumed to be 0.99371 kg/l. TBW (kg) was computed as 3H2O dilution space (liters) x 0.95 x 0.99371. FFM was obtained by dividing TBW by 0.732 (22). Fat mass was obtained as the difference between body weight and FFM.

All procedures and measurements described for the basal study were repeated in the obese subjects participating in the dietary followup.

Euglycemic hyperinsulinemic clamp. Peripheral insulin sensitivity was evaluated by the euglycemic hyperinsulinemic technique (6) at baseline and after diet in obese subjects and at baseline in controls. After the insertion of a cannula in a dorsal hand vein for sampling arterialized venous blood, and another in the antecubital fossa of the contralateral arm for infusions, the subjects rested in the supine position for ≥1 h. They were placed with one hand warmed in a heated air box set at 60°C to obtain arterialized blood samples. Insulin sensitivity was evaluated as the rate of total insulin-mediated glucose uptake (M value) during a 2-h primed constant infusion of insulin at the rate of 6 pmol·min–1·kg–1. The fasting plasma glucose concentration was maintained throughout the insulin infusion by means of a variable glucose infusion and blood glucose determinations every 5 min. The M value was computed in the last 40 min of the clamp after correction for changes in glucose concentration in a total distribution volume of 250 ml/kg and was normalized per kilogram of FFM (M value given in µmol·min–1·kg FFM–1).

Analytical procedures. Plasma glucose was measured by the glucose oxidase technique on a Beckman Glucose Analyzer (Beckman, Fullerton, CA). C-peptide was assayed by radioimmunoassay (MYRIA; Technogenetics, Milan, Italy). Serum NEFAs were measured spectrophotometrically.

Mathematical model. The kinetics of LC-CoA was modeled, following the scheme in Fig. 1. Fp denotes the NEFA concentration in plasma and F the NEFA concentration inside the beta-cell. The simplest model that relates F to Fp is a linear first-order kinetics, that is

Formula 1(1)
According to Eq. 1, the changes in NEFA concentration inside the beta-cell are a "smoothed" version of the changes in NEFA plasma concentration. The term k2F in Eq. 1 represents the LC-CoA formation rate in cytosol from beta-cell NEFA. We assume that the total CoA pool is large enough to permit the conversion of FAs into LC-CoA without any limitation, at least at the concentrations considered. In writing Eq. 1 we have also assumed that beta-cell triglyceride content is constant during the experiment, so there is no net conversion of NEFA into triglycerides or vice versa.


Figure 1
View larger version (19K):
[in this window]
[in a new window]

  		Fig. 1. Schematic representation of the dual pathway involved in the stimulation of insulin secretion by glucose and nonesterified fatty acid (NEFA) (modified from Ref. 32). Variables and parameters of the matematical model are included (symbols explained in the text). The dashed arrows indicate the control actions considered in the model. LC-CoA, long-chain acyl-CoA.

 
Let us now denote by C the cytosolic LC-CoA concentration. As shown in Fig. 1, LC-CoA has two possible fates: transport into mitochondria and utilization in cytosol in the exocytotic machinery. We assume that the kinetics of LC-CoA binding to carnitine palmitoyltransferase I (CPT I) is fast enough to be considered in quasi-equilibrium at each time. The concentration of LC-CoA bound to CPT I may thus be written as RC/(Km + C), where R is the total concentration of the CPT I binding sites and Km is the Michaelis-Menten constant. Still assuming the equilibrium conditions, the rate of LC-CoA formation per unit cytosolic volume, k2F, equals the rate of bound LC-CoA internalization into mitochondria plus the rate of free LC-CoA utilization in the exocytotic machinery. We have

Formula 2(2)
where kint is the rate constant of bound LC-CoA internalization and k3 is the rate constant of cytosolic LC-CoA utilization. In the hypothesis of complete oxidation of internalized lipids, the rate of LC-CoA internalization into mitochondria at the equilibrium is equal to the rate of beta-oxidation in the beta-cell. Equation 2 may be rewritten as the following second-order algebraic equation for C:

Formula 3(3)

As pointed out by Yaney and Corkey (32), the increase in plasma and extracellular glucose concentration results in increased pyruvate availability and malonyl-CoA formation. The glucose-induced inhibition of CPT I via malonyl-CoA will be represented in Eq. 3 as a decrease in the concentration R of CPT I binding sites: in particular, we simply set R = R*/G where R* is a constant and G is glucose concentration in plasma. This leads, taking the positive root of Eq. 3, to the following expression for C as a function of G and F:

Formula 4(4)

According to the view that a dual signaling pathway involving both glucose and LC-CoA (see Fig. 1) regulates the stimulation ofIS by nutrients (32), we express the static component, S, of the IS rate as

Formula 5(5)
where {alpha} is a sensitivity constant. From Eqs. 4 and 5, we finally get the following expression for S:

Formula 6(6)
where p1 = {alpha}k2/k3, p2 = k3Km/k2 and p3 = kintR*/k2 are three parameters to be estimated from the data. It may be seen that S increases with both G and F. In particular, the potentiating effect of NEFA is seen by noting that at any given F, for G very large S increases with slope p1F, and the intercept of this asymptote with G axis is p3/(p2 + F).

In view of Eqs. 1 and 6, the static component of ISR is expressed as a function of both plasma glucose and plasma NEFA concentration. In fact, Eq. 6 shows that glucose has a dual role: it stimulates IS directly and modulates through malonyl-CoA the action of LC-CoA on secretion. This action is represented by the term in square brackets in Eq. 6, which is a sort of "potentiation factor" that accounts for the action of FAs on IS. We observe that the complete inactivation of the citrate-malonyl-CoA-CPT I pathway may be simulated by assuming the total concentration of CPT I binding sites, R, independent of G and equal to a constant Formula 6 in Eq. 3. In this case, the term p3/G in Eq. 6 changes to Formula 63 = kint Formula 6/k2. Moreover, according to Mari and colleagues (15, 16) and Toffolo et al. (26), we add a dynamic component to the static component and obtain the following expression for the IS rate:

Formula 7(7)

As shown by Eqs. 1, 6, and 7, the present model of the ISR contains the following six unknown parameters: k1, k2, p1, p2, p3, and kd.

To analyze the data, the ISR model must be complemented by the equations for the whole body C-peptide kinetics. We have used the validated two-compartment model (18, 27), calculating the standard parameters of C-peptide kinetics for each subject as proposed by Van Cauter et al. (27).

Parameter estimation. All of the parameters, k1, k2, p1, p2, p3, and kd, of the proposed model are a priori uniquely identifiable, as proved by the similarity transformation approach (29). The estimates of model parameters for individual subjects were obtained by assuming k1 = k2 = k, that is, by assuming that equilibrium NEFA concentration inside the beta-cell is equal to NEFA concentration in plasma. Moreover, to take into account the influence on ISR of other stimuli different from glucose and NEFAs, the 24-h time length of the test was subdivided into three phases, of ~8 h each, with possibly different values of the parameter p1 (denoted as p11, p12, p13) for each of these subintervals. The parameters to be estimated were thus the following: p11, p12, p13, p2, p3, kd, and k. In the analysis of data from the hyperglycemic clamp study, the parameter p1 was assumed constant.

To determine the ISR profile, the 24-h experimental data of plasma glucose and plasma NEFA concentration to be used in Eqs. 1, 6, and 7 were approximated by cubic splines, and the model parameters were found for each subject by fitting the plasma C-peptide concentration values. Under the assumption that all measurements had a common coefficient of variation, a weighted least-square fit was performed, with weights given by the inverse of the estimated variance of measurement error (13). The least-square index was minimized by means of a constrained Levenberg-Marquardt routine of the Matlab library. The standard errors of the estimates of individual parameters were evaluated by the Jackknife method (21).

The 24-h profile of the ISR was also reconstructed from plasma C-peptide concentrations by the deconvolution method according to Van Cauter et al. (27).

Statistical analysis. All of the data were expressed as means ± SE unless otherwise specified. Paired two-tailed t-test and unpaired two-tailed t-test were used for intragroup and intergroup comparisons, respectively.


   RESULTS
TOP
 ABSTRACT
 RESEARCH DESIGN AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Twenty-four-hour studies. Six months of diet determined a reduction in BMI from 50.2 ± 2.1 to 41.3 ± 2.0 kg/m2 in obese patients. Fat mass decreased from 62.0 ± 3.9 to 51.1 ± 3.7 kg, whereas FFM decreased from 72.3 ± 4.4 to 60.3 ± 3.9 kg, and the percent reduction of fat mass was 17.5%, whereas that of FFM was 16.3%.

The rate of insulin-mediated whole body glucose uptake (M), normalized per kilogram of FFM, was 39.2 ± 5.5 µmol·kg FFM–1·min–1, and the clamp steady-state level of insulin was 535.0 ± 54.1 pM in controls. The M value was significantly (P < 0.0001) increased in obese subjects after diet, from 17.2 ± 6.1 µmol·kg FFM–1·min–1, with a steady-state plasma insulin concentration of 516.0 ± 60.4 pM, to 27.9 ± 7.3 µmol·kg FFM–1·min–1 and insulin level of 500.2 ± 47.4 pM. Although the glucose uptake was increased in the order of ~62%, it was still significantly (P < 0.05) lower than in controls.

The mean 24-h profiles of plasma glucose, NEFA, and C-peptide concentrations in controls and obese subjects before and after the diet are shown in Fig. 2. After dieting, the plasma levels of C-peptide, averaged over 24 h, became very similar to those of controls (P = not significant), NEFA levels were significantly different (P < 0.01) for obese subjects pre- and postdieting and for obese subjects postdieting and controls (P < 0.05), and NEFA levels of the obese patients before the diet and controls were different with P < 0.001. Average glucose level did not differ significantly in the three groups.


Figure 2
View larger version (25K):
[in this window]
[in a new window]

  		Fig. 2. Time course of glucose, NEFA, and C-peptide plasma concentration (means ± SE) in the obese population before and after the diet, and in control subjects over 24 h. The mean value over 24 h is reported (dashed line). Arrows indicate the time of the meals. The spine approximation is also reported.

 
Figure 3 shows the model fitting of plasma C-peptide concentrations for a representative obese subject before and after dieting. In the same figure, the 24-h ISR, estimated either by the present model or by deconvolution of C-peptide data, is reported. Cumulative 24-h IS, calculated as the area under the ISR curve, was found to attain the same values when computed by the present model or by deconvolution, with a maximal relative difference <1%. Moreover, the cumulative IS was significantly larger (P < 0.01) in obese patients before diet (0.53 ± 0.22 µmol) compared with obese patients after diet (0.33 ± 0.06 µmol) and controls (0.24 ± 0.04 µmol). After the diet, the ISR was markedly reduced, principally as a consequence of the reduction in circulating NEFA levels. Cumulative IS was not significantly different in obese patients after diet and in controls.


Figure 3
View larger version (16K):
[in this window]
[in a new window]

  		Fig. 3. Top: C-peptide plasma concentration before (+) and after (*) diet, with the fitting curves superimposed for 1 representative obese subject. Bottom: ISR time course as estimated by the model (solid line) and as obtained by deconvolution (dotted line). Arrows indicate the time of the meals.

 
Table 1 reports means ± SD over the subject populations of the model parameter estimates and the statistical differences between the obese subjects before and after diet and the controls. For all subjects, the standard error of the individual parameter estimates was consistently <20%. It is remarkable that a weight loss of ~17% resulted in a normalization of the beta-cell parameters, as revealed by t-test. The values of parameter p1 in the three phases of the experiment (p11, p12, p13), as well as p2 and p3, are significantly different in obese patients before diet compared with obese patients after diet and controls, whereas no significant difference was found between obese subjects after diet and controls. Parameters k and kd are not different in the three groups. Table 1 also reports means ± SD of two other quantities. The first one is the product p1mp2 = {alpha}Km, where p1m was computed for each subject as the mean of p1 over the three phases weighted with the duration of each phase. The second quantity is the ratio p3/p2 = kintR*/(k3Km). This ratio represents a balance between the parameters regulating LC-CoA transport into mitochondria (kintR*/Km) and the parameter regulating LC-CoA utilization in cytosol, likely by exocytosis (k3). It is found that p1mp2 is substantially unchanged in the three groups. By contrast, p3/p2 is markedly diminished in the obese group, pointing to a reduction of LC-CoA transport into mitochondria and thus of beta-oxidation rate in these subjects.


View this table:
[in this window]
[in a new window]

  		Table 1. Population parameter estimates for the obese subjects before and after diet and for the controls

 
Figure 4 shows the static component of the ISR as a function of both glucose and NEFA levels. The synergism of high NEFA and high glucose concentrations translates into a large stimulation of IS mainly in controls, whereas in obese subjects this effect is blunted. Thus, although the beta-cell response is increased in obese patients at lower glucose concentrations, the response becomes smaller than in controls as glucose concentration increases. The curves in Fig. 5 depict the change of ISR static component in response to glucose changes when NEFA concentration is kept constant at 0.4 and 0.8 mM, respectively. It is evident that high levels of NEFA strongly influence the ISR at glucose levels in the physiological range. The dashed lines simulate the complete inactivation of the pathway citrate-malonyl-CoA-CPT-1 in controls, with Formula 73 chosen to have the same value of the ISR static component in controls at G = 5 mM. The relationship S vs. G at constant F is now linear, and the potentiation by NEFA only changes its slope.


Figure 4
View larger version (31K):
[in this window]
[in a new window]

  		Fig. 4. Static component (S) of the ISR as a function of both glucose and NEFA levels. C, controls; O, obese subjects before diet. Parameters p1m, p2, p3, as in Table 1.

 

Figure 5
View larger version (13K):
[in this window]
[in a new window]

  		Fig. 5. Static component of the ISR as a function of glucose when NEFAs are kept constant at 0.4 (bottom curves) and 0.8 mM (top curves), respectively. Solid lines, controls; dotted lines, obese subjects before diet; dashed lines, inactivation of the citrate-malonyl-CoA-carnitine palmitoyltransferase I pathway in controls (Formula 73 = 1.7 mM).

 
Hyperglycemic clamp study. Figure 6 shows the ISR profiles predicted by the model during a hyperglycemic clamp (glucose concentration {cong} 14 mM) either after 100 ml of water or 100 g of oral butter load in a representative subject. The overall secretion rate was significantly higher after the butter load. We note that the data in Fig. 6 do not show a first-phase increase in C-peptide concentration. The longer half-life of plasma C-peptide compared with insulin (35 vs. 10 min) may not allow a first phase to be recognized even with a high sampling rate as in Caumo and Luzi (4).


Figure 6
View larger version (14K):
[in this window]
[in a new window]

  		Fig. 6. Top: C-peptide plasma concentration after water (+) and after butter (*), with the fitting curves superimposed for 1 representative subject. Bottom: ISR time course as estimated by the model (solid line) and as obtained by deconvolution (dotted line). The arrow indicates the onset of the hyperglycemic clamp. Water or butter load given at time 0.

 
Table 2 reports the mean (± SD) of estimated model parameters. The values obtained for the hyperglycemic clamp after butter are close to the values obtained in the multiple-meal test in controls. After water, the coefficient p1 is significantly smaller, suggesting that the potentiation of IS mediated by gastrointestinal hormones, such as GIP and GLP1, does not take place.


View this table:
[in this window]
[in a new window]

  		Table 2. Population parameter estimates for normal subjects during the hyperglycemic clamp after butter and water load

 

   DISCUSSION
TOP
 ABSTRACT
 RESEARCH DESIGN AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
There is a strong experimental evidence that changes in circulating NEFA levels are essential for stimulating insulin secretion. In fact, when the elevated level of circulating NEFA in 18- to 24-h-fasted rats was acutely lowered by infusion of the antilipolytic agent nicotinic acid, subsequent GSIS was completely ablated but became supranormal when the NEFA concentration was maintained high by coinfusion of a lipid emulsion plus heparin (24, 25). Qualitatively similar results have also been obtained in humans (7, 14). Therefore, glucose cannot be considered the only secretagogue stimulus for insulin secretion.

The present model, for the first time, takes explicitly into account the role of NEFA in modulating ISR. In the model, glucose exerts a dual role on insulin secretion, with a direct stimulation of ISR and an indirect stimulatory effect through the control of LC-CoA's entrance into mitochondria, where the latter are beta-oxidized. Previous models (15, 16, 26) used the circulating glucose levels as regulators of insulin secretion for relatively short experimental time periods and in a well-defined clinical setting. These protocols include the intravenous glucose tolerance test, the hyperglycemic clamp, the graded glucose infusion, the oscillatory glucose infusion, and the oral glucose tolerance test. All of the above tests provide the beta-cell secretory response to glucose and, in some cases, also the whole body insulin sensitivity.

However, when the 24-h free living conditions are considered, the modeling of the ISR needs to include a series of stimuli that intervene in the regulation of the pancreatic secretory response. A recent model (15) has taken these factors into account by means of an unspecified potentiating factor to satisfactorily represent the 24-h insulin release as calculated by deconvolution of plasma C-peptide concentration data and using the C-peptide standard kinetic model (18, 27). The introduction of plasma NEFA concentration in the present mathematical model of insulin secretion represents an attempt to define a main component of the potentiation factor. In fact, by using NEFA as comodulator of glucose in stimulating insulin secretion we obtained a good fitting of experimental data and explained, at least in part, the potentiating factor that regulates the ISR. Our model is based on previously proposed dual signaling pathways involved in the physiological stimulation of insulin secretion by nutrients (32).

The nutrient-stimulated secretion model here proposed is formulated in terms of the three parameters p1 = {alpha}k/k3, p2 = k3Km/k, and p3 = kintR*/k. The parameter k, which controls the rate of NEFA entry into the beta-cell, is practically unchanged in the three groups shown in Table 1. Moreover, k3, which represents the rate constant of cytosolic LC-CoA utilization, is not likely to be decreased in controls and in insulin-resistant obese subjects after dieting. Thus, the smaller p1 and the larger p2 found in obese patients should reveal a decreased beta-cell sensitivity ({alpha}) to both glucose and NEFA and an increased Km (in fact, the product p1p2 is unchanged in the 3 groups of subjects). The p1 mean value in obese subjects significantly increased after dieting, suggesting a net improvement of beta-cell sensitivity to nutrient stimuli. Finally, p3 is related to the effectiveness of LC-CoA transport into mitochondria as mediated by CPT I. The parameter p3 and the ratio p3/p2 are markedly reduced in the obese subjects, who have a defect in the mitochondrial LC-CoA beta-oxidation (11) compared with healthy controls and with themselves after the diet-induced weight loss.

As shown in Fig. 5, at relatively high NEFA levels (0.8 mM), plasma glucose concentrations larger than 6 mM are able to stimulate insulin secretion more effectively in lean than in obese subjects. This finding agrees with the observations of impaired GSIS in islet cells from Zucker diabetic fatty rats, in which the chronic exposure to elevated levels of long-chain FAs altered a mitochondrial pathway of pyruvate metabolism (1). It has also been found (2) that long-chain FAs inhibited in the INS-1 beta-cell line the accumulation of the enzyme acetyl-CoA carboxylase, which controls the synthesis of malonyl-CoA. The resulting decrease in malonyl-CoA levels was associated with high basal insulin release and marked reduction of GSIS. Overexpression of malonyl-CoA carboxylase in cytosol also reduced malonyl-CoA content and GSIS in INSr3 cell clones and rat islets (20). Moreover, in rat islets infected by an adenovirus encoding a mutant form of CPT I insensitive to malonyl-CoA, GSIS was decreased by 40% compared with the control (10). To evaluate by the model the effect of experimental alterations of the malonyl-CoA-CPT I interaction, the complete suppression of the citrate-malonyl-CoA-CPT I pathway was simulated by deleting the glucose dependence of the binding of LC-CoA to CPT I. In this case, the curves of the static component of ISR vs. glucose concentration in controls (Fig. 5, dashed lines) show a pronounced decrement of potentiation and are similar to the curves obtained for the obese subjects with reduced value of the model parameter p3 and increased p2.

The smaller value of the parameter p1, found in the obese subjects before diet with respect to controls, may be related to other cellular effects of elevated NEFA levels. Decrease of the glucose transporter 2 (GLUT2) was induced in rat pancreatic islets by 48-h exposure to palmitate (8). Also of interest is that the expression of the uncoupling protein-2 (UCP2) that negatively regulates insulin secretion by decreasing ATP synthesis was upregulated in INS-1 beta-cells by high FA levels (12) and in islets of ob/ob mice (33). Both GLUT2 decrease and UCP2 upregulation are likely to cause impairment of beta-cell sensitivity to glucose, which is revealed by a decreased value of parameter p1 with respect to controls.

Campioni et al. (3) have recently reported that incretins increase insulin secretion by enhancing both the dynamic and the static component of insulin response to glucose stimulus after oral glucose load. Incretins alone may not entirely explain the potentiation factor. Indeed, Muscelli et al. (17) suggested that the lack of quantitative correspondence between the incretin-mediated insulin release and the plasma concentrations of GLP-1 and GIP may imply that other unmeasured hormones/substances are involved in the incretin effect as measured in vivo. However, it has to be noted that assessing the actual effect of incretins may be difficult, because their effectiveness on beta-cell response may be more prolonged than their half-life in plasma. Therefore, we propose that NEFA contribute to explain, at least in part, the "potentiation factor" previously described in the literature.

Although our results cannot prove a causative role of NEFA as the potentiation factor, the present model satisfactorily fits the C-peptide concentration data of the multiple-meal test over 24 h as well as of the short-term hyperglycemic clamp, estimating an ISR comparable with that obtained by the deconvolution method. Model parameters highlight important changes that occur in beta-cell function in the obese status, in particular the decreased beta-cell sensitivity to nutrient stimulation and the impairment of LC-CoA transport into mitochondria. However, a more complex model would be required to fully reflect at the molecular level the effects of high NEFA and obesity on beta-cell metabolism and function. The use of NEFA, together with glucose, as comodulator of insulin secretion appears to explain, at least in part, the potentiation factor used in previous models (15, 16) to account for control factors other than glucose after either an intravenous infusion of glucose or a mixed meal.


   FOOTNOTES
 

Address for reprint requests and other correspondence: S. Salinari, Dipartimento di Informatica e Sistemistica, Via Eudossiana, 18, 00184 Roma (e-mail: salinari{at}dis.uniroma1.it)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 RESEARCH DESIGN AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 

  1. Boucher A, Lu D, Burgess SC, Telemaque-Potts S, Jensen MV, Mulder H, Wang MY, Unger RH, Sherry AD, Newgard CB. Biochemical mechanism of lipid-induced impairment of glucose-stimulated insulin secretion and reversal with a malate analogue. J Biol Chem 279: 27263–27271, 2004.[Abstract/Free Full Text]
  2. Brun T, Assimacopoulos-Jeannet F, Corkey BE, Prentki M. Long-chain fatty acids inhibit acetyl-CoA carboxylase gene expression in the pancreatic beta-cell line INS-1. Diabetes 46: 393–400, 1997.[Abstract]
  3. Campioni M, Toffolo GM, Shuster LT, Service FJ, Rizza RA, Cobelli C. Incretin effect potentiates beta-cell responsivity to glucose as well as to its rate of change: OGTT and matched intravenous study. Am J Physiol Endocrinol Metab 292: E54–E60, 2007.[Abstract/Free Full Text]
  4. Caumo A, Luzi L. First-phase insulin secretion: does it exist in real life? Considerations on shape and function. Am J Physiol Endocrinol Metab 287: E371–E385, 2004.[Abstract/Free Full Text]
  5. Culebras JM, Moore FD. Total body water and the exchangeable hydrogen. I. Theoretical calculation of nonaqueous exchangeable hydrogen in man. Am J Physiol Regul Integr Comp Physiol 232: R54–R59, 1977.[Abstract/Free Full Text]
  6. DeFronzo RA, Tobin JD, Andres R. Glucose clamp technique: a method for quantifying insulin secretion and resistance. Am J Physiol Endocrinol Metab Gastrointest Physiol 237: E214–E223, 1979.[Abstract/Free Full Text]
  7. Dobbins RL, Chester MW, Daniels MB, McGarry JD, Stein DT. Circulating fatty acids are essential for efficient glucose-stimulated insulin secretion after prolonged fasting in humans. Diabetes 48: 1613–1618, 1998.
  8. Gremlich S, Bonny C, Waeber G, Thorens B. Fatty acids decrease IDX-1 expression in rat pancreatic islets and reduce GLUT2, glucokinase, insulin, and somatostatin levels. J Biol Chem 272: 30261–30269, 1997.[Abstract/Free Full Text]
  9. Grundy S. Third report of the National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation and Treatment of High Blood Pressure in Adults (Adult Treatment Panel III). Circulation 106: 3145–3421, 2002.[Free Full Text]
  10. Herrero L, RubFormula 7 B, Sebastiàn D, Serra D, Asins G, Maechler P, Prentki M, Hegardt FG. Alteration of the malonyl-CoA/carnitine palmitoyltransferase I interaction in the beta-cell impairs glucose-induced insulin secretion. Diabetes 54: 462–471, 2005.[Abstract/Free Full Text]
  11. Kelley DE, Goodpaster BH, Storlien L. Muscle triglyceride and insulin resistance. Annu Rev Nutr 22: 325–346, 2002.[CrossRef][ISI][Medline]
  12. Lameloise N, Muzzin P, Prentki M, Assimacopoulos-Jeannet F. Uncoupling protein 2: a possible link between fatty acid excess and impaired glucose-induced insulin secretion? Diabetes 50: 803–809, 2001.[Abstract/Free Full Text]
  13. Landaw EM, DiStefano 3rd JJ. Multiexponential, multicompartmental, and noncompartmental modeling. II. Data analysis and statistical considerations. Am J Physiol Regul Integr Comp Physiol 246: R665–R677, 1984.[Abstract/Free Full Text]
  14. Manco M, Bertuzzi A, Salinari S, Scarfone A, Calvani M, Greco AV, Mingrone G. The ingestion of saturated fatty acid triacylglycerols acutely affects insulin secretion and insulin sensitivity in human subjects. Br J Nutr 92: 895–903, 2004.[CrossRef][ISI][Medline]
  15. Mari A, Camastra S, Toschi E, Giancaterini A, Gastaldelli A, Mingrone G, Ferrannini E. A model for glucose control of insulin secretion in 24 h of free living. Diabetes 50, Suppl 1: S164–S168, 2001.[ISI][Medline]
  16. Mari A, Schimtz O, Gastaldelli A, Oestergaard T, Nyholm B, Ferrannini E. Meal and oral glucose tests for assessment of beta-cell function: modeling analysis in normal subjects. Am J Physiol Endocrinol Metab 283: E1159–E1166, 2002.[Abstract/Free Full Text]
  17. Muscelli E, Mari A, Natali A, Astiarraga BD, Camastra S, Frascerra SD, Holst JJ, Ferrannini E. Impact of incretin hormones on beta-cell function in subjects with normal or impaired glucose tolerance. Am J Physiol Endocrinol Metab 291: E1144–E1150, 2006.[Abstract/Free Full Text]
  18. Polonsky KS, Licinio-Paixao J, Given BD, Pugh W, Rue P, Frank B. Use of biosynthetic human C-peptide in the measurement of insulin secretion rates in normal volunteers and in type I diabetic patients. J Clin Invest 77: 98–105, 1986.[ISI][Medline]
  19. Prentky M, Corkey BE. Are the beta-cell signaling molecules malonyl-CoA and cytosolic long-chain acyl-CoA implicated in multiple tissue defects of obesity and NIDDM? Diabetes 45: 273–283, 1996.[Abstract]
  20. Roduit R, Nolan C, Alarcon C, Moore P, Barbeau A, Delghingaro-Augusto V, Przybykowsky E, Morin J, Massé F, Massie B, Ruderman N, Rhodes C, Poitout V, Prentki M. A role for the malonyl-CoA/long-chain acyl-CoA pathway of lipid signaling in the regulation of insulin secretion in response to both fuel and nonfuel stimuli. Diabetes 53: 1007–1019, 2004.[Abstract/Free Full Text]
  21. Shao J, Thu D. The Jackknife and Bootstrap. New York: Springer Verlag, 1995.
  22. Sheng HP, Huggins RA. A review of body composition studies with emphasis on total body water and fat. Am J Clin Nutr 32: 630–647, 1979.[Abstract/Free Full Text]
  23. Siri WE. Body composition from fluid spaces and density: analysis of methods. In: Techniques of Measuring Body Composition, edited by Brozek J and Henschel A. Washington, DC: National Academy of Sciences, National Research Council, 1961, p. 107–141.
  24. Stein DT, Esser V, Stevenson B, Lane KE, Whiteside JH, Daniels MB, Chen S, McGarry JD. Essentiality of circulating fatty acids for glucose-stimulated insulin secretion in the fasted rat. J Clin Invest 97: 2728–2735, 1996.[ISI][Medline]
  25. Stein DT, Stevenson B, Chester MW, Basit M, Daniels MB, Turley SD, McGarry JD. The insulinotropic potency of fatty acids is influenced profoundly by their chain length and degree of saturation. J Clin Invest 100: 398–403, 1997.[ISI][Medline]
  26. Toffolo G, Breda E, Cavaghan MK, Ehrmann DA, Polonsky KS, Cobelli C. Quantitative indexes of beta-cell function during graded up&down glucose infusion from C-peptide minimal models. Am J Physiol Endocrinol Metab 280: E2–E10, 2001.[Abstract/Free Full Text]
  27. Van Cauter E, Mestrez F, Sturis J, Polonsky KS. Estimation of insulin secretion rates from C-peptide levels. Comparison of individual and standard kinetic parameters for C-peptide clearance. Diabetes 41: 368–377, 1992.[Abstract]
  28. Vella A, Rizza RA. Extrapancreatic effects of GIP and GLP-1. Horm Metab Res 36: 830–836, 2004.[CrossRef][ISI][Medline]
  29. Wajda S, Godfrey KR, Rubitz H. Similarity transformation approach to identifiability analysis of non linear compartmental models. Math Biosci 93: 217–248, 1989.[CrossRef][ISI][Medline]
  30. World Health Organization. Globalization Diet and Non Communicable Diseases. Geneva, Switzerland: World Health Organization, 2002.
  31. Yaney GC, Korchak HM, Corkey BE. Long-chain acyl CoA regulation of protein kinase C and fatty acid potentiation of glucose-stimulated insulin secretion in clonal beta-cells. Endocrinology 141: 1989–1998, 2000.[Abstract/Free Full Text]
  32. Yaney GC, Corkey BE. Fatty acid metabolism and insulin secretion in pancreatic beta cells. Diabetologia 46: 1297–1312, 2003.[CrossRef][ISI][Medline]
  33. Zhang CY, Baffy G, Perret P, Krauss S, Peroni O, Grujic D, Hagen T, Vidal-Puig AJ, Boss O, Kim YB, Zheng XX, Wheeler MB, Shulman GI, Chan CB, Lowell BB. Uncoupling protein-2 negatively regulates insulin secretion and is a major link between obesity, beta-cell dysfunction, and type 2 diabetes. Cell 105: 745–755, 2001.[CrossRef][ISI][Medline]




This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
292/6/E1890    most recent
00563.2006v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Salinari, S.
Right arrow Articles by Mingrone, G.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Salinari, S.
Right arrow Articles by Mingrone, G.

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
Visit Other APS Journals Online
Copyright © 2007 by the American Physiological Society.