Simulations

Figure 3.14 shows the results of mathematical modeling experiments that simulate the ALIS response for a protein-ligand complex versus time when subjected to changes in inhibitor concentration and variation in other parameters. Figure 3.14A models a system consisting of 5 mM protein and 1 mM ligand with typical association and dissociation rates (kS-on = 0.1 mM-1 s-1, kS-off = 0.01 s-1, kI-off = 0.01 s-1) to which has been added a large excess of inhibitor by 1:1 dilution of the original, equilibrated protein-ligand mixture with 100 mM inhibitor while keeping the total ligand concentration constant. This would be a typical experimental implementation of the ''cold quench'' method for determining protein-ligand dissociation rates using ALIS. As mentioned above, the rate at which the inhibitor competes with the ligand for the protein depends upon both the dissociation rate of the protein-ligand complex and the rate of association of the inhibitor and protein; this figure shows the expected ALIS protein-ligand recovery for inhibitors of varying association rate. Dilution of the protein with a non-associating inhibitor (kI-on = 0) containing an equal total concentration of

Fig. 3.14 Simulated ALIS-based dissociation rate measurements. See text for details. (A) Quench experiments modeled at varying inhibitor association rates. Even with a very slow-binding inhibitor, the decay curve resembles pure first-order dissociation kinetics. (B) Data in (A), shown on a log axis. (C) Simulated ALIS quench experiment with varying protein-ligand dissociation rates, showing how the method can be used to rank compounds by off-rate. (D) Correlation between the modeled ALIS quench experiment and the theoretical decay curve expected from infinite dilution. The modeled decay curve (solid line) is shown for koff = 0.01 s"1 and theoretical curves (dashed lines) are shown for rates ±10% of this value.

Fig. 3.14 Simulated ALIS-based dissociation rate measurements. See text for details. (A) Quench experiments modeled at varying inhibitor association rates. Even with a very slow-binding inhibitor, the decay curve resembles pure first-order dissociation kinetics. (B) Data in (A), shown on a log axis. (C) Simulated ALIS quench experiment with varying protein-ligand dissociation rates, showing how the method can be used to rank compounds by off-rate. (D) Correlation between the modeled ALIS quench experiment and the theoretical decay curve expected from infinite dilution. The modeled decay curve (solid line) is shown for koff = 0.01 s"1 and theoretical curves (dashed lines) are shown for rates ±10% of this value.

ligand as the equilibrated protein-ligand mixture causes the total protein and protein-ligand complex concentrations to initially drop to 50% of their original value, then (in the absence of active inhibitor) the system restores itself to a new equilibrium. However, in the presence of an excess of an associating inhibitor (ki-on 0 0) any free protein is rapidly quenched by the inhibitor, so no protein-ligand complex ES can re-form. Therefore, as soon as any protein-ligand complex ES spontaneously dissociates, the rate of which depends upon kS-off, the freed protein is quenched by the excess of inhibitor. As such, the measurable concentration of the protein-ligand complex will diminish with time after addition of an excess of inhibitor. it can be seen that even with a very slow-binding inhibitor (kI-on = 0.001 jmM"1 s-1) the slope of the decay curve approaches that of the integrated rate expression resulting from pure first-order dissociation kinetics (for example, under conditions of infinite dilution):

3.6 Protein-Ligand Dissociation Rate Measurement | 147 [ES] = [ESy^ (19)

Since the decay follows an exponential function, the similarity between the simulated decay curve slopes and the theoretical, infinite dilution ideal is even more apparent when the plots are compared in log space, as shown in Fig. 3.14B.

The utility of this method for measuring and comparing multiple ligands' dissociation rates is demonstrated by the simulations in Fig. 3.14C. This figure demonstrates a system consisting of 5 mM protein and 1 mM ligand, with a typical protein-ligand association rate and varying protein-ligand dissociation rates, to which has been added a large excess of inhibitor by 1:1 dilution of the original, equilibrated protein-ligand mixture. The model shows that the ALIS quench method can distinguish compounds of varying off-rate.

Figure 3.14D shows the degree of correlation for the rate of decay of the protein-ligand complex in a modeled ALIS quench experiment and the theoretical decay curve expected from infinite dilution. The modeled decay curve is shown for kS-off = 0.01 s_1 and theoretical curves are shown for dissociation rates +10% of this value. The results indicate that the measured dissociation rate is well within @10% of the actual value, a very good approximation of the actual dissociation rate given the simplicity of this experimental method.

Since the simulated decay curve closely matches the theoretical exponential decay curve expected from pure first-order dissociation kinetics, the experimental data can be fit to this simple function using available curve-fitting algorithms to extract dissociation rate information about each ligand. Following the quench of an equilibrated mixture of a protein and a ligand or ligands of interest, protein-ligand complex concentration values measured by consecutive ALIS experiments yield quantitative estimates of the dissociation rate of each ligand, and the rates of multiple ligands in a mixture can be compared.

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