The simple model of adipocyte hexose transport. Kinetic features, effect of insulin, and network thermodynamic computer simulations

Network thermodynamics and complexity: a transition to relational systems theory

Most systems of interest in today's world are highly structured and highly interactive. They cannot be reduced to simple components without losing a great deal of their system identity. Network thermodynamics is a marriage of classical and non-equilibrium thermodynamics along with network theory and kinetics to provide a practical framework for handling these systems. The ultimate result of any network thermodynamic model is still a set of state vector equations. But these equations are built in a new informative way so that information about the organization of the system is identifiable in the structure of the equations. The domain of network thermodynamics is all of physical systems theory. By using the powerful circuit simulator, the Simulation Program with Integrated Circuit Emphasis (SPICE), as a general systems simulator, any highly non-linear stiff system can be simulated. Furthermore, the theoretical findings of network thermodynamics are important new contributions. The contribution of a metric structure to thermodynamics compliments and goes beyond other recent work in this area. The application of topological reasoning through Tellegen's theorem shows that a mathematical structure exists into which all physical systems can be represented canonically. The old results in non-equilibrium thermodynamics due to Onsager can be reinterpreted and extended using these new, more holistic concepts about systems. Some examples are given. These are but a few of the many applications of network thermodynamics that have been proven to extend our capacity for handling the highly interactive, non-linear systems that populate both biology and chemistry. The presentation is carried out in the context of the recent growth of the field of complexity science. In particular, the context used for this discussion derives from the work of the mathematical biologist, Robert Rosen.

Accelerated net efflux of 3-O-methylglucose from rat adipocytes: a reevaluation

In a study of 3-O-methylglucose transport in insulin-stimulated rat adipocytes (catalyzed primarily by the GLUT4 isoform), it was reported that at 37 degrees C the Km and Vmax were 2.8-fold higher for net efflux than for equilibrium exchange (Vinten, J. (1984) Biochim. Biophys. Acta 772, 244-250). Because of its implications for the relative sizes of steps in the transport cycle, we reinvestigated this phenomenon. Accelerated net efflux was apparent when the extracellular methylglucose was diluted 26-fold but not when it was diluted 11-fold. When analyzed according to the one-site alternating conformation model, the data indicate about a 1.7-fold higher Vmax for efflux than for exchange, only about 40% of the difference reported previously. Together with other results in the literature, the accelerated net flux indicates that the conformational change of the loaded transporter from its outward-facing to its inward-facing form is likely the slowest step in the transport cycle, in contrast to the case for GLUT1. Experiments at 25 degrees C indicate a lower degree of accelerated net flux than at 37 degrees C. This is consistent with the above conformational change being the step with the lowest activation energy, as for GLUT1.

Mathematical model supporting the superoxide theory of oxygen toxicity

The discovery of superoxide dismutase was followed by a proposal that superoxide anion radical (O2.-) is a major factor in oxygen toxicity. The knowledge of superoxide chemistry, however, led some chemists to conclude that since O2.- is not very reactive in aqueous solution, the more reactive hydroxyl radical (HO.) was most likely to be the major damage causing species. Some have defended the superoxide theory by emphasizing that nonindiscriminate and selective reactivity could provide more toxicity than would high, indiscriminate reactivity. In the present study, network thermodynamic simulation was used to create a situation in which O2.- would selectively react with a substrate in a hypothetical sequence of subreactions supporting biological processes. In this situation, when the simulation of the chemical reactions was carried out using reasonable parametric values found in the literature, the selective reaction of O2.- to one molecule in the sequence caused a 95% disruption of the observable process, whereas indiscriminately targeted HO. attack caused only 0 to 35% inhibition. The major cause of the weak effect of HO. was found, in this particular model, to be a lack of sufficient availability of HO. due to both its slow generation by the Fenton reaction and a large demand for reactions with inconsequential targets. This model supports the superoxide theory of oxygen toxicity by demonstrating that a simple set of circumstances can quantitatively lead to the proposed selective superoxide toxicity. The present study also advocates the use of novel network thermodynamic simulation techniques for solving problems concerning biological oxidants and antioxidants.

Coupling of glucose transport and phosphorylation in Xenopus oocytes and cultured cells: determination of the rate-limiting step

The initial events in glucose metabolism by all cells are the transport and phosphorylation of glucose. To quantify the relative contributions of these two processes to overall glucose utilization, we have developed an experimental approach for their in situ measurement as parallel processes. The method is based on the use of intracellular [2-3H]glucose as a substrate for both the transporter and hexokinase, and involves simultaneous measurement of [2-3H]glucose efflux and of 3H2O released by phosphorylation. The Xenopus oocyte expression system was used to test the method, since in these cells transport and phosphorylation activities can be regulated by expression of mRNA or injection of foreign protein. Oocytes microinjected with [2-3H]glucose showed no release of injected glucose, but did have saturable phosphorylation kinetics, with a Km of 40 microM and a Vmax of 0.1 nmol/min/oocyte. Co-injection of yeast hexokinase increased glucose phosphorylation by five-fold. Expression of human glucose transporter (GLUT1) mRNA resulted in a 25-30-fold increase in the rate of saturable efflux of microinjected glucose compared to control oocytes. The kinetics of transport and phosphorylation of [2-3H]glucose were analyzed by a multiple curve-fitting program that provided estimates of kinetic coefficients for both processes from a single time course. The analysis showed that expression of GLUT1 shifted the rate-limiting step in glucose utilization from transport to phosphorylation. A similar shift occurred at a three-fold lower extracellular concentration of 2-deoxyglucose. In a pancreatic beta cell line both transport and phosphorylation showed high Km values, with phosphorylation as the limiting step. The in situ measurement of glucose transport and phosphorylation as parallel processes should be useful in defining the relative contributions of each step to overall glucose metabolism in other cell and tissue models.

The one-site model of human erythrocyte glucose transport: testing its predictions using network thermodynamic computer simulations

Network thermodynamic computer simulations were carried out using parameters experimentally derived by Lowe and Walmsley ((1987) Biochim. Biophys. Acta 903, 547-550) for two tests of the one-site model of human erythrocyte glucose transport. In the temperature-jump experiment, the simulations predicted the amplitude and relaxation time of accelerated uptake, but underestimated the net uptake due to an unexpectedly low measured basal rate. In the maltose-acceleration experiment, the dissociation constant of maltose was assessed at 0 degrees C by measuring the inhibitory effects of maltose on both cytochalasin B binding and on 3-O-methylglucose uptake, and using this value (52 mM) to calculate the dissociation constant (2.9 mM). The simulated experiment then did show a transient acceleration in uptake comparable in magnitude to that observed experimentally, except that the relaxation time was more than 10-fold longer in the simulations. Measurements of the temperature dependence of the inhibition of cytochalasin B binding by maltose and 3-O-methylglucose indicated that apparent sugar affinity is sensitive to carrier orientation at low temperatures, whereas at more physiologic temperatures the intrinsic dissociation constant predominated.

Entropy as a factor in the binding of gamma-aminobutyric acid and nipecotic acid to the gamma-aminobutyric acid transport system

Nipecotic acid is one of the most potent competitive inhibitors and alternative substrates for the high-affinity gamma-aminobutyric acid transport system in neurons, but the structural basis of this potency is unclear. Because gamma-aminobutyrate is a highly flexible molecule in solution, it would be expected to lose rotational entropy upon binding to the transport system, a change which does not favor binding. Nipecotic acid, in contrast, is a much less flexible molecule, and one would expect the loss of conformational entropy upon binding to be smaller thus favoring the binding of nipecotic acid over gamma-aminobutyric acid. To investigate this possibility, the thermodynamic parameters, delta G degrees, delta H degrees, and delta S degrees, were determined for the binding of gamma-aminobutyrate and nipecotic acid to the high affinity GABA transport system in synaptosomes. In keeping with expectations, the apparent entropy change for nipecotic acid binding (112 +/- 13 J.K-1) was more favorable than the apparent entropy change for gamma-aminobutyric acid binding (61.3 +/- 6.6 J.K-1). The results suggest that restricted conformation per se is an important contributory factor to the affinity of nipecotic acid for the high-affinity transport system for gamma-aminobutyric acid.

Network thermodynamic analysis and stimulation of isotonic solute-coupled volume flow in leaky epithelia: an example of the use of network theory to provide the qualitative aspects of a complex system and its verification by stimulation

A network thermodynamic model was developed to provide insights into the nature of isotonic solute-coupled volume flow in "leaky" epithelia, where the transepithelial volume flow is assumed to be primarily through the cellular pathway. The coupled flows of solute and volume at each membrane in this four membrane model are described by the practical phenomenological equations as developed by Kedem & Katchalsky (1958). The model contains one permeable non-electrolyte solute (s) and a fixed amount of an impermeable non-electrolyte (i) inside the cell. The cell is assumed to be capable of volume regulation under the steady-state experimental conditions simulated. A solute-pump, located in the basolateral membrane, uses feedback regulation to adjust Cs in the cell in order to maintain cell volume at or near control levels in all simulations. Model behavior is, in general, very consistent with experimental observations with respect to tonicity and magnitude of volume flow over a wide range of experimental conditions. Examination of the parameter space suggests the following important features when isotonic solute-coupled volume flow moves primarily through the cellular pathway: (1) the apical membrane reflection coefficient must be less than that of the basolateral membrane; (2) the basement membrane reflection coefficient must be small; (3) the apical membrane solute permeability and reflection coefficient are the two most "sensitive" parameters and need to vary in an inverse manner in order to maintain isotonicity when both solute and volume flows increase; and (4) relationships (1) and (3) above imply the need for at least two separate solute pathways in the apical membrane, one that is shared with volume flow and one that is not.

Photolabeling of the adipocyte hexose carrier with an aryl azide derivative of maltose

A nitrophenyl azide derivative of maltose, N-(4-azido-2-nitrophenyl)-maltosylamine (NAP-maltosylamine), was synthesized as a potential photoaffinity label for the hexose carrier of the rat adipocyte. This derivative inhibited 3-O-methylglucose uptake with a Ki of 1.3 mM in the dark, while that of maltose was 10.0 mM. Carbon-14-labeled maltose and NAP-maltosylamine entered adipocytes via the hexose carrier, the latter in a concentrative fashion. Photolysis of NAP-[14C]maltosylamine in the presence of an adipocyte low density microsomal membrane fraction labeled several electrophoretic bands. Among these are a 45 kDa band which showed features expected of the hexose carrier: its labeling was decreased 40% by D- but not L-glucose and pretreatment of intact adipocytes with insulin decreased labeling of the 45 kDa band by 10-40%, as predicted by the translocation theory of insulin-stimulated transport activation. These studies show the suitability of using carbon-1-modified sugar photoaffinity labels as probes for the hexose carrier and possibly of its regulation in rat adipocytes.

Binding of polycation DEAE-dextran to Chinese hamster ovary cells induces reversible Ca2+ influx and inhibits capping of concanavalin A acceptor proteins

Binding of the polycation DEAE-dextran to the cell surface of HA-1 CHO cells caused a marked increase in 45Ca2+ exchange influx. The effect was fairly selective for Ca2+, undirectional (efflux was not increased) and was rapidly reversed by treatment with polyanion dextran sulfate. 45Ca2+ influx could not be stimulated by treatment with multivalent lectins or fibronectin. In addition to stimulating 45Ca2+ flux, DEAE-dextran inhibited the capping of concanavalin-A acceptor proteins. Inhibition of capping occurred over the same DEAE-dextran concentration range (20-200 micrograms/ml) which stimulated 45Ca2+ uptake, possibly implicating increased cellular [Ca2+] in the inhibition of concanavalin A acceptor protein capping in this cell type. The profound effect of DEAE-dextran on cellular Ca2+ uptake and the rapid reversal of the effect by dextran sulfate might make the polycation a useful agent for the induction of transient increases in cellular [Ca2+].

Exploration of apical sodium transport mechanisms in an epithelial model by network thermodynamic simulation of the effect of mucosal sodium depletion: I. Comparison of three different apical sodium permeability expressions

A model based on that of Koefoed-Johnsen & Ussing (1958) and elaborated by Hviid Larsen (1978) and Lew et al. (1979), is designed using network thermodynamic theory and used to simulate experiments performed on epithelia. Three different expressions for the apical sodium permeability are tested for their ability to reproduce the saturation of the short-circuit current with increasing mucosal sodium concentration. Using the parameters from the previous models, the sodium entry step is shown to be the rate limiting step. If the apical sodium permeability is constant, there is no saturation of the short-circuit current with increasing mucosal sodium. The saturation of the short-circuit current is simulated with versions of the model which include a variable apical sodium permeability. The phenomenological expressions used for the variable permeabilities are those proposed by Fuchs et al. (1977) and Civan & Bookman (1982). They describe the so-called feedback effect of the mucosal and intracellular sodium concentrations.

Fluid-phase endocytosis by isolated rat adipocytes

We have developed an assay, which uses radiolabeled sucrose as the marker, to measure the rate of fluid-phase endocytosis in isolated rat adipocytes. In addition, the assay was adapted to allow measurement of the release of sucrose from previously loaded cells (fluid-phase exocytosis). Adipocytes take up sucrose at an approximately linear rate for at least 1.5 hours. A portion of the pinocytosed sucrose is rapidly (half-time about 20 minutes) returned to the medium. The minimal value for fluid uptake by endocytosis is 57 nl/10(6) cells-h at 37 degrees C; this value corresponds to the formation of 110,000 endocytic vesicles of 100-nm diameter per cell per hour and the internalization of about 20% of the plasma membrane per hour. Insulin caused a small and variable increase in the rate of sucrose uptake. The average increase of 31% from 11 experiments is statistically significant at the level of P less than 0.01. A small insulin effect upon the uptake of the calcium complex of [14C]EDTA was also observed. Since this complex was taken up at 2.5 times the rate of sucrose, it probably entered by a combination of fluid-phase and adsorptive pinocytosis. Insulin did not elicit a significant change in the rate of sucrose release from preloaded cells.

Pharmacokinetic–pharmacodynamic modelling and simulation using the electrical circuit simulation program spice2

The use of the electrical circuit simulation program SPICE2 for performing digital computer simulations of linear and non-linear pharmacokinetic-pharmacodynamic models is described. SPICE2 utilizes the principles of network thermodynamics (thermodynamics of electrical circuits). These principles dictate analogy between the conservation laws of chemical reactions and mass transport and Kirchhoff's laws of current and voltage balance, and also prove that Fick's law of diffusion is isomorphous with the conductance form of Ohm's law. Detailed descriptions of program inputs, formats, and options for simulation of linear and non-linear pharmacokinetic-pharmacodynamic systems are provided, with appropriate examples. Single as well as multiple dose simulations (accumulation kinetics and dynamics) are discussed. The advantages of SPICE2 over other available simulation packages, including user-friendliness, ease of operation, versatility, power, and the economy of time and effort afforded, are emphasized. The educational value of SPICE2 as a highly versatile tool for teaching both fundamental and complex pharmacokinetic-pharmacodynamic concepts, as well as its routine usage in elucidating complex research problems, are also discussed.

Plasma ascorbate concentrations and blood cell dehydroascorbate transport in patients with diabetes mellitus

Rates of dehydroascorbate uptake by blood granulocytes and mononuclear cells are slower, and plasma ascorbate concentrations are lower, among persons with diabetes mellitus than in nondiabetic subjects. These measurements do not correlate with one another or with simultaneously measured plasma glucose or glycosylated hemoglobin; they do not differ with type of diabetes or mode of treatment. In those diabetic granulocytes that exhibit slow dehydroascorbate uptake, maximal velocity (Vmax) transport rates for dehydroascorbate, 2-deoxyglucose, and 3-O-methylglucose are decreased, each to the same degree, while Km values for transport of these ligands are not different from those observed in nondiabetic cells. Since diffusion of these ligands is facilitated by a common transporter, these observations may reflect decreased numbers of glucose transporters in the plasma membranes of some diabetic leukocytes.