Kinetics of low-density lipoprotein receptor activity in Hep-G2 cells: derivation and validation of a Briggs–Haldane-based kinetic model for evaluating receptor-mediated endocytotic processes in which receptors recycle

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Abstract
The process of receptor-mediated endocytosis for receptors that recycle to the cell surface in an active form can be considered as being kinetically analogous to that of a uni-substrate, uni-product enzyme-catalysed reaction. In this study we have derived steady-state initial-velocity rate equations for this process, based on classical Briggs–Haldane and King–Altman kinetic approaches to multi-step reactions, and have evaluated this kinetic paradigm, using as a model system the low-density lipoprotein (LDL)-receptor-mediated endocytosis of the trapped label [14C]sucrose-LDL in uninduced, steady-state Hep-G2 cells. Using the derived rate equations, together with experimentally determined values for Bmax (123 fmol/mg of cell protein), Kd (14.3 nM), the endocytotic rate constant ke (analogous to kcat; 0.163 min-1), Km (80 nM) and maximal internalization velocity (26.4 fmol/min per mg), we have calculated the ratio ke/Km (0.00204 nM-1·min-1), the bimolecular rate constant for LDL and LDL-receptor association (0.00248 nM-1·min-1), the first-order rate constant for LDL–LDL-receptor complex dissociation (0.0354 min-1), the total cellular content of LDL receptors (154 fmol/mg of cell protein), the intracellular LDL receptor concentration (30.7 fmol/mg of cell protein) and the pseudo-first-order rate constant for LDL receptor recycling (0.0653 min-1). Based on this mathematical model, the kinetic mechanism for the receptor-mediated endocytosis of [14C]sucrose-LDL by steady-state Hep-G2 cells is one of constitutive endocytosis via independent internalization sites that follows steady-state Briggs–Haldane kinetics, such that LDL–LDL-receptor interactions are characterized by a rapid-high-affinity ligand–receptor association, followed by ligand–receptor complex internalization that is rapid relative to complex dissociation, and by receptor recycling that is more rapid than complex internalization and that serves to maintain 80% of cellular LDL receptors on the cell surface in the steady-state. The consistency with which these quantitative observations parallel previous qualitative observations regarding LDL-receptor-mediated endocytosis, together with the high correlation between theoretical internalization velocities (calculated from determined rate constants) and experimental internalization velocities, underscore the validity of considering receptor-mediated endocytotic processes for recycling receptors in catalytic terms.