Mechanistic interpretation of conventional Michaelis-Menten parameters in a transporter system

Abstract

The aim was to elucidate how steps in drug translocation by a solute carrier transporter impact Michaelis-Menten parameters Km, Ki, and Vmax. The first objective was to derive a model for carrier-mediated substrate translocation and perform sensitivity analysis with regard to the impact of individual microrate constants on Km, Ki, and Vmax. The second objective was to compare underpinning microrate constants between compounds translocated by the same transporter. Equations for Km, Ki, and Vmax were derived from a six-state model involving unidirectional transporter flipping and reconfiguration. This unidirectional model is applicable to co-transporter type solute carriers, like the apical sodium-dependent bile acid transporter (ASBT) and the proton-coupled peptide cotransporter (PEPT1). Sensitivity analysis identified the microrate constants that impacted Km, Ki, and Vmax. Compound comparison using the six-state model employed regression to identify microrate constant values that can explain observed Km and Vmax values. Results yielded some expected findings, as well as some unanticipated effects of microrate constants on Km, Ki, and Vmax. Km and Ki were found to be equal for inhibitors that are also substrates. Additionally, microrate constant values for certain steps in transporter functioning influenced Km and Vmax to be low or high.

Keywords: Apical sodium-dependent bile acid transporter; Michaelis–Menten; Model; Transporter.

Fig 1

Six-state model for unidirectional transporter-mediated substrate translocation in the presence of inhibitor. This model is more briefly denoted the six-state model. The model entails that free drug outside of the cell (S_o) binds with free transporter at exo-face (Y_o) in order to be translocated to be free drug inside of cell (S_in). Three steps are needed for substrate flux: free drug binding to transporter, re-configuration of drug-transport complex from exo-facial oriention to endo-facial oriention, and release of drug intracellularly from transporter. In a fourth forward step, free transporter is re-configured from endo-facially oriented to its initial free, exo-facially oriented configuration. In this model, only unidirectional protein flipping that involves substrate (or inhibitor) translocation or free protein re-configuration is allowed. The model also allows free inhibitor outside of the cell (I_o) to compete for Y_o by an identical process, forming I_in inside the cell. Eqn 10 is the general solution for net transporter-mediated drug flux from outside of cell to the inside of cell when S_in = 0. Subscript o denotes outside of cell or on exo-face (i.e. left side). Subscript in denotes inside of cell or on endo-face (i.e. right side). Each microrate constant except k₋₃ and k₋₇ impacted Km, Ki, and/or Vmax.

Fig 2

ASBT Ki vs Km values of 50 compounds from previous studies (9, 10, 11, 13). Each compound is an ASBT substrate and inhibitor. The trend line shown represents Ki=Km. In Panel A, all 50 compounds are shown, while Panel B is an enlarged view of Km and Ki < 30 µM.

Fig. A1

Six-state model for facilitative transporter-mediated substrate translocation in the presence of inhibitor. Compared to Fig. 1, this model for facilitative transporter-mediated substrate translocation is more complex in that all steps are reversible. Eqn S10 (supplementary material) is the general solution for net transporter-mediated drug flux from outside of cell to the inside of cell when S_in = 0. Subscript o denotes outside of cell or on exo-face (i.e. left side). Subscript in denotes inside of cell or on endo-face (i.e. right side). Each microrate constant except k₋₃ and k₋₇ impacted Km, Ki, and/or Vmax.