The Solvent Isotope and Ionic Effects on Thrombin-Hirudin Interactions
John Paul Sheehy
Biochemistry Comprehensive Submission
April, 24 2008
Abstract
Hirudin, found naturally in medicinal leaches, is the most potent reversible inhibitor of
thrombin known to exist.
It interacts non-covalently over a large area, especially on the
fibrinogen-binding exosite of the enzyme. As hydrogen-bonding interactions play a major role,
this study targeted the dependence of rate constants and the inhibition constant, Ki, on ionic
strength (), sodium ion concentration, nature of buffer, and the presence of D2O in buffers.
Kinetic measurements were conducted spectro-photometrically and spectro-fluorometrically in
the presence of a chromophoric or fluorophoric substrate, respectively. The dissociation constant
and the second-order-rate constant for the slow-tight-binding inhibition of human -thrombin
with r-hirudin1,3 are 1.9 ± 0.4 pM and (7.14 ± 0.07) x 107 M-1 s-1 at [Na+] =  = 0.19 M in pH
8.06, 0.05 M barbital buffer, and 0.56 ± 0.07 pM and (1.50 ± 0.06 ) x 108 M-1 s-1 at Na+ = 0.30, 
= 0.31 M in pH 8.12, 0.02 M Tris buffer at 25.0  0.1 C. There is a strong buffer molecule
dependence, with results in Tris buffers differing consistently from those in barbital buffers.
When this is considered, Na+ ion concentration appears to slightly lower the forward kinetic
constant, k1. The solvent isotope effects on Ki are 1.3 ± 0.5, 0.9 ± 0.1, 1.4 ± 0.7, 1.03 ± 0.7
between pH 8.1 and 8.3 at ionic strength 0.19-0.31 at 25.0 ± 0.1 C. The solvent isotope effect on
the second-order rate constant, k1, is typically lower than unity: 1.04 ± 0.15, 0.71 ± 0.30, 0.64 ±
0.16, 0.68 ± 0.05 under the same conditions.
Introduction
Thrombin (EC 3.4.21.5) is a serine protease which plays an important role in blood
coagulation. It is activated from prothrombin in the final steps of coagulation, and then catalyzes
the conversion of fibrinogen into fibrin, which actually forms blood clots.1 α-thrombin has two
polypeptide chains, a thirty-six residue A-chain and a 259 residue B-chain, connected by a
2
disulfide bridge.
The longer B-chain also includes several internal disulfide bridges.1
α-
thrombin is prone to proteolytic cleavage by trypsin or autolysis at an Arginine 77, and the
resulting form is known as β-thrombin. Other, similar breaks form other versions of thrombin,
including γ-thrombin and ε-thrombin.1 The function of thrombin in the clotting cascade is shown
in Figure 1 below.
Figure 1: Thrombin’s role in clotting cascade.2
Hirudin is one of many substances in the saliva of leeches which helps prevent the
clotting of ingested blood in the digestive tract.3 In fact, it is the most potent natural inhibitor of
thrombin. Its primary structure is shown in Figure 2. It is sixty-five amino acid residues in
length, with glutamine at the C-terminus, and isoleucine as the N-terminal residue.1
The
structure contains three disulfide bridges, between cysteines at the sixth and fourteenth, the
sixteenth and twenty-eighth, and the twenty-second and 39th positions. The latter two bonds
form a “double-loop.”1 From the fortieth to sixty-fifth residue runs the C-terminal tail, which
3
contains no disulfide bonds, but does have one peculiarity at the tyrosine in the sixty-third
position, which is sulfonated in the natural version of the molecule.
Unfortunately, the
recombinant form does not have this sulfate group. Some variant molecules exist with differing
amino acids at a number of positions. In contrast to the long, unbound tail, the N-terminal
domain is compact due to the double loops.1
Figure 2 Primary structure of hirudin.7
Grutter et al. report that the interactions between hirudin and thrombin are quite different
from those of other serine protease inhibitors and their targets. Typically such inhibitors make
contact primarily in the active site region, but hirudin interacts with thrombin over a
comparatively larger area (1400 Å2). This large area of interaction is probably one of the factors
contributing to the extreme tightness of the complex.3 The loop region from residues 5-45 of
hirudin is, for the most part, not in contact with thrombin,3 except for two salt bridges, two
hydrogen bonds, and thee hydrophobic contacts.1 Both N-terminal head and the 18 residue Cterminal tail region of hirudin do make contact.3 The N-terminal three residues of hirudin
occupy the active site of thrombin, but in a novel way. Most serine-protease inhibitors derive
4
their specificity from their ability to bind the primary specificity pocket of thrombin.3 Aside from
the presence of hirudin’s second residue, a threonine, near the entrance to this pocket, the
inhibitor leaves it free, and derives its specificity from numerous interactions both inside and
outside of the active site.3 Fifteen of the first 48 residues of hirudin make some contact with
thrombin, totaling 103 interactions of less than 4 Å.
The C-terminal chain of hirudin binds with the fibrinogen exosite of thrombin.1 This
chain has an unusually long extended conformation, and makes several hundred contacts within
less than 4 Å with thrombin.1 A site-directed mutagenesis study by Betz, Stone, and Hofsteenge
showed that, at least for the acidic residues 53, 55, 57, 58, 61, and 62, the residues contribute to
the total binding energy (75 kJ/mol) in relatively similar amounts (from 2.3 to 5.9 kJ/mol). 4 An
earlier site-directed mutagenesis study of several basic residues in both domains of hirudin found
that only the Lysine 47 made a major contribution to thrombin binding.5 An image of the
interactions can be seen in Figure 3 below.
Figure 3 Thrombin and hirudin interaction.
5
Given the large number of interactions between thrombin and hirudin, it is worth while to
consider whether any short strong hydrogen bonds (SSHB), exist in the thrombin-hirudin
complex. Such bonds, shorter than 2.6 Å, can be important contributors to enzyme catalysis, and
thus also sometimes appear in enzyme-inhibitor complexes.6 They can be as much as six times
stronger than an ordinary hydrogen bond. SSHBs typically form in the absence of a hydrogen
bonding solvent (water) and when the two atoms involved have similar pKa’s and are of the
same element (Oxygen or Nitrogen).6
One example occurs in the catalytic activity of
triosephosphate isomerase, one of the most efficient enzymes known to exist.6,7 Evidence has
been presented that serine proteases, such as thrombin, trypsin, and chymotrypsin, have SSHBs
between the catalytic aspartate and histidine in the active site.”6,7
Hirudin is both a slow-binding and tight-binding inhibitor. “A reversible tight-binding
inhibitor is one that exerts its reversible inhibitory effect on an enzyme-catalyzed reaction at a
concentration comparable to that of the enzyme. Therefore, allowance must be made for the
change in the concentration of free inhibitor that occurs as a result of it undergoing interaction
with one or more forms of the enzyme.”8 This differs from classical inhibitors, which only cause
inhibition at concentrations far greater than that of the target enzyme. This means that such
inhibition cannot be quantitatively described with the Michealis-Menten equation, “since the
assumption that the free inhibitor concentration is equal to the total inhibitor concentration is not
valid.”8
Hirudin is known as a slow-binding inhibitor because the strength of enzyme-inhibitor
interactions lead to a delay in the establishment of a steady state velocity.8 When the equilibrium
for the interaction is not established rapidly, a “transient or pre-steady-state” phase occurs in a
plot of product formation vs. time.8
6
The reaction scheme chosen to describe the inhibition of thrombin by hirudin includes
reversible inhibition of the free enzyme in the presence of substrate. The substrate reaction is
described by two steps: the formation of the enzyme-substrate complex, and the subsequent
formation of product and free enzyme.
Scheme 18
The formation of product vs. time is described by the equation
P= vst + (vs-vo)(1-d)/(dk)*log((1-de-kt)/(1-d))
eq. 19,8
where vs is the steady state reaction velocity, vo is the reaction velocity in the absence of
inhibitor, t is time, P is the amount of product formed, d is a function equivalent to (Ki+Et+It[(Ki+Et+It)2-4EtIt]1/2)/(Ki+Et+It+[(Ki+Et+It)2-4EtIt]1/2)
where Ki is the dissociation constant, Et is the concentration of all enzyme present in solution, It
is the concentration of all inhibitor present in the solution, and k is a sort of second-order rate
constant equivalent to
k1[(Ki+Et+It)2-4EtIt]1/2/(1+S/Km)
where k1 is the forward kinetic constant for inhibition and S is the concentration of substrate.8
According to a study by Stone and Hofsteenge, the dissociation constant of the hirudinthrombin complex depends greatly on ionic strength, increasing approximately twenty fold
between the ionic strengths of 0.1 and 0.4. This increase in dissociation constant is largely
caused by a decrease of k1. In fact, k-1 also decreases with ionic strength, which, by itself, would
7
actually contribute to tighter interactions, but the dependence of k1 on ionic strength is much
more significant.9 According to a later study of Stone, Hofsteenge, and Dennis, each negatively
charged residue in contact with thrombin makes an approximately equal contribution of -4
kJ/mol to the binding energy of the hirudin-thrombin complex. “For native hirudin, ionic
interactions accounted for 32% of the binding energy at a [theoretical] ionic strength of zero.”10
The goal of this study was to determine the deuterium solvent isotope effect on the
interactions of α-thrombin and recombinant hirudin at a number of differing ionic strengths and
sodium concentrations. The data obtained could be useful for better understanding the strength
of the thrombin-hirudin interactions and the potential existence of SSHBs.
Materials and Methods
Materials Anhydrous dimethyl sulfoxide (DMSO), heavy water with 99.9 % deuterium content
and anhydrous methanol, were purchased from Aldrich Chemical Co. All buffer salts were
reagent grade and were purchased from either Aldrich, Fisher, or Sigma Chemical Co. H-D-PhePip-Arg-4-nitroanilide.HCl (pNA) (S-2238) 99% (TLC) was purchased from Diapharma Group
Inc. and Boc-Val-Pro-Arg-7-Amino-4-Methyl Coumarin (VPR-7AMC) was from Sigma
Chemical Co.. Human -thrombin, MM 36,500 d, 3010 NIH u/mg activity in pH 6.5, 0.05 M
sodium citrate buffer, 0.2 M NaCl, 0.1% PEG-8000 was purchased from Enzyme Research
Laboratories, OH.
R-hirudin was purchased from Pentapharm, Lot 40907401/126-05 and Lot
405383/126-05.
Instruments Spectroscopic measurements were performed with a Perkin-Elmer Lambda 6 UVVis Spectrophotometer connected to a PC. The temperature was monitored using a temperature
probe connected to a digital readout device. Either a Neslab RTE-4 or a Lauda 20 circulating
8
water bath was used for temperature control. Fluorometric measurements were performed with
Cary Eclipse fluorometer with a Peltier temperature control system and PC.
Positive
displacement Gilson and Rainin Microman pipettes with plastic tips were used for the delivery of
enzyme solution, substrate solution and inhibitor solution.
Solutions Buffers were prepared by weight from Tris-base and Tris-HCl, Sodium Barbiturate,
and Barbital. The concentrations were 0.02 M Tris, 0.05 M Barbital, or 0.01 M Sodium Barbital,
0.3 M, 0.15 M, or .03 M NaCl, and 0.1% PEG4000 in H2O or D2O. The pH was adjusted to
near 8.0. Water was distilled from a copper-bottom distiller, run through an ion-exchanger and
distilled before use. Buffer solutions in D2O were made identically to their counterpart in H2O,
although one buffer, 0.01 Sodium Barbital, 0.03 NaCl, was prepared by diluting an H2O 1:5 in
D2O to form an 80% D2O buffer. The negative log of the deuteron concentration, pD, in these
solution was measured by the same pH electrode and pD was calculated by adding 0.4 to the
electrode reading.11 The pD was typically near 8.7. Buffer pH and pD was monitored during
storage. Thrombin and hirudin were typically obtained from stock solutions stored at -20° C.
Small stocks of thrombin were prepared identically in advance, and were further diluted in two
steps to about 4 nM in the buffer with the parameters under study. Hirudin stock solutions were
similarly prepared at 180 nM, and just before use were diluted with the buffer under study to
stock solutions of approximately 36 nM and 3.6 nM respectively. The substrate was prepared in
DMSO at a concentration of approximately 5 mM and stored at 0°C.
Protocol
A single set of experimental data was collected in a single session, and the
temperature was maintained at 25.0±0.1°C and monitored with a thermistor in all experiments.
9
In the spectrophotometric studies absorbance was measured at 405 nm to monitor pNA
release from S-2238. Glass cuvettes were placed in the cell compartment before the reaction was
begun so that they would acquire the proper temperature.
The fluorometric studies were performed with excitation set to 365 nm and emission to
445 nm with the PMT sensitivity set to 600 V and both slits to 5 nm. It was determined that 0.57
Arbitrary Units were equal to 1 nM of 7AMC in a fluorometric cell.
Cells were prepared as follows: 10-25 uL of the approximately 4 nM thrombin solution, 5-50 uL
of either the 36 or 3.6 nM hirudin and 10-20 uL of the 5-mM substrate solution were added to
enough of the buffer under study to have a total volume of 2 mL. The order of addition was
always the same: buffer, substrate, inhibitor, enzyme. Before the addition of enzyme, the
instrument reading was be “zeroed.” Upon the addition of enzyme, the number of seconds
between this moment and the time the instrument began recording data was measured with a
stopwatch. Change in fluorescence in the cell was recorded ten times per second for a given
length of time, usually 1000-2000 seconds.
Initial velocities were measured without any
inhibitor in order to measure enzyme activity.
These were typically performed in the
corresponding H2O buffer during D2O experiments. If enzyme activity dropped significantly, a
new stock solution was obtained and the added volume of thrombin would be changed if
necessary to maintain the same activity.
The spectrophotometric experiments were performed similarly, although the cells were
brought to a total volume of 1 mL, no stopwatch was used to measure initial delay, and the
instrument recorded absorbance only once every 1-3 seconds, depending upon the particular
length of the run.
10
Data Processing The time course data curves were first processed in Microsoft Excel. The
fluorometric calibration curve conversion, 0.57 AU/nM or the pNA extinction coefficient, 9920
M-1cm,-1 was applied, so that the concentrations were listed in nM. Also, the number of seconds
recorded on the stopwatch was added to the time values of the ordered pairs, shifting the curve
slightly to the right, and manual curve smoothing was applied. Once the data curves were thus
prepared, they were transferred into the fitting program Graphit and the steady state velocity (the
linear slope which curves ultimately reach, was calculated by means of fitting to a simple version
of the progress curve equation (eq. 1). The actual input in the Graphit equation software was as
follows:
P=vs*(t)+((((vo-vs)*(1-(d)))/((d)*k))*log((1-(d)
*exp(-k*(t)))/(1-(d))))+h
eq. 2
The symbols in eq. 2 are as were defined above, but for this level of fitting, d was simplified, left
merely as d, and h was added as an offset (used because the measurement of the delay between
the start of the reaction and the start of data collection was not always perfect, and occasionally
there was a question as to whether or not a run had been “zeroed.”) P was the dependent
variable, t the independent variable, and d, vo, vs, k, and h were found by means of a non-linear
least squares fit. The Graphit fitting style was “Simple” without “Robust,” and this fitting was
not sensitive to initial estimates within at least one order of magnitude. A full set of data curves
for a single determination may be seen in Figure 4 below.
11
Figure 4: Sample data curves for the inhibition of human α-thrombin by r-hirudin in
pH 8.12, 0.02 M Tris, 0.3 M NaCl, 0.1% PEG at 25.0±0.1°C
The resulting vs values were then collected and plotted against the labeled hirudin
concentration based on the activity determined by Pentapharm, and calculated with the
assumption that one anti-thrombin unit (ATU) was equal to 8.5 pmol of r-hirudin. An additional
12
data point was obtained at the intersection of 0 pM hirudin with the average velocity of the runs
performed without r-hirudin in the experimental buffer.
The dependence of steady state velocity on inhibitor concentration was modeled in Graphit:
vs=(vo/(2*E))*((((Ki+(I*x)-E)^2+(4*Ki*E))^(1/2))-(Ki+(I*x)-E))+h
eq. 3
In this formula, vs and vo are as previously defined. E is enzyme concentration, I is the labeled
inhibitor concentration, x is a factor which represents the ratio of the true inhibitor concentration
to the concentration calculated by Pentapharm, Ki is the apparent dissociation constant Ki’, and h
is an offset which represents activity believed to be due to contaminating β-thrombin and γthrombin which are less susceptible to r-hirudin. Such activity can be eliminated by using an
irreversible covalent inhibitor PPACK, but even substantially large concentrations of r-hirudin
do not eliminate it. In this fitting, vs was the dependant variable, and I was the independent
variable. The offset, h, was arbitrarily decided to be 80% of the activity of the lowest point
measured, and E was calculated using the measured kcat of 73.8 s-1 for VPR-7AMC, and 95 s-1
for S-2238 in pH 8.4-8.6, 0.02 Tris buffer, 0.3 M NaCl, 1% PEG400, and 1-2% DMSO at 25.0 ±
0.1° C.12 Values of kcat in other buffers or at other pH were also determined by measuring the
difference in activity when the same volume of the same solution of thrombin was added to the
different buffers. For the 0.1 M sodium barbital in D2O, the kcat was assumed to be 31.5 s-1, one
third of the corresponding H2O value, due to a large effect of D2O. Ki, vo and x were then fitted
using a non-linear least squares fit with “Simple Robust” fitting. This fit was also not sensitive
to estimates differing within an order of magnitude. A sample fitting is shown in Figure 5
below.
13
Figure 5: Sample fit of data from Figure 4 to eq. 3.
The apparent Ki’ could then be corrected for substrate concentration using the formula:
Ki (corrected) = Ki’ (apparent)/(1+(S/Km))
eq. 4
where S is the substrate concentration for the run (determined from the fluorescence of
completed runs) and Km is the Km for that substrate under the experimental conditions.
The next level of fitting involves the full version of equation 1, the complete progress
curve equation, as described above. The actual Graphit input was as follows:
P=vs*(t)+((((vo-vs)*(1-((Ki+E+(I)-(((Ki+E+(I))^2)(4*E*I))^(1/2))/(Ki+E+(I)+(((Ki+E+(I))^2)(4*E*I))^(1/2)))))/(((Ki+E+(I)-(((Ki+E+(I))^2)(4*E*I))^(1/2))/(Ki+E+(I)+(((Ki+E+(I))^2)(4*E*I))^(1/2)))*k))*log((1-((Ki+E+(I)-(((Ki+E+(I))^2)-
14
(4*E*I))^(1/2))/(Ki+E+(I)+(((Ki+E+(I))^2)-(4*E*I))^(1/2)))*exp(k*(t)))/(1-((Ki+E+(I)-(((Ki+E+(I))^2)(4*E*I))^(1/2))/(Ki+E+(I)+(((Ki+E+(I))^2)-(4*E*I))^(1/2))))))+h
eq. 5
In this version of the equation, where d is fully expanded, all of the other variables are the
same as in equation 2, and Ki, E, and I have the same significance as in equation 3. Ki is here
Ki’, still uncorrected for substrate, and this value was taken from the fit to equation 3. The
symbol k is k’, a type of pseudo-first order rate constant to be used in the next level of fitting.
Also, the labeled concentration, I, was corrected by the factor x fitted in equation 3. E too was a
fixed value, calculated the same way as for equation 2, and h was treated as a fixed value, taken
directly from the fit to equation 1. P and t were, as in equation 2, the dependent and independent
variables respectively. Only vo, vs, and k were left as parameters, and these were fitted by means
of a non-linear least squares regression using “Simple” fitting without “Robust.” As with the
simple version of this fit, initial estimates had little effect.
The “k” values were then collected and plotted against the inhibitor concentrations
corrected by x, and a Km correction was applied at the same time. This was done according to
the following formula described as a Graphit input:
k=k1*Km*((((Ki+E+I)^2)-(4*E*I))^(1/2))/(Km+S)
eq. 6
In this formula k1 is the elementary forward rate constant, and E, I, Km, and S are the same as
listed in the equations above (with the important exception that I is corrected for x, as with
equation 5, but not equation 3). Ki, I, and E, were all provided as they were in the fit to equation
4, leaving only k1 as a parameter. A fit was performed using “Simple” fitting without “Robust,”
and the result can be seen in Figure 6 below. Once again, differing estimates had no effect.
15
By means of the corrected values of Ki and k1, k-1 could be determined using this
equation:
Ki = k-1/k1
eq. 7
The preceding method of analysis
was
applied to
both
fluorometric and
spectrophotometric determinations, but for the spectrophotometric data, the fitting was only
successful up to equation 3.
0.01
0.008
k, s-1
0.006
0.004
0.002
0
0
200
[H], pM
Figure 6: Sample fit of data from Figure 4 to eq. 6.
16
400
Results and Discussion
The study consisted of ten separate determinations of the kinetic parameters of the
thrombin hirudin system in aqueous buffers with varying ionic strength, sodium ion
concentration, and atom fraction of deuterium in the buffer. A summary of the calculated
parameters may be seen below in Tables 1 and 2. Included in Table 1 are several experimental
parameters, the concentration of enzyme and substrate for each determination, the composition
of the buffer, the date on which the experiment was performed, the Km, and the determined
activity fraction of the hirudin, the X-value.
Table 1: Experimental conditions and fitting parameters
Date
Buffer
Enzyme, Substrate,
pM
µM
kcat,
s-1
Km,
µM
X-value
42
95
12*
0.49±0.04
7-20
2006
0.01 M sodium barbital, 0.03 M 95
NaCl, 0.02% PEG, pH 8.11
7-6
2007
27
46
61.3
38*
2.0±0.3
53
46
62.3
24*
5.0±0.3
21
46
73.8
11
1.8±0.1
14
29.1
73.8*
23
0.80±.12
206
29.7
31.5
12*
1.1±0.3
31
42
43.0
42*
3.8±0.02
33
42
55.0
12*
3.7±0.5
33
42
50.4
4.6
2.0±0.3
14
61
25.4*
13
0.69±0.17
0.05 M barbital, 0.03 M NaCl,
0.12 M CholineCl, 0.1% PEG,
pH 8.09
7-2
0.05 M barbital, 0.15 M NaCl,
2007 0.1% PEG, pH 8.06
7-17
0.02 M Tris, 0.3 M NaCl, 0.1%
2007 PEG, pH 8.12
10-13 0.02 M Tris, 0.03 M NaCl, 0.27
2007 M CholineCl 0.1% PEG, pH 8.3
7-25
0.01 M sodium barbital, 0.03 M
2006 NaCl, 0.02% PEG, pD 8.70,
80% D2O
7-23
0.05 M barbital, 0.03 M NaCl,
2007 0.12 M CholineCl, 0.1% PEG,
pD 8.74, D2O
7-12
0.05 M barbital, 0.15 M NaCl,
2007 0.1% PEG, pD 8.74, D2O
7-19
0.02 M Tris, 0.3 M NaCl, 0.1%
2007 PEG, pD 8.74, D2O
11-19 0.02 M Tris, 0.03 M NaCl, 0.27
2007 M CholineCl 0.1% PEG, pD 8.9
D2O
*estimated
17
Table 2 includes the dates and buffer compositions for reference, and then provides the
determinations of Ki, and k1, with standard error of the regressions, and also k-1, which was
calculated from eq. 7.
Table 2: Disassociation constants, rate constants for hirudin inhibition
25.0±0.1°C
Date
Buffer
Corrected
Ki, k1, μM-1s-1
pM
7-20
0.01 M sodium barbital, 0.03 M 0.7±0.3
N/A
2006 NaCl, 0.02% PEG, pH 8.11
7-6
0.05 M barbital, 0.03 M NaCl, 0.12 1.7±0.7
129±8
2007 M CholineCl, 0.1% PEG, pH 8.09
7-2
0.05 M barbital, 0.15 M NaCl, 0.1% 1.9±0.4
71.4±0.7
2007 PEG, pH 8.06
7-17
0.02 M Tris, 0.3 M NaCl, 0.1% PEG, 0.56±0.07
150±6
2007 pH 8.12
10-13 0.02 M Tris, 0.03 M NaCl, 0.27 M 0.35±0.24
206±10
2007 CholineCl 0.1% PEG, pH 8.3
7-25
0.01 M sodium barbital, 0.03 M 23±12
N/A
2006 NaCl, 0.02% PEG, pD 8.70, 80%
D2O
7-23
0.05 M barbital, 0.03 M NaCl, 0.12 1.30±0.03
124±16
2007 M CholineCl, 0.1% PEG, pD 8.74,
D2O
7-12
0.05 M barbital, 0.15 M NaCl, 0.1% 2.2±0.5
101±4
2007 PEG, pD 8.74, D2O
7-19
0.02 M Tris, 0.3 M NaCl, 0.1% PEG, 0.4±0.2
234±6
2007 pD 8.74, D2O
11-19 0.02 M Tris, 0.03 M NaCl, 0.27 M 0.34±0.23
302±14
2007 CholineCl 0.1% PEG, pD 8.9 D2O
of α-thrombin,
k-1,
1000 x s-1
N/A
0.23
0.14
0.084
0.071
N/A
0.016
0.22
0.096
0.010
Dependence of the apparent and corrected disassociation constant on concentration of
sodium ion and ionic strength is tabulated in Tables 3 and 4.
Table 3: Apparent dissociation constant, calculated from data in Tables 1 and 2.
Na+, M
Ionic strength, M
Ki' (H2O), pM
Ki' (D2O), pM
0.03
0.31
0.8±0.5
1.9±1.3
0.04
0.04
3.3±1.4
81±42
0.07
0.19
3.9±1.6
4.2±0.1
0.19
0.19
5.6±1.2
10±2.6
18
0.30
0.31
2.8±0.4
4.2±1.7
Table 4: Corrected dissociation constants from Table 2.
Na+, M
0.03
0.04
0.07
0.19
0.30
Ionic
M
0.31
0.04
0.19
0.19
0.31
Strength, Ki (H2O), pM
Ki (D2O), pM
0.35±0.24
0.74±0.32
1.7±0.7
1.9±0.4
0.56±0.07
0.34±0.23
23±12
1.30±0.03
2.2±0.5
0.4±0.2
Solvent Isotope
Effect
1.03±0.7
0.03±0.02
1.3±0.5
0.9±0.1
1.4±0.7
Tables 5 and 6 show the variation of the kinetic constants with both sodium ion
concentration and ionic strength.
Table 5: Forward second-order rate constants from Table 2
Na+, M Ionic Strength, M
k1 (H2O), μM-1s-1 k1 (D2O), μM-1s-1
0.03
0.07
0.19
0.30
0.31
0.19
0.19
0.31
206±10
129±8
71±7
150±6
302±14
124±16
101±42
234±56
Table 6: Reverse first-order rate constants from Table 2
Na+
Ionic Strength (M)
k-1 (H2O) 1000 X s-1
(M)
0.03
0.31
0.071
0.07
0.19
0.23
0.19
0.19
0.14
0.30
0.31
0.084
Variation in Expected Hirudin Ratio
Solvent Isotope
Effect
0.68±0.05
1.04±0.15
0.71±0.30
0.64±0.16
k-1 (D2O) 1000 X s-1
0.10
0.16
0.22
0.096
The X-value, the ratio of hirudin activity calculated
by fitting to that calculated from information provided by the manufacturer, varied considerably
in a short period of time. The data from 2006 was found with hirudin from a different and older
stock, which explains the differing X-values. The data from 2007 was made with a fresh stock
from Pentapharm, and all of the stock vials of hirudin used on individual experimental days were
19
diluted from the original stock solution at the same time, on the same day, and in the same way.
The lower X-values in October and November are probably due to degradation of these stock
vials in the freezer, but the majority of the data, collected in July 2007, still shows a significant
variation in x from approximately 5 to below 2. This variation with time may be seen in Figure 8
below. Supposing that the “true” value were approximately 3.4, then the extreme variations
would be approximately ± 50%, that is, between 1.7 and 5.1. Some of this could be explained as
human error in dilution, and also as varying levels of condensation forming inside the tubes with
hirudin solutions during experiments. However, a major concern is that the actual fitting process
does not determine hirudin concentration with excellent precision, because increasing the Xvalue and decreasing the disassociation constant have a similar effect on the fitting process, it
does appear that these tend to be directly proportional, as seen in the plot of Ki vs. X-value in
Figure 8.
Hirudin Ratio Concentration
6
Hirudin Ratio
5
4
3
2
1
0
3/24/2006
1/18/2007
11/14/2007
9/9/2008
Date
Figure 7: Variation of X-value with experimental date.
20
Variation of Ratio with Ki
Expected Hirudin Ratio
6
5
4
3
2
1
0
0
1
2
3
Dissasociation Constant (pM)
Figure 8: Variation of X-value with disassociation
constant. H2O buffers are blue and D2O buffers are
pink.
Variation of Kinetic Parameters with Ionic Strength
As Figure 9 shows, the dissociation
constant decreased with increasing ionic strength for both H2O and D2O data. For data collected
fluorometrically, this is completely contrary to the findings of Stone and Hofsteenge, who found
that the dissociation constant increased sharply with increasing ionic strength from 0.1 to 0.4 M.
One possible explanation for this increase is that both experiments at 0.31 M ionic strength were
in a Tris based buffer, whereas the experiments at lower ionic strength were in barbital. Also,
the lowest ionic strength to be studied with the superior fluorometric method was 0.19 M. If the
data obtained in barbital buffer, including the spectrophotometric determination, are examined
separately, as in Figure 9 below, then they do support the trend found by Stone and Hofsteenge.9
21
Ki, pM
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.1
0.2
0.3
Ionic Strength, M
Figure 9: Figure 9 shows the variation in Ki with ionic strength for all determinations except 0.01
M Sodium Barbital, 0.03 M NaCl, 0.02% PEG, pH 8.11. D2O runs are black and H2O are white.
As should be expected from these dissociation constant trends, k-1 increases with ionic
strength, and k1 decreases, as shown in Figures 10 and 11. Interestingly, at 0.31 M ionic strength
and in Tris buffer, both association and dissociation were faster in D2O than in H2O. This is in
contrast to the results obtained at 0.19 M ionic strength in barbital buffer.
Variation of Kinetic Parameters with Sodium Ion Concentration
In both H2O and D2O
buffer systems, the dissociation constant shows a rise with sodium ion concentration, which is
expected based on thrombin’s function, followed by a drop at high sodium concentrations. The
spectrophotometric H2O run was included, and this fits nicely into the apparent trend. Also, in
this case, both Tris (the lowest and highest Na+ concentrations) and barbital data seem to be in
agreement. These data may be observed in Figure 12 below.
22
0.24
0.22
1000 x k-1, s-1
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.2
0.24
0.28
Ionic Strength, M
0.32
Ki, pM
Figures 10 and 11: Variation of k1 (left) and k-1 (right) with ionic strength. D2O runs
are black and H2O are white.
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.1
0.2
0.3
Na+, M
Figure 12: Variation of Ki with sodium ion concentration. H2O determinations are white
and D2O black.
For the association rate constant, k1, the shape of the relationship is, as expected, opposite
of the shape seen for the dissociation equilibrium constant, as shown in Figure 13. Interestingly,
for almost all of the data the k1 was higher in D2O. As the Tris and barbital systems each have
23
constant ionic strength, it is useful to consider them separately. The highest and lowest values
are in the Tris system. In this case, gently decreasing and nearly parallel lines can be drawn for
k1 with increasing sodium ion concentration for all four systems: H2O Tris, H2O barbital, D2O
Tris, and D2O barbital. In the case of k-1, bell shaped dependencies are seen in both the H2O and
D2O buffer systems in Figure 14 below.
If the Tris and barbital systems are considered
separately, the Tris system appears to remain relatively constant, and the barbital system shows
opposite trends for H2O and D2O. These trends appear relatively difficult to interpret.
0.24
0.22
1000 x k-1, s-1
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.1
0.2
Na+, M
0.3
Figures 13 and 14: Variation of k1 (left) and k-1 (right) with sodium ion concentration. D2O
runs are black and H2O are white.
Solvent Isotope Effect
The solvent isotope effects for the parameters were calculated within
approximately 70% error, which is less than ideal, yet the magnitude is established clearly: it is
around unity. The solvent isotope effects on Ki (excluding one) are 1.3 ± 0.5, 0.9 ± 0.1, 1.4 ± 0.7,
1.03 ± 0.7 between pH 8.1 and 8.3 at ionic strength 0.19-0.31. It appears that the slightly higher
values correlate with lower Na+ ion concentrations. The solvent isotope effect on the secondorder rate constant for encounter between thrombin and hirudin is typically lower than unity:
1.04 ± 0.07, 0.71 ± 0.07, 0.64 ± 0.06, 0.68 ± 0.01 from the experiments described in Table 2. It
24
is not possible to discern any effect on these values of ionic strength or Na+ content in the
reaction mixture. The very small isotope effects reveal that SSHBs, i.e. strong hydrogen bridges,
are probably not forming either in the rate determining step in the course of formation of or in
the produced thrombin-hirudin adduct. This is somewhat surprising in the light of the great
number of intermolecular hydrogen bonds between thrombin and hirudin reported from an H
NMR study.13, 14
One value stands out from all the rest in these data, and that is the dissociation constant
determined on 7-25-06 in an 80% D2O buffer with extremely low ionic strength.
This
comparatively large value (23±12 pM) is difficult to dismiss as the data was collected with a
large number of data pairs and the fit does not appear flawed. This point is not shown on any
figures other than Figure 15 below, because its inclusion makes the scale unreadable. Repetition
of this experiment would be desirable.
Ki, pM
40
20
0
0.1
0.2
0.3
Na+, M
Figure 15: Variation of Ki with sodium ion concentration, with data from .01 M sodium
barbital, 0.03 M NaCl, 0.02% PEG, pD 8.70, 80% D2O.
25
Mechanistic Conclusions
While many trends in these data may give rise to speculation, two
are most striking. First, the elementary rate constants tend to be higher in D2O, especially at
higher ionic strength. Second, the k1 values decrease with increasing sodium ion concentration
for every pair of data with the same solvent and ionic strength. Given that at higher ionic
strength the ionic interactions between hirudin and thrombin would be shielded, the hydrogen
bond interactions would become more important. The fact that most of the elementary rate
constants are faster in D2O based solvents would indicate that the hydrogen bonds of the
transition state are more stable in D2O. The decrease in k1 with sodium ion concentration
indicates that the presence of sodium decreases the favorability of hirudin’s extensive binding of
thrombin, most likely because it is an effective shield against the ionic interactions between the
proteins, especially those in hirudin’s C-terminal tail.
26
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