(Received for publication, July 27, 1995; and in revised form, February 7, 1996)
From the
Perlecan is a modular heparan sulfate proteoglycan that is
localized to cell surfaces and within basement membranes. Its ability
to interact with basic fibroblast growth factor (bFGF) suggests a
central role in angiogenesis during development, wound healing, and
tumor invasion. In the present study we investigated, using domain
specific anti-perlecan monoclonal antibodies, the binding site of bFGF
on human endothelial perlecan and its cleavage by proteolytic and
glycolytic enzymes. The heparan sulfate was removed from perlecan by
heparitinase treatment, and the 450-kDa protein core was digested
with various proteases. Plasmin digestion resulted in a large fragment
of
300 kDa, whereas stromelysin and rat collagenase cleaved the
protein core into smaller fragments. All three proteases removed
immunoreactivity toward the anti-domain I antibody. We showed also that
perlecan bound bFGF specifically by the heparan sulfate chains located
on the amino-terminal domain I. Once bound, the growth factor was
released very efficiently by stromelysin, rat collagenase, plasmin,
heparitinase I, platelet extract, and heparin. Interestingly,
heparinase I, an enzyme with a substrate specificity for regions of
heparan sulfate similar to those that bind bFGF, released only small
amounts of bFGF. Our findings provide direct evidence that bFGF binds
to heparan sulfate sequences attached to domain I and support the
hypothesis that perlecan represents a major storage site for this
growth factor in the blood vessel wall. Moreover, the concerted action
of proteases that degrade the protein core and heparanases that remove
the heparan sulfate may modulate the bioavailability of the growth
factor.
Perlecan is a major heparan sulfate proteoglycan (HSPG) ()of the pericellular environment and a ubiquitous component
of basement membranes. These membranes are highly specialized
structures that control tissue architecture, movement of
cells/compounds between the bloodstream and tissues(1) , and
the binding of growth factors(2) . The presence of basic
fibroblast growth factor (bFGF) in the extracellular matrix of cultured
endothelial cells was first demonstrated in 1987(3) .
Subsequently, its release was shown to be modulated by the action of
heparitinase or by competition with heparin(4) , thus
suggesting that the growth factor was bound to a HS component present
in the matrix. Radiolabeled bFGF was also shown to bind ECM and be
released by the enzyme collagenase (4) , thrombin(5) ,
or plasmin (6) and by incubation with unlabeled growth
factor(3) . When bound to HS, bFGF was found to be resistant to
the action of proteases(7) . Recently, perlecan was shown to
bind bFGF and to present the growth factor to its high affinity
receptors on the cell surface, which suggested that this HSPG has an
important role in the regulation of cell growth(8) . When
perlecan was treated with heparinase I it could no longer act as a
co-receptor, suggesting that it was the HS on perlecan that was
responsible for this activity(8) . This is not surprising in
light of the fact that both acidic and basic FGF bind avidly to the
closely related glycosaminoglycan, heparin. bFGF bound to
heparin-Sepharose requires a NaCl concentration greater than 1 M for elution(3, 9) . Highly sulfated regions of
heparin contain a bFGF-binding hexasaccharide sequence, which is
comprised of two trisulfated disaccharides with the structure IdceA
(2-OSO
)
1-4GlcNSO
(6-OSO
)
followed by an IdceA (2-OSO
)
1-4
anhydro-D-mannitol(10) . A similar sequence has been
identified in HS isolated from fibroblasts (11) and from smooth
muscle cells(12) , except that in both cases the proportion of
the disulfated GlcNSO
(6-OSO
) was lower,
suggesting that the presence of the sulfate groups at position 6 of the N-sulfated glucosamine were not involved in mediating the high
affinity binding. HS isolated from whole arterial tissue, which
inhibited the growth of smooth muscle cells(13) , probably by
interfering with the presentation of bFGF to its high affinity
receptors(14) , had a high proportion of the sequence isolated
from fibroblasts and smooth muscle cells. When the proportion of the
IdceA (2-OSO
)
1-4GlcNSO
disaccharide
was decreased with respect to the amount of the IdceA
(2-OSO
)
1-4GlcNSO
(6-OSO
),
the fraction did not inhibit smooth muscle cell growth(13) .
The protein core of perlecan has been divided into five domains on the basis of sequence homology to other proteins and the presence of repeating motifs(15, 16) . Domain I is unique to perlecan and contains three serine-glycine-aspartic acid sequences that may act as glycosaminoglycan attachment sites(16) . Since these HS chains are needed for perlecan to bind FGF, the integrity of domain I is important for anchoring the growth factor activity to the ECM. We reasoned that if this domain were degraded or released by proteases, it could provide a mechanism whereby anchored growth factor molecules could be liberated. It has also been suggested that domain I may be oriented toward the cell surface, which would facilitate its co-receptor activity(17) . Domain II has sequence homology to the low density lipoprotein receptor, domain III has homology to the A chain of laminin, domain IV is composed of immunoglobulin-like repeats that demonstrate homology to the neural cell adhesion molecule, N-CAM, and domain V has regions that have similarity to epidermal growth factor and the globular domains of the laminin A chain(15) .
The fact that bFGF binds a HSPG in the matrix and is released by enzymes such as plasmin, thrombin, heparanase, and collagenase has been known for a number of years. The identity of the HSPG responsible for this binding, however, was unknown until recently when it was shown that perlecan bound bFGF(8) . The major goal of this paper was to investigate which enzymes would degrade the protein component of perlecan and whether these same enzymes could facilitate the release of the bound bFGF. This was facilitated by the use of anti-perlecan monoclonal antibodies, which were characterized with respect to their domain specificity. Plasmin, stromelysin, and rat collagenase significantly degraded the protein core, reduced the immunoreactivity toward domain I, and released significant amounts of the growth factor from the HSPG. Plasmin cleaved the protein core to leave a product that probably contained domain III, whereas stromelysin and rat collagenase degraded perlecan core protein into many fragments. Heparitinase I released bound bFGF, whereas heparinase I did not, a finding consistent with the substrate specificity of heparinase I for highly sulfated regions of heparan sulfate. Platelet extract was the most efficient agent at releasing bound growth factor, and this may be due to the presence of many HS-degrading enzymes. This supports the hypothesis that degranulation of platelets at sites of injury may be very effective at mobilizing growth factor from the matrix, thereby aiding in the wound healing process.
Human
stromelysin-1 (MMP 3) purified from fibroblasts was supplied by Dr.
Jack Windsor from the University of Alabama in Birmingham, Alabama. It
degraded gelatin and casein by SDS-zymography. Human gelatinases (MMP 2
and MMP 9) from
12-O-tetradecanoylphorbol-13-acetate-stimulated HL-60 cells
were supplied by Dr. Guy Lyons at the Kanematsu Institute, Royal Prince
Alfred hospital, Sydney. The presence of active gelatinases was assayed
by zymographic analyses. Rat collagenase was purified from rat mammary
carcinoma cells as described previously (18) and supplied by
Ms. A. Martorana from the University of Technology, Sydney. It was
shown to degrade collagen using a dried collagen film assay (19) and gelatin by zymographic analysis. The human homologue
of rat collagenase has been named collagenase-3 (MMP 13)(20) .
The platelet extract was a gift from Dr. Lloyd Graham of the CSIRO,
Division of Biomolecular Engineering, and had a protein concentration
of 9 mg/ml. One ml was prepared from 1.2 10
platelets by freeze-thawing. This extract was assayed and shown
to contain significant heparin/heparan sulfate-degrading activity using
both a labeled and nonlabeled substrate assay(21) . Human
TIMP-1 was a gift from Dr. Kirby Bodden from the University of Alabama
in Birmingham, Alabama.
For immunoprecipitation, protein A-Sepharose was saturated with rabbit anti-mouse IgG (RAM) by incubating 1 ml of a 50% suspension with 200 µl of the antibody solution for 2 h at room temperature with rocking. The RAM-saturated protein A-Sepharose was washed with Tris-buffered saline (TBS) to remove unbound RAM, and TBS was added to give a final volume of 1 ml (50% suspension). Samples (1 ml) of radiolabeled HUAEC conditioned medium were precleared by a 2-h incubation at room temperature with 100 µl of RAM-saturated protein A-Sepharose suspension. Simultaneously, 100-µl samples of RAM-saturated protein A-Sepharose suspension were incubated with 200 µl of purified monoclonal antibody (mAb) in TBS at 100 µg/ml. The mixtures were microcentrifuged, and the mAb-loaded protein A-Sepharose was washed twice with TBS and resuspended in the precleared medium. After a 2-h incubation at room temperature with shaking, the protein A-Sepharose was washed four times with TBS and resuspended in 50 µl of SDS sample buffer (10% (v/v) glycerol, 0.4% (w/v) SDS, 0.001% (w/v) bromphenol blue, 10 mM Tris, pH 6.8), boiled for 10 min, and microcentrifuged to pellet the protein A-Sepharose. The supernatant was electrophoresed on SDS-PAGE gels, dried, exposed to a phosphor screen (Molecular Dynamics) and imaged on a PhosphorImager (Molecular Dynamics) using ImageQuant software.
Immunoprecipitation
of labeled bFGF-perlecan complexes was achieved using the same protocol
as described above except that the HUAEC conditioned medium was not
labeled and recombinant I-labeled bFGF was added to give
a final activity of 0.2 µCi/ml of medium before precipitation with
mAb-loaded protein A-Sepharose. Treatment of the labeled
bFGF-perlecan-mAb-protein A-Sepharose complexes with NaCl or heparin
was performed at room temperature for 16 h. Treatment with degradative
enzymes was for 16 h at 37 °C (as described below). After all
treatments, the samples were microcentrifuged, and the supernatants
were removed, counted in a
counter (LKB 1275 Minigamma), and
expressed as counts/µl/min. The remaining pellet was washed twice
with phosphate-buffered saline, 50 µl of SDS-PAGE sample buffer was
added, and the samples were prepared for SDS-PAGE analysis. The amount
of labeled bFGF released by the various treatments was expressed as a
percentage of the amount bound in the initial immunoprecipitate, which
was estimated by extraction of the immunoprecipitate with 6 M urea, 0.2% SDS in phosphate-buffered saline. The values were
corrected for the amount of
I-labeled bFGF released by
buffer alone by applying the following formula: corrected % =
(uncorrected % - buffer only %)
100/(100 - buffer
only %).
Figure 1:
Immunoprecipitation of human
endothelial cell-derived perlecan. Human endothelial cells were
cultured with either [S]methionine (25
µCi/ml) or Na
[
SO
]
(25 µCi/ml) in complete medium as indicated and immunoprecipitated
with mAb A76. The immunoprecipitate was electrophoresed through an
SDS-4-15% polyacrylamide SDS gel, stained with Alcian blue,
dried, exposed to a phosphor screen, and analyzed with a
PhosphorImager. Lanes 1 and 4 show the
immunoprecipitated molecules incubated in buffer. Immunoprecipitates in lanes 2 and 5 were incubated with 0.1 units/ml
heparitinase I, and immunoprecipitates in lanes 3 and 6 were incubated with 0.5 units/ml chondroitinase ABC as described
under ``Experimental Procedures.'' The relative positions of
molecular mass standards (in kDa) are shown on the left. Top, the origin of the running gel. The size of the protein
core of perlecan meant that it was running in the region of the
polyacrylamide gel where the estimate of the molecular weight was
relatively inaccurate due to extrapolation of the standard curve and
the low resolution obtained for proteins in this region. However,
multiple estimates of the molecular mass varied by about 10% (i.e.
45 kDa).
Figure 2: Characterization of anti-perlecan antibodies using domain fusion proteins. A, crude lysates from Escherichia coli that were expressing a domain I fusion protein were electrophoresed on a 10% polyacrylamide gel, blotted onto nitrocellulose, and probed with 2 µg/ml of A71 (lane 1), A74 (lane 2), A76 (lane 3), or A81 (lane 4). A71 recognized a major band of approximately 66 kDa as well as some minor domain I components. These are indicated by the arrow. B, fusion proteins containing domain I, II, III, or V of perlecan purified from E. coli. were coated onto wells of an ELISA plate at 2 µg/ml and probed with 2 µg/ml of mAbs. Absorbances for A71 and A74 are shown and have been corrected for the absorbance reading obtained using the irrelevant mouse IgG control. mAbs A76 and A81 did not recognize any of the domain proteins by ELISA.
Figure 3:
Enzyme digestion of perlecan
immunoprecipitates. [S]methionine-labeled
perlecan was immunoprecipitated from HUAEC conditioned medium as
described under ``Experimental Procedures.''
Immunoprecipitated material was incubated with buffer alone (lanes
1 and 7) or with the enzymes indicated by + (lanes 2-6 and 8). Digestion products were
resolved on 4-15% polyacrylamide gels and visualized by phosphor
imaging. This figure is a composite of three gels, two of
which were run in the same experiment (lanes 1-6). The
relative positions of molecular mass standards (in kDa) are shown on
the left. Top, the origin of the running
gel.
Figure 4: ELISA of anti-perlecan antibodies on HUAEC ECM. HUAEC ECM was isolated, and ELISAs were performed as described under ``Experimental Procedures.'' The plates were treated with the various enzymes for 16 h at 37 °C using the same concentrations as those used in Fig. 3. Domain I immunoreactivity was tested with mAb A71, that of domain III with mAb 7B5, and that of domain V with mAb A74.
Figure 5:
Perlecan binds bFGF, and the binding is
competed by heparin. [I]bFGF was added to HUAEC
medium, which was conditioned in either the presence (lanes 2 and 4) or absence (lanes 1 and 3) of
heparin (100 µg/ml). The presence of heparin is indicated by a
+ above the lane. Immunoprecipitated complexes were
collected by centrifugation, resolved on SDS-PAGE, and visualized by
phosphor imaging. Lanes 1 and 2 are
immunoprecipitates using an irrelevant mouse IgG, and lanes 3 and 4 were obtained using mAb A76. The relative position
of molecular mass standards (in kDa) are shown on the left. Top, the origin of the running
gel.
Figure 6:
The
release of bFGF from perlecan by enzymes.
Perlecan-[I]bFGF complexes were
immunoprecipitated using mAb A76 and treated with the same
concentrations of enzymes under the same conditions as those used for
the incubations shown in Fig. 3and Fig. 4. Lanes
1, 8, and 10 are buffer only controls. In lanes 2-6, 8, 9, and 11, the
immunoprecipitated complexes were incubated with the treatments
indicated by a + above the lane. Material
remaining complexed to the protein A-Sepharose beads was collected by
centrifugation, subjected to SDS-PAGE, and visualized with a
PhosphorImager system. This figure is a composite of three
minigels. Lanes 1-6 were run in the same experiment,
whereas lanes 7-9 and lanes 10 and 11 were run in separate experiments. Lanes 1, 8,
and 10 are the buffer only controls from their respective
experiments. The relative positions of molecular mass standards (in
kDa) are shown on the left. Top, the origin of the
running gel.
We tested the hypothesis that bound bFGF
may protect the HS from cleavage by heparinase I by immunoprecipitating SO
-labeled perlecan (from medium containing
heparin that removed any endogenously bound bFGF) and digesting the
immunoprecipitate with either heparitinase I or heparinase I in the
presence or absence of an excess of bFGF. Both enzymes were effective
at removing the heparan sulfate from immunoprecipitated perlecan (Fig. 7, lanes 2 and 5). The intensities of
the various bands were quantitated, using the ImageQuant software, and
compared with the intensity of the control band, which was taken as 0%
digestion. Heparitinase I digested 96 and 98% of the
SO
-labeled HS in either the absence or
presence of 0.5 µg of bFGF, respectively (Fig. 7; compare lanes 2 and 3). Heparinase I was less effective at
digesting the HS, as it degraded 73 and 75% in either the presence or
absence of growth factor, respectively (Fig. 7; compare lanes 5 and 6). These data suggested that the growth
factor was not protecting the HS from cleavage by either heparitinase I
or heparinase I. The reason why bFGF did not protect the HS from
heparinase I cleavage may be due to the fact that although heparinase I
has a preference for highly sulfated regions, it may be capable of
cleaving other regions of the HS chain.
Figure 7:
The presence of bFGF does not affect
digestion of perlecan by heparinases. SO
-labeled perlecan was immunoprecipitated as
described for Fig. 1using A76 antibodies. The
immunoprecipitates were incubated with the treatments indicated by a
+ above the lane, incubated in SDS-PAGE buffer,
electrophoresed through a 4-15% polyacrylamide SDS gel, stained
with Alcian blue, dried, exposed to a phosphor screen, and analyzed
with a PhosphorImager. The intensity of the various bands was
quantitated using ImageQuant software. The concentration of both
heparitinase I and heparinase I used was 0.1 unit/ml. 0.5 µg of
bFGF was added to the immunoprecipitate/enzyme mix in lanes 3 and 6. This figure is a composite of two
minigels run on different days with their appropriate controls. The
relative positions of molecular mass standards (in kDa) are shown on
the left. Top, the origin of the running
gel.
Perlecan derived from human endothelial cells contained HS
and no chondroitin sulfate, as demonstrated by its sensitivity to
heparitinase I and its full resistance to chondroitinase ABC digestion.
This is the most common form of the molecule(1) , although some
forms of the basement membrane proteoglycan have been described that
contain chondroitin sulfate and heparan sulfate on the same core
protein(33) . We estimated the mass of the protein core of
perlecan to be 450 kDa, which was very similar to the published
mass of 467 kDa deduced from cDNA cloning from human tumor and
non-tumor cell lines(15, 16) . The anti-perlecan
monoclonal antibodies were characterized with respect to their domain
specificity and used to study the effects of protease treatment on the
various domains. This study was performed in view of the fact that
perlecan was recently shown to bind bFGF (8) and to have the
necessary HS sequences to cross-link with the high affinity receptors
on the cell surface. Since the HS is attached to domain I of
perlecan(1) , and since the removal of this domain by proteases
would release a HS-growth factor complex, it was of interest to
determine which proteases were effective at degrading the protein core
and in particular which proteases removed domain I. It was of further
interest to determine whether these same proteases were able to release
bFGF that was bound to perlecan.
In the present study we
demonstrated that stromelysin, rat collagenase, and plasmin reduced the
immunoreactivity toward the domain I antibody and were also effective
at releasing bound growth factor. Plasmin was previously shown to
release bound bFGF from whole matrix preparations (6) . It was
not known, however, which component of the matrix functioned as the
plasmin substrate or whether the serine protease released the growth
factor indirectly by activating other latent proteases(34) . We
demonstrated here that plasmin cleaves immunopurified perlecan, leaving
a major product with a molecular mass of 300 kDa, which still
contained domain III, thereby suggesting that the serine protease
cleaved perlecan outside of this domain. In addition to the
demonstration that plasmin cleaved perlecan, we demonstrated the
involvement of metalloproteinases in perlecan degradation, as
stromelysin (MMP 3) and rat collagenase (MMP 13) both degraded the
basement membrane proteoglycan. MMP 3 was first described as a
``proteoglycanase'' because it degraded proteoglycans
isolated from cartilage(35) . More recently, it has been shown
to cleave the aggregating cartilage proteoglycan, aggrecan, at a single
site close to the N-terminal region of the G1 domain(36) . In
contrast, stromelysin cleaved perlecan at many sites, giving rise to
fragments of various molecular weights. This enzyme was also very
efficient at removing the immunoreactivity toward domains I, III, and V
in HUAEC ECM and at liberating bound bFGF from perlecan. Collectively,
the data suggest that the enzyme degraded the protein core at multiple
locations. Rat collagenase also cleaved the protein core of perlecan,
giving rise to a different digestion pattern, which showed no evidence
of smaller fragments. The human homologue of rat collagenase has been
cloned recently and termed collagenase-3. The human recombinant enzyme
was found to degrade fibrillar type I collagen but not gelatin or
casein (20) . The work described in this paper demonstrates
that the native rat enzyme has significant ``perlecanase''
activity. The cleavage of perlecan by stromelysin and rat collagenase
was an attribute not shared by all metalloproteinases, as a mixture of
the two gelatinases (MMP 2 and MMP 9) had no effect on core protein
size or the release of bound growth factor.
The serine protease
thrombin has been shown to release bFGF from native matrix(5) .
However, in our system, it had little effect on either the
immunopurified protein core or the immunoreactivity of domains I and
III of perlecan in matrix. Also, we showed that thrombin released very
little of the growth factor from perlecan. Therefore, thrombin may have
been removing bFGF from native matrix indirectly by degradation of the
surrounding ECM, by activating ECM-bound proteases, or by stimulating
heparanase activity(37) . In contrast, heparitinase I
(heparinase III) and platelet extract released significant amounts of
bFGF from perlecan, whereas heparinase I released a smaller amount.
This is consistent with results obtained elsewhere using native ECM as
the source of binding HSPG(4, 38) . Platelet extract
may contain more than one heparan/heparin degrading activity and has
been used as a starting material to purify platelet
heparitinase(39) . The substrate specificity of the heparan
sulfate lyases may explain why heparitinase I released bFGF from
perlecan at a higher rate than heparinase I. Heparinase I has a
specificity for degrading highly sulfated, heparin-like regions that
have a high proportion of di- or trisulfated
disaccharides(40) . These same regions have been shown to bind
bFGF (10, 41) and have also been shown to inhibit
bFGF-induced mitogenesis (14) . When bFGF was present, however,
our results showed that the growth factor did not interfere with the
activity of either heparitinase I or heparinase I. The reason why a
small amount of the growth factor was released from perlecan by
digestion with heparinase I yet the enzyme was capable, although less
so than heparitinase I, of degrading perlecan-HS in the presence of
bFGF is unknown but may be due to differences between the two
experimental systems (i.e. obtaining I-labeled
bFGF-perlecan complexes and adding enzyme versus obtaining
SO
-labeled perlecan and adding both enzyme and
unlabeled bFGF). Heparitinase I (heparinase III), on the other hand,
preferentially degrades the less sulfated regions of HS, which are more
common in ``non-heparin'' HS (42) and often separate
bFGF binding sequences. Therefore, the action of heparitinase I on
perlecan-bFGF complexes was to liberate more efficiently bFGF bound to
its HS binding sequence.
Bound bFGF can be released from heparin
immobilized to Sepharose beads by treatment with 1.4-1.6 M NaCl(3, 9) , and can be extracted from native
matrix with 3 M NaCl(3) . Our data demonstrate that 5 M NaCl does not remove significant quantities of the growth
factor from perlecan, thereby suggesting that binding between perlecan
and bFGF is very specific and avid. This apparent increase in avidity
may be due to the fact that in our assay incubation mixture we have the
whole proteoglycan bound to immunoglobulin, and incubation with 5 M NaCl may increase any hydrophobic attraction that may exist
between bFGF and either the perlecan protein core or immunoglobulin.
The previous use of 3 M NaCl to remove bound bFGF from matrix (3) may have been possible due to the presence of other HSPGs
besides perlecan in the matrix that bind bFGF with a lower affinity.
The finding that heparin removes bFGF from perlecan is likely due to
the fact that in the competitive reaction mixture, perlecan was present
in much smaller amounts when compared with the 100 µg/ml of
competing glycosaminoglycan. Heparin has also been shown to be a
competitive inhibitor of bFGF binding to matrix at concentrations 10
times lower than those used in these studies(3) . We could not
liberate significant amounts of bound bFGF with up to 15 µg/ml of
``cold'' growth factor. Due to economic constraints and the
logistics of the assay (i.e. 50-µl volume of
perlecan-growth factor complex attached to protein A-Sepharose beads)
we were unable to go above this concentration. Taking the concentration
of bFGF required for 50% displacement of labeled growth factor as in
excess of 15 µg/ml, we calculated that the K had to be less than 800 nM, which is consistent with
previous estimates for the affinity of bFGF for extracellular matrix
and HSPGs(4, 43) . We are planning to isolate perlecan
in the absence of immunoglobulin and protein A-Sepharose and repeat
these experiments.
The binding of bFGF to HSPGs in matrix and its release by incubation with heparin or digestion of the matrix with enzymes are not novel findings. However, in all of the previous experiments used to study bFGF-HSPG interactions, whole native matrix was used as the source of HSPG. Since the matrix may contain more than one HSPG as well as other proteoglycans, it was unknown which HSPG was responsible for the binding of the growth factor. Furthermore, these experiments were complicated by the presence in the matrix of endogenous proteases, heparanases, and other growth factors. Our data demonstrate directly that perlecan binds bFGF very tightly and that significant amounts are released by proteases that degrade the protein component of the proteoglycan, by heparan sulfate-degrading enzymes that remove the HS, or by incubation of the complex with a competitive ligand such as heparin. Because perlecan has been shown to possess the oligosaccharide sequences necessary to activate cell surface receptors(8) , it has been assigned a co-receptor role. Therefore, growth factor bound to perlecan may be very relevant to processes involving cell growth and differentiation. The regulatory mechanisms involved in the synthesis/degradation of this proteoglycan may provide ways of controlling the bioactivity of the growth factor.