Pulsatile Basal Insulin Secretion Is Driven by Glycolytic Oscillations

Abstract

In fasted and fed states, blood insulin levels are oscillatory. While this phenomenon is well studied at high glucose levels, comparatively little is known about its origin under basal conditions. We propose a possible mechanism for basal insulin oscillations based on oscillations in glycolysis, demonstrated using an established mathematical model. At high glucose, this is superseded by a calcium-dependent mechanism.

Introduction

In response to a meal, blood glucose levels rise, and this is sensed by the β-cells of the islets of Langerhans distributed sparsely throughout the pancreas, which then secrete the hormone insulin (1). Once entering the circulation, insulin acts to increase glucose uptake into muscle and adipose tissues while it inhibits hepatic glucose production (2). Glucose-induced insulin secretion is thus a key player in whole body glucose homeostasis, and its dysregulation is a major contributor to type 2 diabetes (3).

The insulin secretory component of this homeostatic control system is regulated by an exquisite set of mechanisms in β-cells (1) (FIGURE 1). In contrast to many other hormones, insulin secretion is regulated directly by the rate of glucose metabolism, which serves as a surrogate for the concentration of glucose in the blood (4). Glucose enters the β-cells through glucose transporters and is metabolized in glycolysis and then by mitochondrial respiration, increasing the ATP/ADP ratio. Insulin secretion is then stimulated via two major pathways: the triggering pathway, which mediates the rise in intracellular Ca²⁺ needed to trigger exocytosis, and the amplifying pathway, which increases docking and priming of insulin-containing granules and brings them into close proximity to Ca_V channels, enhancing the efficacy of Ca²⁺ in driving secretion.

FIGURE 1.

Diagram illustrating the key cellular components and molecular mechanisms involved in oscillations of Ca²⁺ and insulin secretion in the pancreatic β-cell Glucose enters the cell through glucose transporters and is metabolized in glycolysis and the mitochondria. ATP, mostly produced by the mitochondria, closes K_ATP channels in the plasma membrane, leading to depolarization. Additional ion channels, including voltage-gated Ca²⁺ (Ca_V) and K⁺ channels (K_V) and Ca²⁺-activated K⁺ channels (K_Ca), support excitability of the plasma membrane potential (V) and underlie bursting activity at postprandial glucose levels. Depolarization of the membrane leads to Ca²⁺ (c) influx through Ca_V channels, while cytosolic Ca²⁺ levels are reduced by activity of Ca²⁺ ATPase pumps [sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) and plasma membrane Ca²⁺-ATPase (PMCA)]. Exocytosis of insulin-containing granules is triggered by Ca²⁺ and amplified by one or more metabolic signaling factors (AF) that promote the movement of insulin granules towards a releasable state. F6P, fructose-6-phosphate; FBP, fructose-1,6-bisphosphate; PDH, pyruvate dehydrogenase; PFKM, phosphofructokinase, muscle.

Central to the triggering pathway are ATP-sensitive potassium (K_ATP) channels, which close in response to increases in the cytosolic ATP/ADP ratio. K_ATP channels are open in low glucose, maintaining the cells at a negative membrane potential, but when they close, the cells depolarize, opening voltage-dependent calcium (Ca_V) channels and initiating Ca²⁺ entry (c; FIGURE 1). The reciprocal activation of Ca_V and voltage-dependent potassium (K_V) channels generates action potentials (spiking), much like the excitable membranes of neurons and muscle cells. Ca²⁺ then triggers the exocytosis of insulin granules, primarily those located near the Ca_V channels.

In addition to generating ATP, glucose metabolism gives rise to one or more metabolic signals, called amplification factors (AF; FIGURE 1), that mediate the amplifying pathway introduced above. The identity of the AF remains unclear, but some of the suggested candidates include ATP, glutamine, and NADPH (4, 5). A recent review highlights possible roles of reactive oxygen species, lipids and phosphoenolpyruvate (6). The AF is physiologically important, as it is responsible for about half the insulin secretion (7).

The picture described above contains the basic information needed to understand β-cell function but is incomplete, as blood insulin levels in vivo are not steady but oscillatory with a period of about 5 min, as has been observed in humans, rodents, nonhuman primates, and canines (8–11). FIGURE 2 shows an example of insulin levels recorded from the portal vein in a human (FIGURE 2A), with insulin secretion rate reconstructed by deconvolution, as shown below the raw secretory data (FIGURE 2B) (12). Similar data have been recorded from the portal vein in rats (13) and in dogs (14). The latter study looked at oscillations before and after glucose ingestion, indicating an average increase of 400% in pulse amplitude and 40% in frequency. The pulsatile nature of insulin release, which resembles in a general manner that of other hormones (15), is believed to be necessary for the efficacious action of the hormone (16); for a review, see Ref. 17.

FIGURE 2.

Basal and glucose-stimulated insulin secretion are oscillatory in humans

A: insulin oscillations measured from the hepatic portal vein at basal glucose (4.4 mM; left) and high glucose imposed via hyperglycemic clamp (nominally 8–9 mM; right). The ∼5-min period of the oscillations does not change dramatically in response to glucose, but insulin rises about 2-fold in the higher glucose condition (note the difference in scale). B: deconvolution analysis resolves the underlying pulsatile nature of the insulin secretion rate, demonstrating that glucose stimulates a large increase in insulin pulse mass. Reproduced from Ref. 12, with permission from Journal of Clinical Endocrinology & Metabolism.

The insulin oscillations observed in the circulation are driven by insulin secreted in pulses from the islets. Pulsatile insulin secretion from islets in vitro has been shown for both humans and mice (18–24). Notably, the oscillations of isolated islets have the correct period and respond to increasing glucose concentration with increases in insulin pulse amplitude. Despite the pulse-generating capability of individual islets, important questions remain about how the hundreds of thousands of islets within the intact pancreas synchronize their secretory output to generate the insulin pulses of portal blood. Suggested synchronizing signals include acetylcholine, ATP, and nitric oxide, which have been studied by pharmacologically inhibiting the neurons that innervate the pancreas or by vagotomy, but these studies failed to reach a consensus (25–28). While it is also possible that interislet synchronization is different under basal conditions, we assume in the absence of evidence to the contrary that the core oscillation mechanism still resides within individual islets. We proceed to focus here as a first step on the oscillation mechanisms of individual islets.

At higher glucose levels (7–15 mM) corresponding to postprandial or diabetic conditions, oscillations in islet insulin secretion are driven in large part by oscillations in cytosolic free Ca²⁺ (29). These Ca²⁺ oscillations arise in turn from a second role of Ca²⁺ in addition to stimulating the exocytosis of insulin granules shown in FIGURE 1, namely the negative feedback exerted by Ca²⁺ on its own entry. This occurs by two complementary mechanisms. The first mechanism proposed was activation of K_Ca channels, similar to the situation in many other endocrine cells and neurons. This causes the spikes to cluster into bursts rather than occurring continuously [see FIGURE 4 showing simulation of membrane potential (V) and concentration (c)] and was the basis of the earliest mathematical models of Ca²⁺ oscillations in β-cells (30). A number of other models were quickly proposed based on this idea or variations on it, as reviewed in Refs. 31, 32.

FIGURE 4.

The integrated oscillator model with modification can account for basal insulin oscillations A model simulation of a ramped increase in glucose (G) from basal (3 mM) to postprandial to the high levels typically studied in vitro (11 mM). Key dynamic variables shown include the glycolytic metabolites fructose 6 phosphate (F6P) and fructose 1,6 bisphosphate (FBP), AMP, ATP/ADP ratio, membrane potential (V), cytosolic Ca²⁺ concentration (c), an amplifying factor (AF) that enhances exocytosis, and the insulin secretion rate (ISR).

A second, more subtle form of negative feedback was subsequently appreciated: Ca²⁺ entry and accumulation activate Ca²⁺ pumps in the endoplasmic reticulum (ER) and plasma membranes [sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) and plasma membrane Ca²⁺-ATPase (PMCA), as shown in FIGURE 1]. These pumps restore cytosolic Ca²⁺ levels in between bursts of spikes but also consume ATP; see Ref. 33 for experimental evidence that raising Ca²⁺ lowers ATP/ADP. This would reopen some of the K_ATP channels that were closed when glucose was elevated and could contribute to the termination of each burst of spikes, as first proposed in Ref. 33. This is a much slower process than activation of K_Ca channels and is a more appropriate explanation of the 5-min oscillations of insulin observed in the circulation. Current models in which K_ATP channels either drive Ca²⁺ oscillations (34) or are limited to setting the glucose threshold for oscillations driven by other ion channels (35, 36) are reviewed and contrasted in Refs. 37, 38. A further point, which will take on heightened significance below, is that if metabolism oscillates in phase with Ca²⁺, the AF will also oscillate and reinforce the pulses of secretion (39).

We now come to the heart of the matter: oscillations in secretion are also seen in basal glucose in vivo (4–5 mM) (12, 14, 40, 41) and from isolated human (24) and mouse islets in vitro (42, 43). In fact, it has been reported that as much as 70% of the total insulin secreted from the pancreas under basal conditions, where both constant and pulsatile release are observed, occurs in pulses (44). Yet, in vitro data from islets exposed to these low glucose concentrations indicate that the β-cells are not electrically active and do not exhibit large amplitude oscillations in cytosolic free Ca²⁺ concentration in this case. This raises the question: what is the mechanism for oscillatory insulin secretion at basal glucose levels? This is not a purely academic question, because blood glucose is within its basal range most of the time. The high concentrations commonly used in in vitro experiments are typically only experienced by people or animals with diabetes.

Regulation of basal insulin secretion has clinical significance, as elevated basal insulin is a good predictor of future diabetes (45). It occurs years before basal glucose increases and is a marker of insulin resistance, as embodied in the widely used indexes homeostatic model assessment for insulin resistance (HOMA-IR) and quantitative insulin-sensitivity check index (QUICKI) (46, 47). It has also been suggested that in addition to being a marker of insulin resistance, elevated basal insulin may be a cause of insulin resistance (48, 49) as well as obesity (6, 50). A recent review, however, concludes that the preponderance of evidence is against hyperinsulinemia as a primary cause of diabetes in most cases; a good introduction to this debate is the review in Ref. 51 and the commentary responding to it in Refs. 52, 53.

While the mechanism of elevated basal insulin secretion and its contribution to diabetes is not established, various hypotheses have been proposed. Examples include dysregulated basal insulin release due to the interaction between reactive oxygen species (ROS) and long-chain fatty acids (as reviewed in Ref. 6), abnormal levels of cardiolipin in mitochondria due to its altered biosynthesis with concomitant changes in mitochondrial respiration (54), changes in the regulation of sweet taste receptors on the β-cell that normally act as a brake on basal secretion (55), elevation in basal secretion due to fatty acids that does not involve ATP synthesis, mitochondrial lipid oxidation or ROS but does involve Ca²⁺ (56), increased proton leak across the mitochondrial inner membrane mediated by fatty acids independently of ATP synthesis (57), and lastly, a novel Ca²⁺ influx pathway activated by ER stress under low glucose conditions, leading to more insulin secretion (58).

Calcium oscillations have in fact been seen in low glucose (e.g., at 6 mM, just below threshold levels of glucose needed to trigger full blown oscillatory activity) and in islets treated with high glucose and mannoheptulose to inhibit glycolysis (FIGURE 3) (59). However, these small-amplitude Ca²⁺ oscillations are too small to plausibly engage the Ca²⁺ feedback mechanisms acting on K_Ca or K_ATP channels oscillations described above, and it is unlikely that they alone could be the driver of insulin oscillations in basal glucose.

FIGURE 3.

Oscillations in intracellular Ca²⁺ concentration, the main trigger for insulin exocytosis, are observed in islets in vitro A; upon partial block of glycolysis using d-mannoheptulose, large amplitude glucose-stimulated Ca²⁺ oscillations in a mouse islet give way to small amplitude oscillations unlikely to be sustained by ionic mechanisms alone. B: a similar result observed in response to a reduction in glucose from a suprathreshold (11 mM) to a subthreshold (6 mM) concentration. Reproduced with permission from Ref. 59, with permission from Biophysical Journal.

We hypothesize instead that metabolism can oscillate at the level of glycolysis despite low levels of Ca²⁺, as described in detail below. The possibility that glycolytic oscillations can occur in low glucose is supported by recordings of oscillations in K_ATP channel conductance at 3 mM glucose (60) as well as by simulations carried out using mathematical models (61). We further hypothesize that when subthreshold, small-amplitude Ca²⁺ oscillations (henceforth referred to here as subthreshold oscillations) are coupled to coincident oscillations in metabolism, their effect is amplified sufficiently by the AF to produce small amplitude secretory oscillations. Oscillations in secretion driven by oscillations in metabolism with Ca²⁺ fixed, albeit at high-glucose levels, have been seen experimentally (62), making this plausible. Finally, we demonstrate here using a current mathematical model of oscillatory activity in mouse islets that as glucose is increased, the oscillations in the free cytosolic Ca²⁺ concentration, membrane potential, and insulin secretion transform naturally into the patterns that are observed at high glucose. Although our goal is to explain basal insulin oscillations in humans, the model for mouse is the best developed for addressing the interplay between oscillations driven by metabolism versus Ca²⁺, and we expect the general principles to apply.

The Integrated Oscillator Model

Over the past two decades we have developed a mathematical model that can account for most of the oscillatory activity patterns observed in β-cells. This model, the integrated oscillator model (IOM) (37, 63, 64), has been very helpful for generating hypotheses that were subsequently tested in experiments and in the design of those experiments. Here, we use the IOM to illustrate our hypothesis for the origin of oscillatory insulin secretion at basal glucose levels and demonstrate its feasibility. An earlier version of the model demonstrated that subthreshold Ca²⁺ oscillations were indeed possible and would convert to full amplitude oscillations at higher glucose (59, 61), but we did not examine their relationship to secretion oscillations using that model. The model used in this article is closely related to the version previously described in Ref. 64, with the addition only of a previously published set of equations to translate oscillations in Ca²⁺ and metabolism into oscillations in insulin secretion (39). Computer codes for the model are available at https://www.math.fsu.edu/~bertram/software/islet/ (also see Supplementary Material available at https://doi.org/10.6084/m9.figshare.17063984).

We Hypothesize That Glycolytic Oscillations Drive Pulsatile Insulin Secretion at Basal Glucose Levels

Using the IOM, we demonstrate the transitions in electrical activity and secretion that occur as glucose is ramped from basal to suprathreshold levels (FIGURE 4). At subthreshold glucose it is possible to produce oscillations, albeit small, in insulin secretion (see the first 15 min of the ISR in FIGURE 4). In this case, the model β-cell is nearly electrically silent, so the dramatic opening and closing of ion channels that would occur when the cell is electrically active do not take place. In fact, the Ca²⁺ channels that allow Ca²⁺ entry into the cell are mostly closed since the membrane potential (V) is relatively hyperpolarized, so the small changes in the Ca²⁺ concentration (c) observed in this scenario reflect small fluctuations in V and associated changes in the driving force for Ca²⁺ current. These Ca²⁺ oscillations are not by themselves sufficient for basal insulin secretion oscillations.

In the model, the oscillations in the insulin secretion rate (ISR) are driven instead by oscillations in glycolysis, represented here by the intermediate metabolites fructose 6 phosphate (F6P) and fructose 1,6 bisphosphate (FBP). These lead to oscillations in the ATP/ADP ratio and in turn to small oscillations in V and c via changes in K_ATP channel conductance. Additionally, the oscillations in glucose metabolism lead to robust oscillations in the metabolic amplification factor described above (AF; FIGURES 1 AND 4), which enhances the efficacy of Ca²⁺ to trigger the exocytosis of insulin granules. The model calculation in FIGURE 4 suggests that even small excursions of the Ca²⁺ concentration, when combined with large pulses in AF, can result in meaningful oscillations in the secretion rate.

Insulin Pulse Amplitude Increases With Glucose and Activity Patterns Change

As glucose increases above the threshold for electrical activity (∼5 mM), repetitive bursts of action potentials appear (starting at around 17 min; FIGURE 4), mediating large oscillations in the intracellular Ca²⁺ concentration (c; FIGURE 4). The oscillations in FBP and AF persist but do not increase dramatically in amplitude; the large increase in ISR seen here is due mainly to the increased amplitude of the Ca²⁺ oscillations.

As glucose rises further toward the range usually studied in vitro (8–11 mM), oscillations in V, c, and ISR continue but intensify. The active, spiking phases of the bursts become longer, which increases the average level of Ca²⁺, which in turn combines with glucose-dependent increases in AF to increase the amplitude of the ISR pulses. Note that oscillation frequency does not change much, consistent with the experimental data in FIGURE 2.

A subtle but important change in the character of the FBP oscillations in FIGURE 4 also appears at these higher glucose levels: instead of a discrete pulse that precedes each burst and falls nearly to 0, the FBP oscillations become sawtooth in shape, rising slowly throughout the silent phase and falling during the active phase. This is a good sign of the fidelity of the model, as measurements of FBP oscillations at higher glucose levels generally have a sawtooth shape (65, 66). Closer examination elsewhere (37, 63) has revealed that the pulse-like metabolic oscillations do not require oscillations in Ca²⁺, whereas the sawtooth oscillations cease if Ca²⁺ is held constant. We denote these as active metabolic oscillations (AMOs) and passive metabolic oscillations (PMOs), respectively, to distinguish the two cases as previously described in Refs. 37, 63. The existence of AMOs at basal glucose is critical to our hypothesis, as PMOs require large amplitude Ca²⁺ oscillations to occur that would not be possible at basal glucose.

How Do β-Cells Orchestrate Such a Wide Range of Activity Patterns?

Work dating back to the 1970s has demonstrated that metabolic oscillations could be produced in glycolysis, the first stage of glucose metabolism that precedes aerobic respiration. First in yeast (67), and later in muscle extracts (68, 69), it was shown that glycolysis can sustain long-term oscillations. These oscillations are believed to be due to the actions of a key allosteric enzyme, phosphofructokinase (PFK), that converts the substrate fructose-6-phosphate (F6P) into fructose-1,6-bisphosphate (FBP). Importantly, the product FBP is a positive regulator of PFK, and that positive feedback causes a buildup of FBP at the expense of the substrate F6P. At the same time, AMP, which increases the affinity of PFK for F6P, also falls due to increased ATP production downstream in glycolysis and the mitochondria. When F6P and AMP fall too low, PFK activity largely shuts down, ending the positive feedback cycle and resetting the system. This is the basis of the FBP oscillations in FIGURE 4 that underlie oscillatory insulin secretion at low glucose levels. This oscillation mechanism was first proposed in the context of stimulatory glucose levels (69), but we believe that it is actually most important at subthreshold levels.

The PFK isoform that has highest affinity for FBP, PFKM, was long assumed to be the critical player in this scenario, but we and others have found that slow Ca²⁺ oscillations persist in PFKM knockout mice (70, 71). Furthermore, model simulations suggested that other PFK isoforms can take over in the absence of PFKM (70). Regardless of the details regarding this enzyme, as long as glycolytic oscillations can occur independent of Ca²⁺, our basic hypothesis that they are responsible for subthreshold oscillations in insulin secretion would remain viable.

Although we have described how glycolytic oscillations can produce Ca²⁺ oscillations, the reverse can also happen: Ca²⁺ can influence glycolytic oscillations. This is the key to the transformation from AMOs to PMOs as glucose increases, as illustrated in FIGURE 4 and discussed above. At high glucose, glycolysis loses the ability to oscillate independently of Ca²⁺. This is partly due to the intrinsic glucose sensitivity of glycolysis: at high glucose the substrate F6P remains high, so PFK activity remains high, and oscillations are lost. In addition, Ca²⁺ activation of pyruvate dehydrogenase (PDH; FIGURE 1) contributes by increasing the consumption of pyruvate by PDH, which in turn increases the consumption rates of glycolytic metabolites, including FBP. This shuts down the positive feedback of FBP onto PFK and inhibits glycolytic oscillations. The signature of this in FIGURE 4 is the conversion of the FBP waveform from pulses into a sawtooth, as FBP slowly responds to the rise and fall of Ca²⁺.

Nonetheless, oscillations in metabolites, such as FBP and ATP/ADP, can still occur, by a mechanism discussed in the Introduction. When Ca²⁺ is high, ATP is consumed by Ca²⁺ pumps, including the sarco/endoplasmic reticulum Ca²⁺ ATPase and plasma membrane Ca²⁺ ATPase (labeled as SERCA and PMCA in FIGURE 1). This lowers ATP/ADP, allowing some K_ATP channels to reopen, which turns off Ca²⁺ entry. The drop in Ca²⁺ allows ATP/ADP to recover, which again closes K_ATP channels, and electrical activity resumes. Glycolytic metabolites, such as FBP, also oscillate because of the Ca²⁺ dependence of PDH mentioned above—when Ca²⁺ is high, flux through glycolysis and cellular respiration is increased—and also because of feedback of ATP and AMP onto PFK. These repeated cycles of ATP consumption and production underlie the oscillations in Ca²⁺, metabolites, and insulin secretion at high glucose, shown in the simulation in FIGURE 4 starting at around 25 min. In vitro data support this mechanism for PMOs (65).

Summary and Future Directions

We have presented here the hypothesis that oscillations of basal insulin secretion are driven by metabolic oscillations, specifically, oscillations in glycolysis that do not require, but can be modified by, Ca²⁺. We have used model simulations of oscillations in membrane potential, Ca²⁺, and insulin secretion to illustrate and support the feasibility of the hypothesis. Models in which oscillations of metabolism only occur secondary to oscillations in Ca²⁺, which likely occur for the secretory oscillations produced at elevated glucose, cannot account for oscillations observed under basal glucose.

The hypothesis could be tested in islets in vitro by looking for small amplitude oscillations in Ca²⁺ at low glucose, say in the range of 3–7 mM, while simultaneously recording oscillations in metabolites, such as ATP/ADP, FBP, or NAD(P)H. It may take some trial and error to find the right conditions, as the simulations show that the prevailing Ca²⁺ levels may determine whether metabolic oscillations occur at a particular level of glucose.

There are ample data in the literature demonstrating oscillations at stimulatory glucose levels in multiple metabolites, including oxygen consumption (72), mitochondrial membrane potential (73), ATP/ADP (74), and NAD(P)H (75), which are synchronized with membrane potential and Ca²⁺ (65). In addition, a fluorescence resonance energy transfer (FRET) sensor has been developed called the pyruvate kinase activity reporter (PKAR), based on the glycolytic enzyme pyruvate kinase (PK). PK is allosterically activated by FBP, and PKAR FRET is thus an assay to dynamically measure FBP concentration. Fluorescence measurements from islets showed that at stimulatory glucose levels PKAR FRET responses were oscillatory (76) and coincident with Ca²⁺ oscillations (65). Furthermore, metabolic oscillations persisted under conditions where oscillations in membrane potential and Ca²⁺ were abolished with diazoxide, demonstrating the existence of AMOs at high glucose (65). No study has yet been performed using PKAR to look for AMOs at basal glucose levels, so it is not known if oscillations exist in this case. We predict that they would exist for cases in which basal insulin secretion oscillations are present. We also predict that the concentration of ATP would oscillate. As an alternative to PKAR, the fluorescent reporter Perceval-HR, which provides a readout of the cytosolic ATP/ADP ratio, could be used to demonstrate metabolic oscillations in basal glucose.

In addition to offering a plausible mechanism for oscillations in basal insulin secretion, the simulations described here also help resolve a conundrum about how the IOM works. Slow oscillations in Ca²⁺ in the model can result from either AMOs or PMOs. The simulations here suggest that these two modes of operation are most appropriate at different glucose levels. AMOs are the only candidate mechanism of which we are aware that can generate secretory oscillations in basal glucose, and they transition in an orderly way to PMOs as glucose is increased. This was not apparent from previous modeling studies in which glucose was held fixed while other parameters were varied. It is still not apparent why AMOs give way to PMOs at higher glucose, as either mechanism could operate effectively in this range in theory, raising the question of what benefit islets might derive from having two seemingly redundant mechanisms. Nonetheless, AMOs appear to persist in high glucose in at least some islets, as demonstrated by the PKAR measurements mentioned above (65), as well as by the existence of compound oscillations (e.g., slow oscillations that have superimposed fast bursts), which so far have only been plausibly explained by AMOs. However, the observed and detailed characteristics of the slow oscillations indicate that PMOs predominate at higher glucose levels (63, 77).

An analogy for the division of labor between AMOs and PMOs that we find useful is the gas-electric hybrid car, which has two motors. At low speeds, the car is powered by the battery, which energizes the car’s electric motor, while at higher speeds, typically 25–40 mph, depending on the rate of acceleration and battery capacity, the internal combustion engine takes over. This arrangement seems complicated at first glance but is an effective way to exploit the characteristics of each type of engine to produce high fuel efficiency. If pulsatility is important for the efficiency of insulin action (17), it would seem appropriate to maintain such pulsatility over a range of glucose.