Hypothesis: one rate-limiting step controls the magnitude of both phases of glucose-stimulated insulin secretion

Susanne G. Straub and Geoffrey W. G. Sharp

Department of Molecular Medicine, College of Veterinary Medicine, Cornell University, Ithaca, New York 14853


    ABSTRACT
 TOP
 ABSTRACT
 GRANULE POOLS AND GLUCOSE...
 RATE-LIMITING STEPS
 THE MODEL AND THE...
 SIZES OF THE IR...
 CONCLUSION
 GRANTS
 REFERENCES
 
The biphasic secretory response of pancreatic {beta}-cells to abrupt and sustained exposure to glucose is well documented. Some of the ATP-sensitive K+ (KATP) channel-dependent mechanisms underlying the first phase of insulin release are known; the mechanisms underlying the second phase are less well known. The hypothesis we propose is that one rate-limiting step, controlling the conversion of granules in a readily releasable (RR) docked granule pool to an immediately releasable (IR) pool, is responsible for the magnitude of both phases of release. Furthermore, we propose that the KATP channel-independent signaling pathway regulates this rate-limiting step. The size of the IR pool of granules that constitutes the first phase is determined under resting conditions by the forward and reverse rates of conversion of granules in the RR and IR pools. The resulting equilibrium position determines the maximum number of {beta}-cell granules available for release during the first phase upon exposure to glucose. At the nadir between the two phases, the IR pool has been depleted so that the rate of granule release is equal to the low forward rate for the conversion of RR to IR granules. After the nadir, the forward rate is accelerated during the rising portion of the second phase until it reaches a maximum rate at the plateau.

glucose signaling pathways; granule pools


WHEN THE ENDOCRINE PANCREAS is exposed to an abrupt increase in the concentration of glucose, from a nonstimulatory concentration to one that stimulates insulin secretion, the {beta}-cells give a biphasic secretory response. An example of such a response by isolated rat pancreatic islets is shown in Fig. 1. The response is characterized by a first phase of release that is maximal 4 min after onset, a nadir after a further 6 min, and subsequently a second phase characterized by an increasing rate of secretion to a plateau at 30 min. The biphasic response was first reported in vivo in humans in 1963 (11) and subsequently in perfused pancreas in 1968 (14). While such biphasicity is due to the experimental conditions (an abrupt square-wave glucose stimulus) and is unlikely to occur naturally, it is important in that a reduction in the first phase is seen early in the development of type 2 diabetes (16, 40) and may be predictive of the disease (29). The mechanisms responsible for the biphasicity are only partially understood. Nevertheless, at the nadir between the two phases, exocytosis of the insulin-containing granules is clearly rate limited. After the nadir, over the next 20 min, the rate limitation is changed and progressively higher rates of release are achieved until the plateau is reached. Both phases of release have separate rate-limiting steps. We propose that the rate-limiting step for the second phase of glucose-stimulated insulin secretion is the rate at which docked granules are converted to an immediately releasable (IR) state or pool and, as a consequence in an activated cell, the granules undergo immediate exocytosis. Of note, this conversion may be due to a change in the granules themselves, in the state of the plasma membrane (e.g., at an exocytotic site), or in signals to the granules such as the lifting of an inhibitory tone or to the development of a potentiating signal. The hypothesis proposed here is that this step, the conversion of granules to the IR state, determines the magnitude of both the first and second phases of glucose-stimulated insulin release.



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Fig. 1. Glucose-stimulated biphasic insulin release in rat islets. Shown is the response of rat pancreatic islets to an abrupt change in glucose concentration from 2.8 to 16.7 mM, expressed as pg·islet–1·min–1 and as the %insulin content released per minute (n = 8). Freshly isolated rat pancreatic islets were equilibrated by exposure to Krebs-Ringer-HEPES buffer containing 2.8 mM glucose for 35 min before the 5 min time point. At the 5 min point, the islets were exposed to 16.7 mM glucose. The response began after a delay of 1–2 min during which glucose metabolism in the cell was accelerated. This was followed by a rapid increase in the rate of insulin secretion. The increased rate of secretion peaked after 4 min and then declined to a nadir between the first and second phases of release after a further 3 min. The second phase was characterized by a gradually increasing rate of insulin release to the plateau. At the end of the experiment, the islets had released 6.2% of their insulin content. IRI, immunoreactive insulin.

 
It should be stressed at the outset that this review does not attempt to distinguish between the various models that have been proposed to explain the biphasic response (9–11, 21–23, 37, 38); it only identifies the rate-limiting step that is inherent in all of them. Nevertheless, our hypothesis is explained on the basis of the existence of three pools of granules, two of which are docked. In this model, glucose causes first-phase insulin release by depleting a small labile pool and the second phase by gradually increasing a potentiating signal. However, the hypothesis is equally applicable to other models. For instance, it applies to the "feedback" or "excitor-inhibitor" model, in which the first phase is caused by a prompt increase in an excitatory signal followed by a feedback inhibitory signal (21) and has the same potentiating signal during the second phase as it has in the two-compartment model (23). It applies also to what may be described as the immediate and time-dependent effect model (37), in which the first phase of release is caused by the immediate excitatory signal, the nadir is caused by the following time-dependent inhibition (TDI), and the second phase is caused by an increasing time-dependent potentiation (TDP). All three of these models necessarily include the rate-limiting step that occurs at the nadir between the two phases and that must be accelerated to develop the full second-phase response.

More information is available concerning the mechanisms underlying the first phase of glucose-stimulated insulin secretion than those of the second phase. The ATP-sensitive K+ channel (KATP channel) is largely responsible for glucose-induced depolarization of the {beta}-cell, increased Ca2+ entry through voltage-dependent Ca2+ channels, and stimulation of exocytosis (3, 12, 26, 52). This signaling pathway, which directly controls the first phase of release, is termed the KATP channel-dependent or "triggering" pathway of glucose signaling (7, 25).

A second glucose signaling pathway that augments the secretory response to increased intracellular Ca2+ concentration ([Ca2+]i) is a "KATP channel-independent" amplification pathway (6, 19, 43). Thus closure of KATP channels by glucose metabolism triggers the exocytosis of insulin by increased [Ca2+]i, and a KATP channel-independent pathway augments that secretory response (1, 2, 6 19, 43). The mechanisms involved in the KATP channel-independent pathway are not known (7, 25, 34, 36, 44, 46). We favor the hypothesis that glucose-induced anaplerosis generates mitochondrial cataplerotic signals that augment Ca2+-stimulated exocytosis (8, 13, 18, 34, 55). The mitochondrial signals may induce the acylation of proteins critical to the acceleration of the rate-limiting step in the second phase of glucose-stimulated insulin secretion (47, 53, 54).

A second KATP channel-independent pathway of glucose signaling augments insulin secretion in the absence of any rise in [Ca2+]i. This occurs in the presence of agonists that raise intracellular diacylglycerol (DAG) levels and is amplified by increased cyclic AMP levels (31–34). The only difference that has been detected between these two pathways in the presence or absence of Ca2+ is a requirement for GTP. Reducing GTP levels in the islet by the use of mycophenolic acid totally blocks the augmentation of the Ca2+-independent pathway while leaving the Ca2+-dependent pathway untouched (30, 33). The KATP channel-dependent and KATP channel-independent pathways work in synergy to produce the biphasic response to glucose (46, 48). These glucose signaling pathways are illustrated in Fig. 2.



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Fig. 2. Glucose signaling pathways and granule pools. Shown are the glucose signaling pathways and postulated granule pools in a glucose-stimulated {beta}-cell during the second phase of release. The ATP-sensitive K+ (KATP) channel-dependent (triggering) pathway has depolarized the cell and increased intracellular Ca2+ ([Ca2+]i) to stimulate insulin release. Preexisting granules in the immediately releasable (IR) pool have been released during the first phase. The KATP channel-independent (amplification) pathway of glucose signaling is augmenting the rate of insulin release by increasing the rate at which granules in the readily releasable (RR) pool are converted to the IR pool of granules. No granules are shown in the IR pool, because in the activated {beta}-cell they are immediately released. VDCC, voltage-dependent Ca2+ channel.

 

    GRANULE POOLS AND GLUCOSE-STIMULATED INSULIN RELEASE
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 GRANULE POOLS AND GLUCOSE...
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 THE MODEL AND THE...
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The number of insulin-containing granules in the {beta}-cell is large relative to the number required to respond to a single meal. The granules are present in the cell interior or docked at the plasma membrane (7, 39, 46). Those in the interior are of different ages and are described as the reserve pool; some may be newly synthesized, and others may be days old. Those that are docked at the plasma membrane are in different states of readiness for secretion. They may be primed and capable of being released, or they may be unprimed and incapable of being released. However, the primed granules can be defined as present in IR and RR pools (4, 5, 7, 46). These definitions of IR and RR pools are in accord with those of others who have studied biphasic release mechanisms in cells as diverse as murine adrenal chromaffin cells (50), gonadotropes (56), and murine {beta}-cells (4). The reasons for these definitions are as follows. Glucose releases a small number of granules, defined as immediately releasable, that constitute the first phase. However, glucose in the presence of agonists such as GLP-1 or GLP-1 plus gliclazide can release many more granules over the same first-phase time period (37). Therefore, there is a pool of granules larger than the IR pool that is ready for release under specific conditions and can be defined therefore as "readily releasable." They can be converted to immediate releasability with extreme rapidity (37). Despite our scant knowledge of the specific biochemical, geographic, and cytoskeletal distinctions between granules in different pools, it is useful to describe them as either docked or in reserve. The reserve pool contains >90% of the granules in the cell. Two estimates are available for the total number of granules in the murine {beta}-cell: 9,000 (39) and 13,000 (15). By quantitative morphometric analysis of the rat {beta}-cell, we estimated the number of granules at a little over 11,000 (Straub SG, Shanmugam G, and Sharp GWG, unpublished data). For the purpose of this article, we have adopted our rat data and used specific numbers in the figures and in calculations in the text. Obviously, the numbers are not precise and are used only to illustrate the arguments made. We counted the number of "morphologically" docked granules in the rat {beta}-cell under nonstimulated conditions and found them to comprise >6% of the total. This is similar to the murine {beta}-cell (39). Importantly, the percentage of docked granules after 30-min exposure to 16.7 mM glucose increased to 10%. Of the docked granules, the IR granules that are responsible for the first phase of release are estimated by capacitance studies to be in the range of 50–100 granules (4, 5), i.e., <1% of the total number of granules in the cell. They also can be estimated from insulin release studies in which insulin release is stated as a fraction of the total insulin content. For example, from the data in Fig. 1, it can be calculated that with 11,000 granules in the cell, the rate of release per {beta}-cell under basal conditions is one granule every 30 s. At the peak of the first phase, the rate is one granule every 5 s. At the nadir, the release rate is one granule every 7–8 s, and this rate increases over the next 20 min to a maximum rate of one granule every 2 s at the plateau of the second phase. As a consequence of the increase in the size of the docked pool during stimulation with glucose, it is clear that the rate of docking exceeds the rate of granule release during stimulation. Therefore, the rate at which replacement granules from the reserve pool are translocated to the docked pool cannot be rate limiting.

When the stimulation of insulin release is sustained over lengthy periods, there exists a precise coordination of granule movement, including translocation to and docking at the plasma membrane, ATP-dependent priming, conversion to the IR state, and exocytosis. However, while the reserve pool is large relative to the size of the IR pool and to release rates, the morphologically docked pool of granules is also large relative to the IR pool that is contained within it (750 vs. 50–100 granules). The granules in the IR pool that are released in response to glucose display concentration dependence or threshold sensitivity (21, 22, 37). This can be explained by the concentration-dependent depolarization of the cell and different levels of Ca2+ influx and [Ca2+]i, and/or by the fact that not all of the granules in the IR pool have the same sensitivity to increased [Ca2+]i. The latter characteristic would contribute to the similar kinetics of maximal and submaximal first-phase release because the most sensitive granules would be released by a submaximal increase in [Ca2+]i, as they would also by a maximal stimulus. The number of granules released during the first phase of glucose-stimulated insulin release is increased by TDP, which implies an increase in the size of the IR pool. This occurs in association with the increase in the total number of docked granules observed after TDP caused by exposure to 16.7 mM glucose. The {beta}-cell granule pools under nonstimulated conditions are illustrated in Fig. 3.



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Fig. 3. Sizes of the different {beta}-cell granule pools and the transfer rates between the pools in a {beta}-cell under resting conditions. The reserve, newly arrived, RR, and IR pools are shown. Because of the rapidity of ATP-dependent priming, it is assumed that most of the docked granules are in the RR and IR pools. Under nonstimulated conditions, the pools are in equilibrium. K1 = K–1, K2 = K–2, and K3 = K–3. PM, plasma membrane.

 
From the calculated rates of granule release presented earlier, it is clear that the preexisting docked granules are amply sufficient to supply both the first and second phases of glucose-stimulated insulin release. Of 700 docked granules, only 50–100 are released during the first phase. Thus the remaining 600–650 granules could theoretically supply much of the second phase. In the example shown in Fig. 1, the percentage of insulin content released up to the 41st min was just over 6%. Thus the docked granules would be sufficient for all of the insulin secretion shown. Even more striking is our finding that as granules move from the reserve pool to the plasma membrane to replace those that are released during glucose stimulation, the number of docked granules increases. This increased number of docked granules ensures the availability of a large excess of granules for release. This reemphasizes that there is always an ample supply of docked granules for release. Because the number of docked granules cannot be rate limiting for glucose-stimulated insulin release, the rate-limiting step for exocytosis must be the conversion of docked RR granules to the IR state.

The mechanisms involved in preparing granules for the first phase of insulin secretion are presumably the same as those for the second phase. All of the granules have trafficked to the plasma membrane and have been docked and primed before final preparation for exocytosis. All undergo similar events. The distinction between the mechanisms responsible for the two phases is that the first phase is due to the release of granules that have been prepared for immediate release, while the second phase is due to the release of granules that have to be prepared for immediate release. In this model, the order in which the granules are docked does not necessarily dictate the order in which they will be released. Any granule that has recently docked and been primed (a rapid process) and thereby has joined the RR pool may have the same chance as any of the preexisting docked granules of moving into the IR pool.


    RATE-LIMITING STEPS
 TOP
 ABSTRACT
 GRANULE POOLS AND GLUCOSE...
 RATE-LIMITING STEPS
 THE MODEL AND THE...
 SIZES OF THE IR...
 CONCLUSION
 GRANTS
 REFERENCES
 
The overall rate of insulin secretion is controlled by the concentration of glucose to which the {beta}-cell is exposed, the interaction of glucose with glucokinase, and the physiological state of the {beta}-cell (35). Within these constraints, each of the two phases of glucose-stimulated insulin secretion has distinct rate-limiting steps. Beginning when the cell is activated and Ca2+ influx is increased, exocytosis of the IR granules is rate limited by a step involving the recognition and/or transduction of the Ca2+ signal or the rate of exocytosis per se. It is known that the increase in [Ca2+]i results in a spike in exocytosis (the first phase), but we cannot as yet identify the rate-limiting step for this phase. In experiments in which Ca2+ was released by photolysis from "caged Ca2+" and exocytosis was measured by capacitance change, exocytosis occurred within 10 ms (39). Thus this brief period encompasses the recognition and transduction of the stimulatory Ca2+ signal. At the nadir between the first and second phases, the rate of granule exocytosis is clearly rate limited. The IR pool has been discharged (39) and must be resupplied. The replacement granules come from docked and primed granules in the RR pool. In an activated {beta}-cell with constantly elevated [Ca2+]i, granules will be released as soon as they reach the IR state. Therefore, as {beta}-cell granules are released at rates of one every few seconds, the rate-limiting step is the conversion of granules to the IR state. Importantly, as the rate of exocytosis during the second phase increases over time until it plateaus out at a higher level, this rate-limiting step is changed and accelerated over the rising portion of the second phase. This is caused by the time-dependent potentiating signals generated by the KATP channel-independent pathway. A very clear example of the effect of these signals of changing the release rate can be demonstrated as follows. The KATP channel-independent pathway is usually studied by treating islets with KCl and a stimulatory glucose concentration in the presence of diazoxide and comparing the response to KCl and a nonstimulatory glucose concentration and diazoxide. Unfortunately, under these conditions, the biphasicity of the response is less distinct because the nadir is usually small or not present. To "separate" the two phases, experiments were performed in which the stimulatory glucose challenge was added 10 min after the KCl and diazoxide. Under these conditions, the stimulation of release due to KCl was almost over by the time the glucose was added. As can be seen in Fig. 4, the response to KCl was typically "first phase like" and the response to glucose typically "second phase like." The effect of glucose of gradually increasing the rate is obvious.



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Fig. 4. KATP channel-independent action of glucose to induce a "second phase" of insulin secretion after the stimulation of insulin release by KCl in the presence of diazoxide. Freshly isolated rat pancreatic islets were exposed to 2.8 mM glucose for 40 min before the 10 min time point, at which time they were exposed to 40 mM KCl and 250 µM diazoxide. Both sets of islets responded with a prompt first phase that peaked after 2 min and declined thereafter. At the 20 min time point, when most of the response to KCl was over, one set of islets was exposed in addition to 16.7 mM glucose. As a result, there was a typical second-phase response. Values are means ± SE from 6 paired experiments.

 
Because ATP is essential for exocytosis and is required for granule priming (17, 49), the conversion of granules from RR to IR could conceivably involve ATP-dependent priming. In this case, only the IR granules might be primed in the resting cell. It appears, however, that most of the docked granules (RR and IR) are primed. Under capacitance conditions for the measurement of exocytosis, endogenous cellular ATP was removed and exocytosis was blocked. Subsequently, when caged ATP was released in the {beta}-cell in the presence of a permissive [Ca2+]i, exocytosis began within 400 ms (39). This time therefore is sufficient for ATP-dependent priming of the granules, conversion to the IR state, recognition of the Ca2+ signal, and exocytosis. Because the rate of granule release in the {beta}-cell has a time scale of seconds, ATP-dependent priming of 400 ms or less and a docked pool of several hundred granules will not be rate limiting. Virtually all of the docked granules will be primed (for a recent review of granule dynamics in the {beta}-cell, see Ref. 42).


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The granule pools in the pancreatic {beta}-cells under basal conditions can be defined as a large reserve pool in the cell interior with >90% of the granules and a docked granule pool with 6–7% of the granules. The docked granules differ in their ability to undergo exocytosis. Thus, upon glucose stimulation, an IR pool of granules undergoes exocytosis in response to depolarization and increased Ca2+ entry. This constitutes the first phase of glucose-stimulated insulin release. The number ofgranules released is small compared with the total number in the docked pool (50–100 of 750). At the nadir after the first phase, the IR pool is depleted, granule release is slow, and granules must be converted to the IR pool (or state) before they can undergo exocytosis. The rate of conversion of docked granules to the IR pool is controlled by the KATP channel-independent pathways. As the rate of conversion is increased, so the rate of insulin release during the second phase of secretion is increased until the plateau is reached. This model does not assume that the docked granules are released in the order in which they are docked. ATP-dependent priming is rapid relative to the rate of exocytosis such that within 400 ms after docking, the granule should be available for conversion to the IR pool. This implies that granules from the reserve pool could be released early in the second phase and will certainly be released during prolonged stimulation. One of the most important unknowns is the nature of the step that determines whether a granule is in the IR pool or not. Suggestions include the need for a close association with Ca2+ channels or specific exocytotic sites (4, 5, 39, 41, 51) and changes in Ca2+ sensitivity so that exocytosis occurs at lower [Ca2+]i. In addition to the IR pool, granules in the RR pool can be mobilized rapidly by cyclic AMP (37). The biochemical mechanisms by which cyclic AMP acts at this site are unknown, although the involvement of PKA and/or Epac is likely (27, 28). Regardless of the mechanism involved, the result will be the same as that of the effect of the KATP channel-independent pathway; i.e., the conversion of granules in the RR pool to the IR pool will be accelerated. In addition, DAG is reported to be involved in a similar effect via Munc-13 (45). The action of DAG could be similar to that of a KATP channel-independent pathway if the latter involves the synthesis of DAG as previously suggested (13).


    SIZES OF THE IR POOL AND OF THE FIRST-PHASE RESPONSE ARE DETERMINED BY THE TDP OF THE KATP CHANNEL-INDEPENDENT PATHWAYS
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Under nonstimulated conditions, the docked granules exist in a state of equilibrium between RR and IR (Fig. 3). The equilibrium position depends on the ambient glucose concentration, on the activity of the KATP channel-independent pathways, and on the history of exposure to glucose (i.e., on the effect of TDP). The TDP effect of the KATP channel-independent pathway drives the equilibrium positions to the right, increasing the size of the RR and IR pools and thereby maximizing the size of any subsequent first phase of glucose-stimulated insulin release. Low ambient glucose concentrations such as those that occur during fasting may allow the equilibrium position to move to the left so that the size of the IR pool and a subsequent first phase of release are reduced. Similarly, by increasing the rate of conversion from the RR to the IR state, glucose determines the magnitude of the second-phase response. Note also that a leftward shift to the unprimed state (unpriming) has been suggested as the mechanism whereby physiological inhibitors of secretion block exocytosis (24). In Fig. 3, the cell is shown in the resting, nonstimulated state with the pools in equilibrium. In Fig. 5A, the cell is shown after TDP has developed. The number of granules in the IR pool has increased (K3 > K–3). Our recent data show that glucose increases the size of the docked granule pools (from 6 to 10% of the granules in the cell) so that the RR pool is also increased (K2 > K–2). Consequently, all of the forward rates (K1, K2, and K3) were greater than their corresponding backward rates at the time the pool sizes were increasing, K1 was greater than K2, and K2 was greater than K3. In Fig. 5B, the {beta}-cell has been stimulated with glucose, the first phase is over, and the response is assumed to be at some point just beyond the nadir at the start of the second phase. The IR pool is shown without granules because by definition they are "immediately" released in an activated cell. The forward rates K1 and K2 are now greater than the corresponding backward rates; K3 equals the rate of granule release. K–3 no longer exists because exocytosis is irreversible. To reach the plateau of the second phase, all of the forward rates must increase until they reach their maximum values at the plateau.



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Fig. 5. Sizes of the different {beta}-cell granule pools and rate constants for transfer between the pools after time-dependent potentiation (TDP) and at the start of the second phase. Shown are the reserve, newly arrived, RR, and IR pools. A: the cell has undergone glucose-induced TDP and has just been returned to basal conditions. The number of granules in the IR pool has increased. Because of the exposure to a high glucose concentration, the number of granules in the RR pool has also increased. During the development of TDP, the forward rates are greater than the backward rates. Under basal conditions, TDP dissipates over time so that the backward rates exceed the forward rates or the granules undock. B: the {beta}-cell has been stimulated with glucose, the first phase is over, and the response is just after the nadir at the start of the second phase. The IR pool is empty because in the stimulated cell, the granules from this pool are immediately released. K1 > K–1, and K2 > K–2. K–3 no longer exists, because exocytosis is irreversible. During the ascending portion of the second phase, K1, K2, and K3 and the size of the RR pool continually increase. The rate-limiting K3 reaches its maximal rate at the plateau.

 
It should be noted that none of the rate constants can yet be defined quantitatively and that they are used here and in Figs. 3 and 5 only for illustration. However, in one case, if we assume that the reverse rates are negligible under stimulated conditions during the second phase, then K1 and K2 will be greater than K3 as the RR pool increases in size. K1 and K2 will be equal to K3 when the RR pool size and release rates are maximal at the plateau of the second phase. In applying the concept that K3 is the rate-limiting step for the second phase of insulin release to existing models of {beta}-cell biphasicity, K3 is driven by the TDP signal in the two-compartment and excitor-inhibitor models (21, 22). K3 will be controlled by the balance between TDP and TDI in the immediate and time-dependent effect models (37).


    CONCLUSION
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 GRANULE POOLS AND GLUCOSE...
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 THE MODEL AND THE...
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 CONCLUSION
 GRANTS
 REFERENCES
 
The KATP channel-independent pathways control the rate of conversion of granules in the RR pool of docked granules to the IR pool. This rate-limiting step determines the equilibrium position between the two pools and therefore the magnitude of the first phase of glucose-stimulated insulin release. In addition, the rate of this conversion directly controls the rate of the second phase of release. Recent evidence suggests that both phases of insulin secretion are reduced in people who are destined to develop type 2 diabetes and that this may precede the onset of insulin resistance (20). Therefore, the rate-limiting step between the RR and IR pools may prove to be a unifying link and the site of a primary genetic risk factor in the disease.


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Our work in this area was supported by a Research Award from the Alexander von Humboldt Foundation and National Institute of Diabetes and Digestive and Kidney Diseases Grants DK-54243 and DK-56737 (to G. W. G. Sharp) and a Career Development Award from the Juvenile Diabetes Research Foundation International (to S. G. Straub).


    FOOTNOTES
 

Address for reprint requests and other correspondence: G. W. G. Sharp, Dept. of Molecular Medicine, College of Veterinary Medicine, Cornell Univ., Ithaca, NY 14853 (E-mail: gws2{at}cornell.edu).


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