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Endocrine Care |
Divisions of Pediatric Nephrology (R.F., M.S., O.M., F.S.) and Clinical Nephrology (E.R.), Faculty of Medicine, and Institute of Pharmacology and Toxicology (R.F.), Faculty of Clinical Medicine Mannheim, Ruperto-Carolus University, 69115 Heidelberg, Germany; and Department of Internal Medicine (J.D.V.), University of Virginia Health Sciences Center and General Clinical Research Center, Charlottesville, Virginia 22908
Address all correspondence and requests for reprints to: Franz Schaefer, M.D., Pediatric Nephrology Division, University Childrens Hospital, Im Neuenheimer Feld 150, 69120 Heidelberg, Germany. E-Mail: . franz_schaefer{at}med.uni-heidelberg.de
Abstract
Chronic renal failure (CRF) is associated with mechanistically unexplained impaired insulin sensitivity. Erratic insulin secretory patterns typify other states of insulin resistance. We sought to investigate possible alterations of plasma insulin oscillations in CRF. We assessed high- and low-frequency insulin and glucose oscillations in 7 male CRF patients and 11 controls by multiparametric deconvolution analysis and cluster analysis, approximate entropy (ApEn) statistic, and cross-ApEn statistics. Insulin sensitivity was appraised by euglycemic hyperinsulinemic clamps. Despite impaired glucose disappearance rates in CRF, fasting and 24-h mean insulin and glucose concentrations did not differ between patients and controls. However, patients showed a 2.5-fold increase of insulin elimination half-life, reduced frequency of both rapid (6.1 ± 0.4 vs. 7.1 ± 0.2 h-1, P < 0.001) and slow oscillations of insulin release (0.54 ± 0.11 vs. 0.71 ± 0.1 h-1, P < 0.001), lack of acceleration and paradoxically more orderly slow insulin and glucose pulses after meals, and increased temporal coupling between insulin and glucose patterns (cross-ApEn: 0.58 ± 0.13 vs. 1.37 ± 0.23, P < 0.001). Postprandial glucose intolerance was inferable by prolonged and amplified blood glucose excursions despite exaggerated insulin bursts of almost 3-fold higher area. In summary, CRF is associated with a complex disruption of the temporal organization of insulin release, which differs from abnormalities observed to date in other states of insulin resistance.
INSULIN RESISTANCE IS an early complication and an important predictor of long-term morbidity in patients with chronic renal failure (CRF) (1, 2, 3). Although uremic insulin resistance appears to reside primarily in the peripheral tissues, additional defects of the pancreatic insulin secretory capacity have been demonstrated (4). However, previous studies did not take into account the impaired renal elimination of insulin in CRF (5, 6) and the episodic nature of endogenous insulin secretion.
Insulin is secreted in a pulsatile fashion with two dominant frequencies of insulin release (7, 8, 9). Whereas the precise biological functions of these low-amplitude/high-frequency and high-amplitude/low-frequency oscillations are still unknown (10), alterations of pulsatile insulin release occur in non-insulin-dependent diabetes mellitus patients and even in their relatives who have minimal or no reduction of glucose tolerance but are predisposed to insulin resistance (11, 12, 13, 14). Pulsatile insulin delivery exerts a greater hypoglycemic effect than continuous delivery (15). Moreover, recent research using genetically modified animals has identified common molecular mechanisms regulating ß-cell function and peripheral insulin sensitivity (16, 17, 18).
We hypothesized that the alterations of insulin signaling in CRF might be associated with abnormalities in spontaneous insulin pulsatility. To test this notion, we compared both types of insulin oscillations in a group of patients with moderately advanced CRF with patterns in healthy controls matched for age, body mass index, and waist to hip ratio.
Subjects and Methods
Patients and control subjects
Seven male patients with CRF and 11 healthy male volunteers participated in the study. The anthropometric and endocrine characteristics are given in Table 1
. Relevant diseases other than CRF were excluded by history, physical examination, and routine laboratory investigation. There was no known diabetes mellitus in first-degree relatives of all patients and control subjects. The primary renal disease was IgA glomerulopathy in four patients and nephrotic syndrome, renal artery stenosis, and Alports disease in one patient each.
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Study protocol
All studies were performed after an overnight fast. At 0730 h a cannula was inserted into a cubital vein for blood sampling. From 0800 h (d 1) to 0800 h (d 2), 0.7-ml blood specimens were withdrawn at 15-min intervals without tourniquet use.
Three meals were prepared on the basis of low sodium and phosphate content. The meals were standardized with respect to carbohydrate, protein, and fat content and were consumed at 0800 h, 1300 h, and 1900 h. Each meal contained 45% carbohydrates, 20% protein, and 35% fat, delivering 36 ± 7 kcal/kg body weight·d. The subjects were allowed to walk in a quiet environment and went to bed at 2300 h. Sleep was confirmed by inspection and interview in the morning. Starting at 0600 h on the second day, a blood sample was withdrawn every minute for 2 h. Thereafter, a 2-h hyperinsulinemic euglycemic clamp study was performed. For this procedure, a second iv line was inserted immediately before the clamp study. After the end of the clamp study, a sample was drawn every 0.5 min for 20 min to measure directly the individual plasma half life of insulin.
The study protocol was approved by the Ethics Committee of the University of Heidelberg. All participants gave their voluntary written informed consent before the study.
Analytical methods
One aliquot of the blood sample was used for measurement of electrolytes and pH immediately after sampling. The remainder was stored on ice and centrifuged after clotting. The serum was stored at -80 C. All measurements were performed within 2 wk after the study.
Serum insulin concentrations were determined using an insulin ELISA (DAKO Corp. Diagnostika, Hamburg, Germany), a highly sensitive two-site immunospecific ELISA with two monoclonal murine antibodies to human insulin. The detection limit of the assay is 0.5 mU/liter. There is no cross-reactivity with human C-peptide and virtually none with intact human proinsulin (0.3%), 3233 split proinsulin (0.3%), and des-3132 split proinsulin (0.5%). The antibodies cross-react with 6566 split proinsulin (45%) and des-6465 split proinsulin (66%). The concentrations of the latter two split products in healthy humans and uremic patients are negligible (20). The interassay coefficient of variation was 8.4%. The intraassay coefficient of variation was 6.3%, 5.0%, and 4.9% at 05, 510, and more than 10 mU/liter, respectively. Each sample was assayed in duplicate.
For the 24-h profiles, blood glucose was measured using the hexokinase method on a Hitachi 705 autoanalyzer (Roche Molecular Biochemicals, Mannheim, Germany). During the euglycemic clamp studies, glucose concentrations were determined by the glucokinase method, using a Glucose Analyzer II (Beckman Coulter, Inc. Instruments, Munich, Germany). Sodium and pH were measured using an ion-selective electrode device (Ionometer EF-H, Fresenius, Bad Homburg, Germany).
Euglycemic hyperinsulinemic clamp studies
The euglycemic hyperinsulinemic clamp studies were performed as described in detail by DeFronzo et al. (21), with slight modifications. A priming bolus of insulin (100 mU/m2 per minute, H-Insulin, Hoechst, Frankfurt, Germany) was infused iv for 2 min. The insulin infusion rate was decreased stepwise every 2 min from 90 to 80 and 60 mU/m2 per minute to reach a constant maintenance rate of 40 mU/m2 per minute. Five minutes after the start of the insulin infusion, a 20% glucose infusion (Glucosteril 20%, Fresenius) was started through the same venous line. Arterialized plasma glucose levels were determined at 5-min intervals throughout the insulin infusion. Starting at a glucose dose of 2.5 mg/kg per minute, the infusion rate was subsequently adjusted continuously to keep the blood glucose concentration within ± 10% of the baseline level. The mean intrastudy coefficient of variation of plasma glucose concentrations was 9% in the control subjects and 5% in the patients (not significant).
Data analysis
Calculation of insulin sensitivity, half-life, and volume of distribution. The glucose disposal rate (insulin-mediated glucose uptake, M value), the ratio of the M value to the insulin plasma concentrations, and the metabolic clearance rate of insulin were calculated for the last 100 min of the hyperinsulinemic euglycemic clamp studies at 20-min intervals as described previously (21). Insulin half-life was calculated according to a biexponential model, using the decay curves obtained after the stop of the insulin infusion.
The volume of distribution of insulin was calculated based on the results of the hyperinsulinemic euglycemic clamp studies and the analysis of the postinfusion plasma insulin disappearance rate. The distribution volume was calculated according to the following equation:
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Peak detection and pulse analysis
The Cluster Analysis program was used as a waveform-independent technique to detect significant ultradian peaks in each plasma analyte profile (22) in the 24-h insulin, glucose, pH, and sodium profiles. Nadir test cluster sizes were set to 2 and peak test cluster sizes were set to 1. Minimum t statistics of 1.96 were used as a stringency criterion both for upstrokes and downstrokes. These settings detect significant fluctuations with 2.1% false-positive and less than 10% false-negative errors provided that the signal-to-noise ratio in the profile is 1.3 or higher.
Each insulin concentration was assigned an SD value based on a concentration-dependent power function relating assay variance to sample concentration based on all duplicate measurements in an individual profile. The same procedure was applied for the glucose measurements, using an assay variance curve derived from 500 duplicate measurements obtained in quality control series assessed in duplicate.
The profiles measured during the 2-h study period in which blood was withdrawn every minute were analyzed by deconvolution analysis. Deconvolution was carried out with a previously validated iterative multiparameter technique, using the assumptions that insulin is secreted 1) in a finite number of bursts of a 2) common half-duration but 3) with individual amplitudes and that insulin removal 4) can be modeled by a biexponential elimination model as described previously (23, 24). Because individual elimination parameters were obtained for each study subject separately after the euglycemic hyperinsulinemic clamp studies, we used these parameters in deconvolution analysis.
Approximate entropy statistics (ApEn)
The scale- and model-independent ApEn provides a measure of regularity (orderliness) of fluctuations in a given hormone time series (25, 26). This statistic is complementary to, but distinct from, pulse analysis. It quantifies the serial regularity or degree of recurrence of subordinate patterns in time series or sample-by-sample irregularity, i.e. it may be interpreted as the predictability of the next measurement when prior measurements are known (27). ApEn evaluates the negative logarithm of the probability that any given particular data pattern length of m consecutive points will be repeated within a tolerance or distance r on next incremental comparison. Here, m was set at 1 and r at 0.2 (20%) of the respective series SD to normalize ApEn against different absolute substrate concentrations (28, 29). ApEn values typically lie between 0 (perfectly ordered) and 23 (highly random) for series of this approximate length.
Temporal relationship of insulin and glucose blood concentrations
Cross-correlation analysis was applied to quantify the temporal relationship between the blood concentrations of insulin and glucose. The cross-correlation coefficients between the concentrations of a pair of analytes at individual lags of -150 to +150 min at 15-min intervals were transformed to standardized z-scores according to the equation:
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Additionally, to quantify pattern asynchrony (conditional irregularity), we used cross-ApEn. Cross-ApEn evaluates the degree of pattern synchrony defined as the tendency of patterns in one series to be reproduced in the other. Cross-ApEn can be employed to compare sequences from two distinct yet intertwined variables in a network, herein applied to the joint insulin and glucose time series. The precise definition is thematically similar to that for ApEn. For this study, we applied cross-ApEn with m = 1 and r = 0.2 to standardized time-series data, i.e. for each subject, we applied cross-ApEn (1, 0.2) to the [u*(l), v*(l)] series, where u*(l) = (u(i) - mean u)/SD u and v*(i) = (v(i) - mean v)/SD v. This standardization, in conjunction with the choice of m and r, ensures good replicability properties for cross-ApEn for the data lengths studied (30).
Statistics
For analytical purposes, the 24-h observation period was subdivided into a daytime and nighttime period. The former started with the first blood sample at the start of breakfast at 0800 h and was further subdivided in pre- and postprandial periods. The postprandial state was defined by the broad waves of insulin release that regularly occurred after each of the three meals. The end of the postprandial insulin waves was defined as the first of two consecutive plasma insulin values that were within 1 SD of the mean baseline insulin concentration, as calculated by cluster analysis. The start of the nighttime period was given by the end of the postprandial period after dinner.
Data are given as mean ± SD, unless indicated otherwise. Statistical contrasts, Pearsons correlation coefficients, and z-scores were assumed to be significant at P less than 0.05.
Results
Euglycemic clamp study
Plasma insulin levels were raised to 68.6 ± 39.8 mU/liter in the patients and to 69.1 ± 20 mU/liter, i.e. approximately 10 times the basal level, in the control subjects (NS). The M value was 3.6 ± 1.1 mg/kg per minute in patients and 8.4 ± 2.7 mg/kg per minute in controls (P < 0.001), resulting in a ratio of the M value to the insulin plasma concentrations of 3.8 ± 1.7 in patients and 14.6 ± 7.5 in controls (P < 0.001). The metabolic clearance rate of insulin tended to be lower in patients (616 ± 360 ml/m2 per minute) than in controls (936 ± 323 ml/m2 per minute). The results of the euglycemic hyperinsulinemic clamp studies were independent of age, body mass index, or waist to hip ratio, which might be owing to the limited variability of these parameters in our study population.
Insulin half-life and volume of distribution
The decay curve of plasma insulin after discontinuation of the insulin infusion post steady-state (euglycemic clamp) infusion was best described by a biexponential elimination function superimposed on constant basal insulin release. The first-component half-life of insulin was similar in controls (2.04 ± 0.64 min) and patients (2.46 ± 1.57 min). In contrast, the terminal half-life of insulin was prolonged more than 2-fold in CRF (13.5 ± 6.2 min), compared with controls (5.7 ± 2.1 min, P = 0.01) (Fig. 1
).
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High-frequency insulin oscillations
The frequency of the insulin secretory bursts determined by 1-min sampling was significantly reduced (P < 0.001), and the interpeak interval prolonged (P < 0.001), in the patient group, compared with controls (Table 2
and Fig. 2
). No differences were observed in the mass of posthepatic insulin appearance per burst and the cumulative pulsatile, basal, or total posthepatic insulin appearance rates.
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Whereas patients and controls had similar integrated mean plasma insulin concentrations throughout the 24 h, the frequency of ultradian insulin pulses detected by 15-min sampling was lower in the patient group both during daytime and at night (Table 3a
). The mean interpulse interval for the 24-h period was 95 min, compared with 111 min in the patients (P < 0.005). In contrast, daytime insulin pulses were prolonged (P < 0.05) and tended to have a higher amplitude in patients (40 ± 20.8 vs. 27.1 ± 17.2 mU/liter, NS).
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Significant fluctuations of glucose were noted in all subjects. Fewer glucose oscillations than insulin pulses were detectable in both patients and controls during the preprandial period (patients: 0.24 ± 0.11 h-1, controls: 0.47 ± 0.19 h-1 glucose pulses, Fig. 3
) and during nighttime (patients: 0.23 ± 0.14 h-1, controls: 0.30 ± 0.14 h-1, Table 3b
). The frequency of the postprandial glucose oscillations was similar to that of insulin in both groups. The patients glucose levels oscillated at a slower pace (0.56 ± 0.16 h-1) than the controls (0.79 ± 0.18 h-1, P < 0.05, Fig. 3
). The amplitudes of the glucose oscillations relative to the preceding baseline were smaller for glucose than for insulin (P < 0.0001). Whereas preprandial glucose pulse areas were similar in patients and controls, pulse areas increased postprandially by 2.5-fold in the controls but 6-fold in the patients owing to exaggerated increases in both pulse amplitude and duration (Fig. 4
).
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The slow insulin fluctuations were generally more regular than the corresponding blood glucose fluctuations (P < 0.01 for total observation period) (Table 3, a
and
b), and the regularity of both insulin and glucose fluctuations was higher at night than during daytime (P < 0.05). During daytime, both insulin and glucose fluctuations were significantly more orderly in the patients than in the controls (P < 0.05).
Cross-correlation analysis was used to evaluate nonrandom temporal associations between the concentration vs. time profiles of insulin and glucose. Because the changes of blood glucose concentrations during the 2-h study period did not exceed the measurement error, we performed cross-correlation analysis for the 24-h study period only. During daytime, significant temporal associations were detected between insulin and glucose (P < 0.01) in patients and controls. Changes in blood glucose concentrations preceded those of insulin by 0 to 15 min. During the nighttime observation period, no coupling between insulin and glucose profiles was detected.
The pattern synchrony of insulin and glucose was significantly higher in the patients than in the controls for the total observation period (cross-ApEn: 0.58 ± 0.13 vs. 1.37 ± 0.23, P < 0.001) and during daytime (0.72 ± 0.16 vs. 1.19 ± 0.11, P < 0.001). The increased temporal synchrony of blood insulin and glucose fluctuations in the patients tended to persist during nighttime (0.89 ± 0.39 vs. 1.1 ± 0.47, P = 0.08).
The analysis of the rapid insulin oscillations disclosed no difference in system orderliness between patients and controls (Table 2
).
Discussion
The present study provides a detailed examination of plasma insulin oscillations in patients with CRF. Despite equivalent mean plasma insulin and blood glucose concentrations, CRF was marked by distinct alterations of the dynamic behavior of insulin release: Principal features included a prolonged insulin elimination half-life, a slowing of both high-frequency and low-frequency insulin oscillations, and a hypersynchronization of insulin and glucose patterns. Insulin resistance was manifested by a reduced glucose utilization rate, exaggerated postprandial insulin, and glucose pulses, with a failure of physiological postprandial acceleration of coupled oscillations.
Earlier studies have reported elevated plasma immunoreactive insulin concentrations in patients with CRF (31). In this investigation, we eliminated a possible confounding effect of cross-reacting proinsulin, which accumulates in uremia (32), by use of a highly specific insulin ELISA. Although fasting plasma insulin concentrations tended to be elevated in the CRF patients, significance was not reached because of marked individual variability and limited sample size. To further dissect possible changes in insulin secretion from changes in elimination in CRF, the multiparameter deconvolution methodology was applied. The deconvolution model assumes that the plasma concentrations of insulin are the net result of insulin pulses appearing in the peripheral circulation after hepatic passage, acted on by continuous exponential decay (23, 24). Assuming that hepatic insulin extraction is constant, the posthepatic insulin appearance rate is representative of the pancreatic insulin secretion rate. We used direct measurements of the subject-specific insulin elimination half-life to calculate the underlying mass of hormone released by episodic bursts or continuous secretion. Patients and controls did not differ with respect to the early elimination phase, which may reflect transition from the intravascular into the interstitial space and/or initial hormone binding and internalization in target tissues such as liver and muscle.
In contrast, the half-life of the terminal disappearance phase, thought to indicate irreversible hormone elimination, was increased 2.5-fold in the CRF group. This finding confirms previous clinical and experimental evidence that the kidney is a major source of insulin degradation (5, 6). Renal insulin clearance occurs by tubular uptake both via the luminal membrane following free glomerular filtration and by direct basolateral uptake from interstitial capillaries. Specific insulin scavenger receptors have been demonstrated on the luminal side and on the basolateral surface of proximal tubular epithelial cells (33). Although an additional impairment of insulin removal by extrarenal tissues cannot be completely excluded, normal or even increased insulin receptor binding has been found in liver, muscle, and adipose tissue of uremic animals and humans (34) Hence, diminished renal insulin elimination may contribute to the high-normal or elevated fasting plasma insulin concentrations observed in CRF.
Notably, fasting insulin appearance rates were quantitatively unchanged in the CRF patients despite severe insulin resistance. Again, we cannot entirely exclude that a markedly increased first-pass insulin extraction by the liver masked pancreatic hypersecretion in the CRF patients. Nevertheless, because systemic plasma insulin concentration is the central controlling element in the endocrine regulation of energy metabolism, the normal plasma insulin levels in the presence of severe insulin resistance indicate a relative failure of secretory adaptation in CRF.
Further analyses unveiled an array of distinct abnormalities in the dynamic regulation of fasting and postprandial insulin release. Appraisal of minute-to-minute insulin release disclosed a small but consistent slowing of the physiologically rapid, low-amplitude insulin bursts in the CRF patients. Likewise, the slow insulin oscillations occurred at a reduced frequency in the patients, with a 33% increase in interval from 90120 min. The mechanism underlying the deceleration of both dominant frequencies of oscillatory insulin release remains to be elucidated. The high-frequency insulin pulses are believed to be driven by wavelike increases in intracellular calcium ions in ß-cells rapidly spreading via gap junctions and possibly other synchronizing mechanisms (35). Even less is known about the mechanisms causing the low-frequency insulin pulses, which are readily entrained by glucose fluctuations in vivo. However, the slow insulin oscillations persist during constant glucose exposure in isolated organs and islets of Langerhans monitored in vitro, consistent with possible local synchronization by episodic calcium superwaves (36, 37).
Previous experimental work has provided indirect evidence for chronically increased basal intracellular calcium concentrations in Langerhans islets in CRF (38). The increase of resting intracellular calcium levels is a general phenomenon in CRF, which has been attributed to partial Na/K-ATPase inhibition by accumulating ouabainlike substances (39). Islets from chronically uremic rats have a reduced insulin secretory capacity, which is normalized by addition of calcium channel blockers (40). Because insulin secretory bursts are triggered by dynamic increases in calcium oscillations above a certain threshold, we speculated that elevated resting intracellular calcium concentrations in uremia may limit suprathreshold changes in intracellular calcium, resulting in a reduced frequency of episodic insulin secretion bursts.
During daytime, food intake influenced the underlying pattern of slow insulin pulses. In the control subjects, insulin pulses were more frequent postprandially, causing a more irregular pulse pattern. In contrast, insulin pulse frequency was less responsive to food intake in the CRF patients, in whom the mean degree of orderliness (repetitive patterns) of daytime pulses even increased. The latter diminished postprandial modulation of burst frequency could indicate a subtle defect in glucose sensing by the pancreatic islets in uremia. A similar alteration of frequency-encoded modulation of pulsatile hormone release arises in uremic hyperparathyroidism, wherein patients display impaired adaptations of PTH pulse frequency to acute induced variations in plasma ionized calcium (41). The tendency toward hyperregularity of the low-frequency insulin oscillations appears to be unique to CRF. Indeed, diminished orderliness of insulin release has been documented in people with other disorders of carbohydrate metabolism, including patients with non-insulin-dependent diabetes, minimally or non-insulin-resistant relatives, obesity, and ageing (11, 12, 13, 14, 42).
Significant oscillations of blood glucose were also detectable in the 24-h concentration profiles. At least during daytime, the glucose oscillations were coupled to the pulsations of plasma insulin. The apparently lower frequency of the glucose, compared with the insulin pulses, is likely because of the limited detection of small glucose pulses, the relative amplitude of which was on average only one-tenth of that of the plasma insulin pulses. The frequency of daytime glucose oscillations tended to decrease in the CRF patients, although significance was not reached, most likely because of sensitivity problems. The high degree of temporal coupling between insulin and glucose fluctuations, with glucose preceding insulin by 15 min, is consistent with a dynamic feedback interaction between glucose and plasma insulin. The cooscillatory pattern is enhanced by oral glucose intake and maintained into the fasting periods. Surprisingly, we observed a markedly increased temporal coupling of the glucose and insulin oscillation patterns throughout the 24 h in the CRF patients by cross-ApEn analysis. Because our study represents the first application of cross-ApEn methodology to glucose-insulin time series in a nonhealthy population, it is currently unclear whether the observed phenomenon is common to insulin resistant states or denotes a specific abnormality associated with uremia.
In keeping with previous investigations (1, 3), patients with CRF exhibited severely diminished glucose uptake during constant hyperinsulinemia. Our quantitative analysis of the blood glucose and insulin patterns relative to the daily meals revealed that under fasting conditions, normal fasting plasma insulin and glucose concentrations were maintained. However, hyperglycemia occurred after meals despite an augmented insulin response. The postmeal insulin response in CRF was characterized by pulses of exaggerated width and amplitude but subnormal frequency. The almost 3-fold greater postmeal insulin pulse area, compared with controls, did not prevent a 2-fold higher area of the postprandial glucose pulses. Hence, postcibal insulin resistance is manifested in this context.
In summary, we observed multiple abnormalities in the temporal regulation of insulin secretion in uremia. The defects are most marked postprandially but persist in part under fasting conditions. The deceleration of both the rapid and slow frequencies of insulin secretory pulses, heightened orderliness of the slow insulin pulses and the enhanced pattern synchrony between insulin and glucose oscillations identify a distinct neurosecretory phenotype in CRF.
It is unclear whether the deceleration and hypersynchronization of insulin oscillations is causally related to the severe peripheral insulin resistance. In this context, recent work in transgenic mouse models has provided evidence for a direct molecular link between insulin secretion and action, e.g. a selective deficiency of the insulin receptor on ß-cells impairs glucose-regulated insulin secretion glucose sensing (17). It is tempting to speculate about a common molecular mechanism causing the observed peripheral insulin resistance, relative insulin hyposecretion, and defective modulation of insulin oscillations in uremia.
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Ilona Gomminginger (AOK Heidelberg) kindly supported the recruitment of control subjects. Expert laboratory assistance was provided by Renate Nitze from the Department of Medicine. We are grateful to P. Bahrmann and D. Fliser for their helpful instructions with the euglycemic clamp technique.
Footnotes
This work was supported by the Else Kröner-Fresenius Stiftung (Bad Homburg, Germany), Novo Nordisk (Copenhagen, Denmark), DAKO Corp. Diagnostika (Hamburg, Germany), the General Clinical Research Center, and Center for Biomathematical Technology. R.F. received a postgraduate scholarship from the Deutsche Forschungsgemeinschaft.
Abbreviations: ApEn, Approximate entropy; CRF, chronic renal failure; M value, insulin-mediated glucose uptake.
Received May 18, 2001.
Accepted January 16, 2002.
References
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