Kinetic Analysis of Antithrombin Inhibition

Second order association rate constants for antithrombin inhibition of proteases in the absence and presence of saturating pentasaccharide were measured under pseudo-first order conditions as in the kinetic titrations. Reactions of antithrombin with thrombin were done only in the absence of pentasaccharide in 20 mM sodium phosphate, 0.1 mM EDTA, 0.1% PEG 8000, pH 6.0 at 25°C. Reaction mixtures (100 μl) containing fixed concentrations of antithrombin and thrombin were incubated for varying times and then quenched with 900 μl 100 μM S-2238 substrate in 10.15 sodium phosphate buffer, pH 7.4 and residual thrombin activity measured from the initial rate of substrate hydrolysis at 405 nm. Reactions of antithrombin with factor Xa or with factor IXa were conducted in 20 mM MES, 5 mM CaCl₂, 0.1% PEG 8000, pH 6.0 at 25°C in the absence and presence of the natural pentasaccharide. For reactions in the absence of pentasaccharide, fixed antithrombin and factor Xa or factor IXa concentrations were incubated for varying times or fixed protease and varying antithrombin concentrations were incubated for a fixed reaction time in 50–100 μl and then quenched with 1 ml chromogenic substrate to measure residual protease activity from the initial rate of substrate hydrolysis at 405 nm. The factor Xa substrate was 100 µM Spectrozyme FXa and the factor IXa substrate was 300 μM Pefachrome FIXa, both in 0.1 M Hepes, 0.1 M NaCl, 0.1 mM EDTA, 0.1% PEG 8000, pH 7.4. Factor IXa substrate solutions were supplemented with 33% ethylene glycol and 10 mM CaCl₂ to enhance factor IXa activity (39 (link)). The loss in protease activity as a function of time or as a function of antithrombin concentration was fit by the exponential function:
$${\text{v}}_{\text{obs}}={\text{v}}_{\mathrm{o}}\hspace{0.33em}\text{x}\hspace{0.33em}\text{exp-}\left({\text{k}}_{-\text{H}}\text{x}{\left[\text{AT}\right]}_{\text{o}}\text{x}\hspace{0.33em}\text{t}\right)$$
where v_obs and v_o are the observed velocity of substrate hydrolysis by protease after inhibitor reaction and control velocity without inhibitor, respectively, and k_−H is the second order association rate constant for the free antithrombin reaction. Dividing the fitted exponential constant by the antithrombin concentration when time was varied or by the fixed time when the antithrombin concentration was varied then yielded k_−H.
For reactions in the presence of pentasaccharide, fixed concentrations of antithrombin, protease and saturating pentasaccharide were reacted for varying times or varying antithrombin concentrations were reacted with fixed concentrations of protease and saturating pentasaccharide for a fixed reaction time in 50–100 μl and then quenched with 1 ml chromogenic substrate to measure residual protease activity at 405 nm. The loss of protease activity as a function of time or as a function of antithrombin concentration was fit by the exponential equation above with k_-H replaced by k_H, the second order association rate constant for the antithrombin-heparin complex reaction. Dividing the fitted exponential constant by the antithrombin concentration when time was varied or by the fixed time when the antithrombin concentration was varied yielded k_H. Alternatively, fixed concentrations of antithrombin and protease were reacted with varying subsaturating pentasaccharide concentrations ([H]_o « [AT]_o) for a fixed reaction time. Fitting the loss of protease activity as a function of pentasaccharide concentration by an exponential function in this case gives a fitted exponential constant that must be divided by the product of the fixed reaction time and the factor, [AT]_o/(K_D,obs + [AT]_o), to correct for the fraction of antithrombin that is complexed with pentasaccharide so as to obtain k_H(19 (link)).