A model for single-substrate trimolecular enzymatic kinetics

Abstract

We developed a kinetic model for a single-substrate trimolecular enzymatic system, where a receptor binds and stretches a substrate to expose its cleavage site, allowing an enzyme to bind and cleave it into product. We demonstrated that the general kinetics of the trimolecular enzymatic system is more complex than the Michaelis-Menten kinetics. Under a limiting condition when the enzyme-substrate binding is in fast equilibrium, the enzymatic kinetics of the trimolecular system reduces to the Michaelis-Menten kinetics. In another limiting case when the receptor dissociates negligibly slowly from the substrate, the trimolecular system is simplified to a bimolecular system, which follows the Michaelis-Menten equation if and only if there is no enzyme-substrate complex initially. We applied this model to a particular trimolecular system important to hemostasis and thrombosis, consisting of von Willebrand factor (substrate), platelet glycoprotein Ibalpha (receptor), and ADAMTS13 (enzyme). Using parameters from independent experiments, our model successfully predicted published data from two single-molecule experiments and fitted/predicted published data from an ensemble experiment.

Figure 1

Model for binding and enzymatic kinetics of the GPIbα-VWF-ADAMTS13 trimolecular system. The k_f, k_r, k_u, k_c, k₊₁, and k_-1 are kinetic rates (see text for details). VWF^∗ and ^∗VWF present the cleaved VWF products. Three states of VWF are highlighted in different colors. Dashed box includes the kinetic processes of GPIbα-VWF binding and VWF unfolding, which is added to the main model only for treating the experiment of agglutination of platelet-VWF.

Figure 2

Probability density of the lifetimes of the tethered platelets, f(t), plotted versus k₋₁, the dissociation rate of the ADAMTS13-VWF interaction (A), k_c, the cleavage rate of VWF by ADAMTS13 (B), k_r, the dissociation rate of the GPIbα-VWF interaction (C), and c, the ADAMTS13 concentration (D).

Figure 3

Randomness parameter r versus ADAMTS13 concentration c with k₊₁ = 0.001 nM⁻¹ s⁻¹, k₋₁ = 0.01 s⁻¹, k_c = 3 s⁻¹, and k_r = 3 s⁻¹.

Figure 4

Comparison between the predicted and measured enzymatic kinetics of a VWF-ADAMTS13 bimolecular system. Predictions were calculated from Eqs. 10 (solid curve) and 14 (dashed curve) with measured kinetic rates (K_M = 1.61 μM, k_c = 0.14 s⁻¹, and K_D = 20 nM) from Zanardelli et al. (16). Experimental data (points, mean ± SE) are from Zhang et al. (5).

Figure 5

Comparison between the calculated and measured enzymatic kinetics of a GPIbα-VWF-ADAMTS13 trimolecular system. Predictions (solid curves) and fitting (dashed curves) of the averages (A) and the standard deviations (B) of lifetimes were calculated by Eqs. 7 and 16. For predictions, the kinetic rates (K_M = 5.81 μM, k_c = 4.43 s⁻¹, K_D = 4.6 nM) are from the literature (14,15) and the GPIbα-VWF dissociation rate (k_r = 3.06 s⁻¹) is from Wu et al. (6). Experimental data (points, mean ± SE) are also from Wu et al. (6).

Figure 6

Comparison of platelet agglutination between calculations (curves) and experiments (points). Calculations are based on Eqs. 21 and 22. The kinetic rates (K_M = 5.81 μM, k_c = 4.43 s⁻¹, K_D = 4.6 nM) are from the literature (14,15). Experimental data and parameters (L = 20 mm, h = 0.25 mm, c = 33.35 nM, N_p = 10⁸ mL⁻¹, R_b = 3 μm, and R_p = 1 μm) are from Yago et al. (17).