A computer model simulating human glucose absorption and metabolism in health and metabolic disease states
The roles of apical SGLT1 and GLUT2 intestinal glucose absorption
The sodium dependent glucose transporter SGLT1 is the only active component of intestinal transport sugar absorption. When SGLT1 is deficient, as in glucose-galactose malabsorption syndrome1–3, or inactivated by specific inhibitors, such as phloridzin, or similarly acting high efficacy inhibitors e.g. GSK16142354, small intestinal sugar absorption is blocked and the ingested sugar load is relegated to the large intestine where it becomes subject to fermentation processes.
It has been argued that exposure to high intestinal luminal glucose concentrations ≥ 15mM, or more modest glucose loads, supplemented with artificial sweeteners, induces small intestinal apical membrane passive glucose transport via GLUT25,6. This process is stimulated by enterocyte AMP kinase(AMPK), triggered by opening of Cav 1.3 Ca2+ channels following SGLT1-dependent depolarization of the apical membrane potential7. However, whether apical GLUT2 has any functional role in net glucose absorption has been questioned. No discernible effect on net intestinal glucose absorption in vivo is observed in GLUT2 knock out, (KO) mice,8.
Glucose absorption can only be enhanced by apical GLUT2, when the enterocyte and submucosal glucose concentrations are lower than in the intestinal lumen. The time required to reach steady state glucose accumulation within the enterocytes in vitro following exposure is ≤ 2 min9,10 and within 5 to 10 minutes in vascularly perfused frog11. As net glucose transport across the basolateral membranes is entirely due to passive processes, it follows that this can only occur when intracellular glucose exceeds the submucosal concentrations. Estimates of enterocyte glucose concentrations that are lower than that within the submucosa have been reported12, but as glucose accumulation only occurs in a small proportion of the enterocytes within the intestinal villus, are ascribable to overestimates of the compartmental volume into which glucose is actively accumulated;13. When the intestinal luminal glucose is lower than the enterocyte concentration, any apical component for passive glucose absorption, such as GLUT2, will hinder, rather than assist, net absorption14.
The experimental evidence supporting the accelerant role of apical GLUT2 in glucose uptake is based on data obtained with pharmacological concentrations of inhibitors, such as phloretin and cytochalasin B. These agents have multiple inhibitory effects, on glucose, Cl-, urea and water permeability. When phloridzin is already present, additional high phloretin concentrations may further inhibit any residual SGLT1 glucose transport activity1 and also prevent paracellular sugar absorption by blocking solvent drag effects14,15. Additionally, any of the pro-absorptive roles of apical GLUTs seen with phloridzin present will be artificially enhanced by the depressed cytosolic glucose concentration14.
Paracellular glucose absorption
When the intestinal luminal glucose concentration is higher than mesenteric capillary glucose concentration transcellular glucose transport may be supplemented, by passive flow via paracellular routes from the intestinal lumen16–19. With luminal glucose concentration > 15 mM the passive transport mode becomes predominant. A variable paracellular sugar permeability explains the non-saturable nature of intestinal glucose transport over a concentration range from 15mM to 100mM20,21 and how ingested ligands that are not transported via either SGLT1 or GLUT2, e.g. rhamnose, L-glucose, or mannitol, rapidly appear in human urine. Paracellular shunts also explain why molecules show size selectivity of transepithelial flows,22–24 and how inflammatory intestinal diseases, known to loosen intercellular junctions25,26 induce large increases probe entry into both plasma and urine27.
The highest rates of glucose transport obtained in exercising dogs are more than an order of magnitude higher than those obtained in vitro20,28. In vitro experimentation on isolated intestine or intestinal tissue or cells, which has become the normal mode of investigation of intestinal absorption, necessarily removes the intestinal capillary network. This capillary plexus provides the essential bridging component between the proximal sugar absorptive process and its distribution to the splanchnic and systemic circulations. So when it is removed, the major part of the sugar absorption control system is destroyed20,29–31. It is evident that lack of capillary perfusion of in vitro intestine heavily masks optimal absorptive performance21,32.
Integration of intestinal glucose absorption with splanchnic circulation
Superior mesenteric artery and incretins
The discovery that oral glucose generates a more rapid and larger metabolic response to insulin than equivalent amounts of intravenous glucose suggested that substances secreted by the gut wall during glucose absorption augment insulin release from pancreatic islets and its activity on liver and muscle33–36. It was inferred that a portal venous signal raises hepatic glucose uptake and stimulates hepatic glycogen synthesis, independent of a rise in insulin.
The superior mesenteric artery (SMA) supplies 600–1800 ml min-1 blood to the glucose absorptive portion of the proximal small intestine (Figure 2A and 2B). When ingested glucose is present in the intestinal lumen, splanchnic capillaries channel the absorbate via the portal vein to the liver. Splanchnic blood has approximately double the concentrations of absorbed materials and also of pancreatic hormones and incretins that are present in the systemic circulation (37,38; Figure 3E–G).
An integrated model of glucose transport and metabolism
It is evident that the incretin response to luminal, submucosal and splanchnic venular glucose; the pancreatic islet secretory response to systemic glucose; the hepatic response to incretins; the intrahepatic circulatory responses to portal blood pressure and the systemic metabolic responses to systemic blood concentrations of glucose, insulin and incretins are interrelated and interdependent39–41.
A quantitative model of the integrated response to glucose ingestion is both lacking and needed to assimilate the extent to which the incretin response to intestinal glucose load affects the balance between splanchnic–systemic blood flow and hepatic and peripheral glucose metabolism. Although there are several compartmental models that simulate intestinal glucose absorption and its subsequent metabolism by liver, none take account of the altered splanchnic blood flows that accompany and accommodate glucose absorption. These models assume that the splanchnic blood compartment imposes no impediment to flows into the liver42–44. As will be seen from the simulations here, the GLP-1 controlled flows of SMA are an important component in glucose absorption.
Other models, based mainly on the work of Cherrington’s and Bergman’s laboratories,45,46 give predictive indices of glucose metabolism and insulin-sensitivity in humans with normal and diabetic metabolism. The HOMA model of whole body glucose metabolism in relation to insulin secretion47,48 accounts for the hepatic contribution to homeostatic control of plasma glucose, but lacks an account of the incretin response, or splanchnic flow response to glucose ingestion, or how hepatic steatosis and/or portal-systemic venous shunting affect these responses. These issues are addressed by the current model.
Methods
Replication of the human response to oral glucose ingestion necessitates simulation of the circulatory response to glucose, integrated with hormonal (insulin and glucagon) and incretin (GLP-1) secretion and their effects on the liver and pancreas, also both the peripheral insulin-sensitive (muscle and adipose) tissues and insulin-insensitive (brain, skin and bone) glucose uptakes and metabolism (Figure 1).
This model of glucose absorption and metabolism was created with several aims. The first was to provide a quantitative simulation of the effects of changes of capillary perfusion rates on intestinal glucose absorption in health and disease. The second was to provide a broader understanding of how incretins affect the whole body response to glucose. The third aim was to demonstrate how metabolic diseases such as NAFLD, NASH and T2DM alter glucose and uptake and metabolism.
The model of whole body glucose absorption builds on those of Granger and Pappenheimer,29,49. The salient features of the current model are simulation of resting human systemic and splanchnic blood flows and pressures before, during and after glucose absorption. Sets of sub-models simulating the time course of changes in flows and concentrations of glucose, insulin, glucagon and the incretin GLP-1 following intra-duodenal glucose gavage, are embedded within this circulation model (Figure 1; for specific details of the model parameters given in parameter Table 2, see also Table 1). Intestinal glucose absorption is simulated here following initiation of a standard glucose tolerance test by duodenal gavage. By-passing the stomach avoids the extra complexities resulting from control of gastric emptying rates. Although these factors are important, they are inessential to the intestinal absorptive and subsequent vascular and metabolic processes50.
| Where RSMA(0) is th… |
| 2A ∫t=0t=txddt (Sys… |
| SMA flow = aortic B… |
| 2B Total blood vol … |
Table 1A. The number prefixes in equations refer to the positions in Figure 1.
| 1 Intestinal Glucos… |
| 2∫t=0t=txddt(Sys V … |
| 4A ∫t = 0t = txddt(… |
| 4B Hepatic glucose… |
Table 1B. Glucose equations (number prefixes refer to positions in Figure 1).
| 2 insulin secretion… |
| 4 ∫t = 0t = txddt (… |
| 4A Hep insulin ina… |
| 5 ∫t=0t=txddt (sys … |
Table 1C. Insulin equations.
| Glucagon release fr… |
| Glucagon secretion … |
| The exponent n is f… |
| 4∫t=0t=txddt (Hep G… |
Table 1E. Glucagon Flow sub-model.
Number prefixes refer to position in Figure 1.
All the simulations were generated using Berkeley Madonna version 9.0. (http://www.berkeleymadonna.com), a modelling and analysis program that solves simultaneous non-linear differential equations. It runs on Microsoft Windows 7–10, Macintosh and Linux platforms. The computer simulations are done using the option solving stiff non-linear simultaneous differential equations using the Rosenbrock simulation method51 with a step time of 100 µs and error tolerance of 1×10-8. Simulations usually extend for 1500 virtual seconds, normally outputted at 5 second intervals. The numerical data output tables were subsequently processed in Microsoft Excel 2013 for Windows 2013 and graphed using the build-in Chart facility. Further analysis was done using self-generated Excel Solver macros, and the Levenberg-Marquardt, L-M, least squares minimizing routines available with Synergy Software Kaleidagraph version 3.52, (www.synergy.com). This conveniently includes error estimations of the derived parameters.
Model description
Cardiac output at rest is set at approximately 5.5 L/min and mean aortic blood pressure at ≈ 105 mm Hg. The core model blood vessel resistances and compliances are adjusted to obtain appropriate normal human steady state flows and pressures. The compartmental volumes are determined by their compliances, C and the transluminal pressure. Their initial and steady state values are adjusted to match known human values. The most pertinent compartmental compliances are the superior mesenteric capillary (SM cap) and hepatic sinusoidal beds. The circulating blood volume is assumed to be a third of the extracellular volume into which glucose, insulin and glucagon are distributed rapidly.
The main components of the model of glucose circulation and metabolism. Intestinal absorption, is modelled as active and passive parallel transmission elements connecting the intestinal lumen with the submucosal capillary bed. Passive glucose flows depend on the glucose concentration gradient existing between the intestinal lumen and modal sub-mucosal glucose concentration and linked via the passive intestinal paracellular glucose permeability. The active component to intestinal uptake is assumed to be a saturable function of luminal concentration with constant Na+concentration = 140 mM (Figure 1 (1), Table 1B equation 1).
Net hepatic glucose uptake NHGU and hepatic glucose metabolism. Glucose flows via the portal circulation into the liver, where it is absorbed via sinusoidal GLUT2 and metabolized by insulin and GLP-1-dependent processes, the non-absorbed glucose flows via to the hepatic vein to the systemic circulation. The rate of hepatic glucose uptake and metabolism is controlled by the synergistic incretin and insulin dependent Vmax of hepatic GLUT2 and are tightly coupled to glucokinase activity, Glucose can also be regenerated by glucagon-dependent gluconeogenesis and glycogenolysis (Figure 1 (4), Table 1B equation 4).
Systemic glucose metabolism
Glucose enters into the systemic circulation via the hepatic vein (Figure 1 (2), Table 1B equation 2). It is metabolized by either insulin-dependent processes in muscle and adipose tissue, to which is entry is controlled by the insulin- and GLP-1-dependent Vmax of GLUT4 (Km 2.5 mM glucose), Figure 1 (5), Table 1B equation 5. Additionally, insulin-independent glucose uptake processes in brain, bone and skin consume glucose, entry to these tissues is controlled via GLUT1 parameters (Vmax and Km) Figure 1 (6), Table 1B equation 6.
Insulin flow sub-model
Insulin is released by pancreatic islet β cells into the superior mesenteric blood compartment, partially in response to a Michaelis-Menten function of systemic arterial glucose concentration. GLUT2 is a rate determining step of this process (Figure 1, Table 1C equation 1).
Glucagon flow sub-model
Glucagon, like insulin, is released from the pancreatic islets (α-cells) into the superior mesenteric blood compartment and circulates in the splanchnic and systemic circulations its release is suppressed by raised systemic glucose as a hyperbolic function of glucose concentrations Ki controlled by GLUT2 (Figure 1, Table 1E equation 1).
GLP-1 sub-model
In contrast with glucagon and insulin, which are sensitive to systemic arterial glucose, incretin secretion rates are controlled by the splanchnic capillary glucose concentration. Incretins (GLP-1 and GLP-1-2) are released from proximal intestinal enteroendocrine L cells and flow directly into the portal blood compartment, the stimulus for their release is assumed to be the glucose concentration within this superior mesenteric capillary compartment, determined by GLUT2 Km (Table 1E equation 2).
Estimation of the sensitivities of the flow and concentration variables. Altering single parameters e.g. intestinal paracellular glucose permeability, Pgl, or the glucose sensitivity of enteroendocrine cell GLP-1secretion have many important quantitative and qualitative effects on the flows of blood glucose hormones and incretins. These responses may be linear, where it is simple to estimate the sensitivity by linear regression, or hyperbolic. In this latter case the function is normally fitted to a hyperbolic curve, defined by two parameters, the maximal rate, Vmax, or the concentration of e.g. GLP-1, or the resistance to blood flow giving half maximal concentration, K½ or flow rates. These parameters are estimated by non-linear least squares fits of the hyperbolic function to the observed data. The standard error of these fits is < 5% and as it does not represent an experimental error is omitted. As there is significant interaction between several key effectors, e.g. GLP-1secretion rate and paracellular glucose permeability, Pgl, a measure of this interaction is required. All of the 3D surface plots of the dependent variable, z with respect to alterations in the independent variables x and y can be fitted using least square regression or minimal Chi2 fits either to the second order surface equation, where z = a.x2 + b.y2 + c.x.y + d.x + e.y + f or the equivalent third order equation.
The key coefficient required to estimate the degree of second order interaction between the two variables x and y is c. Forpositive x*y interactions c > 0 for negative x*y interactions c < 0. Examples of positive interaction are seen in Figure 5A, where SM arterial flow varies as an increasing function of both GLP-1secretion and paracellular glucose permeability, Pgl. However, with Pgl = 0 or GLP-1≅ 0, SM flow is small 200 ml min-1. SMA flow after feeding increases as a linear function of GLP-1 and as a hyperbolic function of Pgl; K½ = 0.02 μm s-1 and the interaction coefficient c for Figure 5D = 4.1, indicating a strong positive interaction between Pgl and GLP-1secretion, as can be seen from the upward elevation of the surface towards higher values of both independent variables. In contrast, during fasting, when intestinal glucose absorption is absent, although SMA increases with GLP-1secretion, there is no effect of altering Pgl, so coefficient c = 0. Where the independent variables both independently x and y cause a reduction in response, i.e. negative response, as is the effect of increasing GLP-1secretion on SM capillary glucose during feeding, then when both are increased, c = -4.58 during feeding, but during fasting the response c = 0.
Blood flow. The simulations are simplified by assuming that superior mesenteric artery supplying blood to the small intestine is the only flow resistance directly responsive to glucose (Table 1A equation 7, Figure 1 (7)).
All other blood flow changes are indirect reactions to this primary response. Blood flows are determined directly by the pressure gradients ΔP between the neighbouring nodal points in the circulation model (Table 1A equation 7, Figure 1 (7)).
As blood flows and pressures within the network obey Kirchoff’s laws, flow changes in other parts of network result from passive reactivity. The initial and steady state compartment volumes are adjusted to match known human values. For typical compartmental pressure change generated by change in volume see Figure 2D and 2E and Table 2. Changes in compartmental volumes (ml) following perturbations in blood flow are determined by their compliances, C and changes in transluminal pressure, generated by the blood flows.
All other compartments in Figure 1 depend on their assigned initial volumes and compliances and the integrated inflows and outflows. The most relevant compartmental compliances are those determining the splanchnic blood volumes, i.e. the superior mesenteric capillary bed and the hepatic sinusoidal bed resulting from glucose-dependent alteration of SMA flow.
The total circulating blood volume is assumed to be a third of the extracellular volume into which glucose, insulin and glucagon are rapidly distributed in all accessible compartments52. It is assumed that all the circulating glucose, hormones and incretin concentrations rapidly equilibrate between the circulating blood and their neighbouring extracellular fluid compartments. Thus the total circulating blood volume is 5 L and the fluid volume is initially and remains at approximately 15 L.
Glucose flow sub-model. Both splanchnic and systemic glucose circulations are incorporated within the core blood circulatory model. Ingested fluid entry and exit from the stomach, intestine and colon are programmed in order to fully replicate oral glucose tolerance tests. However, only a standard glucose dose via duodenal gavage delivery is shown in this present study. The key equations determining glucose flows are outlined in Figure 1. The parameters determining the rates of glucose flow and metabolism are shown in the Table 2.
Explanation of the model components of glucose circulation and metabolism. Intestinal absorption, is modelled by parallel active and passive transmission elements connecting the intestinal lumen with the submucosal capillary bed (Table 1B Glucose equation 1).
Passive glucose flows depend on the glucose concentration gradient existing between the intestinal lumen and sub-mucosal capillary glucose concentration and the passive intestinal paracellular glucose permeability, Pgl. The active component to intestinal uptake is assumed to be a saturable function of luminal concentration with constant Na+concentration = 140 mM. In addition to glucose entry via the superior mesenteric capillary bed, glucose also enters the splanchnic circulation via the superior and inferior mesenteric arteries, splenic and coeliac arteries (Table 1B Glucose equations 2–7). Glucose concentrations, mM within each body compartment are obtained from the amounts of glucose (mmoles)/volumes (L) within each compartment.
Net hepatic glucose uptake, NHGU and hepatic glucose metabolism (Glucose equation 4B). Glucose flows via the portal vein, PV into the liver, where it is absorbed via sinusoidal GLUT2 and metabolized by insulin and GLP-1-dependent processes starting with the enzyme glucokinase, the remaining non-absorbed glucose flows onwards via the hepatic vein, HV to the systemic circulation (Table 1B Glucose equation 4A). The rates of hepatic glucose uptake and metabolism are controlled by the synergistic incretin and insulin-dependent Vmax of hepatic GLUT2/glucokinase complex (Table 1B Glucose equation 4A). It is assumed that GLUT2 and glucokinase activities are tightly coupled, so hepatic glucose metabolism is synergistically controlled by activation of coupled insulin and GLP-1 receptor53,54 that modulates the combined GLUT2- glucokinase Vmax. Glucose can also be added to the hepatic sinusoidal circulation by glucagon-dependent gluconeogenesis and glycogenolysis, ultimately rate-limited by hepatic glucose 6 phosphatase activity55.
Systemic glucose metabolism. Glucose enters the systemic circulation via the hepatic vein (HV). It is consumed by insulin-dependent processes in muscle and adipose tissue, entry to which is controlled by the insulin- and GLP-1-dependent Vmax of the glucose transporter GLUT4 (Table 1B Glucose equation 5B).
Additionally, insulin-independent glucose uptake processes in brain, bone and skin consume glucose, entry to these tissues is controlled via GLUT1 parameters (Vmax and Km)56,57 (Table 1B Glucose equation 5A).
Renal glucose excretion. When the renal artery glucose concentration exceeds the ceiling for renal glucose reabsorption, glucose is excreted in urine at a rate proportional to the difference between renal glucose filtration rate (approximately 10% of renal artery flow and renal glucose re-absorptive capacity (Table 1B Glucose equation 6). Urinary glucose loss does not significantly affect glucose metabolism in any of the simulations.
Insulin flow sub-model. Insulin is released from pancreatic islet β cells into the superior mesenteric blood compartment, partially in response to a GLUT2 Michaelis-Menten function of systemic arterial glucose concentration (Table 1C Insulin equation 2, Figure 10A). Glucose uptake via GLUT2 is the rate determining step of this process. However this rate is modulated by a glucose sensitivity coefficient, which is a function of systemic GLP-1 concentration,58,59. Like glucose, insulin circulates to the liver via the splanchnic circulation, but is partially inactivated within liver before passing to the systemic circulation, where it is also partially degraded60 (Table 1C Insulin equations 4A and 5A).
Insulin secretion rates are adjusted to give concentrations within the systemic circulation, similar to known concentrations in normal and T2DM states (Table 2). The rates of insulin inactivation/degradation correspond with the reported inactivation rates t½ ≈ 2–3 min33,48) and adjusted to give a ratio of SMA insulin/peripheral venous insulin ≈ 2.061.
Glucagon flow sub-model. Glucagon, like insulin, is released from the pancreatic islets (α-cells) into the superior mesenteric blood compartment and circulates in the splanchnic and systemic circulations. Glucagon release responds as an inverse hyperbolic function of the systemic glucose concentration and is regulated only with a glucose-sensitive coefficient (Figure 1C, Table 1E Glucagon equation 2, Figure 10C).
On contact with hepatocytes glucagon stimulates hepatic glucose production by gluconeogenesis and glycogenolysis (Table 1B Glucose equation 4B). These processes result in net glucose release, into the systemic circulation. Glucagon, like insulin, decays within the circulation with a similar degradation half-time of 2–3 min, but is more slowly degraded by liver than insulin, so that the portal to arterial glucagon ratio is reported to 1.2–1.461. For present purposes the liver is assumed to be a limitless source, of gluconeogenesis from either glycogen or from fat and protein stores. This condition obviously applies only to the short term (1–2 days).
Incretin sub-model. Incretin secretion rates are controlled by the splanchnic capillary glucose concentration and like insulin and glucagon, incretins flow directly into the portal blood compartment (Table 1D GLP-1 equation 1). The stimulus for GLP-1 release is dependent on glucose concentration within this superior mesenteric capillary SM cap compartment, determined by GLUT2 Km35,62–64. Thus incretin release from enteroendocrine L cells differs from glucagon and insulin release from pancreatic islets; these are sensitive to systemic arterial glucose; whereas GLP-1 release is activated by splanchnic glucose concentrations. Like insulin and glucagon, GLP-1 has a half-time of degradation of 2–3 min; this is modelled by Table 1D GLP-1 equation 2, and Figure 10C.
In Figure 2–Figure 4 the effects of altering the glucose sensitivity over a range from (0.1–100) of GLP-1 release are shown on the key pressure, volume, flow and concentration variables affecting glucose distribution and metabolism, as functions of time after initiation of duodenal glucose gavage at 100min. Increasing glucose sensitivity over the range (0.1–100) increases the GLP-1 concentration in both splanchnic and systemic circulation by around 20 fold, (Figure 3D and 3H) (The linear regression coefficient of splanchnic capillary GLP-1 concentration with GLP-1-glucose sensitivity coefficient is 0.58 ± 0.01 and for systemic arterial GLP-1, the coefficient is 0.5 ± 0.007).
The effects of a standard oral glucose tolerance test, OGTT of 50 G glucose delivered by duodenal gavage over a period of twenty minutes are used in all simulations to demonstrate the comparative effects of these altered conditions on glucose flows and metabolism.
The effects of two major physiological variables, the GLP-1 sensitivity to glucose and the paracellular glucose permeability, Pgl on glucose absorption and its distribution and metabolism are displayed in the first part of this paper. Glucose sensitivity of GLP-1 release is the main regulator of superior mesenteric arterial response to glucose and the second variable Pgl affects the passive paracellular rate of glucose flow and hence its sensitivity to splanchnic capillary flow rates. The other major effects of altered GLP-1 secretion rates will be described in the first part of the Results section.
In the second part of this paper variations of two parameters, hepatic pre-sinus resistance and portosystemic shunt resistance, PSS R associated with NAFLD and NASH on hormonal and incretin changes affecting glucose absorption and metabolism will be examined.
No other parameters, or coefficients are altered during these simulations. All the other parameters used are the same as in Table 2.
Most of the graphs shown are 3D representations in which the arrays of dependent variable z are plotted versus array vectors of x (time) and y {independent variables, (resistances, permeabilities, etc.)}. This method of variable mapping using 3D surface graphs with Excel Chart facilities demonstrates the non-linear interactions between variables, however, only the time axis and the dependent variable are an exact linear or logarithmic maps of the independent variable The K½and “c” estimates of x, y interactions are all obtained with exact fits.
Comments
Post a Comment