Simulations of pentasaccharide binding to native and latent forms of antithrombin by the 2-step mechanism of scheme 1 or the 3-step mechanism of scheme 2 were done by numerical integration of the differential equations for these mechanisms using Scientist software (Micromath) and the indicated values for K1, k+2, k−2, k+3, and k−3 in Table 3. These values were chosen based on apparent kinetic parameters obtained in kinetic studies of the binding interactions. For the initial binding step, the forward rate constant, k+1, was set at the diffusion-limited value of 100 μM−1s−1 and the reverse rate constant, k−1, was set at 1000 s−1 to provide a K1 of 10 μM close to the measured value and rapid equilibrium binding (k−1≫k+2). The predicted value for KD was calculated from the kinetic parameters as K1K2/(1+K2) for the 2-step mechanism and K1K2K3/(1+K2K3+K3) for the 3-step mechanism where K1, K2 and K3 equal k−1/k+1, k−2/k+2, and k−3/k+3, respectively [29]. Progress curves for pentasaccharide binding to antithrombin were generated for pentasaccharide concentrations ranging from 0.25–15 μM and fixed antithrombin concentrations of 0.025 μM. The curves for formation of the final complex were fit well by a single exponential function to yield kobs. kobs values were then plotted against the pentasaccharide concentration and fitted by the rectangular hyperbolic equation in the text to generate values for K1,app, k+lim.app, k−lim,app= koff and k+lim,app/K1,app = kon.