©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
Prothrombin Activation by Prothrombinase in a Tubular Flow Reactor (*)

(Received for publication, April 28, 1994; and in revised form, August 23, 1994)

Didier Billy Han Speijer George Willems H. Coenraad Hemker Theo Lindhout (§)

From the Department of Biochemistry, Cardiovascular Research Institute Maastricht, University of Limburg, P. O. Box 616, 6200 MD Maastricht, The Netherlands

ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
FOOTNOTES
REFERENCES

ABSTRACT

Thrombin production by the phospholipid-bound complex of blood clotting factors Xa and Va (prothrombinase) was studied in a tubular flow reactor. The inner wall of a glass capillary was coated with a phospholipid bilayer of 25% phosphatidylserine and 75% phosphatidylcholine. Prothrombinase was assembled on this bilayer by perfusion with a mixture containing an excess of factor Va (2 nM) and a limiting amount of factor Xa (1-100 pM), either in the absence or presence of prothrombin. The rate of assembly of prothrombinase in the presence of prothrombin appeared to be limited by the transfer rate of factor Xa to the phospholipid surface. A good agreement was found between the predicted mass transfer coefficient for factor Xa and the observed pre-steady state rate of thrombin production. The eventually obtained steady state rates of thrombin production were proportional to the prothrombin concentration and independent of the surface density of prothrombinase. The observed rate of thrombin production was in excellent agreement with the predicted mass transfer rate for prothrombin. Transport-limited prothrombin conversion was observed for prothrombinase densities exceeding 1 fmol/cm^2, which corresponds to 0.05% occupation of available binding sites. The kinetic parameters of the reaction were determined at low prothrombinase densities (0.02-0.04 fmol/cm^2). Even in this situation the Michaelis-Menten equation had to be corrected for substrate depletion near the catalytic surface. We hereto employed an accurate approximation of the mass transfer coefficient. The kinetic parameter k was 60 s and the intrinsic K had a surprisingly low value of 3 nM. Both parameters were not influenced by the wall shear rate.


INTRODUCTION

The process of blood coagulation encompasses a complex system of enzymatic reactions in flowing blood at the surface of damaged blood vessels. One of the final steps in this process is the conversion of prothrombin to thrombin(1, 2) . The activator of prothrombin is a multicomponent complex that consists of the serine protease factor Xa and the non-enzymatic cofactor factor Va. In the presence of calcium ions, the complex of factor Xa and factor Va assembles on a membrane containing negatively charged phospholipids, i.e. phosphatidylserine(3, 4) . These membranes become available when blood platelets are activated(5, 6) . Other cells like monocytes and endothelial cells have also been reported to support prothrombin activation by providing such a procoagulant surface(7, 8) .

Prothrombin activation at a macroscopic surface under flow conditions has been studied in our laboratory. We previously reported on prothrombin activation in a tubular flow reactor(9) . The findings of that study seemed to contrast with the findings on prothrombin activation at planar phospholipid bilayers(10, 11) . That is, during continuous flow through the tubular flow reactor, the rate of thrombin production appeared to be dependent on the prothrombin concentration in the bulk solution up to about 1 µM. Studies with an uniformly accessible surface, as offered by the rotating disc, however, showed that the concentration of prothrombin in the bulk solution that is required for the half-maximum rate of prothrombin conversion was about 7 nM(10) .

In the present paper we describe the results of a kinetic study on prothrombin activation in a tubular flow reactor. Our major goal was to identify the experimental settings, with respect to flow rate, substrate concentration, and prothrombinase surface density, that allow us to derive kinetic parameters from the thrombin production data. Hereto we explored the conditions that gave rates of thrombin production proportional to the true catalytic activity of prothrombinase and thus independent of the rate of transfer of prothrombin from the bulk solution to the catalytic surface. We, therefore, have carefully evaluated the transport limit in the flow reactor and used the theoretical considerations of mass transfer given by Brown(12) . Our findings support previous proposals that at a macroscopic phospholipid surface prothrombin activation by prothrombinase is extremely efficient because very low concentrations of prothrombin (a few nanomolar) are required to obtain half-maximal velocity of thrombin production(10, 11) . We also addressed the question whether the catalytic efficiency of prothrombinase was influenced by the wall shear rate, as has been reported for factor X activation in a flow reactor(13, 14) .


EXPERIMENTAL PROCEDURES

Materials

Fatty acid-free bovine serum albumin was from Sigma. The chromogenic substrate for thrombin, S2238, was from Chromogenix, Möhldal, Sweden. All chemicals used were of the highest grade commercially available.

Proteins

Human factor Xa, human prothrombin, and bovine factor Va were prepared and quantified as described(9) . Bovine factor Va was further purified on a Mono S column (Pharmacia Biotech, Uppsala, Sweden) as described by Rosing et al.(15) . Briefly, after loading the column with bovine factor Va, a linear gradient of 0.05-1 M NH(4)Cl was applied. Factor Va activity was eluted in two peaks at 0.45 and 0.75 M NH(4)Cl. Throughout this study we used factor Va eluted at the higher salt concentration.

Preparation of Phospholipid-coated Capillaries

The glass capillaries (0.65 and 0.29 mm internal diameter and 127 mm length) obtained from Brand AG, Wertheim, Germany were boiled for 10 min in a 1:1:5 solution of NH(4)OH (25%), H(2)O(2) (30%), and H(2)O for 10 min and rinsed in deionized water. They were then boiled in a 1:1:6 solution of HCl (37%), H(2)O(2) (30%), and H(2)O for 10 min and rinsed in deionized water. The clean and hydrophilic capillaries were kept at 4 °C in deionized water. Before use the capillaries were dried under a stream of N(2). The capillary was filled with a suspension of unilamellar phospholipid vesicles composed of 75 mol % egg phosphatidylcholine and 25 mol % brain phosphatidylserine, prepared as described before(15) . After 20 min of incubation with the 1 mM phospholipid suspension, the capillary was rinsed with Tris-buffer (50 mM Tris-HCl, 175 mM NaCl, and 0.5 mg bovine serum albumin/ml, pH 7.9) containing 3 mM CaCl(2) at a flow rate of 1.2 ml/min for 2 min to remove non-bound phospholipid(9, 13) .

The Flow System

The flow system was as described by Contino et al.(16) . Briefly, the phospholipid-coated capillary is attached to a Hamilton gas-tight syringe. The flow is controlled by a syringe pump (Harvard Apparatus Co., South Natich, MA). An XYZ translation table (Isel, Eiterfelt, Germany) was used to collect samples (typically 30 µl) from the tip of the flow reactor into disposable cuvettes (Sarstedt, Nümbrecht, Germany) containing 20 mM EDTA in Tris-buffer. Thrombin was measured in the cuvette after the addition of the chromogenic substrate S2238 as described previously(9) . All procedures were performed at 37 °C.

Determination of Factor Xa Bound to the Surface of the Flow Reactor

The amount of factor Xa bound to the phospholipid bilayer in the flow reactor was determined at the end of each experiment. To this end the capillary was rinsed with Tris-buffer containing 3 mM CaCl(2) and factor Va (2 nM) at a flow rate of 30 µl/min for 5 min to remove prothrombin and thrombin. The capillary was then eluated with Tris buffer containing 5 mM EDTA at 30 µl/min for 5 min. The effluent was collected and assayed for factor Xa.

The factor Xa-containing samples were diluted in Tris buffer containing 3 mM CaCl(2). An aliquot (30 µl) of the dilution was added to a cuvette containing 108 µl of Tris buffer containing 1.4 nM factor Va, 14 µM phospholipid (25% phosphatidylserine, 75% phosphatidylcholine), and 3 mM CaCl(2). Thrombin production was started by the addition of 12 µl of a 5 µM prothrombin solution and stopped after 4 min by the addition of 390 µl of 20 mM EDTA in Tris buffer. The amount of thrombin formed was determined by adding 60 µl of S2238 (2.5 mM) and reading of the optical density at 405 nm. Reference curves were constructed from known amounts of factor Xa.

Prothrombin Transport from Perfusion Solution to the Catalytic Surface as Rate-limiting Step of Thrombin Production

The transfer of prothrombin by convection and diffusion to the capillary wall becomes easily rate-limiting(17, 18) . This results in depletion of the prothrombin in the solution near the wall and thus a steady state concentration C(r,z) is established, which depends on the radial co-ordinate r and on the axial co-ordinate z. The concentration C(r,z) is a solution of the convective diffusion equation(17, 18) :

with D the diffusion constant of the protein, V(f) the mean fluid flow velocity and R the radius of the capillary. At the entrance of the capillary, z = 0, C is equal to the perfusion concentration C(b):

and at the capillary wall the diffusional flux must balance the conversion rate:

with V the maximal conversion rate per unit area and K the Michaelis constant.

Diffusion-controlled Prothrombin Conversion

For high values of V, i.e. for high densities of prothrombinase at the capillary wall, maximal thrombin production and therefore maximal mass transfer of prothrombin by convection and diffusion is attained. According to boundary condition (c), this corresponds to a concentration at the wall that approaches zero. The boundary condition (c) thus can be replaced by

A convenient and simple approximate solution of the boundary value problem (a, b, and d) was derived by Leveque (19) using the assumption that the boundary layer of substrate depletion is small compared to the capillary diameter. With this so called Leveque approximation, the total mass transfer, J(t) (mol/s), is given by:

where D is the diffusion constant of the substrate (cm^2/s), Q the volumetric flow rate (cm^3/s), L the length of the capillary (cm), and C(b) the substrate concentration at the inlet (mol/cm^3). The total mass transfer can thus expressed as the mass transfer coefficient Delta(t) (cm^3/s) times the substrate concentration C(b). It should be noted that the mass transfer rate J(z), expressed in mol/cm^2/s, depends on the distance z downstream from the capillary inlet:

with C the solution of boundary value problem (a, b, and d) with C = 1 and Delta the local mass transfer coefficient (cm/s) which declines steeply in the downstream direction.

For low flow rates and relatively long capillaries of small diameter, the depletion layer, however, spans the entire capillary and the Leveque approximation becomes invalid. The depletion at the end of the capillary can be estimated by as:

For a capillary with R = 0.032 (cm), L = 12.7 (cm), a diffusion constant D = 10 (cm^2/s) and a flow rate Q = 5 times 10 (cm^3/s), this amounts to C/C(b)= 0.53 and will overestimate the transport rate by about 20%. Errors of this size can be avoided by employing the semianalytical approximate solution to the full problem (a, b, and d) as presented by Brown (12, and Equation 15 and Table I therein). The equation, which allows the calculation of the total mass transfer coefficient Delta(t) for a given flow rate and diffusion coefficient, is rather unwieldy. We, therefore, should like to confine ourselves to refer the reader to the paper of Brown(12) . Table 1lists the numerical values calculated on basis of Brown's semianalytical approximate solution for the total mass transfer coefficient, Delta(t), for prothrombin and factor Xa under the flow conditions used in our experiments. Also given are the mass transfer coefficients calculated on the basis of the Leveque approximation(19) . It is apparent that prothrombin transport is overestimated by 10-30% in the latter approximation.



Intermediate Kinetics of Prothrombin Conversion

For lower surface concentrations of prothrombinase, a partial depletion of prothrombin near the capillary wall is obtained, i.e.C(b) >C(R,z) >0, and in this situation the thrombin generation rate is determined by the solution of the boundary value problem (a, b, and c). Due to the non-linearity in the boundary condition (c) this boundary value problem is intractable for analytical solutions for general distributions of enzyme activity V(z) and requires a numerical treatment(18) . The special situation, however, is that the enzyme activity on the capillary wall is proportional to the local mass transfer rate:

with beta as proportionality constant, allows a simple solution of this problem. It is easily verified that

with C(w) the substrate concentration at the capillary wall (independent of z) and C(o) the solution of (a, b, and d) with C(b) = 1 satisfies a and the boundary condition (b). Boundary condition (c) is equivalent to second-order equation in C(w), which is independent of z:

Integration of this expression over the inner surface of the capillary results in

with J(t) the total thrombin generation (mol/s) and V(m) the maximal thrombin production rate (mol/s) of the capillary. allows the following explicit solution:

Non-linear regression of this equation to measured thrombin production rates as a function of the perfusion concentration C(b) of prothrombin then allows the determination of the parameters V(m) and K(m).


RESULTS

Rate of Thrombin Production as a Function of the Surface Prothrombinase Density

Phospholipid-coated capillaries were perfused with solutions containing factor Va (2 nM), prothrombin (0.2 µM), and varying amounts of factor Xa (5-20 pM). It was expected that ongoing perfusion would result in assembly of increasing amounts of prothrombinase at the inner wall of the phospholipid-coated capillary which in turn results in increasing rates of thrombin production.

Fig. 1illustrates that the time to reach the steady state levels of thrombin production decreased with increasing amounts of factor Xa in the perfusion solution. Evidently, because a molar excess of factor Va over factor Xa was used, the rate of assembly of the prothrombinase complex at the macroscopic surface is limited by the transport of factor Xa and/or preformed factor Xa-factor Va complexes from the bulk solution to the surface. The initial part of the thrombin generation curve, therefore, reflects the rate of formation of prothrombinase activity at the phospholipid bilayer, and this rate will increase with increasing amounts of factor Xa in the perfusion mixture.


Figure 1: Rate of thrombin production as a function of factor Xa concentration. Phospholipid coated capillaries (internal diameter of 0.32 mm) were perfused at 30 µl/min (wall shear rate 20 s) with Tris buffer containing prothrombin (0.2 µM), factor Va (2 nM), 3 mM CaCl(2), and varying concentrations of factor Xa: 5 pM (box), 10 pM (up triangle), and 20 pM (circle).



It is also evident from Fig. 1that the rate of thrombin formation reached a steady state value independent of the amount of factor Xa present. Under the flow conditions used and with 0.2 µM prothrombin in the perfusion solution, the maximum rate of thrombin formation was 1.5 pmol/min. Table 1predicts a maximal mass transfer of 2.2 pmol prothrombin/min for a prothrombin concentration of 0.2 µM. Therefore, an obvious explanation for the identical steady state levels is that in each experiment the prothrombin converting capacity of the capillary wall ultimately exceeded the transport limit. The alternative explanation that in all experiments the prothrombinase concentration at the wall surface reached a maximal value was refuted by determination of the prothrombinase densities attained in these experiments. The amount of phospholipid-bound factor Xa at the end of the perfusion increased linearly with the factor Xa concentration in the perfusion mixture. Thus, 0.34, 0.65, and 1.13 fmol factor Xa/cm^2 was bound after 28 min perfusion with a mixture containing 0.2 µM prothrombin, 2 nM factor Va, and 5, 10, or 20 pM factor Xa, respectively. Thus, despite widely different surface densities of prothrombinase we observed identical rates of thrombin production. It is important to note that when factor Xa was perfused in the absence of factor Va, no factor Xa could be detected in the EDTA effluent of the capillary. Thus, the amount of prothrombinase in the phospholipid-coated capillary is represented by the amount of factor Xa found in the EDTA effluent.

Since the rate of thrombin production seemed to be limited not by the prothrombinase binding capacity of the phospholipid-coated capillary, but by the rate of supply of substrate to the catalytic surface, we expected to find that the steady state rate of thrombin production should be proportional to the concentration of prothrombin in the perfusion solution (see ). Thus, phospholipid-coated capillaries were perfused with varying concentrations of prothrombin in the presence of fixed amounts of factor Xa (50 pM) and factor Va (2 nM). The steady state rates of thrombin production are presented in Table 2as a function of the prothrombin concentration. It is seen that the rate of thrombin production increased linearly with the prothrombin concentration. Table 2also gives the rate of transport of prothrombin to the catalytic surface as a function of the prothrombin concentration in the perfusion solution. These values were calculated as described under ``Experimental Procedures.'' The mass transfer coefficient was taken from Table 1. The close agreement between the experimental rate of thrombin production and the rate of prothrombin transport to the catalytic surface strongly indicates that the system employed behaves as predicted by the hydrodynamic theory.



Steady State Rate of Thrombin Production as a Function of Prothrombinase Surface Density

Phospholipid-coated capillaries were first perfused with factor Va (2 nM) and varying concentrations of factor Xa (2.5-100 pM) during 10 min at a flow rate of 30 µl/min to obtain controlled amounts of prothrombinase. Subsequently, the prothrombinase-containing capillaries were perfused with prothrombin (0.5 µM) in the presence of factor Va (2 nM). An increase of the factor Xa concentration in the first perfusion solution from 2.5 to 25 pM gave an increase of the steady state rate of thrombin production upon perfusion with 0.5 µM prothrombin. Preperfusion of the phospholipid capillaries with factor Xa concentrations higher than 25 pM did not result in higher rates of thrombin production. To assess the amount of prothrombinase in the capillary, we rinsed the capillary at the end of the perfusion experiment with EDTA and assayed the effluent for factor Xa activity. Fig. 2clearly shows that whereas the amount of factor Xa bound to the inner wall of the phospholipid-coated capillary increased proportionally with the factor Xa concentration of the first perfusion mixture, that also contained a fixed amount of factor Va (2 nM), the steady state rate of thrombin production did not further increase when the factor Xa (prothrombinase) surface density was greater than 0.6 fmol factor Xa/cm^2. We note that the maximum steady state rate of thrombin production in this experiment was 2.5-fold higher than the maximum rate found when a phospholipid-coated capillary was perfused with a mixture that contained factor Xa, factor Va, and prothrombin as shown in Fig. 1. This difference in rates of thrombin production is readily explained by a 2.5-fold difference in prothrombin concentration of the perfusion solutions. It is apparent that under the conditions of this experiment (wall shear rate of 20 s and prothrombin concentration of 0.5 µM) the rate of thrombin production becomes independent of the amount of phospholipid-bound enzyme when the prothrombinase density exceeded 0.6 fmol/cm^2.


Figure 2: Rate of thrombin production as a function of prothrombinase density. Capillaries were first perfused with Tris buffer containing factor Xa, at the concentrations indicated, factor Va (2 nM), and 3 mM CaCl(2). Steady state rates of thrombin production (bullet) were determined by perfusion with 0.5 µM prothrombin and 2 nM factor Va. At the end of the perfusion experiment, the amount of phospholipid-bound factor Xa () was determined by rinsing the capillary with EDTA containing Tris buffer. The wall shear rate was 20 s. Further experimental conditions were as described under ``Experimental Procedures.''



Determination of the Kinetic Parameters of Thrombin Production by Prothrombinase in the Flow Reactor

To assess the kinetic parameters of prothrombinase bound to a macroscopic phospholipid bilayer under flow, phospholipid-coated capillaries were first perfused with 0.5 pM factor Xa in the presence of 2 nM factor Va during 10 min at a wall shear rate of 20 s. This preperfusion resulted in about 0.02 fmol of prothrombinase/cm^2 which was assumed to be sufficiently low to avoid significant depletion of prothrombin near the catalytic surface (Fig. 2). Subsequently, the capillaries were perfused with varying concentrations of prothrombin in the presence of factor Va (2 nM), and rates of thrombin production were determined from the steady state levels of thrombin at the outlet of the flow reactor. At the end of each perfusion experiment, factor Xa was quantitatively recovered from the flow reactor to establish the prothrombinase surface density. Fig. 3gives the rates of thrombin production obtained from perfusion experiments in which a capillary with a prothrombinase density of 0.014 fmol/cm^2 was perfused with increasing prothrombin concentrations (2-80 nM) at a wall shear rate of 20 s and another capillary (0.018 fmol prothrombinase/cm^2) at a wall shear rate of 3000 s. The different wall shear rates were obtained by using capillaries with an internal diameter of 0.65 mm at a flow rate of 30 µl/min and capillaries with an internal diameter of 0.29 mm at a flow rate of 440 µl/min. The data as shown in Fig. 3were analyzed by a non-linear fit to a rectangular hyperbola to obtain apparent K(m)(m) and V(max) values. The calculated data points are presented by the solid line. The same experiment was performed with a 2-3-fold higher prothrombinase density in the flow reactor. Table 3summarizes the apparent kinetic constants that were determined under the different experimental conditions. A large variation in K(m) as well as k is seen. Noteworthy is the high K(m) when a small diameter capillary with a high prothrombinase density is perfused with prothrombin at a low wall shear rate. This difference is readily explained by depletion of prothrombin near the catalytic surface. That is, when thrombin production is partly limited by the transport of prothrombin to the catalytic surface, higher prothrombin concentrations in the perfusion solution are required to saturate half the prothrombinase in the flow reactor. Kinetic parameters should be calculated from the steady state rate of thrombin production and the prothrombin concentration near the catalytic surface. Therefore, K(m) and k values were obtained by fitting observed rates of thrombin production and prothrombin concentrations in the perfusion solution to (see ``Experimental Procedures''). The intrinsic kinetic parameters thus obtained are also listed in Table 3. From these data we conclude that both K(m) and k are independent of the experimental conditions such as the prothrombinase density and the wall shear rate. Of particular interest is the low K(m) of 3 nM.


Figure 3: Rate of thrombin production as function of prothrombin concentration, shear rate, and prothrombinase density. Capillaries containing phospholipid bound prothrombinase, 0.014 fmol/cm^2 (bullet) and 0.018 fmol/cm^2 () were perfused with Tris buffer containing the indicated concentrations of prothrombin, 2 nM factor Va and 3 mM CaCl(2), at a wall shear rate of 20 s (bullet) and 3000 s (). The solid lines represent the result of a non-linear fit to the Michaelis-Menten equation. The estimated kinetic parameters are listed in Table 3.






DISCUSSION

We have characterized the kinetics of prothrombin activation by the complex of factor Va and factor Xa assembled at the macroscopic phospholipid surface of a tubular flow reactor. The present study confirms an earlier observation from our group (10, 11) that on macroscopic lipid bilayers the Michaelis constant K(m) is much lower than reported for prothrombin activation at the surface of unilamellar vesicles with a radius of 20-30 nm. It was noticed that the K(m) decreased with increasing phospholipid area per molecule of the factor Xa-factor Va complex. Indeed the K(m) was depressed by a factor of 4 when large unilamellar vesicles (radius of 60-80 nm) were used. Moreover, it was shown that on planar phospholipid bilayers, with an area of 1 µm^2/prothrombinase complex, the K(m) was 6-7 nM and thus 25-fold smaller than the K(m) (170 nM) on small unilamellar vesicles. This marked difference was attributed to an efficient collection of prothrombin from solution by a macroscopic surface, whereas the K(m) on small unilamellar vesicles represents an apparent value reflecting the limited transport rate of prothrombin from solution to the vesicle(10, 11) . The phospholipid bilayers in these studies were present on a slide opposite a stirring bar or on a rotating disc. The latter system especially has the advantage that it presents a uniform accessible surface, with a uniform mass transfer coefficient over the entire surface. The capillary flow system used in the present study has the advantage of an extremely stable and well defined fluid flow. Another advantage is the high surface/volume ratio (0.05 cm^2/µl) of the capillary. Its potential disadvantage is the steep decline of the mass transfer rate in the downstream direction (). This could complicate the analysis of the intermediate enzyme kinetics. This potential disadvantage is, however, largely circumvented by the transport limited assembly of prothrombinase (see below), which implies a local prothrombinase activity proportional to the mass transfer coefficient and therefore the applicability of and (see ``Experimental Procedures'') for the analysis of the experimental data.

Our initial experiments, in which the phospholipid-coated capillary was perfused with a solution of factor Xa, factor Va, and prothrombin showed that at a shear rate of 20 s the rate of thrombin production became independent of the prothrombinase density at the surface when that density was greater than 1 fmol/cm^2 and the prothrombin concentration of the perfusion solution was 0.5 µM. From reported binding data(20, 21, 22) , we could calculate a maximum binding capacity of our phospholipid bilayer between 2 and 10 pmol prothrombinase/cm^2. Thus, a fractional occupation of about 0.05% is sufficient to enter a regime of thrombin production that is controlled by the mass transfer rate of prothrombin. From the data shown in Fig. 1, we also could estimate the rate at which prothrombinase was assembled during the initial phase of the thrombin production curve. If we assume a turnover of 60 s (Table 3), then the initial slopes of thrombin production indicate rates of prothrombinase formation of 0.05, 0.10, and 0.18 fmol/min with, respectively, 5, 10, and 20 pM factor Xa in the perfusion mixtures. As a matter of fact these rates of prothrombinase formation are in good agreement with the mass transfer of 0.01 fmol factor Xa/min/pM factor Xa in the perfusate (Table 1).

The validity of our theoretical considerations regarding the thrombin production data in the flow reactor also became evident from the excellent agreement between the observed steady state rates of thrombin production under diffusion-controlled conditions (high prothrombinase density and low wall shear rate) and the calculated mass transfer of prothrombin as shown in Table 2. We like to note that the theory was developed for reactions at a homogeneously catalytic surface like that of platinum. The fact that catalysis at a macroscopic surface with a very low enzyme density follows the same theory is compatible with the notion that the lateral diffusion of reactants at the surface exceeds the flux of reactants toward the apparent non-homogeneously catalytic surface(11) .

When capillaries with prothrombinase density below 0.6 fmol/cm^2 were perfused with 0.5 µM prothrombin at a wall shear rate of 20 s, the steady state rate of thrombin production became a linear function of the surface density of prothrombinase (Fig. 2). Yet, we have to emphasize that this observation does not exclude prothrombin depletion at the catalytic surface. As outlined under ``Experimental Procedures,'' thrombin production causes a partial dependence of the rate of thrombin production on the mass transfer rate of prothrombin to the catalytic surface. This is clearly demonstrated by the results presented in Table 3. The apparent K(m) for prothrombin is much higher at a low shear rate and high prothrombinase density than the K(m) determined under conditions where much less depletion of prothrombin near the catalytic surface was expected. The apparent difference in K(m) disappeared when the prothrombin concentration was corrected for depletion of prothrombin near the catalytic surface (). The results as summarized in Table 3show that both the V(max) and K(m) did not vary with the shear rate. In this respect prothrombinase bound to a macroscopic surface seems to behave differently from the factor X converting complex tissue factor-factor VIIa. Nemerson and co-workers (13, 14) reported that the V(max) of factor X activation in a tubular flow reactor increased with increasing wall shear rate.

Whereas the k value for prothrombin activation in the tubular flow reactor is in accordance with those reported for prothrombin activation by prothrombinase in a vesicle system(3, 4) , we found a much lower K(m). However, the value 3 nM is in close agreement with the K(m) value (6 nM) determined for phospholipid bilayers on a rotating disc(10) .

The Michaelis constant observed for macroscopic lipid bilayers, which is about 1000-fold lower than the plasma concentration of prothrombin, might have interesting implications for the regulation of thrombin generation in vivo. This low value of K(m) implies the existence of two control regimes: (i) for low surface densities of prothrombinase, with V(max) below the mass transfer coefficient times the plasma concentration of prothrombin, the thrombin generation is completely determined by the amount of prothrombinase, and (ii) for high surface concentrations of prothrombinase the thrombin generation rate is completely determined by the transport limit and thus by the plasma concentration of prothrombin. The two regimes might also have consequences for the inhibitor-regulated thrombin production. Because of the high catalytic efficiency of prothrombinase for prothrombin, inhibition by pseudo-substrates, like antithrombin, is hardly to be expected. However, when thrombin production is limited by the supply of substrate, inhibition by pseudo-substrates has to be expected, but will not result in a reduced rate of thrombin production. In this respect, it is of interest to see that these transport phenomena have the very same implications for other surface-bound reactions involved in blood coagulation like the activation of factor X(23) .


FOOTNOTES

*
This work was supported by Program Grant 900-526-192 from the Dutch Organization for Scientific Research (NWO). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore by hereby marked ``advertisement'' in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

§
To whom correspondence should be addressed: Dept. of Biochemistry, Cardiovascular Research Institute Maastricht, University of Limburg, P. O. Box 616, 6200 MD Maastricht, The Netherlands. Tel.: 31-43-881674; Fax: 31-43-670988.


REFERENCES

  1. Jackson, C. M., and Nemerson, Y. (1980) Annu. Rev. Biochem. 49, 765-811 [CrossRef][Medline] [Order article via Infotrieve]
  2. Mann, K. G., Nesheim, M. E., Church, W. R., Haley, P., and Krishnaswamy, S. (1990) Blood 76, 1-16 [Abstract]
  3. Nesheim, M. E., Taswell, J. B., and Mann, K. G. (1979) J. Biol. Chem. 254, 10952-10962 [Abstract]
  4. Rosing, J., Tans, G., Govers-Riemslag, J. W. P., Zwaal, R. F. A., and Hemker, H. C. (1980) J. Biol. Chem. 255, 274-283 [Abstract/Free Full Text]
  5. Bevers, E., Comfurius, P., van Rijn, J. M. M. L., Hemker, H. C., and Zwaal, R. F. A. (1982) Eur. J. Biochem. 122, 429-436 [Medline] [Order article via Infotrieve]
  6. Mann, K. G. (1987) Trends Biochem. Sci. 12, 229-233 [CrossRef]
  7. Tracy, P. B., Nesheim, M. E., and Mann, K. G. (1981) J. Biol. Chem. 256, 743-751 [Abstract/Free Full Text]
  8. Rodgers, G. M., and Shuman, M. A. (1983) Proc. Natl. Acad. Sci. U. S. A. 80, 7001-7005 [Abstract]
  9. Schoen, P., Lindhout, T., Willems, G., Hemker, H. C. (1990) Thromb. Hemostas. 64, 542-547
  10. Willems, G. M., Giesen, P . L. A., and Hermens, W. Th. (1993) Blood 82, 497-504 [Abstract]
  11. Giesen, P. L. A., Willems, G. M., and Hermens, W. Th. (1991) J. Biol. Chem. 266, 1379-1382 [Abstract/Free Full Text]
  12. Brown, G. M. (1960) A. I. Ch. E. Journal 6, 179-183
  13. Gemmell, C. H., Turitto, V. T., and Nemerson, Y. (1988) Blood 72, 1404-1406 [Abstract]
  14. Gemmell, C. H., Nemerson, Y., and Turitto, V. (1990) Microvasc. Res. 40, 327-340
  15. Rosing, J., Bakker, H. M., Thomassen, M. C. L. G. D., Hemker, H. C., and Tans, G. (1993) J. Biol. Chem. 268, 21130-21136 [Abstract/Free Full Text]
  16. Contino, P., Repke, D., and Nemerson, Y. (1991) Thromb. Hemostas. 66, 138-140
  17. Levich, V. G. (1962) Physicochemical Hydrodynamics , pp 112-116, Prentice-Hall, Englewood Cliffs, NJ
  18. Kobayashi, T., and Laidler, K. J. (1974) Biotech. Bioeng. 66, 99-118
  19. Leveque, M. A. (1928) Ann. Mines Mem. 13, 201-239
  20. Pusey, M. L., Mayer, L. D., Wei, G. J., Bloomfield, V. A. and Nelsestuen, G. L. (1982) Biochemistry 21, 5262-5269 [Medline] [Order article via Infotrieve]
  21. Higgins, D. L., and Mann, K. G. (1983) J. Biol. Chem. 258, 6503-6508 [Abstract/Free Full Text]
  22. Krishnaswamy, S. (1990) J. Biol. Chem. 265, 3708-3718 [Abstract/Free Full Text]
  23. Andree, H. A. M., Contino, P. B., Repke, D., Gentry, R., and Nemerson, Y. (1994) Biochemistry 33, 4368-4374 [Medline] [Order article via Infotrieve]
  24. Lim, T. K., Bloomfield, V. A., and Nelsestuen, G. L. (1977) Biochemistry 16, 4177-4181 [Medline] [Order article via Infotrieve]

©1995 by The American Society for Biochemistry and Molecular Biology, Inc.