From the Department of Biochemistry, Queen's University, Kingston,
Ontario K7L 3N6, Canada and the
Academic Medical Center,
Department of Biochemistry, University of Amsterdam,
1105 AZ Amsterdam, The Netherlands
INTRODUCTION
The major protein constituent of blood clots, fibrin, is degraded
to soluble products by plasmin, which displays a broad trypsin-like specificity. The activity of plasmin is restricted as a result of the
fibrin-specific way in which its inactive precursor plasminogen is
activated by tissue-type plasminogen activator
(t-PA)1 (1). Fibrin, therefore, not only
serves as a substrate for plasmin, it is also required for its
production. Both t-PA and plasminogen are built from autonomous
domains, and those involved in binding to fibrin have been identified
(2, 3). Native [Glu1]plasminogen, however, exhibits a
very tight spiral structure (4), thereby shielding the activation
cleavage site (Arg561-Val562) from easy access
by plasminogen activators (5) and attenuating the interaction of the
kringle domains with fibrin (2, 6, 7). A change in hydrodynamic
properties is observed when the NH2-terminal acidic domain
of native [Glu1]plasminogen is removed by limited
plasmin-catalyzed proteolysis, resulting in a truncated form of
plasminogen having Lys78 as the new
NH2-terminal residue (5, 8).
[Lys78]plasminogen has been shown to be a significant,
although not essential, intermediate in the activation of
[Glu1]plasminogen during in vitro fibrinolysis
(9-11), where its formation is strictly dependent on the presence of
polymerized fibrin (10, 12). The work of Violand et al. (5)
suggested that [Glu1]plasminogen bound to fibrin adopts a
[Lys78]plasminogen-like conformation.
The kinetics of fibrin-stimulated plasminogen activation by
"native" t-PA are currently described by an ordered sequential mechanism (cyclic ternary complex model), in which solution phase plasminogen interacts with high affinity only with fibrin-bound t-PA
(13). Subsequent studies employing [Glu1]- and especially
[Lys78]plasminogen or variants of t-PA have shown
deviations from this kinetic model (14-17).
A detailed kinetic analysis of plasminogen activation necessitates the
performance of steady-state measurements during the different stages of
fibrin degradation. Since the reaction generates active plasmin,
however, the structure of the cofactor fibrin is subject to continuous
change. In the accompanying paper (18), we describe the expression of a
variant of recombinant human [Glu1]plasminogen, in which
serine of the active site of plasmin has been replaced by cysteine and
labeled with fluorescein: Plg(S741C-fluorescein). Employing this
plasminogen variant and the Lys78 form of it, we quantified
by fluorescence the activation rate of these zymogens without
generating active plasmin. The impact of fibrin affinity of the
activator on these kinetics was studied by employing deletion variants
(del.K2 and del.F) that show altered affinity for fibrin (17). In the
present paper we describe a detailed study of the kinetics of
t-PA-mediated plasminogen activation in a fully polymerized, intact
fibrin clot. Analysis of the kinetics led to a new, modified model for
fibrin-stimulated plasminogen activation within fully intact,
polymerized fibrin.
EXPERIMENTAL PROCEDURES
Materials
Native (recombinant) t-PA was Activase, a generous gift of Dr.
G. Vehar (Genentech, San Francisco, CA. SDS-polyacrylamide gel
electrophoresis indicated that the material is predominantly in the
single-chain form. Single-chain t-PA and its deletion variants were
obtained as described previously (17). The production and purification
of recombinant Plg(S741C-fluorescein) and the human proteins
-thrombin and fibrinogen are described in the accompanying paper
(18). The chromogenic substrate
D-Glu-Gly-Arg-p-nitroanilide (S2444) was
obtained from Chromogenics (Molndal, Sweden).
Fluorescent Activation Assay of [Glu1]- and
[Lys78]Plg(S741C-fluorescein)
Activation experiments were performed in 96-well plates
(Dynatech) at 20 °C, using a Perkin Elmer LS50B Luminescence
Spectrometer equipped with a fluorescence plate reader. Fluorescence
intensities were measured at excitation and emission wavelengths of 495 and 535, respectively, employing a 530-nm emission cut-off filter. In
this instrument the sample is excited from above and emitted light is
collected from above. Wells were pre-equilibrated with 20 mM HEPES-NaOH, pH 7.4, 150 mM NaCl (HBS) plus
1% Tween 80 (w/v) for 1 h to prevent adsorption of proteins to
the plastic. Subsequently, wells were loaded with 90 µl of HBS,
0.02% Tween 80 (w/v) (HBST) containing various concentrations of
[Glu1]- or [Lys78]Plg(S741C-fluorescein)
and fibrinogen and equilibrated at 20 °C. Stability of the
fluorescence intensity was verified for 5 min. The reaction was
initiated by adding 10 µl of HBST, 100 mM
CaCl2 containing 60 nM human
-thrombin and
various concentrations of t-PA (1-10 nM final
concentration). Data were collected every 60 s and stored as print
files for each individual well using a data acquisition program written
by Dr. W. K. Stevens in our laboratory. Initial rates of fluorescence
decrease were determined by linear regression analysis and converted to
rates of zymogen activation according to Equation 1, in which
dPn/dt is rate of cleavage of the zymogen,
Po is initial [Glu1]- or
[Lys78]Plg(S741C-fluorescein) concentration,
Io is initial fluorescence intensity, and
r represents the ratio of the fluorescence intensities of
the fluorescent analogues of plasmin and plasminogen. The values of
r for the Glu1 and Lys78 forms of
Plg(S741C-fluorescein) are 0.5 and 0.4, respectively (18).
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(Eq. 1)
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Competition Kinetics
The impact of the presence of
[Glu1]Plg(S741C-fluorescein) as a competing substrate on
the t-PA-catalyzed hydrolysis of S2444 was measured in microtiter wells
in a Titertek Twinreader at 37 °C. In brief, 10.0-µl aliquots of
200 nM t-PA were added to 90.0 µl of HBST containing 1 mM S2444 and various concentrations of
[Glu1]Plg(S741C-fluorescein), and hydrolysis was
monitored at 1-min intervals at 405 nm. The influence of fibrin was
measured by adding 10.0-µl aliquots containing 200 nM
t-PA, 60 nM
-thrombin, and 100 mM
CaCl2 to 90 µl of HBST containing 1 mM S2444,
3.3 µM fibrinogen, and various concentrations of
[Glu1]Plg(S741C-fluorescein). Clotting was complete
within 1 min, as seen from the rapid increase in turbidity, which
remained constant during the remainder of the experiment. The apparent
Km for the interaction of t-PA and
[Glu1]Plg(S741C-fluorescein) was deduced from Equation 2,
which describes the relationship between activity toward a chromogenic
substrate in the presence of increasing concentrations of a competing
substrate, and in which vo and v
represent rates of S2444 hydrolysis in the absence and presence of
[Glu1]Plg(S741C-fluorescein), F is the fibrin
concentration, K1 is the dissociation constant for t-PA and
fibrin, P is the [Glu1]Plg(S741C-fluorescein)
concentration, and K2 is the apparent Km
for the t-PA-[Glu1]Plg(S741C-fluorescein)
interaction.
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(Eq. 2)
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Models of Plasminogen Activation
In order to interpret the dependences of initial rates of
plasminogen activation on fibrin and plasminogen concentrations, a
model of the reaction was sought. The model, in order to accurately reflect the data, would need to predict Michaelis-Menten behavior with
respect to the substrate concentration at all fibrin concentrations; saturation in kcat with respect to the fibrin
concentration; template-like, biphasic behavior with respect to the
fibrin concentration at all fixed substrate concentrations; and a very
high Km in the absence of fibrin. In addition, it
would need to fit all accumulated data accurately, with randomly
distributed residuals over the entire data set, and not predict values
for parameters, such as dissociation constants for binding
interactions, that are inconsistent with independently measured values.
In an effort to find a model that satisfies the above criteria, all
possible equilibrium models that describe three component systems were constructed and examined with respect to their ability to predict the
experimental data. In addition, a steady-state model was constructed. These models and the derivations of their corresponding rate equations are shown below.
Equilibrium Models
Since general experience has shown that
significant plasminogen activation occurs only when all three
components are present (activator (A), plasminogen (P) and fibrin (F)),
the assumption is made that catalysis occurs from a ternary complex of
the three components (AFP) which turns over into product. The rate
constant for the turnover step is designated
kcat. In addition, the assumption is made that
the ternary complex is assembled through binary interactions among the
individual components and subsequent interactions of the binary
complexes with the third component. Furthermore, all interactions are
assumed to be essentially at equilibrium. The three components can form
three individual binary complexes (AF, FP, PA). Thus, seven equilibrium
models of the assembly of AFP are possible, as indicated by Boskovic
et al. (19). Three models involve only one of each of the
binary complexes, three involve the three possible pairs of components,
and one involves all three components. Expressions relating the
equilibria among components and the conservation of fibrin, concepts of
the seven models, and derivations of their rate equations are as
follows.
Equilibrium interactions are shown by Equations 3, 4, 5, 6, 7, 8.
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(Eq. 3)
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(Eq. 4)
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(Eq. 5)
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(Eq. 6)
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(Eq. 7)
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(Eq. 8)
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From Equations 3, 4, 5, 6, 7, 8, Equation 9 results.
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(Eq. 9)
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Conservation of fibrin is given by Equation 10.
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(Eq. 10)
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Since [A]o
[F]o, we get Equation 11.
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(Eq. 11)
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All rate equations below are expressed as the ratio
v/[A]o, where v is the rate and
[A]o is the total concentration of activator (t-PA). [P] is
the free concentration of plasminogen (when [FP] exists in the model)
and [P]o is the total concentration of plasminogen (when
[FP] does not exist in the model). [F]o is the total
concentration of fibrin. The rate equations were obtained using the
expressions for v/[A]o given below, the
equilibrium expressions of Equations 3, 4, 5, 6, 7, 8 and the conservation equation
for fibrin (Equation11).
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(Eq. 12)
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(Eq. 13)
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(Eq. 14)
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(Eq. 15)
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(Eq. 16)
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(Eq. 17)
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(Eq. 18)
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(Eq. 19)
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(Eq. 20)
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(Eq. 21)
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(Eq. 22)
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(Eq. 23)
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(Eq. 24)
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(Eq. 25)
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(Eq. 26)
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(Eq. 27)
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(Eq. 28)
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(Eq. 29)
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Steady-state Model
The concepts and equations of this model
are as follows. Protomers of fibrin possess unique binding site(s) for
t-PA and plasminogen and can interact with either to form the
respective binary complexes, activator-fibrin(AF) and
plasminogen-fibrin(PF). These binary complexes can interact further to
form the ternary activator-fibrin-plasminogen complex (AFP) in which
catalysis occurs to yield Pn (plasmin) and AF. The events are
characterized by their respective rate constants, as depicted
below.
Model VIII
The rate of the reaction is given by Equation 30.
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(Eq. 30)
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The steady-state equations for [AF] and [AFP] are given by
Equations 31 and 32.
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(Eq. 31)
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(Eq. 32)
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The conservation equation for the enzyme (Ao) is given
by Equation 33 and that for fibrin (Fo) is given by Equation 11, above.
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(Eq. 33)
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Because the concentrations of fibrin and plasminogen are
typically so much greater than that of t-PA, the interaction of plasminogen with fibrin is assumed to be at equilibrium. The
equilibrium interaction between fibrin and plasminogen is expressed in
Equation 34, where KF is the dissociation
constant.
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(Eq. 34)
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Equations 11 and 34 can be combined to give equation
(35)
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(Eq. 35)
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Equations 30, 31, 32, 33 can be used to express v and
[A]o in terms of [F], [PF], [P], and the rate
constants. The results are given in Equations 36 and 37, where
D is the determinate of the matrix defined by Equations
31, 32, 33, and the term [PF] has been substituted by [PF] = [P][F]/KF, according to Equation 34.
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(Eq. 36)
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(Eq. 37)
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The ratio of Equations 36 and 37 yields the rate Equation 38,
with the rate expressed per unit nominal concentration of
enzyme.
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(Eq. 38)
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This equation predicts that at high levels of [P], the
reaction kinetics with respect to [P] will deviate from the
Michaelis-Menten relationship because of the terms containing
[P]2. Since this was not the case over the range of [P]
concentrations used presently, terms in [P]2 were
considered negligible and therefore not included in the rate equation.
With this approximation and with Equation 35 used to substitute for
[F] in Equation 38, the rate Equation 39 results, which is written in
a simpler format in Equation 40. This later equation shows that, at any
fixed concentration of fibrin, plasminogen activation conforms to the
Michaelis-Menten equation when the plasminogen concentration is
expressed as the free concentration. The
kcat(app) and
Km(app) values depend on the fibrin concentration as indicated in Equations 41 and 42.
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(Eq. 39)
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(Eq. 40)
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(Eq. 41)
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(Eq. 42)
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The definitions of kcat, K,
Km, and KA of Equations 39,
41, and 42 are given in terms of rate and equilibrium constants in
Equations 43, 44, 45, 46. In these equations, KA and
KF are the dissociation constants for the
respective binding interactions of t-PA and plasminogen with
fibrin.
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(Eq. 43)
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(Eq. 44)
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(Eq. 45)
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(Eq. 46)
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Equations 41 and 42 predict that
kcat(app) and
Km(app) approach the true
kcat and Km (Equations 43 and 45) at high fibrin concentrations.
Equation 39 predicted well all experimental data and therefore was used
to calculate, by nonlinear regression analyses (SYSTAT, NONLIN module),
best values for the parameters kcat,
K, Km, and KA.
Free concentrations of plasminogen were calculated from the total
concentrations of plasminogen and input fibrinogen by using the binding
parameters reported previously:
[Lys78]Plg(S741C-fluorescein): KF = 1.2 µM, n = 1.8;
[Glu1]Plg(S741C-fluorescein): KF = 30 µM, n = 1 (17, 18), and the quadratic
equation [P] = [P]o
0.5·(KF + [P]o + [F]o·n
((KF + [P]o + [F]o·n)2
4&
#183;[P]o[F]o·n)1/2).
RESULTS
Activation of [Glu1]- and
[Lys78]Plg(S741C-fluorescein) in a Fully Polymerized
Fibrin Clot
The fibrin-stimulated substrate activation by t-PA
was studied by measuring rates of activation of the recombinant,
fluorescently labeled Glu1 and Lys78 forms of
variant plasminogen Plg(S741C-fluorescein). This system allows
steady-state measurements of plasminogen activation without the
concurrent formation of active plasmin, thereby preventing any possible
feedback by plasmin-mediated proteolytic alterations of t-PA,
plasminogen, and fibrin. The turbidity of the fibrin clot does not
change under this experimental setup, allowing the performance of the
fluorimetric analysis within a fully polymerized fibrin clot. This
precludes the introduction of potential artifacts by chemical and/or
physical treatment of the fibrin stimulator, and allows determination
of the role of fibrin polymer formation, which has been shown to be
essential for full stimulatory activity (20). Large data sets were
obtained at fibrin concentrations ranging from 20 nM to 10 µM, [Glu1]Plg(S741C-fluorescein)
concentrations ranging from 50 nM to 2.5 µM,
and [Lys78]Plg(S741C-fluorescein) concentrations ranging
from 25 nM to 1 µM. The concentration of
native t-PA and deletion variants was constant within each data set
(1-10 nM), although the turnover number was shown to be
independent of t-PA concentrations ranging from 0.5 to 50 nM (not shown). Representative sets of the kinetic data for
native t-PA and its variants and
[Glu1]Plg(S741C-fluorescein) are shown in Fig.
1. At any given fibrin concentration, the rate of
activation by native t-PA (Activase and sct-PA) as a function of
plasminogen concentration approximates a Michaelis-Menten rectangular
hyperbola as shown previously (13). Similar profiles are observed for
del.K2, but apparent saturation takes place at higher
[Glu1]Plg(S741C-fluorescein) concentrations. In the case
of del.F, rates increase linearly with the substrate concentration in
the measured range.
Fig. 1.
Kinetics of
[Glu1]Plg(S741C-fluorescein) activation in a fibrin
clot. Rates of [Glu1]Plg(S741C-fluorescein)
activation at the indicated t-PA or t-PA variant and fibrin
(F) concentrations were determined in a fluorescent plate
reader at 20 °C as described under "Experimental Procedures." Results are expressed as rates per unit concentration of t-PA or t-PA
variant (s
1). Panel A, Activase (t-PA);
panel B, sct-PA; panel C, del.K2; panel
D, del.F. The lines represent the fibrin and
plasminogen dependences of rates as calculated from Equation 39 (see
"Experimental Procedures") and derived parameter values (Table
I).
[View Larger Version of this Image (23K GIF file)]
With [Lys78]Plg(S741C-fluorescein) as the substrate, and
t-PA as the activator, hyperbolas were observed as for
[Glu1]Plg(S741C-fluorescein) (Fig.
2A). Similar profiles were observed for
del.K2, whereas no saturation was evident in the case of del.F (not
shown). Further analysis of the data with t-PA indicated that even
though Michaelis-Menten behavior with respect to the substrate
concentration is exhibited at any particular, fixed fibrin
concentration, rates exhibit a biphasic dependence on the fibrin
concentration at any fixed [Lys78]Plg(S741C-fluorescein)
concentration (Fig. 2B). Similar behavior was described by
de Vries et al. (16) and is typical of template-like mechanisms (21).
Fig. 2.
Kinetics of
[Lys78]Plg(S741C-fluorescein) activation in a fibrin
clot. Rates per unit concentration of t-PA or t-PA variants (s
1) were determined as in Fig. 1. Panel A,
Activase (t-PA): rate as a function of the
[Lys78]Plg(S741C-fluorescein) concentration at various
fibrin concentrations (F). panel B, Activase
(t-PA): rate as a function of log [F]o at various
[Lys78]Plg(S741C-fluorescein) concentrations
(Po, µM). The lines
represent the dependences of rates on fibrin and
[Lys78]Plg(S741C-fluorescein) concentrations as
calculated from Equation 39 (see "Experimental Procedures") and
derived parameter values (Table I).
[View Larger Version of this Image (31K GIF file)]
Fig. 3 shows the responses of apparent
kcat and Km values to
increasing fibrin concentrations with both forms of the substrate for
t-PA (A and B) and del.K2 (C and
D). With both forms of the activator,
kcat increases and saturates with increasing fibrin, and values at saturation with
[Lys78]Plg(S741C-fluorescein) are 1.5-fold (t-PA) and
2.6-fold (del.K2) greater than those with
[Glu1]Plg(S741C-fluorescein). The Km
value decreases with increasing fibrin concentrations for
[Glu1]Plg(S741C-fluorescein) and is approximately
constant with [Lys78]Plg(S741C-fluorescein). Since
[Lys78]Plg(S741C-fluorescein) has a high affinity for
fibrin (1.2 µM) and
[Glu1]Plg(S741C-fluorescein) a low one (30 µM), this behavior would be expected for a template
mechanism in this range of fibrin concentrations (21). Notably, both
kcat and Km values at
saturating fibrin are approximately 3-fold higher for del.K2 than for
t-PA, making their catalytic efficiencies very similar. The individual kcat and Km values for del.F
were not determined due to linear activity/substrate concentration
relationships. kcat/Km values, however, were 20-fold lower for this variant and did saturate with fibrin (Fig. 3E).
Fig. 3.
Fibrin dependence of the kinetic parameters
for [Glu1]- and
[Lys78]Plg(S741C-fluorescein) activation. A
and B, t-PA (Activase); C and D,
del.K2; E, del.F. The open symbols represent
[Glu1]Plg(S741C-fluorescein), and the closed
symbols represent [Lys78]Plg(S741C-fluorescein). The
experimentally determined kcat and Km values, plus and minus standard errors, for each
fibrin concentration were calculated by fitting rate data
versus the free Plg(S741C-fluorescein)
concentration to the Michaelis-Menten equation. The values represented
by solid lines for kcat and
Km were calculated by Equations 41 and 42 and the
parameters of Table I. For symbols not accompanied by error bars, the
magnitude of the error was less than the size of the symbol.
[View Larger Version of this Image (15K GIF file)]
In order to determine whether fibrin facilitates an active
site-dependent association between t-PA and
[Glu1]Plg(S741C-fluorescein), we performed competition
kinetics with the amidolytic substrate S2444 in the absence and
presence of fibrin (Fig. 4).
[Glu1]Plg(S741C-fluorescein) does not compete for the
t-PA-catalyzed hydrolysis of the amidolytic substrate S2444 in the
absence of fibrin, therefore precluding the presence of an active
site-dependent high affinity interaction between these
proteins. The presence of a fibrin clot results in a modest increase in
activity of the fibrin-bound single-chain t-PA as a result of a
decreased Km for the amidolytic substrate in
accordance with published data (22). In contrast to the lack of
interaction between t-PA and plasminogen in the absence of fibrin, an
interaction between [Glu1]Plg(S741C-fluorescein) and t-PA
with a Kd value of approximately 0.5 µM can be inferred in the presence of a 3 µM fibrin clot (Fig. 4). Thus, we conclude that f
ibrin
promotes the association between the enzyme and the substrate. The
value of the apparent Km (0.5 µM)
indicates in this three-component system the substrate concentration at
which half of the t-PA molecules are involved in a Michaelis complex
with plasminogen.
Fig. 4.
The influence of
[Glu1]Plg(S741C-fluorescein) on the t-PA-catalyzed
hydrolysis of S2444 in the presence or absence of a fibrin clot.
The activity of t-PA toward 1 mM S2444 was determined at
37 °C as described under "Experimental Procedures" either in the
absence (
) or presence (
) of a 3 µM fibrin clot.
The lines represent the calculated activities based on
Equation 2 of "Experimental Procedures" with the apparent
Km set at 0.5 µM.
[View Larger Version of this Image (17K GIF file)]
Data Analysis and Selection of a Steady-state Template Model for
Plasminogen Activation
In order to summarize and interpret the
rate data, we sought a model that describes the kinetics of fibrin
stimulated plasminogen activation under each of the permutations of
t-PA and plasminogen species. We tested the seven equilibrium models
derived for a three-component system as described by Boskovic et
al. (19) and examined their ability to predict the present data.
One of these models (Model I; see "Experimental Procedures")
embodies the Hoylaerts mechanism (13). In addition, we constructed a steady-state template model. The analyses of the data eventually indicated that the steady-state model fit all of the data very <
/SUP>well and
predicted no values for parameters (e.g..
Kd for the tPA-fibrin interaction), which are
inconsistent with independent measures of those values. This was not
true for any of the equilibrium models. Since the template model is
described by the rate equation derived above (Equation 39), the
difficulties with the equilibrium models can be most readily identified
by comparing their predicted behavior to observed behavior and their
rate equations to Equation 39.
Thus, the specific difficulties with each of the equilibrium models
(Experimental Procedures) are as follows.
Model I, which is identical to the model of Hoylaerts et
al. (13), includes only the AF binary complex and has the rate equation V/[A]o = kcat[P]o/(Km(1 + KA/[F]o) + [P]o). Thus, it
does not predict a variation of kcat with the
concentration of fibrin, which is inconsistent with the data of Fig. 3
and Equation 39. It does, however, fit the data reasonably well at
fibrin concentrations in excess of 1.0 µM, where the
activator is completely bound and kcat no longer
varies with the fibrin concentration.
Model II includes only the FP binary complex and has the rate equation
V/[A]o = kcat
[P][F]o/(KmF + [F]o)/(KmFKF/(KmF + [F]o) + [P]). This equation pre
dicts the expected
behavior of kcat(app) as a function of
[F]o, but the Km(app) = KmFKF/(KmF + [F]o) term does not conform to the data o
r to the equation above.
Model III includes only the AP binary complex and has the rate equation
V/[A]o = kcat[P]o[F]o/(KmF + [F]o)/(KmFKF/
(KmF + [F]o) + [P]o). It has a problem very similar to
that of Model II; it predicts the proper variation in
kcat(app), but not in Km(app), with the fibrin
concentration.
Model IV, like the steady-state template model, includes both the AF
and PF binary complexes and has the rate equation:
V/[A]o = kcat[P][F]o/(KmF + [F]o)/(KmA(KA +
[F]o)/(KmF + [F]o) + [P]). This equation is identical in form to the Equation 39 for the
steady-state template model; thus, it fits the data very well. The
physical meanings of the constants in the two models are different,
however. In addition, Model IV has the restraint
KAKmA/KmF = KF (see Equation 9 in "Experimental
Procedures"), which implies that the fit parameters
KA, KmA and
KmF should predict the dissociation
constant for the binding of fibrin to plasminogen
(KF). When the data were fit to this equation,
predicted values of KF were 1.6 µM
and 0.15 µM for the Glu1 and
Lys78 forms of Plg(S741C-fluorescein), which are smaller
than the experimentally measured values by factors of 19 and 8.0, respectively, Thus, in spite of the excellent fit of the rate equation
of Model IV to the data, the model was excluded because of the latter
difficulty.
Model V includes the AF and AP binary complexes and has the rate
equation V/[A]o = kcat[P]o[F]o/(KmP + [F]o)/(KmA(KA + [F]o)/(KmP + [F]o) + [P]o). This equation is similar to that of Model IV, except
that the concentration of plasminogen is expressed as the nominal
([P]o) rather than free ([P]) concentration. This is
because Model V does not include the binary plasminogen-fibrin
interaction. The data, especially those with the Glu1 form
of the substrate (which only binds fibrin weakly, such that [P]
[P]o), fit this equation well. Because of the restraint KAKmA/KmP = KP; however, values of
KP = 1.2 µM and
KP = 0.03 µM were predicted for
the dissociation constants for solution phase interactions between t-PA
and the Glu1 and Lys78 forms of the substrate.
These high affinity interactions are not consistent with the high
Km values (
50 µM) reported for the
solution phase reaction (13) or the lack of saturation of rates of
reactions in the absence of fibrin (18).
Model VI includes the FP and AP binary complexes and has the rate
equation V/[A]o =
kcat[P]/(KmF + KmP + [F]o)/(KmFKF(KmF + KmP + [F]o) + [P] + KmF[P]2/KP/(KmF +
KmP + [F]o)). Nonlinear regression analyses would not converge upon efforts to fit this equation to the data with the Glu1 form of the substrate.
With the Lys78 form and with KF (the
dissociation constant for the plasminogen-fibrin interaction) fixed at
1.2 µM, convergence was obtained. Again, however, the
restraint that
KmF·KF/KmP = KP predicted a high affinity solution phase
interaction between t-PA and the Lys78 form of plasminogen
(KP = 0.13 µM), which is not
consistent with independent observations.
Model VII includes all three binary complexes, AF, FP, and AP, and has
the rate equation V/[A]o =
kcat[P][F]o/(KmF + KmP + [F]o)/(KmA(KA + [
F]o)/(KmF + KmP + [F]o) + [P] + KmP[P]2/KF
/(KmF + KmP + [F]o)).
This equation has five parameters (kcat,
KmF, KmP,
KmA, and KA),
which proved one too many for a unique solution to be found. By fixing
the dissociation constant for the tPA fibrin interaction
(KA) at the experimentally measured value
KA = 0.36 µM (17), however, a
unique solution for the remaining four values was obtained for both the
Glu1 and Lys78 forms of plasminogen. The
quality of the fit, as inferred by random residuals and values of the
loss function, was equivalent to that obtained with the template model
and Model IV above. However, the restraint
KAKmA/KmP = KP again predicted high affinity solution
phase interactions between t-PA and the Glu1
(KP = 3.2 µM) and
Lys78 (KP = 0.21) forms of
plasminogen. Since these predicted high affinity interactions are
inconsistent with independent experimental observations, model VII also
is excluded.
Thus, of the seven equilibrium models, model IV, which is similar to
the template model because it includes the two binary complexes AF and
FP, and model VII, which includes all three possible complexes, fit the
data well. The former was excluded, however, because it predicted
binding affinities between fibrin and plasminogen too high to be
consistent with observations, and the latter was excluded because it
predicts binding affinities between t-PA and plasminogen too high to be
consistent with observations.
Since the steady-state model, unlike the equilibrium models, both fit
the data well and did not predict unrealistic properties of the binary
interactions, it was chosen to represent and interpret the data.
Parameters of Kinetics of Plasminogen Activation
The
steady-state model predicts the behavior of the reaction over the
entire data set and provides a means of summarizing the results through
the four parameters kcat, Km,
KA, and K. The ability of the model
to reflect the data with reasonable accuracy is attested to by the fact
that the solid lines indicated in Figs. 1, 2, 3 all are
regression lines obtained upon fitting the data globally to a single
rate equation (Equation 39). The values of the parameters of kinetics
obtained by nonlinear regression analysis over the entire range of
fibrin and plasminogen concentrations for each type of activator and
either [Glu1]- or
[Lys78]Plg(S741C-fluorescein) (up to 200 points/analysis)
are provided in Table I.
With [Glu1]Plg(S741C-fluorescein) as the substrate, the
respective kcat values (s
1) for
t-PA, sct-PA, del.K2, and del.F were 0.058, 0.078, 0.176, and 0.041. The corresponding Km values (µM) were
0.41, 0.78, 1.23, and 2.46. These values can be interpreted as those which are obtained at saturating levels of fibrin. With
[Lys78]Plg(S741C-fluorescein) as substrate,
kcat values of t-PA, del.K2, and del.F were
greater than those with [Glu1]Plg(S741C-fluorescein) by
factors of 1.5, 1.9, and 2.6, respectively. Corresponding
Km values were smaller by factors of 13, 8, and 7. KA values (µM, dissociation
constant for the activator-fibrin interaction) for t-PA, del.K2, and
del.F, inferred from the kinetics of cleavage of
[Glu1]Plg(S741C-fluorescein) were 0.30, 0.71, and 2.88;
the corresponding values obtained with
[Lys78]Plg(S741C-fluorescein) were 0.13, 0.53, and 1.61. These values for each form of the activator are relatively insensitive
to the identity of the substrate, as expected, and are consistent with the values obtained previously in independent measurements of binding
(KA t-PA = 0.36 µM;
KA del.K2 = 1.1 µM; and
KA del.F = 1.4 µM), as
reported by Horrevoets et al. (17).
The values for the catalytic efficiency
(kcat/Km,
M
1·s
1) of t-PA, del.K2, and
del.F in [Glu1]Plg(S741C-fluorescein) activation were:
1.42 × 105, 1.43 × 105, and
0.17 × 105. When
[Lys78]Plg(S741C-fluorescein) is the substrate the
corresponding values for t-PA, del.K2, and del.F are: 26.9 × 105; 20.7 × 105, and 3.2 × 105. Thus, the catalytic efficiencies of t-PA and del.K2
are very similar to one another with either form of the substrate,
whereas those of t-PA are larger than those of del.F by a factor of 8.4 with either form of the substrate. The
kcat/Km values of t-PA,
del.K2, and del.F with [Lys78]Plg(S741C-fluorescein)
were, respectively, 19-, 12-, and 19-fold greater than those with
[Glu1]Plg(S741C-fluorescein).
The effect of fibrin on the catalytic efficiency of t-PA in catalysis
of cleavage of the two forms of the substrate can be quantified by
comparing kcat/Km values
obtained in the presence and absence of fibrin. In the absence of
fibrin, the relationship between rate and the concentration of
substrate is strictly linear and values of the slopes
(kcat/Km,
M
1·s
1) are 3.44 × 102 and 1.43 × 1
03 for the
Glu1 and Lys78 forms of the substrate,
respectively (18). The corresponding values in fibrin for
Glu1 and [Lys78]Plg(S741C-fluorescein) thus
exceed those obtained in the absence of fibrin by factors of 413 and
1,881, respectively.
DISCUSSION
Previous efforts to elucidate the kinetics of
fibrin-dependent activation of plasminogen by t-PA have
been complicated by two features of the reaction. The first is that the
reaction occurs within a clot, thereby complicating the measurement of
the time course of the generation of plasmin. The other is that plasmin can modify the properties of fibrin, plasminogen, and t-PA during the
interval over which plasmin generation is measured; thus, the kinetics
of the process are relatively complex and difficult to interpret
clearly. The approach described here was taken in order to circumvent
both of these difficulties. The recombinant, labeled derivative of
plasminogen was used to both provide an easily measured signal change
upon cleavage of the zymogen, even within a clot, and to eliminate the
plasmin-catalyzed feedback reactions, thereby simplifying the
interpretation of data.
The results of these studies indicate that at any particular input
concentration of fibrin, the kinetics of plasminogen activation conform
to the Michaelis-Menten equation, v =
kcat(app)
[S]/(Km(app) + [S]), so long as the
substrate (plasminogen) concentration is expressed as the free, rather
than total, concentration. Although not shown here, conformity to the
Michaelis-Menten equation also is achieved if the substrate
concentration is taken as that bound. The
kcat(app) and
Km(app) values vary with the input concentration of fibrin, such that kcat(app) = kcat[F]o/(K + [F]o) a
nd Km(app) =
Km(KA + [F]o)/(K + [F]o). Thus, the rate
equation that describes the kinetics of fibrin-dependent
plasminogen activation is given by Equation 47.
|
(Eq. 47)
|
The four characteristic parameters of this equation are
kcat, K, Km, and
KA. Except for KA, which
is the dissociation constant for the activator-fibrin interaction,
these parameters are related in somewhat complex ways to the individual
rate constants for assembly and turnover of the ternary
activator-plasminogen-fibrin complex, as indicated by Equations 43, 44, 45, 46
(see "Experimental Procedures"). In the absence of experimentally
determined values for the individual rate constants, the values of
kcat, Km, K,
kcat(app), and
Km(app) unfortunately cannot be
interpreted with mechanistic rigor. Nonetheless, they have the
conventional meanings in that kcat(app) at any
particular fibrin concentration yields the maximum rate at
saturating substrate and kcat yields the rate at
both saturating substrate and fibrin. Km and
Km(app) are both numerically equal to
the concentration of free substrate when the rate is one-half the
maximum, and Km is the limiting value of
Km(app) at saturating fibrin. The
parameter K provides the value of the fibrin concentration at which kcat(app) is one-half of the
kcat value at saturating fibrin.
As the data of Table I indicate, kcat values are
fairly insensitive to the identity of either the activator or the
substrate. Thus, because the affinities of the various forms of the
activators and the two substrates for fibrin vary quite substantially,
kcat is not very sensitive to the affinities of
the activators and substrates for fibrin. In contrast,
Km values increase and
kcat/Km values decrease, with
decreasing affinity of either the substrate or the activator for
fibrin. Equations 43 and 45 of the model described under
"Experimental Procedures" provide a reasonable explanation for
these behaviors. According to those equations,
kcat and Km are defined as
shown below in Equations 48 and 49.
|
(Eq. 48)
|
|
(Eq. 49)
|
Therefore,
|
(Eq. 50)
|
The relative invariance of kcat can be
explained if the denominator of the equation for
kcat is dominated by the term
KFk2 + KAk4. Since the
denominator also can be written as
KFk2 + k4(k
1 + k
2 + k5)/k1, domination of the
denominator by KFk2 + KAk4 implies that
k
1
(k
2 +&
nbsp;k5), i.e. the rate constant for
dissociation of t-PA from fibrin greatly exceeds those for dissociation
of t-PA from the ternary complex and substrate turnover. In this case
kcat is approximately equal to
k5, the turnover number of the ternary complex.
kcat therefore is not sensitive in this case to
the affinity of either the activator or substrate for fibrin, as
observed experimentally. Similarly, under these conditions the term for
Km would approximate as Km
(k
2&nbs
p;+ k
4 + k5)·KF/(KFk2 + KAk4). This equation
predicts an increase in Km with an increase in
KF (the dissociation constant for the
plasminogen-fibrin interaction), which is consistent with
observations (KF for
[Glu1]Plg(S741C-fluorescein) = 30 µM,
KF for
[Lys78]Plg(S741C-fluorescein) = 1.2 µM);
and Km for
[Glu1]Plg(S741C-fluorescein) = 0.41 µM,
Km for
[Lys78]Plg(S741C-fluorescein) = 0.032 µM). It also predicts, however, a decrease in
Km with an increase in KA,
which is not consistent with observations (i.e. the
Km does not decrease when the affinity of the
activator for fibrin decreases). However, if k2
and k4 are approximately equal to one another
(k2
k4 = k), then k2KF
is always much larger than
k4KA, (especially with [Glu1]Plg(S741C-fluorescein), because
KF exceeds KA by a factor
of 10-100 depending on the activator). Under these circumstances, Km approximates as Km
(k
2 + k
4 + k5)/k2. Thus, the
magnitude of Km depends on the values of
k
2 and k
4, which are
the off-rate constants for dissociation of t-PA or plasminogen from the
ternary plasminogen-fibrin-t-PA complex, rather than on values of the
dissociation constants for binary interactions between fibrin and the
substrate or the activator. Thus, the value of the
Km is predicted to change linearly with changes in
either k
2 or k
4; that
is, with the stability of the ternary complex. That
k2 and k4 are equal is reasonable, because these are the on-rate constants for the binding of
similar proteins (t-PA and plasminogen) to similar structures (binary
complexes between a fibrin protomer and plasminogen or t-PA).
Similarly, the catalytic efficiency is given by
kcat/Km
k2/(1 + (k
2 + k
4)/k5), which
therefore changes reciprocally with changes in either
k
2 or k
4. Since k
2 and k
4 are the
off-rate constants for the dissociation of t-PA and plasminogen from
the ternary complex, their magnitudes are directly related to the
stability of complex. When these rate constants are small, such
that the complex is stable, the Km value is small,
the kcat/Km value (catalytic
efficiency) is high, and vice versa.
According to this interpretation, the Km and
catalytic efficiency
(kcat/Km) values are not
determined directly by the affinities of the binary interactions
between the activator and substrate with fibrin, but rather by the
stability of the ternary plasminogen-fibrin-activation complex. This
uncoupling of fibrin binding affinity from catalytic properties is
illustrated by comparing the results with t-PA or the variant del.K2
with those of del.F. They have very similar Kd
values in fibrin binding (17) but substantially different
kcat, Km, and
kcat/Km values (Table I).
A representation of the steady-state model is presented in Fig.
5. The figure depicts a fibrin protomer with a binding
site (a) for the activator (A) and another
(p) for plasminogen (P). The activator and
substrate can add in either order to form the respective binary
species. Further interactions produce the ternary complex, from which
plasmin is generated. Also depicted is an interaction between the
activator and plasminogen within the ternary complex. This interaction
would contribute to the stability of the complex. The
plasminogen·fibrin interaction is assumed to be essentially at
equilibrium because of the high plasminogen and fibrin concentrations,
relative to the activator concentration. The analysis presented in the
preceding paragraph applies to conditions in which the rate constants
k
2 and k5 are much
smaller than k
1, i.e. where the
rate constant for dissociation of the activator from fibrin is large
compared to those for dissociation of the activator from the ternary
complex (k
2) and substrate turnover
(k5). Under these circumstances
kcat is approximately equal to
k5, and Km and
kcat/Km are largely determined by the values of k
2 and
k
4, i.e. by the stability of the
ternary complex. Thus, according to the model, catalytic efficiency,
expressed through k
2,
k
4, and k5, can be
dissociated from the binding of activator
(k1,k
1) and substrate
(k3,k
3) to fibrin.
Essentially, the potential exists that the catalytic efficiency of
fibrin-potentiated plasminogen activation is determined by the
stability of the three component complex rather than the affinities of
the binding interactions of the substrate and activator with
fibrin.
Fig. 5.
Steady-state template model of plasminogen
activation. The model embodies the independent binding of
activator (A) and plasminogen (P) to their unique
binding sites on fibrin (F) and formation of the ternary
catalytic complex (AFP), from which plasmin (Pn)
is formed. The symbol (·) between A and P in the ternary complex
implies a template-dependent interaction between them.
Under the conditions described in the text, the turnover number, the
stability of the ternary complex, and the catalytic efficiency are
determined primarily by the steps with corresponding rate constants
k
2, k
4, and
k5.
[View Larger Version of this Image (11K GIF file)]
The above considerations are relevant to efforts to use recombinant
technologies to produce modified forms of plasminogen activators with
catalytic properties that are improved compared to those of the wild
type form of the activator. An intuitively obvious change includes
producing variants with enhanced fibrin binding, an effect that
presumably would improve both fibrin specificity and enhanced
catalysis. The possibility exists, however, that changes in the
structure of t-PA could be introduced through protein engineering that
greatly amplify fibrin binding but do not contribute to enhanced
catalytic efficiency. Conversely, changes in structure could
potentially be incorporated, which, although not appreciably altering
the affinity of the activator for fibrin, could substantially increase
or decrease the catalytic efficiency, depending on whether such changes
enhance or diminish the stability of the ternary activator-fibrin-plasminogen complex. This distinction between fibrin
binding and the stability of the ternary complex, and the elements of
structure that contribute to them, may rationalize the frequently
observed lack of correlation between the fibrin binding affinities of
variants of t-PA and their potencies in plasminogen activation or
thrombolysis (23, 24, 25). Perhaps those structural modifications that
will prove efficacious in optimizing the catalytic efficiency of
variant forms of the activator will be those that maximize the
stability of the ternary complex rather than the fibrin binding
properties of the variants.