Fig 3. Numerical example for induced-fit binding with the rate constants k₊ = 100 μM⁻¹s⁻¹, k₋ = 100 s⁻¹, k_e = 1 s⁻¹, and k_r = 10 s⁻¹.

(a) Relaxation data for the bound complex obtained by numerical integration of the rate equations and subsequent addition of Gaussian noise with amplitude 0.004 μM at the total protein concentration [P]₀ = 1 μM and exemplary total ligand concentrations [L]₀. The black lines represent multi-exponential fits of the data points. (b) to (d) Comparison of k_obs values obtained from multi-exponential fits of numerical relaxation data (points) to our theoretical results for k_obs (lines) at the three different total protein concentrations [P]₀ = 1 μM, 2 μM, and 3 μM and total ligand concentrations [L]₀ between 0.1 μM and 10 μM. The full lines represent fits of Eq (1) for induced-fit binding (blue) and of Eq (6) for conformational-selection binding (orange), with fit parameter values specified in the figure. In these fits, the dissociation constant K_d = 1/11 μM is assumed to be known from equilibrium data. The dashed blue lines are obtained from Eq (1) for the ‘true’ rate constants of the numerical example.