Involvement of heparin chain length in the heparin-catalyzed inhibition of thrombin by antithrombin III.

The mechanism of the heparin-promoted reaction of thrombin with antithrombin III was investigated by using covalent complexes of antithrombin III with either high-affinity heparin (Mr = 15,000) or heparin fragments having an average of 16 and 12 monosaccharide units (Mr = 4,300 and 3,200). The complexes inhibit thrombin in the manner of active site-directed, irreversible inhibitors: (Formula: see text) That is, the inhibition rate of the enzyme is saturable with respect to concentration of complexes. The values determined for Ki = (k-1 + k2)/k1 are 7 nM, 100 nM, and 6 microM when the Mr of the heparin moieties are 15,000, 4,300, 3,200, respectively, whereas k2 (2 S-1) is independent of the heparin chain length. The bimolecular rate constant k2/Ki for intact heparin is 3 X 10(8) M-1 S-1 and the corresponding second order rate constant k1 is 6.7 X 10(8) M-1 S-1, a value greater than that expected for a diffusion-controlled bimolecular reaction. The bimolecular rate constants for the complexes with heparin of Mr = 4,300 and 3,200 are, respectively, 2 X 10(7) M-1 S-1 and 3 X 10(5) M-1 S-1. Active site-blocked thrombin is an antagonist of covalent antithrombin III-heparin complexes: the effect is monophasic and half-maximum at 4 nM of antagonist against the complex with intact heparin, whereas the effect is weaker against complexes with heparin fragments and not monophasic. We conclude that virtually all of the activity of high affinity, high molecular weight heparin depends on binding both thrombin and antithrombin III to heparin, and that the exceptionally high activity of heparin results in part from the capacity of thrombin bound nonspecifically to heparin to diffuse in the dimension of the heparin chain towards bound antithrombin III. Increasing the chain length of heparin results in an increased reaction rate because of a higher probability of interaction between thrombin and heparin in solution.

Active site-blocked thrombin is an antagonist of covalent antithrombin 111-heparin complexes: the effect is monophasic and half-maximum at 4 nM of antagonist against the complex with intact heparin, whereas the effect is weaker against complexes with heparin fragments and not monophasic.
We conclude that virtually all of the activity of high affinity, high molecular weight heparin depends on binding both thrombin and antithrombin I11 to heparin, and that the exceptionally high activity of heparin results in part from the capacity of thrombin bound nonspecifically to heparin to diffuse in the dimension of the heparin chain towards bound antithrombin 111. Increasing the chain length of heparin results in an increased reaction rate because of a higher probability of interaction between thrombin and heparin in solution.
* This work was supported in part by grants from the Geconcerteerde Onderzoeksactie (project 80-85/ 3) and Grants HL-22471-05 and HL 14230 (Specialized Center for Research in Atherosclerosis) from the National Heart, Lung and Blood Institute. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "aduertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. Antithrombin I11 (heparin cofactor) is a plasma protein that can inhibit several serine proteinases, including thrombin, factors IXa, Xa, XIa, XIIa, and plasmin (1). Antithrombin I11 is distinguished from other protease inhibitors by the capacity of catalytic amounts of heparin to enhance the rate of enzyme inhibition; the 1:l stoichiometry of the enzymeinhibitor reaction is, however, unaffected (2, 3). Three mechanisms have been proposed to account for the activity of heparin. One involves allosteric activation of antithrombin I11 (3-6) upon binding to heparin (7)(8)(9)(10). A second mechanism (11- 14) operates via enhancement of the reactivity of thrombin with antithrombin I11 by binding of heparin to the enzyme. A third hypothesis proposes that a ternary complex, stabilized at least in part by interaction of both proteins with heparin, is required for enhanced inhibition (15)(16)(17).
The procoagulant enzymes may be divided into two groups on the basis of their kinetics of inhibition by antithrombin I11 in the presence of heparin. In one group, e.g. factors Xa and XIIa, the reaction rate is proportional to the concentration of heparin-antithrombin I11 complex. In the second group, i.e. factor IXa, and thrombin, the inhibition rate increases with increasing heparin concentration but reaches a pseudo-plateau and decreases again at higher heparin concentrations. Furthermore, with thrombin the activity of heparin increases with molecular weight, whereas inhibition of factors Xa and XIIa is enhanced equally by heparin and by heparin fragments with molecular weights as small as 3400 (18,19). These and related kinetic properties have been used as arguments for a mechanism in which the activated reactant is heparin-antithrombin I11 complex, with minor additional rate enhancement contributed by interaction of thrombin (but not factor Xa) with the heparin bound to antithrombin I11 (18,20,21).
A major problem in the interpretation of thrombin-antithrombin I11 kinetics is that, in spite of high binary affinities, measurements are carried out in ternary mixtures of enzyme, antithrombin 111, and heparin, where stoichiometries and concentrations of binary complexes must be inferred.
We have synthesized covalent 1:l complexes of antithrombin I11 and heparin (22,23). These complexes inhibit factor Xa with second order rate constants very similar to those obtained with the corresponding reversible complexes. Because the system is now binary, kinetic analysis is greatly simplified. Therefore, we have investigated the inhibition of thrombin by antithrombin I11 coupled to native heparin (average M, = 15,000) or to heparin fragments with M, = 3,200 (hI2l) or M , = 4,300 (hI6). The results suggest a mechanism involving specific binding of antithrombin I11 to a unique site on the heparin molecule, and one-dimensional diffusion along the heparin of cationic thrombin bound by electrostatic association to polyanionic heparin. This interaction of thrombin with heparin makes a major contribution to the rate of thrombin inhibition, increasing the inactivation rate by three orders of magnitude. The mechanism of inhibition of thrombin by antithrombin 111 in the presence of heparin bears some similarities to that of diffusive protein translocation on nucleic acids (24-26).
Bovine a-thrombin was purified from Topostasine (Roche, Brussels, Belgium) by chromatography on sulfopropyl (SPbSephadex and elution with a linear NaCl gradient (0.05-0.25 M NaC1) in 0.05 M imidazole-HC1 buffer, pH 6.3, containing 0.1% polyethylene glycol 6000 and 1 mM benzamidine. The preparation showed one band at the a-thrombin position on sodium dodecyl sulfate-gel electrophoresis and separated into A and B chains upon reduction. The preparations were stored at -80 "C in 0.1 M Na,HPO, buffer, pH 6.5, and had an average clotting activity of 3000 USP units/mg. Antithrombin 111, factor Xa, high affinity heparin, and the heparin fragments with M , = 3200 (h12) and with M, = 4300 (h16) were obtained as described previously (22,23). Extinction coefficients At2m (280 nm) used were 6.1 for antithrombin 111 and 18 for thrombin (29).

Methods
Covalent Heparin-Antithrombin III Complexes (AT-H, AT-hlG, and AT-h,,i-The coupling of H and of the heparin fragments (h16 and h12) to antithrombin 111 was performed as previously described (22,23). Primary amino groups were introduced in the mucopolysaccharide by reaction with hexamethylenediamine and the fraction of the substituted heparin having a high affinity for antithrombin 111 was linked to antithrombin 111 with the bifunctional reagent tolylene-2,4diisothiocyanate. The covalent complexes were purified by chromatography on DEAE-Sephacel (23).
The antithrombin 111-heparin complex was purified further by gel filtration on Ultrogel AcA 44 in 0.1 M Tris-HC1 buffer, pH 7.6, to remove complexes between one heparin molecule and two antithrombin 111 molecules (22) and most of the unreacted free heparin.
To remove residual free heparin (about lo%), the preparations, dissolved in 0.05 M NaCl, 0.1 M Tris-HC1, pH 7.6, were applied to columns of concanavalin A-Sepharose equilibrated in the same buffer. About 10% of the heparin but no antithrombin 111 appeared in the breakthrough. The columns were washed with 1 bed volume of 1 M NaCl, 0.1 M Tris-HC1, pH 7.6, and then were eluted with 0.5 M amethylglucoside, 0.5 M NaCl, 0.1 M Tris-HC1, pH 7.6. The products contained no free heparin detectable by sodium dodecyl sulfate-gel radioelectrophoresis and no free antithrombin 111 as determined by crossed immunoelectrophoresis (23,30).
For all preparations, antithrombin 111 concentration determined by titration with thrombin was greater than 85% of that estimated by the method of Lowry et al. (31). Covalent Heparin-Thrombin Complex-Heparin was substituted with hexamethylenediamine in the presence of l-ethyl-3-(3-dimeth-ylaminopropy1)carbodiimide hydrochloride and the high affinity fraction was treated as follows: per ml of substituted heparin (6 mg) diluted to 7 ml with N,N-dimethyl-N-allylamine buffer, pH 9.2, were added 100 mg of tolylene-2,4-diisothiocyanate, which corresponds to a 1,200-fold molar excess. After stirring for 1 h at 45 "C, the reaction mixture was extracted four times with 7 ml of benzene and three times with 7 ml of a mixture of heptane/ethyl acetate (2:l). The aqueous phase was then immediately added to 13 mg of bovine thrombin (equimolar amount) in 0.1 M NaHC03, pH 8.6, containing 0.1% polyethylene glycol 6,000, at 30 "C in a final volume of 30 ml. During this incubation, the enzymatic activity as measured with the chromogenic substrate S-2238 remained constant. After 1 h the mixture was dialyzed at 4 "C against 0.05 M Tris-HC1 buffer, pH 7.2, containing 0.1% polyethylene glycol 6,000. Sodium dodecyl sulfategel electrophoresis of the reaction mixture showed formation of a complex with M, = 46,000 and small concentrations of higher M, complexes. Measurement of radioactivity in the slices revealed that 30-35% of the heparin was complexed with thrombin.
The thrombin-heparin complex was purified by chromatography on a column (1.5 X 20 cm) of heparin-Ultrogel equilibrated with the dialysis buffer. The unbound fraction (containing heparin and thrombin-heparin complex) was then applied to a column (1 X 10 cm) of benzamidine-Sepharose, and eluted with a linear NaCl gradient (0.1-2 M) in 0.05 M imidazole buffer, pH 7.35. Sodium dodecyl sulfate-gel electrophoresis revealed that the complex was of high purity; the final recovery of the complex was about 15%. Determination of the specific radioactivity of the heparin, amino acid analysis, and assay of the enzymatic activity with S-2238 revealed that the purified complex had a 1:l stoichiometry. The final product was stored in 0.1 M phosphate buffer, pH 6.3, a t -80 "C.
Kinetic    (H, hI6, and hI2) on the Inhibition of Thrombin by Antithrombin ZZZ-In agreement with previous data (18,34) we found that the apparent rate constant of the inhibition of thrombin by antithrombin 111 increased in the presence of H to reach a plateau followed by a decrease at higher concentrations (Fig. 1 A ) . At concentrations of H above 1 p~, the reaction rate in the presence of 10 nM of antithrombin I11 was too slow to be measured accurately. However, (lo) incubation of thrombin with 100 nM antithrombin 111 revealed that the reaction rate decreases further (Fig. l A , inset), and that it gradually levels off at 10 p~. In the absence of NaCl essentially the same pattern was observed (Fig. l A , squares) but with a 7-fold lower maximum value of kapp. With hI6 (Fig.  lB), the initial rise in k,,, is followed by a plateau region  (Fig. 2 ) . With kz = 2 s" (see below) and [ATl0 of 10 nM, the ordinate intercepts yield KTH = 80 nM and c h l E = 160 nM. The abcissa intercepts then yield KATH = KATh,, = 70 nM. At extreme concentrations of [HI (up to 100 p~) , no further decrease occurs in kapp (Fig. l A , inset), which implies a shift to pathway  (AT-H, AT-h16, AT-hlz)-With AT-H (or AT-h16, AT-h,,) concentrations large relative to [TI, inhibition of thrombin followed pseudo-first order kinetics until thrombin became undetectable. Fig. 3A shows thrombin in-  hibition by 1-15 nM AT-H, from which pseudo-first order rate constants (In 2/t1,,) were obtained and then plotted according to Equation 20 (Fig. 3B). The abscissa intercept indicates that K, = 7 nM, the ordinate intercept indicates that k2 = 2 s-'. The bimolecular rate constant calculated as the ratio k,/Ki = klkJ(k-, + k2) equals 3 X lo8 M" s-'.

Inhibition of Thrombin by Covalent Complexes of Heparin with Antithrombin ZII
Likewise, pseudo-first order rate constants obtained with AT-h16 (Fig. 4A), yield a linear Kitz-Wilson plot (Fig. 4 B ) and estimates of K; = 100 nM, kz = 2 s" and k,/K, = 2 x lo7 M-' s-'. Similar analysis of AT-hlz (Fig. 5) Table I. netics of thrombin inhibition in a binary reaction, where the many competing interactions of the ternary (thrombin-antithrombin-heparin) system have been eliminated. Irrespective of the chain length of the heparin moiety, the complexes inhibit thrombin in the manner characteristic of active site directed, irreversible inhibitors in steady state: shown recently (35) to be the pathway of the thrombin-Use of covalent complexes of antithrombin 111 with heparin antithrombin I11 reaction. In keeping with recent findings of and heparin derivatives have enabled an analysis of the ki-Olson and Shore (35), heparin has little or no effect on k, and thus, may be regarded as a catalyst that acts by stabilizing the transition state, E . I . However, Ki = + k,)/k, is strikingly sensitive to the chain length of the heparin moiety, decreasing approximately 60-fold when the chain length increases from 12 to 16 monosaccharide units, and another 15fold from 16 to about 40-60 monosaccharide units. Because, as shown by Figs. 1C and 2, the affinity of antithrombin I11 for heparin is relatively insensitive to chain length, the decreasing Ki must reflect an increasing contribution of the thrombin-heparin interaction.
The magnitude of the rate enhancement that depends on interactions of thrombin with heparin may be addressed in two ways. First, the capacity of FPR-thrombin to inhibit the reaction of the covalent heparin-antithrombin 111 with thrombin must arise from competition for the heparin moiety, as thrombin with an occupied catalytic center does not inhibit the reaction of thrombin with free antithrombin I11 (18, 36), and competition of FPR-thrombin for the antithrombin 111 binding site is precluded by the covalent coupling of the inhibitor to heparin. Compared with that of free antithrombin 111, the maximum bimolecular rate constant of 3 X 10' M" s-I obtained with AT-H or with high affinity heparin saturated with antithrombin I11 represents an increase in reaction rate of about 50,000-fold, the greatest so far observed. Because even AT-h,, is partially inhibited by FPR-thrombin, we may conclude that no less than 1,000-fold, or 99.9% of the rate enhancement catalyzed by high molecular weight, high affinity heparin depends on noncovalent bonds between heparin and thrombin.
From a comparison between the values of KTH (80 nM) and KFh16 (160 nM) on the one hand and KATH = (70 nM) on the other hand, it can be assumed that the stability of the final transition state is equal but not higher than predicted by the electrostatic interactions between proteins and heparin. Therefore the reaction can be interpreted in terms of electrostatic interactions of thrombin with a site on the heparin chain adjacent to antithrombin 111. Thus, in K!TH = (k!;TH + kz)/(kfTH), eTH equals that fraction of the association rate constant between thrombin and heparin that is directed to the site adjacent to antithrombin 111. Similarly, kATH equals the same fraction ( f ) of the corresponding dissociation rate constant. In addition, the interaction between FPR-thrombin and AT-H (Fig. 6) is suggestive of a single association between both molecules. Therefore, the IC50 of 4 nM represents the dissociation constant of the equilibrium as follows. From Fig. 1B it appears that hI6 consists of two slightly different heparin populations. Yet, assuming that the IC50 (60 nM) (Fig. 6) represents the average dissociation constant of the equilibrium k Ln T + AT-h16 T. hlG-AT, k it can similarly be calculated that IZfThle = 5.0 X lo7 M" S-' and that k!Th16 = 3 s-'.
These findings indicate that the dissociation rate constant of thrombin from the antithrombin I11 binding site ( k -1 ) on heparin is independent of the chain length of the remaining heparin part, whereas the second order rate constant (kl) of the association between enzyme and inhibitor on the heparin chain is strongly dependent on the total chain length.
The exceptionally high second order rate constant of 6.7 X 1 0 ' M" s" suggests that the reaction is proceeding faster than might be expected for a diffusion-limited bimolecular reaction between two macromolecules (37). Because thrombin carries a net charge at pH 7.6 of about +9 (38), the initial encounter of thrombin with heparin may represent geometrically random ion pairing. If thrombin then were much more likely to diffuse in the dimension of the heparin chain than to dissociate, the probability that any interaction of thrombin with heparin may lead to reaction with bound antithrombin I11 is greatly enhanced. Thus, steric restrictions of the initial encounter are minimized or eliminated, and as the heparin chain elongates, the probability of an interaction increases, and may exceed the usual expectations of second order reactions. An analogous mechanism, termed "sliding" and reviewed recently by Berg et al. (25) accounts for the rapid association of regulatory proteins with their target base sequences on DNA (24). Also consistent with such a process is the relatively narrow maximum in the second order rate constant of thrombin inhibition when ionic strength is varied (Fig. 1A) (24) and the insensitivity to heparin chain length of the rate of reaction of the anionic enzyme, factor Xa (23). In addition, preventing restricted diffusion of thrombin on the heparin chain by covalent attachment results in abolishment of the heparin catalysis as evidenced by the reduction of the inhibition rate to the value observed in the absence of heparin.
Because the covalent and noncovalent complexes yield virtually identical bimolecular rate constants, the findings with the binary system may now be used to rationalize the ternary system of heparin, antithrombin 111, and thrombin. From the values of the various equilibrium and inhibition constants, it is clear that, as concluded recently by Griffith (39), the pathway of the reaction is random but may be restricted by the appropriate concentrations of any of the three components. This is illustrated by Fig. 1. The ascending limb in Fig.  1A can be explained by considering both the 10-fold greater affinity of thrombin than antithrombin I11 for heparin, and the 10-fold greater reaction rate of heparin-antithrombin I11 with thrombin than that of heparin-thrombin with antithrombin 111. Upon saturation of thrombin with heparin, the formation of ternary complex shifts from a random to a sequential pathway, in which heparin-thrombin is inhibited by antithrombin 111. Thus, the descending limbs in Fig. 1, A and B, reflect a decreasing concentration of antithrombin 111, which is being saturated with heparin. At complete saturation of both proteins the reaction rate minimizes to a rate comparable to the reaction of AT-H with T-H, which interestingly compares with similar rates of reaction of either covalent or noncovalent hlz-antithrombin I11 with either free thrombin or thrombin saturated with heparin. Furthermore, the reaction of factor Xa with heparin-antithrombin 111 proceeds at only a slightly faster rate (23). This convergence of rate constants to between IO5 and IO6 M" s" suggests the minimum rate above which additional rate enhancement arises only from additional interactions of the thrombin with the heparin chain.