A.A. Gruzdkov*, L.V. Gromova, Yu.V. Dmitrieva, A.S. Alekseeva. FREE CONSUMPTION OF GLUCOSE SOLUTION BY RATS AS A CRITERION FOR EVALUATION ITS ABSORPTION IN THE SMALL INTESTINE (Experimental study and mathematical modeling) I.P. Pavlov Institute of Physiology RAS, St. Petersburg, 199034, Makarova Nab., 6, Russia,
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The aim of this studyis study is to analyze the relationship between consumption of glucose solution by rats and its absorption, and to use it thitem for assessment of the absorptive capacity of the small intestine in non anesthetized animals in vivo. Consumption of glucose solution (200 g / l) by fasted rats was recorded in the( control), and after administration of phloridzin (inhibitor of glucose active transport) or 3 hours after the immobilization stress. On the mathematical model wase studied the relative role of factors that can influence the temporal dynamics of glucose consumption by rats. The rate of glucose consumption was observed to be decreased in the presence of phloridzin (1 mM), and increased after the stress. The results of modeling are consistent with the experimental data and show that the rate of consumption of glucose solutions depends more on the transport activity of the small intestine than on glucose concentration in the solution, or on the substrate regulation of the stomach emptying. Analysis of dynamics of consumption of glucose solution by intact rats may be considered as one of promising approaches to assess the absorptive capacity of the small intestine under natural conditions.
Key words: consumption of glucose, glucose absorption, small intestine, mathematical modeling, stress
INTRODUCTION
Under normal conditions, the amount and the rate of food absorption depend on nutritional requirements of the organism, as well as on ability of the gastrointestinal tract to assimilate food [4, 14, 16]. The optimal rate of food consumption during a single act of meal is achieved by regulation of evacuative functions of the stomach and intestine and depends on the concentration of the final products of nutrients hydrolysis (predominantly, monomers) in proximal and distal segments of the small intestine [6, 12, 13, 15, 20].
In frame of these views, virtually constant average rate of free consumption of concentrated (400 g / L) glucose solution by intact fasted rats (observed by Ugolev and coworkers [4]), may be explained by existence of regulation of the stomach emptying according to the rate of glucose absorption in the small intestine.
In the early '90s the American physiologist J. Pappenheimer [18], when assessing the role of different mechanisms of transport of glucose in the small intestine, made an assumption that the rate of free consumption a concentrated glucose solution of glucose by rats reflects the true capacity of the small intestine to absorb this monosaccharide. Later, this assumption was confirmed in our experiments, which showed that the average consumption rate of glucose solution (200 g / l) by fasted rats with the intact small intestine (after laparotomy) was higher than after the surgical isolation of 30 cm of jejunum, though before this operation the animals in the both groups showed the similar rates of consumption of glucose consumption [3].
Given these circumstances, the aim of this work was to analyze the relationship between the free consumption of glucose solution and its absorption in the intestine, and to use this relationship to assess the absorptive capacity of the small intestine in non anaesthetized animals. The free consumption of concentrated glucose solution by intact rats (preliminary starved) was recording for 5 - 6 hours without any additional actions (control), and after administration of phloridzin ( inhibitor of active transport of glucose) into the solution, or after immobilization stress for 3 hours.
The mathematical model has been used to study the relative role of various factors that affect glucose consumption in rats (substrate concentration in the initial solution, maximum volume of the stomach, parameters of gastro-duodenal and gastro-ileal loops controlling the evacuation function of the stomach, the level of the active transport of glucose), and also a degree of correlation between the rate of consumption of glucose, and absorptive capacity of the gut.
MATERIALS AND METHODS
EAll experimental procedures were performed according to the ethical principles and in full compliance with the European Council Directive (86/609/EEC) and were approved by the ethical committee of the I.P. Pavlov Institute of Physiology, RAS.
Before and after each experiment, the rats were kept in common cages (5 animals in each cage) and received a standard diet. In preliminary experiments, for 10–12 days, twice a week, rats were trained to drink a glucose solution (200 g / L) after starvation for 18–20 hours. For this, they were placed in individual cages with two vessels, one – with plain water * and the other – with glucose solution. For 5–6 hours every 30 minutes the consumption of this solution was recorded. in each animal . Rats with too low consumption of glucose (usually not more than 10% of the total) were not taken in the subsequent experiments.
Using the software resource «ORIGIN 7» (OriginLab Corporation, USA) and linear regression analysis, the average rate of free consumption of glucose (in mL/min) for each rat in the time interval from 60 to 300–360 min from the start of the experiment has been determined. In this range, in contrast to the initial period, the average volume of glucose solution consumed by several animals, increases almost linearly with time.
Based on the results of preliminary experiments, we have formed two groups of animals – the experimental and the control (7–10 rats in each group) – so that the average rates of glucose consumption in the time interval from 60 to 300–360 minutes from the beginning of experiment were close for both groups.
Statistical analysis was performed using Student's t-test. Differences were considered to be statistically significant when P <0.05.
2. Mathematical modeling. A model developed earlier [3], has been used with minor modifications. The model is based on current ideas of glucose absorption in the small intestine and mechanisms regulating the stomach and the intestine emptying. It isThe model represents ed by a set of series-connected compartments that mimic the stomach (compartment 1), and the small intestine (compartments 2-21). The absorbed solution enters the compartment 1, and then is evacuated to the compartments 2 – 21, where glucose is absorbed due to active and passive transport mechanisms. In the simulation of this process, the same basic assumptions have been taken into considereation as in determining the values of the kinetic constants of glucose transport in the isolated loop of the small intestine in chronic experiments using the previously developed mathematical approaches [1, 2, 9]. It was assumed that the "intestinal" compartments were identical in all properties except the value of Jmax, which varies from one compartment to the other according to the proximal- distal distribution of the active glucose transport along the intestine [3].
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*) In all experiments the animals practically did not drink water.
The rate of exchange between the contents of adjacent compartments depends on the volume of each compartment taking into account a polarity of intestinal peristalsis (Equation 1):
(1)
i = 2, 3, . . . 21 (1а)
Xi - volume of the i -th compartment at time t; X0i - the initial volume of the i-th compartment; Di - intermediate variable; k1 and k2 - coefficients characterizing the relationship between volumes of the compartments and the evacuation rates of their contents; k' and k"- are factors that characterize the predominant direction of evacuation of the contents from the compartment i and imitate a polarity of intestinal peristalsis (k' > k").
The rate of gastric emptying is determined by volume of its contents, as well as an inhibitory effect from the "intestinal" compartments; the extent of these effects depends on the concentration of monomers at the absorptive surface in the second and third compartments (analogue of the duodenum), and in the three final compartments (analogues of terminal part of the ileum) (equation 2):
(2)
(2а)
(2б)
U1 reflects the inhibition of evacuation from cell i depending on the concentration of glucose on the absorptive surfaces of cells 2, 3 and 19 – 21; X1 - the volume of the first cell ("stomach") at time t; X01 is the initial volume of the first cell; kж' and kж"- constant coefficients characterizing evacuation rate from the compartment 1 ("stomach") to the compartment 2 and in opposite direction, respectively (to simulate "gastrointestinal reflux"); Cm2 and Cm3 are glucose concentrations at the absorptive surfaces in the compartments 2 and 3 (analogue duodenum); , and in the past (the analogue of the terminal ileum) kторм1, a1, a2, b1, b2 and b3 – constant coefficients.
It is assumed that the solution flow to the compartment 1 ("stomach") occurs continuously in small portions, interrupted when the maximal volume of the compartment 1 (X1max) is reached. Increase or decrease of the X1max value imitates the amplification or reduction of emptying function of the stomach, accordingly.
Exit of the content from the n-th compartment may also be inhibited by enhanced concentration of glucose at the absorptive surface of this compartment (Equation 3):
(3)
(3а)
(3б)
U2 reflects an inhibition of emptying from the compartment 21, depending on the glucose concentration at its absorptive surface (); Dn – intermediate variable; kinhib 2 and d2 are constant coefficients.
The model also takes into account changes in the volume of the stomach and small intestine due to changes in volumes of gastric and pancreatic juices and water absorption or secretion.
The distribution of substrates in space (between the compartments) and in time is described by ordinary differential equations of the first order, a solution which wereas carried out by conventional methods on a personal computer using a program, written in the language of "Quick Basic".
A choice of the model’s parameters was based on previously obtained data on the absorption of glucose in the isolated loop of the rat small intestine under chronic experiment [1-3, 9], and literature data on the structural and functional parameters of the digestive tract and their rates. It should be noted that when comparing the results of simulation with experimental data, in order to achieve the closest correspondence between them, a correction was performed for only one or (in some cases two) parameters of the model, while the rest parameters were constant.
RESULTS
1. Dynamics of free consumption of glucose (200 and 400 g/L) by rats. We have previously shown that in rats subjected to laparotomy or with isolated jejunum, the consumption rate of glucose with an initial concentration of 200 g/L was 1.7 times higher than in the case of glucose concentration of 400 g / L. [3].
In this study, similar experiments were carried out on non-operated, intact rats.
In preliminary experiments animals were divided into two groups (Fig. 1, A). In the range of 60-360 min from the onset of the experiment the average amount of glucose solution, consumed by rats of both groups, increased almost linearly in time (correlation coefficient r = 0.996). The average rates of free consumption of glucose by rats of Groups 1 and 2 were 35.1 ± 0.9 and 36.5 ± 1.5 µL/min.
After 4 days, these same animals after preliminary starvation for 18-20 hours, consumed glucose solutions with concentrations of 200 g / L (group 1) or 400 g / L (group 2).
The mean consumption rate of glucose solution, which was determined by linear regression in the range 60-360 min after the onset of the experiment, amounted 33.5 ± 1.2 µL / min (group 1) and 18.6 ± 0.7µL / min (group 2) (Fig. 1, B). But the average consumption rates of glucose itself were not significantly different: 36.9 ± 1.3 and 40.9 ± 1.5 µmol / min (6.7 ± 0.2 and 7.4 ± 0.3 mg / min), respectively (P> 0.05).
The mathematical model (Fig. 1, B, lines 1 and 2) in the range of 90-360 minutes reproduces satisfactorily the experimental results.
ImportantlyInterestingly, this wasis achieved usingat the same values of parameters of the model except for a slight correction (25% reduction of parameter X1max, simulating a maximum volume of the stomach) in the case of consumption of glucose solution with concentration of 400 g / L.
2. Dynamics of free consumption of glucose solution (200 g / l) by rats in presence of phloridzin in the solution.
Phloridzin - a competitive inhibitor of active transport of glucose - causes a decrease in the ability of the small intestine for absorption of the monosaccharide [7]. If the hypothesis about a correlation between the rate of consumption of glucose and absorptive capacity of the small intestine is correct, then, in the case ofafter adding phloridzin to glucose solution, one should expect a decrease in the rate of its consumption of this solution.
To test this hypothesis, rats, after preliminary experiments were divided into two groups (N1 = N2 = 8) with close values of average consumption rates of glucose solution of 200 g / L: 65.0 ± 3.4 and 63.4 ± 3.0 µL / min in groups 1 and 2 corresponbdingly.
After 5 days, a consumption of glucose solution by the same animals was been recording in presence of 1 mM phloridzin 1 mM in the glucose solution (experiment – Group 1) or without phloridzin (control– Group 2). As shown in Fig. 2, A, when the inhibitor of active glucose transport was added to the solution the rate of its consumption by the rats in group 1 was 54.0 ± 1.6 µL / min and was significantly lower compared to the control: 69.7 ± 2.2 µL / min (P <0.003), confirming the hypothesis mentioned above.
In the mathematical model the change of absorptive capacity of the small intestine was simulated by the change in parameter SJmax – the sum of the maximum rates of active glucose transport in all compartments (2–21). When SJmax = 106.4 and 145.1 µmol / min with a minor correction of parameter X1max (6.3 instead of 6.7 ml), and other variables being constant, the model satisfactorily reproduces the experimental data obtained on rats in groups 1 and 2 correspondingly (Fig. 2, A, lines 1 and 2).
Thus, the experimentally observed 1.3 times reduction of glucose( 200 g / L) consumption rate of glucose 200 g / L by the rats after the addition of phloridzin may be due to a decrease of the total transport activity of the mucosa of the small intestine. This confierms a correlation between the capacity of the small intestine to for glucose absorbption glucose from the lumen and the rate of free consumption of its concentrated solution by rats.