The Brain-Gut-Islet Connection

  1. Stephen C. Woods,
  2. Stephen C. Benoit and
  3. Deborah J. Clegg
  1. From the Department of Psychiatry and the Obesity Research Center, University of Cincinnati, Cincinnati, Ohio
  1. Address correspondence and reprint requests to Stephen C. Woods, Department of Psychiatry, University of Cincinnati, 2170 E. Galbraith Rd., Cincinnati, OH 45237. E-mail: steve.woods{at}


Peptide signals from the pancreatic islets and the gastrointestinal tract influence the regulation of energy homeostasis by the brain, and the brain in turn influences the secretions of both the islets and the gut. This article focuses on how insulin interacts with the brain to influence food intake, blood glucose, and cognitive behavior. Insulin is secreted in response to changes of ambient glucose, and the levels achieved are directly proportional to body adiposity. Hence, insulin, like leptin, is an adiposity signal. An increased insulin signal in the mediobasal hypothalamus indicates that ample or excess energy is available in the body and elicits responses that limit food intake and reduce hepatic glucose secretion. Increased insulin (and leptin as well) locally within the brain complements other signals that indicate a surfeit of energy in the body, including satiety signals generated by the gut during meals, glucose, and some fatty acids. There is compelling evidence that overlapping intracellular signaling pathways within the mediobasal hypothalamus mediate the overall catabolic response to these diverse metabolic signals. Insulin receptors are also densely expressed in the hippocampus, and insulin acts there to facilitate learning and memory. The function of insulin receptors in other brain areas is poorly understood. Obesity and/or the consumption of diets high in fat render the brain as well as the body insulin resistant. In the hypothalamus, this is manifest as a reduced ability of insulin to reduce food intake and body weight, and in the hippocampus, it is manifest as a reduced ability of insulin to improve learning and/or memory.

The brain-gut-islet connection refers to the myriad ways in which signals arising in the three arms of this important axis interact among themselves, and at least one overall function of this integrated control system is the regulation of energy homeostasis throughout the body. Many of the interactions of this triad are well known. The brain regulates activity in both the gut and the pancreatic islets directly via the autonomic nervous system and indirectly via changes in food intake and energy expenditure. Peptide hormones and other signals secreted from the gut, in addition to coordinating the digestion and absorption of nutrients, provide the incretin effect that augments prandial insulin secretion. Many of these peptides also serve as critical satiety signals to the brain that limit meal size. Islet hormones influence digestion and control the disposition of ingested nutrients in addition to providing key signals to the brain regarding the level of adiposity and circulating energy. This review focuses on one aspect of this complex network, i.e., the actions of pancreatic insulin within the brain and the pathologies that occur when insulin signaling within the brain is compromised. The topic is timely, with relevant new information appearing almost monthly, and it is also an area of knowledge where the basic tenets are being challenged, since insulin was historically thought not to interact with the brain and subsequently was thought to mainly influence the control of food intake and body weight.


The energy equation holds that for body weight to remain relatively stable over time, food intake must match energy expenditure, and deviations in either direction will result in weight gain or loss. Humans and most mammals consume food in discrete episodes or meals. When there are no restrictions on when or how much individuals are allowed to eat (i.e., when they are in a free-feeding or ad lib condition), the impetus to begin a meal is rarely if ever caused by a biological deficit or need such as insufficient glucose. Rather, evidence indicates that the timing of meals is based on psychological factors such as habit, time of day, the social situation, convenience, and others (13). Because of this, body weight regulation, the continuous process that ties energy intake to energy expenditure, must logically be manifest as a control over how many calories are consumed once a meal begins, i.e., on meal size. Consistent with this, during meals, the gut responds to ingested nutrients by secreting peptide signals proportional to the quantity and quality of calories consumed, and some of these secretions function as satiety signals to the brain to limit meal size (47). The prototypical satiety signal is the duodenal peptide cholecystokinin (CCK). Humans and animals that are administered CCK just before eating consume smaller meals, and when administered a selective CCK-1 receptor antagonist, they consume larger meals (5,8). Table 1 lists gut and islet signals secreted during meals that influence meal size and are considered to be satiety signals.

Adiposity signals are hormones secreted in direct proportion to body fat. In contrast to satiety signals that are secreted mainly during meals, adiposity signals are tonically present, providing a relatively continuous message to the brain concerning fat stored within the body. Pancreatic insulin and the adipocyte hormone leptin are the two best-known adiposity signals, and others such as amylin and adiponectin also circulate in proportion to body fat and share many of the same properties. Administering either insulin or leptin directly into the brain results in reduced food intake and body weight, and reductions of either insulin or leptin signaling locally within the brain results in overeating and weight gain. When an individual’s weight (i.e., body fat) changes, insulin and leptin secretion change in parallel, and this is manifest as an altered adiposity signal to the brain. There are many reviews of these phenomena (914).

The interaction of adiposity signals with satiety signals in the control of food intake is a topic of considerable interest and beyond the scope of this review. The basic principle is that adiposity signals modulate the sensitivity of the brain to meal-generated satiety signals (10,12,15). As an example, the administration of very low doses of either insulin or leptin directly into the brain enhances the efficacy of systemic CCK to reduce food intake (1622), and a reduced leptin signal in the brain, which also reduces brain insulin signaling (23), lowers CCK sensitivity (24). The implication is that when an individual loses weight and insulin and leptin secretion are reduced, brain circuits that control meal size are consequently rendered less sensitive to meal-generated satiety signals such as CCK. As a result, more calories than normal must be consumed before a satiety signal of sufficient magnitude to terminate a meal is generated. Individuals consequently eat larger than normal meals until body weight returns to normal. Conversely, when an individual gains excess weight, the increased insulin and leptin signal in the brain causes increased sensitivity to satiety signals, and relatively small meals are consumed until the excess weight is lost.


Basal plasma insulin is low and increases during meals or when stimulated by glucose. Basal, prandial, and stimulated insulin levels are all direct functions of stored fat, with leaner individuals having lower levels and more obese individuals having higher levels (2527). Plasma insulin is therefore positioned to convey an important signal to the brain indicating the degree of adiposity, and as discussed below, some insulin enters the brain from the circulation and provides a key negative feedback signal in the regulation of body fat as originally proposed by Kennedy (28) (Fig. 1). When exogenous insulin is administered near or directly into the mediobasal hypothalamus, animals behave as if they have excess fat, i.e., they eat less and lose weight. The response is dose dependent (17,29), occurs in all species assessed, and is not secondary to illness or incapacitation (30). When insulin levels in the brain are clamped by means of slow steady local infusions, body weight is maintained and defended at a level determined by the dose of insulin administered (rev. in 13,3133). The response to changes of the insulin signal is bidirectional in that the administration of insulin antibodies into or near the mediobasal hypothalamus causes overeating and weight gain (34,35). Likewise, reducing hypothalamic insulin receptor activity either genetically by a neuronal-specific knockout of insulin receptors or pharmacologically via antisense oligonucleotides against the insulin receptor leads to increased food intake and body fat (36,37). Although insulin has not been administered directly into the brains of humans, certain formulations of insulin have been administered intranasally to humans with a consequent increase of cerebrospinal fluid but not plasma insulin. Humans receiving insulin in this way eat less food and lose body fat (38).

Insulin enters the brain via receptor-facilitated transport through capillary endothelial cells. The process is saturable, selective for insulin, and regulated (3942). Insulin transport into the brain is reduced during fasting (43), by maintenance on a high-fat diet (44), and in genetic and dietary-induced obesity (45,46). Because brain insulin derives from plasma insulin, it should be the case that experimentally induced increases of plasma insulin enter the brain and result in reduced food intake and body weight. Such procedures are confounded by hypoglycemia and a consequent increased tendency to eat more food. However, when insulin is administered systemically at doses sufficiently low to preclude hypoglycemia, food intake is reduced (47). Likewise, when sufficient glucose is administered in conjunction with systemic insulin to circumvent hypoglycemia, food intake is also reduced (48).

Autoradiographic insulin binding, as well as immunohistochemical analyses, reveal that insulin receptors are selectively located in several brain regions (4952). The areas of highest concentrations are the olfactory bulb, hypothalamus, cerebellum, cortex, and hippocampus (5355), and most insulin receptor immunoreactivity occurs on neurons and not on glia.


As discussed above, insulin reduces food intake and body weight when delivered into the third cerebral ventricle (i3vt) or directly into the hypothalamus in or near the arcuate nucleus (ARC). Conversely, reduction of insulin signaling has the opposite action. Insulin signaling in the ARC also initiates a signal via the vagus nerve to the liver to reduce glucose synthesis and secretion into the blood (5658). Hence, insulin’s action in the hypothalamus is consistent with its better-known systemic actions, i.e., its net effect is to lower blood glucose (9,11). Reducing the amount of food consumed and neurally reducing hepatic glucose output both complement insulin’s ability to facilitate glucose uptake by muscle, liver, and other tissues, as well as complement insulin’s direct action in the liver. It has recently been reported that administering oleic acid or glucose into or near the ARC also reduces food intake (57,5962). Leptin may also act there to influence glucose homeostasis (63). Hence, ARC neurons respond to diverse signals indicative of a surfeit of available energy (i.e., elevated insulin, fatty acids, or glucose) by reducing the ingestion of energy and decreasing the secretion of utilizable energy (especially glucose) into the blood. Rossetti’s group has postulated that manipulating intracellular metabolic signaling pathways, especially those involved with the oxidation of lipids, comprises the actual stimulus that is important in controlling both food intake and hepatic glucose production by the hypothalamus (61,6467).


As discussed above, both leptin and insulin function as adiposity signals, and the two have overlapping actions with regard to the hypothalamic control of metabolism. While the existence of two or more adiposity signals might seem redundant, insulin and leptin in fact reflect different fat stores, sexes, and risk factors for developing type 2 diabetes, cardiovascular problems, and the metabolic syndrome.

Fat stores.

Insulin is secreted in proportion to visceral fat, whereas leptin reflects total fat mass and especially subcutaneous fat (68,69). This is an important distinction with regard to the message conveyed to the brain, since visceral fat carries a greater risk factor for the metabolic complications associated with obesity than does subcutaneous fat. Elevated visceral fat carries an increased risk for insulin resistance, type 2 diabetes, hypertension, cardiovascular disease, and certain cancers (68,70,71). Hence, leptin and insulin each convey specific information to the brain regarding the distribution of fat, and the combination of the two additionally conveys information as to the total fat mass of the body.


Women have relatively more subcutaneous fat and higher plasma leptin, whereas men have relatively more visceral fat and higher plasma insulin (68,70,71). Likewise, male rats have relatively more visceral fat and higher plasma insulin, whereas female rats have more subcutaneous fat and higher plasma leptin (72). We have found that the brain of females is more sensitive to the catabolic action of leptin, whereas the brain of males is more sensitive to the catabolic action of insulin (73), and that estrogen mediates this difference (72). These data are consistent with a growing literature documenting sex differences in the actions of many compounds that influence energy homeostasis, including CCK (74), insulin (38,73), leptin (73), and ghrelin (D.J.C., L.M. Brown, C.J. Kemp, A.D. Strader, S.C.B., S.C.W., M. Mangiarachina, N. Geary, unpublished data), and this may be manifest in the selection of foods (75,76) as well as the preferred strategy used by males and females to defend their body weight (77). The physiological basis of these sex differences is an important clinical issue, since males are far more likely to develop symptoms of the metabolic syndrome (70), whereas females are far more likely to develop eating disorders (78).

Risk factors for developing type 2 diabetes.

Although insulin and leptin each signal the degree of adiposity to the brain, and whereas each lowers food intake as well as hepatic glucose secretion, they do so by stimulating different ARC neurons and circuits (79) as well as by altering different hepatic enzyme systems (80). Further, each has important other functions. Insulin is a major controller of the levels and utilization of glucose throughout most of the body, including the brain (9,11). Leptin also influences glucose parameters via the brain, although via different neural circuits than stimulated by insulin (80). Low circulating leptin and the resultant decrease of leptin signaling have been hypothesized to regulate many vital systems when animals are severely hypocaloric and have low body fat (8183). The secretion of insulin is adjusted in response to every acute change of metabolism (9,84), with levels increasing during meals or when glucose is elevated for some other reason and decreasing during stress and exercise. The half-life of insulin in the blood (2–3 min) is consistent with its role as a minute-to-minute indicator of ongoing metabolism, and all of its fluctuations are directly proportional to total body fat (26). Leptin is secreted from adipocytes in direct proportion to the amount of stored fat (85) (although the actual stimulus is related more to the metabolic activity of the fat cell than to actual fat storage [86] such that dissociations can occur between stored fat and leptin release, particularly during a fast [8688]). Nonetheless, under normal conditions and with a half-life of 45 min, plasma leptin levels are a reliable and relatively stable indicator of body fat. Hence, insulin levels reflect the interaction of ongoing metabolic processes and body adiposity, whereas leptin levels reflect the activity of adipose cells more directly.

As described above, both insulin and leptin act in the ARC (and probably other brain areas) to reduce food intake and body weight, and both also act in the ARC to reduce hepatic output of glucose. In some instances, the overlap of function may result from common intracellular signaling pathways of insulin and leptin, since both activate a pathway using insulin receptor substrate 1 and 2, and both cause increased intracellular cAMP degradation (8991). Insulin upregulates the expression of mRNA of the long form of the leptin receptor (OB-Rb) in neuronal but not other cell types (92), and insulin facilitates leptin’s ability to activate the JAK-STAT pathway in the hypothalamus (90,93). Both leptin (94,95) and insulin (94,95) exert their catabolic action through phosphatidylinositol 3-kinase.


Insulin and leptin interact with two populations of ARC neurons. Activity of those that synthesize proopiomelanocortin, the precursor molecule of the melanocortins, is stimulated by insulin and leptin, whereas activity of those that synthesize neuropeptide Y plus Agouti-related protein is inhibited by insulin and leptin. α-Melanocyte–stimulating hormone is a melanocortin that is derived from ARC proopiomelanocortin and is an agonist at melanocortin receptors (MC3R and MC4R) in several hypothalamic nuclei; Agouti-related protein is an endogenous antagonist of these same melanocortin receptors. Central administration of insulin or leptin, or the administration of α-melanocyte–stimulating hormone or synthetic agonists for melanocortin receptors, or the application of treatments that reduce ARC neuropeptide Y (e.g., antisense oligonucleotides administered directly into the ARC [96]), all result in reduced food intake and body weight. Conversely, the administration of neuropeptide Y, Agouti-related protein, or synthetic melanocortin antagonists, or the absence of endogenous insulin or leptin signaling, all result in a net increase of food intake and body weight (rev. in 11,83,97101).


It is important to consider what a change in the insulin signal at its receptor in diverse brain areas actually signifies. The obvious answer is that acute changes of insulin reflect an increase (or decrease) in energy in the form of glucose interacting with the pancreas, whereas sustained changes additionally reflect the amount of fat stored in the visceral or abdominal region. Based on this, it is easy to generate an explanation for why neurons in the mediobasal hypothalamus express insulin receptors, since these neurons are intimately involved in the regulation of energy homeostasis. An intriguing related question, however, concerns the rationale for more remote areas of the brain to express insulin receptors, such as the hippocampus or the olfactory bulb.

In the hippocampus, immunoreactivity for insulin receptors is found in the molecular layer of the dentate gyrus and on dendrites of CA1 pyramidal cells (51,102). Insulin binding in the hippocampus is colocalized with immuno-labeled phosphotyrosine (54) and insulin receptor substrate 1 (103), and as is discussed above, these compounds are important for the insulin receptor’s intracellular signaling pathways (104). Thus, the binding of insulin in the hippocampus, as it is in the hypothalamus, appears to be closely associated with functional effects of insulin. Glucose metabolism in hippocampal cells is sensitive to application of exogenous insulin (105), and this sensitivity depends on the insulin receptor (106,107). Further, insulin receptors in the hippocampus are localized in dendritic fields, suggesting a neuromodulatory role (51,54,55). Furthermore, there is a relationship between certain metabolic disorders and cognitive decline (108). In diabetes, for example, patients must rely on exogenous insulin administration to keep blood glucose levels within a life-sustaining range. These patients also often exhibit increased cognitive impairment correlated with the progression of their diabetes (109). Other disease states are also accompanied by changes in metabolic status. The progression of diverse central nervous system disorders such as Huntington’s disease (110), Parkinson’s disease (111), and schizophrenia is correlated with changes in glucose levels, insulin, and metabolic activity. Likewise, the progression of Alzheimer’s disease is correlated with disturbances in basal insulin levels as well as glucose metabolism (112).

More striking is the finding that when Alzheimer’s patients are made hyperinsulinemic, their performance on several assessments of memorial tasks is improved (113). Importantly, this occurs even at doses of insulin that do not affect peripheral glucose levels. Further, hyperinsulinemic states do not appear to increase Alzheimer’s patients’ performance on visual-spatial or physical-coordination tasks. This finding adds support to the hypothesis that insulin levels are specific to cognitive process (e.g., memory) in Alzheimer’s patients. Finally, patients with type 2 diabetes who are insensitive to the effects of insulin (i.e., who are insulin resistant) are also impaired on some measures of cognitive ability (114117). These and other findings encourage the hypothesis that insulin plays an important role in normal cognitive functions and memorial processes. Moreover, it encourages the hypothesis that alterations in insulin signaling may play an important role in neurodegenerative disease.

In addition to the epidemiological and clinical studies, a growing body of evidence from animal experiments also implicates insulin as an important factor in learning and memory (118). Experimental removal of insulin leads to disrupted learning and performance. For example, administration of streptozotocin leads to impaired learning on a number of learning tasks in mice (119). In rats, streptozotocin-induced diabetes leads to disrupted performance on avoidance tasks and in Morris water mazes (109,120123). Central streptozotocin also produces impairment in working and reference memory in rats (124), and it alters intracellular signaling by N-methyl-d-aspartate (125) and α-amino-3-hydroxy-5-methyl-4-isoxaziole-propionate (126) receptors that are implicated in the development of long-term potentiation (127). Thus, disruption of systemic insulin signaling is associated with impairments of memorial processes in rodents.

Importantly, administration of exogenous insulin improves performance on some learning tasks and corrects the learning and memory deficits produced by streptozotocin or diabetes. For example, administration of exogenous insulin improves rats’ performance in the one-trial learning of a passive avoidance task (128,129). It also ameliorates the diabetic impairments observed on radial-arm maze tasks and water mazes (122,123). A key point is that administration of insulin directly into the brain, where it does not improve peripheral glucose metabolism, also improves learning (128,130), although some studies have reported contradictory findings, i.e., that administration of insulin impairs learning and memory performance (131134).

Therefore, data from both humans and animals support the hypothesis that insulin is an important factor in memorial processes. However, the exact nature of that role remains elusive. This is due, in part, to the fact that much of the previous work suffers from one or both of two serious confounds. First, it is often difficult to disentangle the effects of altered insulin from the effects of altered metabolism. Large changes in basal insulin levels can produce profound disruptions in metabolic status that might account for some of the observed disruptions in learning in and of themselves. Second, because most manipulations of insulin occur systemically, it is difficult to identify the effects of insulin uniquely in regions of the brain known to be important for learning and memory. Finally, the ability of insulin to improve cognitive behavior might be task or reinforcement specific. It might be, for example, that increased insulin in the hippocampus, which reflects an increase of available energy in the body, facilitates learning tasks that help procure food. That is, elevated insulin might well enable remembering where food is located, or the best time to access it, or related factors. Likewise, increased insulin activity in the olfactory bulb could help form associations between specific odors and food. The point is that any general hypothesis of insulin action in the brain must account for what changes of insulin actually reflect.


As previously mentioned, when leptin is administered into the brains of experimental animals, there is a selective reduction of body fat, with lean body mass being spared (135). Likewise, when insulin is administered into the brain, there is a reduction of the respiratory quotient, suggesting that the body is oxidizing relatively more fat (136). These observations suggest that one action of these adipose signals within the brain is to reduce body fat, and a corollary of this is that fat ingestion would be expected to be reduced as well. Consistent with this, we have observed that when insulin is administered into the third cerebral ventricle of rats, fat intake is selectively reduced (137). Hence, it is reasonable to hypothesize that leptin and insulin, acting in the brain, reduce body fat by increasing lipid mobilization and oxidation and simultaneously by reducing the consumption of dietary fat.

When animals become obese after exposure to high-fat diets, they become resistant to leptin and insulin’s ability to regulate food intake and body weight. The epidemiological data that increasing dietary fat accelerates the development of obesity are quite compelling and have been summarized in several reviews (138140). Animal studies provide strong corroborative evidence, i.e., across numerous experiments, diets, and species, and the conclusion that increased consumption of high-fat diets leads to increased body fat is inescapable (141148). Importantly, there are strong genetic influences that dictate whether or not a given individual will be prone or resistant to becoming obese when exposed to a high-fat diet (141,146,149153). As Bray and Popkin (138) point out, a high-fat diet can be viewed as the environmental agent that acts on a susceptible host animal to produce the noninfectious disease obesity. Importantly, the consequences of obesity, including dietary-induced obesity, are well documented and include type 2 diabetes and insulin insensitivity. Further, some detrimental effects of dietary fat are not limited to obese individuals. For example, we have recently demonstrated that while high-fat diet–induced obesity decreases central sensitivity to the anorexic effects of central insulin administration, increased dietary fat, in the absence of frank obesity, also attenuates the potency of central insulin to reduce food intake and body weight (148; K. Gotoh, M.D. Wortman, S.C.B., D.J.C., D. D’Alessio, P. Tso, R.J. Seeley, S.C.W., unpublished data).


Consistent with the concept that insulin acts in multiple regions of the brain to influence multiple processes, dietary-induced insulin resistance has recently been linked to impaired cognitive function in both humans and animals. Specifically, high levels of dietary saturated fats and simple carbohydrates (which promote insulin resistance and obesity) have been demonstrated to reduce hippocampal-dependent memory processes. For example, Gomez-Pinilla and colleagues (154) have shown that long-term access to obesigenic diets impairs rats’ performance in the Morris water maze task, a classic measure of spatial memory. These deficits are associated with reductions in hippocampal expression of brain-derived neurotrophic factor mRNA (155). We and others have found that increased body weight and peripheral metabolic disruptions are also associated with reduced insulin receptor gene expression in the hippocampus. Several important questions remain unanswered, however, including the specific molecular mechanisms by which central insulin resistance might lead to decreased expression of such factors as brain-derived neurotrophic factor.


To summarize, increased insulin in the mediobasal hypothalamus provides a signal that ample or excess energy is available in the body, and one consequence is a reduction of food intake. It has recently been reported that the increased hypothalamic insulin signal also elicits a vagal reflex to the liver that reduces glucose secretion. Increased insulin (and probably leptin) locally within the hypothalamus therefore can be considered to be analogous to other signals that indicate a surfeit of energy in the body. In addition to satiety and adiposity signals, this includes certain lipids and glucose, and there is compelling evidence that overlapping intracellular signaling pathways within the mediobasal hypothalamus mediate the overall catabolic response to these diverse metabolic signals. Insulin receptors are also densely expressed in the hippocampus, and there is evidence that insulin acts there to facilitate certain cognitive functions. The function of insulin receptors in other brain areas is poorly understood. Obesity and/or the consumption of diets high in fat render the brain as well as the body insulin resistant. In the hypothalamus, this is manifest as a reduced ability of insulin to reduce food intake and body weight, and in the hippocampus, it is manifest as a reduced ability of insulin to improve learning and/or memory. Figure 2 is a model depicting some of the feedback loops involving insulin in the brain.

FIG. 1.

Insulin is secreted into the blood from the pancreas in direct proportion to the amount of fat stored in white adipose tissue. As it circulates through brain capillaries, a small amount of insulin is transported into the brain, where it acts on insulin receptors on neurons with either net catabolic or anabolic activity, for example, in the ARC of the hypothalamus. These neurons in turn influence energy homeostasis (food intake and energy expenditure) and ultimately the amount of fat stored in the body by exerting a net catabolic or anabolic action.

FIG. 2.

Insulin has many actions in the brain. A: Insulin circulates in the blood in direct proportion to stored calories. Within the hypothalamus, it regulates food intake and energy expenditure, thus contributing to the maintenance of a relatively stable body weight. B: Insulin levels are also a function of blood glucose. Elevated glucose increases insulin secretion, and the increased insulin signal in the hypothalamus reduces hepatic glucose secretion, thus contributing to the regulation of blood glucose. C: Insulin stimulates receptors in the hippocampus, facilitating certain kinds of learning and memory. This action, as well as an action in the olfactory bulb, is hypothesized to facilitate foraging behavior.


Gastrointestinal hormones that affect satiety


  • This article is based on a presentation at a symposium. The symposium and the publication of this article were made possible by an unrestricted educational grant from Servier.

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

    • Accepted April 27, 2006.
    • Received March 25, 2006.


| Table of Contents