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The Functional Expression of Tissue Factor by Fibroblasts
and Endothelial Cells Under Flow Conditions
By Eric F. Grabowski, Dina B. Zuckerman, and Yale Nemerson
The expression of tissue factor (TF) by a variety of vascular
cell types under physiologic flow conditions is critical t o
factor X activation and invivo clotting. Therefore, in a parallel-plate flow chamber (volume 40 pL) w e mounted monolayers of human embryonic fibroblasts (FBs) or interleukinl a (IL-la) (5 U/mL X 4 hours)-stimulated human umbilical
vein endothelial cells (ECs). Inflow buffer contained 10
nmol/L factor Vlla, 100 nmol/L factor X, and 2.0 mmol/L
CaCI,. With FBs, production of factor Xa (product of outflow concentration of factor Xa and flow rate) increased
ZOO-fold over the range of shear stress from 0 to 2.7
dynes/cm2. Production values (mean f SE (N)) were 7.93
2 0.024 (6). 3 1 2 f 7.3 (6), 688 f 33.1 (8). 1,033 f
119 (6). and 1,601 f 183 (7)fmol/cm2 * minute at shear
stresses of 0. 0.27, 0.68, 1.35, and 2.7 dynes/cm2, respectively. Further experiments at 0.68 dynes/cm2 indicated that factor Xa production increased with factor X
concentration over the range from 3 t o 100 nmol/L, but
changed little from 300 to 1,000 nmol/L. With ECs, productionwas0.13 f 0.86(6),8.17 -C 1.65(13),and1.66 f
1.66 (5) fmol/cm2 minute at 0,0.68, and 2.7 dynes/cm2,
respectively. However, in the presence of an antibody directed against tissue factor pathway inhibitor (TFPI) production with ECs was augmented t o 16.46 f 0.80 (8),
149.8 2 18.6 (8). and 48.9 f 10.3 (10), respectively, at
these same shear stresses. Control experiments with factor Vlla, factor X, or both absent confirm for both cell types
the specificity of the reaction for the TF pathway. Similarly, specificity for TF itself is shown by the virtual absence of factor Xa generation in the presence of the monoclonal antibody HTFl -788 directed against human TF. We
conclude that ECs, even when activated, are normally unable t o generate significant quantities of factor Xa in the
presence of factors X and Vlla. However, significant quantities of factor Xa are possible in the presence of an inhibitor of TFPI. On the other hand, production of factor Xa by
fibroblasts is markedly augmented by shear stress, yet independent of the availability of substrate factor X above an
inflow concentration of 100 nmol/L. The latter suggests a
direct effect of flow on the fibroblast monolayers, not substrate limitation by convective diffusion.
0 1993 by The American Society of Hematology.
W
HILE THE INTACT vascular endothelium norflow directly augments the expression of T F by monolayers
mally acts to inhibit coagulation and thrombosis, reof FBs, while ECs, even when activated, are normally limcent work suggests that under certain circumstances endoited with respect to TF expression, in large part because of
thelial cells may actively promote coagulation and
tissue factor pathway inhibitor (TFPI).
thrombosis by various mechanisms. These include the expression of tissue factor (TF)'-", platelet-activating f a c t ~ r , ~
MATERIALS AND METHODS
and binding of activated factors IX and X.6 In particular,
endothelium can be stimulated to express TF-like procoaguEC monolayers. Primary passage monolayers of human umbililant activity (PCA) in a manner independent of cyclooxycal vein endothelial cells (ECMs) were grown to confluence on 25 X
genase inhibitors. Along with endotoxin' and tissue necrosis
76 mm Permanox tissue culture slides (Laboratory Disposable Prodfactor,' a key stimulus is interleukin-1 (IL-l), a multifuncucts, North Haledan, NJ) according to established techniques.16
Owing to the slight buoyancy of Permanox, special metal retainers
tional inflammatory/immune mediator that is produced by
were used to keep the cover slides at the bottom of square Petri
stimulated mononuclear phagocytes. The effect of 5 to 10
dishes holding three slides each. Plastic was used because we have
U/mL IL-1 on cultured human umbilical vein endothelium
is detectable after 30 minutes and maximal by 4 h o ~ r s . ~ , ~previously determined that human ECs grow poorly on glass (Grabowski EF, McDonnel S, unpublished observations, August 199I).
PCA has usually been measured by means of a clotting assay
Culture medium was Medium 199 containing human and bovine
performed either with cell lysates or intact monolayers.
calf sera (5% and 15%, respectively), 40 pg/mL of EC growth factor
Tissue-factor-producing cells have been identified in hu(Meloy Laboratories, Springfield, VA), 90 pg/mL of heparin (from
man vessels by in situ hybridization and immunohistocheporcine intestinal mucosa: Sigma, St Louis, MO), 2 mmol/L L-glumistry using a riboprobe for TF mRNA and a polyclonal
antibody directed against human TF. While present in fibroblast (FB)-likeadventitial cells, in cells present in atheroscleFrom the Department ojpediatrics, Massachusetts General Hosrotic plaques, and in scattered cells of the tunica media, TF
pital, and Harvard Medical School, Boston, MA: and the DepartmRNA and protein are not found in endothelial cells (ECs)
ments of Medicine and Biochemistry, School ojMedicine of the City
lining normal arteries, veins, and
Therefore,
University of New York, New York, NY.
the antigenic, as well as functional, expression of T F on
Submitted August 29, 1991; accepted January 25, 1993.
Supported by Grant No. H L 33095 from the National Heart,
intact endothelium in vivo is in doubt.
Lung, and Blood Institute.
Nevertheless, certain EC products and functional properAddress reprint requests to Eric F. Grabowski, MD, ScD, Pediatties have been found to be augmented by shear stresses of
ric Hematology/Oncology Unit, Massachusetts General Hospital,
physiologic flow, including prostacyclin," tissue plasmino15 Parkman St, Boston, MA 02114.
gen activator,'' and a K+ current.12 However, cellular T F
The publication costs of this article were defrayed in part by page
has not been studied in this regard, although Gemmel et
charge payment. This article must therefore be hereby marked
aIL3-l5
have observed increased production of factor Xa in a
"advertisement" in accordance with 18 U.S.C. section 1734 solely to
nonbiologic system that incorporated TF in a lipid bilayer
indicate this fact.
immobilized on the inner surface of a glass capillary tube,
0 1993 by The American Society of Hematology.
The purpose of the present communication is to show that
0006-49 71/93/81 12-0005%3.00/0
Blood, Vol81, No 12 (June 15). 1993: pp 3265-3270
3265
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3266
tamine, and 100 U/mL of penicillin and 100 pg/mL streptomycin
(Whittaker Bioproducts, Walkerville, MD). The ECMs were used
after 4 to I I days of culture. Just before study, the ECMs were
activated with recombinant human (rh) IL- I-a (Genzyme, Inc,
Boston, MA) at 5 U/mL for 4 hours. A few ECMs received no
IL- 1-a.
During the last 60 minutes of activation with IL-]-a, some
ECMs were incubated with a 1:30 dilution (44 pg/mL protein) ofan
antibody isolated from a rabbit antiserum against TFPI” (courtesy
of G. Broze, Washington University School of Medicine, St Louis,
MO) by chromatography on a protein A-Sepharose 4B column
(kindly performed by A. Guha, Mt Sinai Medical Center, New
York, NY). This antiserum is believed to be specific to TFPI insofar
as reactivity with TF, as well as with factors VII. IX, and X, cannot
be shown by Western blotting (G. Broze, personal communication,
September 1992).The dilution chosen was based upon factor X
activation (see below) that in preliminary experiments was enhanced 10-fold with I: 10 and 1:30 dilutions, but was enhanced less
than twofold with a 1:lOO dilution. Control ECMs were incubated
with like dilutions of a nonspecific rabbit serum.
FB monolayers. Monolayers of human embryonic lung FB
(American Type Culture Collection [ATCC], Rockville, MD) of
passage I3 to I6 were grown to confluence on 22 X 60 mm, gelatincoated (0.2%) cover glasses (thickness I 1/2; Fisher Scientific,
Springfield, NJ). Culture medium used was EMEM (Minimum Essential Medium, Eagle) containing 10%bovine calf serum, 100 vol/
mL penicillin and 100 pg/mL streptomycin (Whittaker Bioproducts, Walkersville, MD), and 2 mmol/L L-glutamine. The
monolayers were used aRer 7 to 24 days of culture.
Flow system. An infusion pump (model no. 27 16; Harvard Apparatus Co, South Natick, MA) drove buffer (see below) through a
30-cm length of 0.20-cm internal diameter Silastic tubing (Dow
Corning, Indianapolis, IN) to the inlet port of a parallel-plate flow
chamber, mounted on the stage of an inverted-phase microscope
(model TMS; Nikon, Inc, Garden City, NY) coupled to a SIT camera (Cohu Inc, San Diego, CA). An air-stream incubator(Nicho1son
Precision Instruments, Gaithersburg, MD) maintained tubing,
chamber, and microscope stage at 37”C, as confirmed by a temperature probe (model no. TH-5; Bailey Instruments, Inc, Saddlebrook,
NJ). The chamber’s construction” provided for the thin-film flow
of medium past a cell monolayer as well as vacuum “clamping” of
the periphery of the cover glass or Permanox slide to assure constancy and uniformity of film thickness (290 pn). Flow rates of
0.10,0.25,0.5,
and 1.O mL/min were used. For a buffer (see below)
viscosity of 1.0 cp, these correspond to shear stresses at the medium-monolayer interface of 0.28,0.68,1.35, and 2.7 dynes/cm2,
respectively. Such shear stresses are characteristic of small and large
veins.’’ Monolayer confluence at the beginning and end of each
experimental run was confirmed by in situ inverted-phase videomicroscopy and recorded on videotape.
Static system. Zero shear-stress control studies were performed
with monolayers of ECs or FBs also grown on Permanox or glass
but retained in tissue culture dishes (Petri or 4-well multidishes;
Nunc, Inc, Naperville, IL). Passage numbers and culture media
were identical to those used in flow studies.
Chromogenic assay. Chamber inflow buffer consisted of 0.0 1
mol/L HEPES containing 0.14 mol/L NaCI, 10 nmol/L factor
VIIa, 100 nmol/L factor X, 2.0mmol/L CaCI,, and 1 mg/mL bovine serum albumin (BSA). However, just before being mounted in
the chamber, monolayers on slides or cover glasses were washed
three times with inflow buffer free of factor VIIa and factor X. This
step was necessary to eliminate interference of pH indicator dyes
(present in Medium 199 and EMEM) with measurements of tissue
factor activity by means of a chromogenic assay for factor Xa. This
GRABOWSKI, ZUCKERMAN, AND NEMERSON
step also served to minimize serum-derived factor VIIa and factor
X.
Outflow samples (0.5 and 1.0 mL) were collected into an equal
volume of 75 mmol/L EDTA on ice to prevent any further generation of factor Xa. The samples were next combined with a 9:l solution of a chromogenic substrate (0.5 mmol/L, Spectrozyme Xa;
American Diagnostica, Inc, Greenwich, CT) for the amidolytic assay of factor Xa production, and incubated at 37°C for 30 minutes.
At the end of this time period, further production of free chromophore was blocked with a 30% solution ofacetic acid (200pL/mL of
sample) and the absorbance of the free chromophore (para-nitroaniline) generated was promptly read for all samples in a spectrophotometer (model 1234X; Gilford Instrument Lab, Inc, Oberlin, OH)
at 405 nm. Blanks used samples of inflow buffer collected in parallel. Purified factor Xa of known concentration (courtesy of Dr. A.
Guha, Mt Sinai Medical Center, New York, NY) allowed generation of a calibration curve linear down to approximately 20 pmol/
L. However, the presence of factor Xa could be detected qualitatively down to at least I pmol/L. Production ofa free chromophore
in femtomoles per square centimeter of monolayer per minute was
calculated as the product of outflow concentration of free chromophore and flow rate.
Monolayers in tissue culture dishes were treated similarly, except
that there was no flow and a single 60-minute sample was collected
into EDTA on ice. Dish volume was 4.0 mL per Permanox slide
and I .O mL per glass slide.
Experiments. There were three principal experiments. In the
first, factor Xa production by FBs was compared with that by activated endothelium, the latter without or with anti-TFPI, as a function oftime and shear stress. In control experiments, anti-TFPI was
added directly to inflow buffer in the absence of cells. Factor Xa
production by unactivated endothelium was also measured at 0.68
dynes/cm2 in three experiments without anti-TFPI. Monolayers
and inflow buffer were in contact with one another in the flow
chamber at 37°C for less than 2 minutes before the start offlow. In
preliminary experiments with FBs, factor Xa production for all
flow rates generally decreased with time (Fig I). However, in some
experiments production increased or remained the same from the
first to the second sample. For a subset of these studies, 30 nmol/L
of an antihuman tissue factor murine monoclonal antibody
(MoAb) (HTF1-7B8)’’ before the onset of flow was incubated with
the monolayers for 230 minutes. Control experiments used 30
nmol/L of nonspecific mouse Ig.
In the second set of experiments, factor Xa production by FBs at
0.68 dynes/cm2 was measured as a function ofinflow concentration
( 3 , IO, 30, 100,300, and 1,000nmol/L) of factor X. The purpose of
these experiments was to determine whether factor Xa production
in this situation was limited by the convective diffusion of factor X.
In the third set of experiments, factor Xa production by fibroblasts and activated ECs (without anti-TFPI) at 0.68 dynes/cm2 was
studied in the absence of factor Vlla, factor X, or both. The aim
here was to confirm the specificity of factor Xa production for factors VIIa and X.
RESULTS
ECs versus FBs. Figure 1 shows that at 0.68 dynes/cmz
and for factor VIIa and X concentrations of I O and 100
nmol/L, respectively, factor Xa for both FBs and ECs was
maximal in the first few minutes of flow, decreasing slowly
thereafter. Because at constant flow rate factor Xa production is proportional to factor Xa concentration, factor Xa
production had the identical behavior. However, EC pro-
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3267
CELLULAR TISSUE FACTOR UNDER FLOW CONDITIONS
A
0
Activated endothelialcells
a-*-
8
12
Min
--
16
e
20
Factor Xa production, factor X , and factor VIIa. Figure
4 shows that FB production of factor Xa at 0.68 dynes/cm2
increased over the range of inflow factor X from 3 to 100
nmol/L. However, between 100 and 1,000 nmol/L it increased only a further 12%.Fitting the data at and above 30
nmol/L factor X to a rectangular hyperbola, as is typically
done for Michaelis-Menten kinetics (ENZFITTER, Elsevier, Amsterdam, Holland), yields a value for V,,, of 792 f
47 fmol/cm2. minute at 0.68 dynes/cm2. Note that the data
of Fig 2 indicates that V,, must increase with shear stress.
Km, the concentration at which the reaction velocity is onehalf V,,, was determined to be 35.7 -t 8.4 nmol/L.
In further experiments (Table I), the absence of inflow
factor VIIa, factor X, or both led to production rates relative
to FB and EC controls of 0 to 3.1 % for FBs, and 0 to 5.0%for
ECs, respectively.
Fig 1. Factor Xa concentration and production rate for FBMs
and ECMs versus time. Shear stress was 0.68 dyneslcm’.
duction in the absence of anti-TFPI was of the order of only
1% of that for FBs.
The specificity of the process for TF was confirmed by
preincubation of monolayers with antihuman TF murine
MoAb HTF1-7B8. As compared with controls using 30
nmol/L of a nonspecific murine IgG, factor Xa levels and
factor Xa production were each inhibited by 100%. This was
true in six experiments with each cell type over the range of
0.68 to 2.7 dynes/cm2. Even the minimal activity associated
with activated ECs was totally eliminated. Similarly, zero
factor Xa production was seen in the experiments with unactivated ECMs.
Because of the above time-dependence of factor Xa levels
and production, all subsequent figures and tables use values
for outflow samples collected immediately after the first 1
mL of flow. This has the advantage of yielding maximal
values likely independent of any kinetic t r a n ~ i e n t asso’~
ciated with the binding of inflow factor VI1 to T F to produce
the TFVIIa surface enzymatic complex. At 0.25 mL/min
(0.68 dynes/cm2), for instance, the values used exclude the
first 4 minutes of flow.
Factor Xa production and shear stress. Figure 2 indicates that for FBs at 0.68 dynes/cm2 and for factor VIIa and
X concentrations of 10 and 100 nmol/L, respectively, factor
Xa production increased 200-fold over the range from 0 to
2.7 dynes/cm2. Factor Xa levels themselves decreased over
the range of shear stress from 0.27 to 2.7 dynes/cm2 (data
not shown), but not as rapidly as would have been the case
had production been independent of shear stress.
EC production in the absence of anti-TFPI over the same
range of shear stress remained of the order of 1% of that for
FBs (Fig 3). However, in the presence of anti-TFPI, production was augmented markedly (P< .001 at each of three
shear stresses), peaking at 22% that for FBs at 0.68 dynes/
cm’. While there appeared to be shear-stress enhancement
of this augmentation, the augmentation was not a simple
function of shear stress. Anti-TFPI added to inflow buffer in
the absence of cells (10 experiments) did not enhance the
absorbance of free chromophore.
DISCUSSION
Our demonstration of TF activity on the surface of intact,
activated endothelium is in agreement with previous observations by others of a procoagulant activity associated with
such endothelium by one- and two-stage clotting
Nevertheless, the amount of such activity is at most 1% of
that seen in the present work with FBs. This finding is consistent with the absence of TF mRNA and protein in ECs
lining human blood vessel^*^^ and, further, is all the more
striking in that it applies to cells possessing some degree of
activation. The finding is also consistent with the work of
Ryan et a12’ who noted the presence of T F antigen by immunoperoxidase staining chiefly in the interior of cultured
human ECs activated with tissue necrosis factor and permeabilized with saponin, or in matrix proteins of the abluminal surface. Very little T F was found at the intact cell
luminal surface. Preliminary studies of our own indicate
that activated ECs lysed by exposure to sterile water for 20
minutes are able to generate factor Xa at a rate enhanced
FIBROBLASTS
7
1600 1400 1200 -
6
1000 -
i
X
600
I
1.35
1
2.7
Shear stress, dynes/cm2
Fig 2. Factor Xa production rate for fibroblasts versus shear
stress.
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GRABOWSKI, ZUCKERMAN, AND NEMERSON
3268
Table 1 . Factor Xa Production in the Absence of Factor Vlla,
Factor X, or Both
.-c
E
N.
E,
Cells
Factor
Vlla Absent
FBs
ECs
3.12 k 0.97 (5)
5.0 1.5 (4)
*
Factor
X Absent
Both
Absent
0 (6)
0 (4)
0 (6)
0 (2)
FB or EC factor Xa production at 0.68 dynes/cm2 as a percent (mean
* SE, N) of FB or EC production with 10 nmol/L factor Vlla and 100
nmol/L factor X.
m‘
X
L
0
c
0
LL
5
T
Oo
0.27
0.68
2.7
1.35
Shear stress, dyneslcm2
Fig 3. Factor Xa production rate for activated ECs versus shear
stress. Open circles (0)
denote absence of anti-TFPI, while closed
circles (01 indicate presence of anti-TFPI. Note that ordinate has
been expanded 10-fold compared with that for Fig 2.
10- to 20-fold. All of these observations indicate that either
TF is expressed to a minimal extent on the plasma membrane of activated ECs, or that T F expression is subject to
powerful local regulation, such as by EC TFPI.23
Our findings of markedly augmented T F expression with
activated ECs in the presence of anti-TFPI suggest that T F
expression by ECs may indeed be normally under tight control by TFPI. One might speculate that procoagulant states
exist in which the efficacy or production of TFPI is impaired. The absence of a direct effect of anti-TFPI, added to
inflow buffer in the absence of cells, on the chromogenic
assay indicates that the anti-TFPI contained little or no factor Xa-like activity directed against the chromogenic substrate. One might hypothesize that anti-TFPI caused some
1000 -
300 -
7
4
51
/1-
degree of EC contraction and, therefore, enhanced exposure
of matrix-associated TFVIIa at intercellular junctions.
However, addition of anti-TFPI did not alter the morphologic appearance of the EC monolayers by inverted phasecontrast microscopy.
The rather marked increase in factor Xa production by
FBs with shear stress does not seem to be caused by substrate factor X limitation by convective diffusion, at least
for inflow factor X concentrations of 100 nmol/L or higher.
Calculations based on the boundary layer theory of convective diffusion indicate that the amval rate of factor X at the
FB (or EC) surface is of the order of 20 pmol cm2/min at
0.68 dynes/cm2 and for 1,000 nmol/L factor X (Appendix).
This rate is an order of magnitude greater than the observed
factor Xa production rate (Fig 4) of 0.8 pmol/cm2 minute
at the same shear stress. Therefore, the shear-stress dependence of FB factor Xa production must be caused by a direct effect of flow on the cell monolayers. Possible mechanisms for such a direct effect include: (1) increased efficacy
of an antigenically small amount of cell surface TFVIIa
complex (ie, a shear stress-induced steric or conformational
change); (2) decreased cell association, internalization and
degradation of factor Xa; and (3) increased exposure of matrix-associated TF:VIIa at intercellular junctions.
The first possibility is consistent with studies by Gemmell
et al,L3-’5
who used a tubular reactor whose inner walls were
coated with a bilayer of phospholipid (30%phosphatidylserine and 70% phosphotidylcholine) into which a known
quantity of T F was inserted. As in the present system, the
maximum rate of factor Xa production was found to increase with shear rate while remaining independent of factor X concentration above a certain factor X level. Because
Gemmell’s experiments used no cells, possibilities (2) and
(3) above do not apply. Interestingly. production rates at
100 seconds-’ ( I .O dyne/cm2) for FB monolayers and the
tubular reactor were comparable: 800 (by interpolation)
and 300 fmol/cm2 minute, respectively. In other words,
V,,, in each case increases with shear stress and is of the
same order of magnitude. The present Km (36 nmol/L),
however, is somewhat lower than Gemmell’s value of 438
nmol/L, indicating a greater affinity of FB TFVIIa for factor X.
With respect to the second possibility, ECs, and perhaps
also FBs, have a variety of mechanisms by which factor Xa
may become cell associated and/or degraded. These mechanisms include binding to a specific receptor with a Km of
3.6 n m ~ l / L association
,~~
with a covalent ~ o m p l e x , ’and
~
internalization and degradation by ECS.’~
.
-
6
X
L
fi
LL
Factor X, nM
Fig 4. Factor Xa production rate for fibroblasts versus Factor X
concentration. Shear stress was 0.68 dynes/cm2.
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CELLULAR TISSUE FACTOR UNDER FLOW CONDITIONS
Information concerning the third possibility is currently
lacking. However, exposure to shear stress did not alter the
morphologic appearance of the FB monolayers by inverted
phase-contrast microscopy.
Because production of factor Xa by activated ECs is normally two orders of magnitude smaller than that for FBs,
EC generation of factor Xa can only be even less dependent
on the convective diffusion of factor X. Such production
should, in fact, be virtually entirely dependent on local reaction kinetics involving TFVIIa. However, the data of
Nawroth et a126suggest for 35-mm wells that the upper limit
for EC internalization and degradation is only 0.2 fmol/
cm2.minute. This value is too small to affect the observed
production at 0.68 dynes/cm2. Larger rates of EC production of Xa may be possible after mechanical injury exposing
extracellular or subcellular TF, inhibition of TFPI (such as
by human leukocyte elastase), and viral infection leading to
an altered cell phenotype having enhanced expression of
functional TF. These possibilities are under current investigation.
Notwithstanding the likely independence of convective
diffusion of factor Xa production by activated ECs, this production still depends on shear stress, the manner being complex compared with that for fibroblasts. In particular, production by activated ECs peaks at 0.68 dynes/cm2 in both
the absence and presence ofanti-TFPI, while the augmentation with anti-TFPI increases from 18-fold at 0.68 dynes/
cm2to 30-fold at 2.7 dynes/cm2. One possible explanation is
that TFPI synthesis by ECsZ3increases with shear stress
above 0.68 dynes/cm2. TFPI binding to cultured cell surf a c e may
~ ~ ~also be modified by shear stress.
The experiments performed in the absence of factor VIIa,
factor X, or both, confirm that for either cell type factor Xa
production is specific to the TFVIIa pathway. Therefore,
there is no significant contamination of the buffers used
with factor VI1 or factor X that may have been present in
the serum employed in culture media used. Similarly, studies with the MoAb HTF1-7B8 confirm the specificity ofthe
expressed procoagulant activity to human TF. Virtual elimination of factor Xa production with this antibody agrees
with the 295% inhibition observed by Carson et alZofor T F
from extracts of human brain and placenta.
The present shear stresses are in the range found in small
to large veins. Nonetheless, such shear stresses exist also in
the arterial circulation in slow-flow regions immediately
distal to stenoses and in ischemic vessels.
APPENDIX
The diffusional flux of factor X to the monolayer (EC or
FB) surface can be approximated as:
-D6c/6y
=
D
(v)
where D is the Brownian diffusion coefficient for factor X,
c(x,y) is factor X concentration in a convective diffusion
boundary layer, x is the axial (downstream) coordinate, y is
the distance from the monolayer into the flowing medium,
C, and C, are bulk and surface concentrations, respectively,
3269
of factor X, and 6(x) is the effective boundary-layer thickness. The coefficient D can be estimated by extrapolation
from the known values for small molecular weight hydrophilic solutes under the assumption that the diffusion coefficient varies inversely as the Stokes radius, itself proportional
to the cube root of molecular weight.” For D (sucrose) of
0.543 X
cm2/s at 37”C, and for molecular weights of
sucrose and factor X of 342 and 52,000, the extrapolation
cm2/s at 37°C. Assuming diffusion-limyields 1.02 X
ited transport of factor X (maximum transport; C, = 0), one
finds that the boundary-layer thickness can be estimated
from the Leveque solution of the convective diffusion equation2’ to be
6
=
(Dx/y)’I3
where y is the wall shear rate and is approximately numerically equal to lOOX the perfusate shear stress. For x of 1.8
cm (chamber midpoint) and y of 68 seconds-’, 6 is 3.0 X
I 0-3 cm (30 pm). Consequently, the maximum diffusive
flux of factor X, DC,/6, is of the order of 340 fmol/
cm2.second for C, of 1,000 nmol/L. This value is equivalent to 20 pmol/cm2. minute.
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The functional expression of tissue factor by fibroblasts and
endothelial cells under flow conditions
EF Grabowski, DB Zuckerman and Y Nemerson
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