Shear Stress Decreases Endothelial Cell Tissue Factor Activity by Augmenting Secretion of Tissue Factor Pathway Inhibitor
Abstract—Monolayers of human umbilical vein endothelial cells were activated with 50 U/mL interleukin-1α (IL-1α) for 3 hours and simultaneously conditioned with shear stresses of 0, 0.68, or 13.2 dyne/cm2 in a parallel-plate flow chamber. In the presence of an inflow buffer containing 100 nmol/L factor X and 10 nmol/L factor VII, production of factor Xa, a measure of functional tissue factor (TF), was determined as the product of outflow concentration of factor Xa (chromogenic assay performed under quasi-static flow conditions after the shear period) and flow rate. Similarly, production of TF pathway inhibitor (TFPI) was estimated as the product of antigenic TFPI (by enzyme-linked immunosorbent assay) in the supernatant and flow rate. In parallel experiments, total RNA was isolated for determination of amplification products of TF mRNA by reverse transcription–polymerase chain reaction. We found that shear stress reduced factor Xa production (mean±SE; n=number of experiments) from 13.33±1.14 (n=16) fmol/min×cm2 at 0 shear stress to 5.70±2.51 (n=5) and 0.54±0.54 (n=4) fmol/min×cm2 at shear stresses of 0.68 and 13.2 dyne/cm2, respectively. At the same time, immunogold labeling showed that TF antigen on the endothelial surface increased >5-fold with shear stress, whereas TFPI antigen on the surface increased 2-fold. The secretion of TFPI (appearance of new supernatant TFPI) rose from 7.4±2.4 (n=12) ×10−3 fmol/min×cm2 at 0 shear stress to 23.7±7.3 (n=9) and 50.2±14.3 (n=4) ×10−3 fmol/min×cm2 at 0.68 and 13.2 dyne/cm2, respectively. TF mRNA amplification products were not markedly changed by shear stress. We conclude that acute application of shear stress reduces functional, but not antigenic, expression of TF by intact, activated endothelial cell monolayers in a manner associated with shear stress–augmented endothelial cell secretion of TFPI.
Reprint requests to Eric F. Grabowski, MD, Dr Eng Sci, Pediatric Hematology/Oncology, Blake 255, Massachusetts General Hospital, Fruit St, Boston, MA 02114.
May 22, 2000; revision accepted November 1, 2000.
Tissue factor (TF) is the membrane-bound glycoprotein that serves as the nonenzymatic cofactor for factor VII/VIIa in the initiation of blood coagulation, whereas TF pathway inhibitor (TFPI), its principal inhibitor, binds to both activated factor X and the ternary complex formed by TF, factor VIIa, and factor Xa. Both TF and TFPI are synthesized by endothelial cells (ECs), the former usually only after cell activation.1 With regard to increasing shear stress, functional TF has been shown to increase over a wide range of shear stress for a noncellular system of lipid bilayers, to which has been added exogenous TF that has been immobilized on the inner surface of a glass tube.2 A similar increase has been demonstrated for monolayers of human fibroblasts,3 which express TF in the absence of cytokine activation. With respect to monolayers of activated human ECs, however, the dependence on shear stress is more complex, passing through a maximum with respect to shear stress under 1 set of conditions3 or decreasing monotonically with shear stress under another.4 Prior work has not established whether this complex dependence is due predominantly to a reduction in TF protein and TF mRNA, augmentation of cell-associated TFPI, or other factors.
This flow dependence itself, moreover, may explain the fact that TF activity has not normally been found on human endothelium in vivo, whereas TF activity has long been identified on the surface of activated, cultured endothelial monolayers under static conditions in vitro.5 6 TF is not found on normal coronary endothelium or on saphenous veins and internal mammary arteries obtained during coronary bypass surgery, although TF mRNA and protein are expressed in macrophages, foam cells, monocytes adjacent to cholesterol clefts, and smooth muscle cells.7 8 More recently, on the other hand, digoxigenin-labeled factors VIIa and X have been used to demonstrate the presence of TF not only in atherosclerotic plaques but also in a subset of ECs overlying these plaques.9
In the present work, therefore, we explored the effects of fluid shear stress (none, venous, and arterial) on the expression of TF by interleukin-1α (IL-1α)–activated EC monolayers. We found that for acute changes in shear stress simultaneous with EC activation with IL-1α and of 3 hours’ duration or less, dependence of the expression of TF on shear stress is regulated largely by levels and secretion rates of TFPI and not by a reduction in TF antigen (nonfunctional plus functional TF) or TF mRNA.
Human umbilical vein ECs were harvested as described elsewhere10 and seeded on Permanox chamber slides (21×45 mm, Nalge Nunc, Inc) or on glass slides (38×75 mm, Fisher Scientific Co) precoated with fibronectin (10 μg/mL). The medium consisted of medium 199 (Whittaker Bioproducts), 20% fetal calf serum, 150 μg/mL heparin (from porcine intestinal mucosa, Sigma Chemical Co), 50 μg/mL EC growth supplement (Biomedical Technologies), 2 mmol/L l-glutamine, 100 U/mL penicillin, and 100 μg/mL streptomycin (both from Sigma). Monolayers were used when fully confluent, generally at 3 to 7 days of age, as assessed by means of phase-contrast microscopy.
Monolayers were mounted in specially designed parallel-plate flow chambers, 1 of which11 accommodated the 21×45-mm Permanox slides, while the other12 accepted the larger 38×75-mm glass slides. Both chambers were placed within an incubator and perfused with complete culture medium containing 50 U/mL IL-1α (Genzyme, Inc) by interposing a given chamber between a sterile reservoir and a withdrawal pump (shear stress of 0.68 dyne/cm2) or by placing the chamber in a recirculating-flow device driven by a gravity head, in turn maintained by a roller pump (shear stress of 13.2 dyne/cm2). The second chamber required larger flow rates for the same shear stresses, given its larger cross-sectional area. While the first chamber (endothelial surface area of 1.9 cm2) was used for measurements of TF antigen, TFPI antigen, TFPI protein in the supernatant, and factor Xa production (see below), the second chamber (surface area of 13.2 cm2) was necessary for both accurate measurements of TFPI secretion and harvest of large numbers (0.5 to 1×106) of shear-exposed ECs for studies of TF mRNA. Control (static) monolayers, both large and small, were placed in an incubator in a tissue culture dish containing complete medium and the same concentration of IL-1α. Duration of flow (or stasis) was always 3 hours. Unless otherwise stated, IL-1α exposure was simultaneous with flow.
In further experiments with the first chamber type concerning factor Xa production, monolayers were (1) exposed to a shear stress of 0.68 dyne/cm2 for 3 hours in the absence of IL-1α and then exposed to IL-1α in the absence of shear for an additional 3 hours or (2) exposed to IL-1α in the absence of shear for 3 hours and then exposed to a shear stress of 0.68 dyne/cm2 for 3 more hours in the absence of IL-1α.
Immunogold Labeling for TF and TFPI Antigens
TF and TFPI antigens were identified by immunocytochemistry for light microscopy. After exposure to shear stress, monolayers were fixed in 4% paraformaldehyde solution, washed 3 times in PBS, coated with 10% normal goat serum (as the blocking agent) in PBS for 20 minutes, and then incubated for 1 hour at room temperature with either 30 nmol/L of a polyclonal anti-TF antibody (raised in rabbits to the extracellular domain of recombinant soluble TF, residues 1 to 218; courtesy of Dr Yale Nemerson, Mt Sinai Medical Center, New York, NY) or 30 nmol/L of a monoclonal antibody against TFPI (mouse anti-human; American Diagnostica). The primary antibodies were detected with a secondary gold-conjugated antibody (goat anti-rabbit with 10-nm gold particles, or goat anti-mouse with 5-nm gold particles; Amersham Life Science). As a control for nonspecific binding of the secondary antibody, the primary antibody was omitted from a portion of every monolayer that nonetheless received the secondary antibody. Monolayers were then postfixed with 2.5% glutaraldehyde in cacodylate buffer. For light microscopy (Optiphot, Nikon), the bound gold particles were subsequently enhanced with silver (IntenSE M silver enhancement kit RPN491, Amersham Life Science) and visualized with dark-field and interference reflection contrast microscopy. Quantification of bound antibody against TF or TFPI was performed on light microscopy specimens by interference reflection contrast microscopy with a ×20 objective. Interference reflection contrast microscopy was favored over dark-field microscopy because epi-illumination prevented scattered light from the ECs and revealed only the silver-enhanced gold particles. By means of a CCD camera (model 300-RC, Dage-MRI, Inc) and a frame grabber with Inspector software (Matrox Electronics Systems, Ltd), 5 random images of each immunolabeled EC monolayer were digitized, recorded onto hard disk (Dimension XPS P120C, Dell Computer Corp), and analyzed for the percentage of image pixels occupied by silver-enhanced gold particles. Because immunolabeling may have varied on different days, we compared EC labeling performed on the same day only.
Chromogenic Assay for Factor Xa Under Nearly Static Flow Conditions
As a measure of functional TF, we determined levels of activated clotting factor X (factor Xa) that appeared in the supernatant of intact endothelium or subendothelial matrix by using an amidolytic technique.3 For this purpose, EC monolayers (on Permanox slides) after exposure to shear stress and IL-1α were incubated at 37°C under nearly static conditions (see below) with a “reaction complex” consisting of 0.01 mol/L HEPES, 0.14 mol/L NaCl, 10 nmol/L factor VII, 100 nmol/L factor X (both from American Diagnostica), 5.0 mmol/L CaCl2, and 1 mg/mL bovine serum albumin. Aliquots of postincubation reaction complex were mixed with an equal volume of 75 mmol/L EDTA to inhibit further activation of factor X and then incubated with Spectrozyme Xa (0.5 mmol/L final concentration, American Diagnostica) at 37°C for 30 minutes. To block further action of factor Xa on the chromogenic substrate, we then added 30% acetic acid (1 part to 5 parts reaction complex). Samples were read in a microplate reader at 405 nm for the increase in absorbance of free chromophore; a calibration chart had been constructed previously by using known concentrations of purified factor Xa (A. Guha, Mt Sinai Medical Center, New York, NY).
Factor Xa production was assayed under nearly static conditions at 0.054 dyne/cm2 in the same flow chamber used for shear preconditioning or, when true static conditions were used, monolayers were mounted for assay purposes in an identical chamber (control static monolayers) at 0.054 dyne/cm2. The low shear stress (0.054 dyne/cm2) during the factor Xa assay, which characterized the nearly static conditions, was sufficient to allow chamber outflow sampling (over a 40-minute period) without disassembly of the flow chamber yet approximated well the true static conditions when compared with either of the shear preconditioning stresses (0.68 or 13.2 dyne/cm2). Factor Xa production was estimated as the product of the nearly static flow rate and the steady-state outflow concentration of factor Xa (achieved after 15 minutes).
The specific TF origin of factor Xa activity was confirmed by additional experiments in which activated monolayers under “true” static conditions were incubated for 30 minutes with 100 nmol/L of the above polyclonal anti-human TF antibody, versus 100 nmol/L of a nonspecific rabbit IgG. Factor Xa production was calculated from the rate of increase of factor Xa over time.
In view of the reported equilibrium13 14 that is believed to exist between supernatant “free” TFPI and EC-associated TFPI, we previously15 characterized the affinity in solution of a monoclonal antibody directed against Kunitz domain 1 of human TFPI (American Diagnostica) for EC-associated TFPI in terms of Michaelis-Menten kinetics. For human umbilical vein ECs,15 we estimated an apparent rate constant, k, of 8.68±3.08 μg/mL (mean±SE) and a maximum production rate of factor Xa, Fmax, of 1.385±0.191 fmol/cm2 per 100 000 cells (mean±SE). Therefore, some monolayers were washed with HEPES buffer with 0.1% bovine serum albumin and incubated with 100 nmol/L anti-TFPI for 30 minutes at 37°C. After a single wash with the same HEPES buffer, the monolayers were assayed for factor Xa production as described above. Control experiments were carried out in which TF activity was assessed in the absence of cytokine activation (“baseline” activity), without and with anti-TFPI.
Assay for TFPI
Antigenic levels of TFPI in cell culture supernatants were determined by using an ELISA for total (full-length plus truncated) TFPI (product 849, American Diagnostica). TFPI secretion after IL-1α activation with shear preconditioning at 0.68 dyne/cm2 or IL-1α activation during a period of true stasis was measured from chamber outflow sampling in a manner similar to that described above for factor Xa production; ie, nearly static conditions were used. TFPI secretion after 3 hours at 0.68 dyne/cm2 or after 3 hours under static conditions was calculated as the product of the nearly static flow rate and the steady-state outflow concentration of TFPI (achieved after 30 minutes). For 13.2 dyne/cm2, samples after 3 hours were taken directly from the upper reservoir of the recirculation device, which had been filled with medium containing or not containing IL-1α. TFPI secretion was then calculated as the product of the rate of rise of TFPI concentration and the total volume (15 to 20 mL) of the recirculation device. Preliminary experiments had shown that TFPI levels in complete media were <0.1 ng/mL and were augmented to only a minor extent by cytokine activation without or with shear preconditioning.
Quantitative RT-PCR Amplification Products of TF mRNA
Total RNA from guanidine isothiocyanate extracts of cell cultures (isolated as indicated for Northern blot analysis) was used for reverse transcription–polymerase chain reaction (RT-PCR). First-strand cDNA synthesis (RT reaction) used 4 μg of total RNA and 0.2 A260 U of random-hexamer primers (Boehringer-Mannheim) and was performed for 1 hour at 37°C with 400 U of M-MLV reverse transcriptase (Promega) in Promega reaction buffer and 40 U of RNase inhibitor (Boehringer-Mannheim). PCR was performed in a Mini Cycler (MJ Research). In each reaction we used 5% of the RT reaction (2 μL of a 40-μL RT total volume), 2 pmol of primer oligonucleotides for TF, 1 pmol of primer nucleotide for glyceraldehyde 3-phosphate dehydrogenase (GAPDH), and 2 U of Taq polymerase (Fisher Scientific), in PCR reaction buffer B (Fisher Scientific) supplemented with 4 μL of 25 mmol/L MgCl2 to a final concentration of 4 mmol/L in a final reaction volume of 25 μL. Oligonucleotide primers for TF were synthesized from published primer sequences4 and yielded a product of 204 bp. Those for GAPDH were constructed complementary to the known sequence for GAPDH. The primer sequences for GAPDH were AAG GTG AAG GTC GGA GTC AA for the 5′ end and TGA GTC CTT CCA CGA TAC CA for the 3′ end, resulting in a 511-bp product. Thermal cycling parameters were as follows: initial denaturation at 95°C for 1 minute followed by 94°C for 30 seconds, annealing at 50°C for 30 seconds, and extension at 72°C for 2 minutes per cycle, with a final extension at 72°C for 5 minutes. Linear amplification (log optical density of RT-PCR amplification products) was established with respect to cycle number for both TF and GAPDH primer pairs. Quantification of the products was performed by measuring optical density in the range of 20 to 22 cycles.
Endothelial Monolayer Morphology
No loss of EC monolayer integrity was observed at 4 hours and over the range of shear stress used (0 to 13.2 dyne/cm2). ECs also did not undergo elongation and alignment with flow direction, a phenomenon observed by others16 after longer periods of shear stress.
Immunogold Labeling for TF and TFPI Antigens
Because unstimulated ECs do not express TF antigen at their surfaces, we considered the weak immunolabeling (0.5%) found at those cell surfaces to be nonspecific (Figure⇓ I; published online at http://atvb.ahajournals.org), an impression confirmed in every 1 of our experiments by a similar degree of weak labeling observed in the absence of primary antibody but in the presence of the secondary antibody (Figure⇓ II; published online at http://atvb.ahajournals.org). Cytokine activation of the ECs increased TF labeling from this background level to 5% to 8% (n=3, Figure 1a⇓ versus Figure⇓ I). Subjecting ECs to venous and arterial shear stress while simultaneously being activated with IL-1α further increased surface TF antigen expression by 2-fold and 5-fold, respectively (n=3 in each case, Figures 1b⇓ and 1c⇓). As for TFPI antigen, a baseline level of detectable antigen was present in the absence of IL-1α, which was not detectably increased after cytokine activation, in accord with only a modest 25% increase observed by others17 after stimulation with thrombin. However, this baseline level in the presence of cytokine activation was increased ≈2-fold by shear stress over the range of shear stress investigated (Figures 2a⇓ and 2b⇓). In the absence of primary antibody but in the presence of secondary antibody, only weak labeling was observed (Figure⇓ III; published online at http://atvb.ahajournals.org).
Factor Xa Production
Preconditioning of the ECs with a shear stress of 0.68 dyne/cm2 for 3 hours, with simultaneous activation with IL-1α, reduced functional TF to 43% of baseline, while detectable factor Xa was not significantly different from 0 at 13.2 dyne/cm2 (Figure 3⇓). When shear stress preconditioning for 3 hours in the absence of IL-1α preceded cytokine activation under static conditions for 3 hours, functional TF was reduced to 12% of control. However, when cytokine activation preceded shear preconditioning, functional TF declined to only 71% of baseline (Figure 4⇓). Control experiments under static conditions with 100 nmol/L of the polyclonal antibody to human TF reduced functional TF by 92±6.8% (n=4).
Under static conditions, the presence of 100 nmol/L anti-TFPI augmented (P<0.01) measurable factor Xa production after IL-1α stimulation by 2.1-fold, from a mean±SE (n=number of experiments) of 1.27±0.25 (n=6) to 2.61±0.19 (n=6). In the absence of IL-1α activation, factor Xa production was similar with and without anti-TFPI: 0.11±0.016 (n=4) and 0.08±0.020 (n=4) fmol/min×cm2, respectively.
TFPI secretion after IL-1α activation increased significantly with simultaneous shear stress (P<0.01), attaining 3-fold and nearly 7-fold increments at 0.68 and 13.2 dyne/cm2, respectively, over that under no shear stress (Figure 5⇓). Results did not differ significantly in the presence versus absence of IL-1α stimulation.
In 3 separate experiments, the RT-PCR amplification products for both TF mRNA and control GAPDH mRNA neither increased nor decreased significantly with shear stress (Figure 6⇓).
We report here that shear stress reduces functional, but not antigenic (nonfunctional plus functional) expression of TF by intact, activated EC monolayers in a time- and shear stress level–dependent manner. Indeed, the expression of surface TF antigen was markedly enhanced by shear stress, whereas for acute changes in shear stress investigated in this study, there was no significant change in TF mRNA. The decrease in functional TF instead may be due to secretion into the medium of sufficient TFPI to offset any increased production of factor Xa. The endothelium accomplishes this by ensuring that its rate of secretion of TFPI (and any component of “secretion” that may be new TFPI synthesis) is both shear rate augmented and always just large enough so that the rate-limiting step for transport into the culture medium (or, in vivo, into the blood) is convective diffusion, not the rate of secretion itself. The net result is the maintenance, despite increasing shear rates, of a relatively constant concentration of TFPI in a “boundary layer” immediately adjacent to the endothelium. (See the Appendix.) This boundary layer concentration is believed to be in equilibrium with cell surface–associated TFPI.13 14 Therefore, cell surface–associated TFPI need not increase markedly with shear stress (see below). We also have previously reported no significant change in TFPI secretion after cytokine activation,15 an observation consistent with that of Ameri et al,18 who found increases in TFPI levels only of the order of 25%.
In parallel with this mechanism, shear stress may also favor, to a modest extent, the redistribution and increased exposure of TFPI on the EC plasma membrane, such as has been reported for thrombin stimulation under static conditions.17 Such TFPI is believed to “encrypt” TF by forming TF/factor VIIa/factor Xa/TFPI assemblies that inhibit TF/factor VIIa in glycosphingolipid-rich microdomains and translocate into low-density, detergent-insoluble cellular fractions enriched in caveolin (caveolae19 20 ). In this regard, we note that surface TFPI antigen in the present study, as assessed by immunogold labeling, was maintained—even doubled—over the range of shear stress from 0 to 13.2 dyne/cm2. A third mechanism for the effects of shear stress on functional TF may be a shift in the partitioning of TF between apical and basolateral surfaces, possibly by bringing more TF to the apical surface where it can be inhibited by the formation of TF/factor VIIa/factor Xa/TFPI assemblies.
Whatever the mechanism, a potent role for TFPI is supported by our findings under static conditions of a 2.1-fold increase in functional TF with 100 nmol/L anti-TFPI and by our earlier observation under static conditions15 of a 3.7-fold increase with a molar excess of anti-TFPI. Under flow conditions with a lower concentration of IL-1α, we demonstrated increases in functional TF of 15-fold and 25-fold at shear stresses of 0.68 and 2.7 dyne/cm2, respectively, with the use of 300 nmol/L of a polyclonal anti-TFPI (calculations from data of Figure 3⇑ of Reference 33 ). TFPI, therefore, may have an even more potent role under shear stress conditions.
Matsumoto et al4 have reported a decrease with respect to shear stress in functional TF, surface TF antigen, and TF mRNA by tumor necrosis factor-α–activated ECs, the magnitude of the decrease in functional TF being dependent on both shear intensity and duration. In most of their experiments, the ECs were preconditioned with shear stress for 15 hours before the onset of stimulation with tumor necrosis factor-α. Shorter periods of preconditioning led to lower degrees of reduction in TF mRNA (Y. Ikeda, unpublished data, August 1999). These workers interpreted their findings to be indicative of shear attenuation of TF mRNA, a conclusion that may apply to longer (eg, 15-hour) periods of preconditioning, but not to shorter (eg, 3-hour) periods.
In the “closed” cone-in-plate system used by Matsumoto et al,4 it is furthermore probable that TFPI accumulated over time and contributed to the observed reduction in functional TF for intact endothelium. In contrast, the reduction in functional TF of the present study was observed at 0.68 dyne/cm2 in a single-pass system, which eliminates the possibility of such TFPI accumulation. This is not a trivial matter, because the presence of an antibody directed against Kunitz domain I of human TFPI was found in the present work and in previous work15 to more than double measurable production of factor Xa under static conditions, indicating a marked downregulation by TFPI of EC functional TF even under static circumstances. We hypothesize that the downregulation of functional TF under flow conditions is due chiefly to TFPI when changes in shear stress are acute (eg, nearly simultaneous with the onset of cytokine exposure) but may be due as well to downregulation of TF mRNA (and possible upregulation of TFPI mRNA) when changes in shear stress are more chronic (eg, lasting several hours or more).
Lin et al21 and Houston et al22 both reported that shear stress alone (no cytokine exposure) transiently induced TF mRNA over periods of 1 to 3 hours. Transcription factors likely involved in these shear stress–induced changes in TF mRNA include Sp1, whose increased activity is associated with hyperphosphorylation,21 and/or Egr-1,22 23 24 but not nuclear factor-κB.4 In those studies, either human umbilical vein ECs were subjected to 12 dyne/cm2 for 1 to 2 hours21 or human aortic ECs were exposed to 15 dyne/cm2 for 1 to 3 hours.22 Lin et al found that TF mRNA by Northern blotting was essentially no longer present after 6 hours; Houston et al, who performed RT-PCR, did not look beyond 3 hours. Although the present work does not address this issue, we did find that TF antigen at 3 hours increased with increasing shear stress. Although we also found no significant effect of shear stress on TF mRNA at 3 hours, it is possible that shear stress may have shortened the time required for TF mRNA to attain a “ceiling” level, thereby still having an effect on the area under the curve for TF mRNA. A further point is that both Matsumoto et al4 and the present work used cytokine stimulation, whereas Houston et al and Lin et al did not: stimulation with tumor necrosis factor-α or IL-1α may have quantitatively masked any response due to shear stress itself. In support of this is our earlier observation with a 10-fold lower concentration of IL-1α: factor Xa production, with or without anti-TFPI, was actually enhanced at a shear stress of 0.68 dyne/cm2 compared with no shear stress.3
These findings suggest that flow has a direct effect on diminishing the ability of activated ECs to generate functional TF. One may speculate that stasis in vivo may therefore promote coagulation by permitting the relative upregulation of TF and TF mRNA and downregulation of TFPI secretion. Such a process may be operative in deep venous thrombosis or in coronary artery thrombosis as a compounding event after acute near-closure due to platelet thrombi and/or vessel spasm. This remains to be clarified in future work.
Convective Diffusion of TFPI
The convective diffusion of a substance from a surface can in general be considered a 2-step process. Step 1 is the local “production and/or release rate” of the substance at the surface itself, which for TFPI in the current study is its rate of secretion. Step 2 is convective diffusion of the substance into the bulk of the adjacent flow and downstream. When the first step is rate limiting, the gradient in the concentration of the substance normal to the surface is fixed, while the surface concentration diminishes with increasing flow rate. Convective diffusion is then said to be surface reaction–rate limited. When the second step is rate limiting, the surface concentration of the substance is fixed, while the surface concentration gradient increases with increasing flow rate. Convective diffusion is then said to be diffusion limited. Because the secretion rate of TFPI in the current work was found to increase with increasing shear stress (or shear rate), it is likely that the latter condition well approximates the convective diffusion of TFPI. Mathematically, such a diffusion-limited process for a concentration boundary layer confined to a fraction of the thickness of the chamber flow path and for isotropic diffusion (according to the Fick equation) in a homogeneous, incompressible fluid25 is described by the Leveque26 equation:
where −D(dc/dy)y=h is the diffusion (production) rate of TFPI, in mol/cm2×s, from the EC surface; D is the Brownian diffusion coefficient for TFPI, in cm2/s; c is the local concentration of TFPI, in mol/cm3; y is the distance from the plane bisecting the chamber flow path, in cm; C0 is the concentration of TFPI at the EC surface, in mol/cm3; h is half of the height of the flow chamber, in cm; U is the mean flow velocity in the flow chamber, in cm/s; and x is the axial (downstream) position from the chamber inlet, in cm.
For an increase in shear stress (or mean flow velocity) from 0.68 to 13.2 dyne/cm2, −D(dc/dy)y=h should increase by a factor equal to the one-third power of (13.2/0.68), or by a factor of 2.7. The observed increase is a factor of 2.4. The present TFPI data are therefore consistent with diffusion-limited convective diffusion, which predicts a surface concentration of TFPI that changes little with shear stress. This is also in accordance with the present experimental observations involving immunogold labeling of surface TFPI, which showed that the surface antigen concentration of TFPI changes at most by a factor of 2 over the range of shear stress studied.
This work was supported by grant No. HL33095 from the National Heart, Lung, and Blood Institute, Bethesda, Md. Dr Reininger’s salary was supported by DFG grant No. RE-1293/3–1.
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