Steady-state brain glucose transport kinetics re-evaluated with a four-state conformational model

Abstract

Glucose supply from blood to brain occurs through facilitative transporter proteins. A near linear relation between brain and plasma glucose has been experimentally determined and described by a reversible model of enzyme kinetics. A conformational four-state exchange model accounting for trans-acceleration and asymmetry of the carrier was included in a recently developed multi-compartmental model of glucose transport. Based on this model, we demonstrate that brain glucose (G(brain)) as function of plasma glucose (G(plasma)) can be described by a single analytical equation namely comprising three kinetic compartments: blood, endothelial cells and brain. Transport was described by four parameters: apparent half saturation constant K(t), apparent maximum rate constant T(max), glucose consumption rate CMR(glc), and the iso-inhibition constant K(ii) that suggests G(brain) as inhibitor of the isomerisation of the unloaded carrier. Previous published data, where G(brain) was quantified as a function of plasma glucose by either biochemical methods or NMR spectroscopy, were used to determine the aforementioned kinetic parameters. Glucose transport was characterized by K(t) ranging from 1.5 to 3.5 mM, T(max)/CMR(glc) from 4.6 to 5.6, and K(ii) from 51 to 149 mM. It was noteworthy that K(t) was on the order of a few mM, as previously determined from the reversible model. The conformational four-state exchange model of glucose transport into the brain includes both efflux and transport inhibition by G(brain), predicting that G(brain) eventually approaches a maximum concentration. However, since K(ii) largely exceeds G(plasma), iso-inhibition is unlikely to be of substantial importance for plasma glucose below 25 mM. As a consequence, the reversible model can account for most experimental observations under euglycaemia and moderate cases of hypo- and hyperglycaemia.

Keywords: GLUT; blood-brain-barrier; glucose transport; mathematical modelling.

Figure 1

(A) Schematizes the alternating-conformation kinetics of the glucose carrier. In the absence of glucose (G_out or G_in), the carrier can exist in two inter-converting isomers that are ready to bind glucose either outside (C_out) or inside (C_in) the membrane. When loaded, the carrier can also assume two isomeric forms favouring glucose release to the outer (C_outG) or inner (C_inG) side of the membrane. The rate constants k₁ and k₋₃ define glucose binding while k₋₁ and k₃ define its dissociation from the carrier. The rate constants k₂ and k₋₂ or k₄ and k₋₄ reflect the isomerisation of the loaded or unloaded carrier. Panel (B) Shows the simplest model of bidirectional glucose transport (T^f and T^r) represent the forward and reverse fluxes of glucose diffusion) through a BBB that was considered as a single membrane. In panel (C), the compartment composed by the endothelial cells was included and thus four unidirectional fluxes (T) are required to describe glucose flow through the BBB. The glucose consumption rate CMR_glc was considered as a metabolic compartment in the system.

Figure 2

Brain glucose concentration as function of plasma glucose concentration in three different studies. (A) Human brain, in Gruetter et al. (1998); (B) rat brain (under α-chloralose anaesthesia), in Choi et al. (2002); (C) rat brain, in Morgenthaler et al. (2006). The data sets were analysed with the reversible (solid lines) and the conformational four-state exchange (dashed lines) models (see kinetic parameters in Table 1). In these experimental conditions and for the range of glucose concentrations studied, the reversible MM model is clearly able to describe the brain-blood glucose relationship, with the advantage of requiring the estimation of only two kinetic parameters.

Figure 3

Brain glucose concentration as function of plasma glucose concentration in two extreme cases, when the experimental curve is ill-defined at lower (A) or higher (B) plasma glucose concentrations. In panel (A), the model takes the form of the standard MM model (results from the whole rat brain reported in Lei and Gruetter, 2006); in panel (B), the model superimposes the reversible MM model (results from the rat cortex reported in Poitry-Yamate et al., 2009).