Haloacetamidine-based inactivators of protein arginine deiminase 4 (PAD4): Evidence that general acid catalysis promotes efficient inactivation

Article abstract of DOI:10.1002/cbic.200900698

Dysregulated protein arginine deiminase (PAD) activity, particularly PAD4, has been suggested to play a role in the onset and progression of numerous human diseases, including rheumatoid arthritis (RA). Given the potential role of PAD4 in RA, we set out to develop inhibitors/inactivators that could be used to modulate PAD activity and disease progression. This effort led to the discovery of two mechanism-based inactivators, denoted F- and Cl-amidine, that inactivate PAD4 by the covalent modification of an active-site cysteine that is critical for catalysis. To gain further insights into the mechanism of inactivation by these compounds, the effect of pH on the rates of inactivation was determined. These results, combined with the results of solvent isotope effect and proton inventory studies, strongly suggest that the inactivation of PAD4 by F- and Cl-amidine proceeds by a multistep mechanism that involves the protonation and stabilization of the tetrahedral intermediate formed upon nucleophilic attack by the active-site cysteine, that is, Cys645. Stabilization of this intermediate would help to drive the halide-displacement reaction, which results in the formation of a three-membered sulfonium ring that ultimately collapses to form the inactivated enzyme. This finding - that protonation of the tetrahedral intermediate is important for enzyme inactivation - also suggests that, during catalysis, protonation of the analogous intermediate is required for efficient substrate turnover.

Full text of DOI:10.1002/cbic.200900698

DOI: 10.1002/cbic.200900698
Haloacetamidine-Based Inactivators of Protein Arginine Deiminase 4
(PAD4): Evidence that General Acid Catalysis Promotes Efficient Inactivation
Bryan Knuckley,[a] Corey P. Causey,[a] Perry J. Pellechia,[a] Paul F. Cook,[b] and Paul R. Thompson*[a]
Dysregulated protein arginine deiminase (PAD) activity, particu-
larly PAD4, has been suggested to play a role in the onset and
progression of numerous human diseases, including rheuma-
toid arthritis (RA). Given the potential role of PAD4 in RA, we
set out to develop inhibitors/inactivators that could be used to
modulate PAD activity and disease progression. This effort led
to the discovery of two mechanism-based inactivators, denot-
ed F- and Cl-amidine, that inactivate PAD4 by the covalent
modification of an active-site cysteine that is critical for cataly-
sis. To gain further insights into the mechanism of inactivation
by these compounds, the effect of pH on the rates of inactiva-
tion was determined. These results, combined with the results
of solvent isotope effect and proton inventory studies, strongly
suggest that the inactivation of PAD4 by F- and Cl-amidine
proceeds by a multistep mechanism that involves the protona-
tion and stabilization of the tetrahedral intermediate formed
upon nucleophilic attack by the active-site cysteine, that is,
Cys645. Stabilization of this intermediate would help to drive
the halide-displacement reaction, which results in the forma-
tion of a three-membered sulfonium ring that ultimately col-
lapses to form the inactivated enzyme. This finding—that pro-
tonation of the tetrahedral intermediate is important for
enzyme inactivation—also suggests that, during catalysis, pro-
tonation of the analogous intermediate is required for efficient
substrate turnover.
In nature, a myriad of post-translational modifications are
found in proteins. These modifications, and the requisite modi-
fying enzymes, can have far-reaching effects on living systems.
Within the family of protein-modifying enzymes are the pro-
tein arginine deiminases (PADs). These enzymes catalyze the
hydrolysis of arginine residues to form citrulline.[1–3] Much
effort from our laboratory has been focused on gaining insight
into the mechanism of the PADs, and, in particular, PAD4.[3–5]
Our interest in PAD4, and the PADs in general, was piqued as
evidence emerged that linked dysregulated PAD activity to the
increased incidence and severity of rheumatoid arthritis
(RA).[2,3,6] This disease, which afflicts nearly 1% of the popula-
tion, is an autoimmune disorder that appears to be triggered,
at least in part, in response to aberrant citrullination, a result
of dysregulated PAD activity. Based on this apparent causal
relationship, we set out to develop inhibitors/inactivators that
could be used to modulate PAD activity and disease progres-
sion. This effort led to the discovery of two mechanism-based
inactivators, denoted F- and Cl-amidine, which are the most
potent PAD inhibitors described to date.[7,8] At the same time,
Fast and colleagues reported that 2-chloroacetamidine, that is,
the warhead in Cl-amidine, also inactivates PAD4 and other
members of the guanidinium-modifying family of enzymes.[9]
Much work has been done to characterize the mechanism of
inactivation, including dialysis experiments to verify irreversible
inhibition. Additionally, analysis of the kinetics of inactivation
demonstrated that F- and Cl-amidine possess kinact/KI values of
3000 and 13000mꢀ1 minꢀ1, respectively.[7,8] Subsequent crystal-
lographic data confirmed that inactivation was due to the co-
valent modification of an active-site cysteine (Cys645) that is
critical for catalysis—this residue promotes arginine deimina-
tion by covalent catalysis according to a mechanism that is
analogous to that of the Cys proteases.[5] While this finding
conclusively demonstrated the mode of inactivation–alkylation
of the thiolate, the precise mechanism of inactivation has yet
to be established.
Although unclear, the mechanism of inactivation presumably
proceeds through one of at least two routes: direct displace-
ment of the halogen through an SN2 mechanism or initial
attack on the iminium carbon, followed by displacement of
the halide to form a sulfonium ring, and ending with concomi-
tant re-formation of the imine and opening of the sulfonium
ring (Scheme 1). While the former possibility is the more intui-
tive, the latter is analogous to the mechanism by which the
fluoromethylketones inactivate the cysteine proteases,[10–12] and
therefore warranted further investigation.
[a] B. Knuckley, C. P. Causey, P. J. Pellechia, Prof. P. R. Thompson
Department of Chemistry and Biochemistry, University of South Carolina
631 Sumter Street, Columbia, SC 29208 (USA)
We began our investigations by examining the influence of
pH on kinact/KI, that is, the second-order rate constant of
enzyme inactivation. These studies were pursued because pH
rate profiles can suggest the identity of catalytically important
functional groups, in the inactivator or free enzyme, up to and
including the first irreversible step of the reaction. For these
studies, kinact/KI values were determined for both Cl- and F-ami-
E-mail: thompson@mail.chem.sc.edu
[b] Prof. P. F. Cook
Department of Chemistry and Biochemistry, University of Oklahoma
620 Parrington Oval, Norman, OK 73019 (USA)
Supporting information for this article is available on the WWW under
http://dx.doi.org/10.1002/cbic.200900698.
ChemBioChem 2010, 11, 161 – 165
ꢀ 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
161

similar (i.e., decreased inactivation at pH values >8), thereby
suggesting that general acid catalysis also plays a role in the
inactivation of PAD4 by this compound.
To gain further insight into this process, the effect of pH on
PAD4 inactivation by 2-fluoroacetamidine (FA)—the fluoroacet-
amidine warhead alone—was examined. As with Cl- and F-ami-
dine, the rates of inactivation are roughly bell-shaped (Fig-
ure 1C). In contrast, the rate at which 2-chloroacetamidine
(CA) inactivates PAD4 does not decrease with increasing alka-
linity (Figure 1D).[5] This break from the trend suggests that CA
inactivates PAD4 through a mechanism that is different from
the mechanism by which F-amidine, Cl-amidine, and FA inacti-
vate the enzyme. Given that chloride is an inherently better
leaving group than fluoride, the most reasonable assumption
is that inactivation by CA can proceed through the direct SN2
displacement of chloride, that is, mechanism 1 in Scheme 1.
Based on the fact that general acid catalysis is unlikely to
enhance the rate of this reaction, this assumption is not only
plausible, but likely.
Scheme 1. Structures of compounds described in this communication and
proposed mechanisms of PAD4 inactivation by Cl- or F-amidine.
dine over a pH range of 6.0–8.5. Interestingly, the rates of
inactivation increased until ~pH 8.1, after which point further
increases in alkalinity resulted in a dramatic drop in the rates
of inactivation (Figure 1A and B).
Fits of the F-amidine versus pH rate data give estimates of
the pKa values for the ascending and descending limbs of
7.05 and 8.05, respectively, with a pH-independent value of
1425mꢀ1 minꢀ1. Interestingly, these values are in reasonable
agreement with those obtained for substrate turnover (i.e., 7.3
and 8.2) and, as such, they likely correspond to the pKa values
of His471 and Cys645, respectively. Given that His471 is
thought to act as a general acid in the acylation step of the
reaction, and that this drop in reactivity mimics the pH profile
for substrate turnover,[5] these data suggest that general acid
catalysis also contributes to enzyme inactivation by F-amidine.
Although the data for Cl-amidine fit poorly to canonical pH
versus rate equations, the trends of the pH rate profiles are
The break in the trend for CA also argues, albeit indirectly,
that PAD4 inactivation by Cl-amidine, F-amidine, and FA pro-
ceeds through the proposed multistep mechanism, that is,
mechanism 2. This argument, however, does not explain why
the chloride of Cl-amidine is not directly displaced. The sim-
plest and most reasonable hypothesis to explain this discrep-
ancy is that CA, lacking any peripheral structural elements, has
far fewer limitations on its orientation within the active site. As
such, this molecule can inactivate PAD4 by a direct SN2 dis-
placement that is solely dependent on the concentration of
the thiolate. By contrast, the “backbone” amide groups of Cl-
amidine are instrumental in binding,[4,7,8,13] and therefore re-
strict conformational freedom, and lead to a mode of binding
that is not conducive to an SN2
displacement.
While this hypothesis ration-
alizes the observed differences
in the kinetics of inactivation, it
does not directly explain the
observed decrease in inactiva-
tion rate at higher pH. Although
we have suggested that this
drop in reactivity suggests a
role for general acid catalysis,
alternative explanations for the
observed drop in reactivity in-
clude deprotonation of the war-
head and or decomposition of
the inhibitors.
Warhead
deprotonation
would be expected to decrease
the rate of inactivation because
the positive charge of the pro-
tonated arginine side chain is
crucial for substrate binding
and catalysis.[4] To investigate
this possibility, the pKa of the
fluoroacetamidine warhead in
Figure 1. Inactivation pH profiles of Cys645 by using A) F-amidine, B) Cl-amidine, C) 2-fluoroacetamidine, and D) 2-
~
*
chloroacetamidine. : D2O, : H2O.
162
www.chembiochem.org
ꢀ 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ChemBioChem 2010, 11, 161 – 165

F-amidine was determined by NMR. By monitoring the chemi-
cal shifts of the protons that are in closest proximity to the
amidine, that is, the protons adjacent to the fluoride and the
protons on the d-carbon, the pKa of the warhead was found to
be 10.2 (Figure 2). Virtually identical results were obtained by
fluorine NMR (Figure S1 in the Supporting Information). While
this pKa is significantly lower than that of arginine (pKa =12.5),
it is high enough to ensure complete protonation in the pH
regime of our experiments.
As described above, the dramatic loss in inactivator potency
could be due to inhibitor decomposition at higher pH values.
To test this possibility, samples of the inhibitors were subjected
to reaction conditions in the absence of enzyme, and subse-
quently analyzed by analytical HPLC. Essentially no decomposi-
tion was observed (Figure S2). This possibility was further ruled
out by a slight modification to our assay procedure. Typically,
the inactivator was incubated in assay buffer for 10 min prior
to the addition of PAD4 to initiate the inactivation reaction.
Decreasing this time to 2 min did not affect the rate of inacti-
vation (data not shown).
Having ruled out inactivator deprotonation and decomposi-
tion as reasons for the sharp decline in inactivation rates
above pH 8.0, the most reasonable explanation for the ob-
served effect on kinact/KI, which reports on ionizable groups in
the free enzyme, is the presence of a protonated active-site
residue that is important for binding and orienting the war-
head for nucleophilic attack by the active-site thiol. If, as we
expect (see below), this group represents the imidazolium
form of His471, it could polarize the acetamidine, fix the
charge on one of the two NH2 groups, and thereby promote
reaction with the active-site thiolate.
To gain further insights into this process, kinact values were
determined for F- and Cl-amidine as a function of pH. These
experiments were performed to identify catalytically important
functional groups in the enzyme·inactivator complex. Addition-
ally, we reasoned that for mechanism 1, the simple SN2 mecha-
nism, the plots of kinact versus pH should rise with increasing
pH and plateau at a limiting value that is dependent on the
concentration of the active-site thiolate. In contrast, for the
more elaborate mechanism depicted in Scheme 2, we rea-
soned that if general acid catalysis plays a role in promoting
enzyme inactivation after the inactivator has bound the
enzyme, then kinact would rise to a limiting value and then fall
Scheme 2. Proposed general acid-catalyzed mechanism of inactivation.
as the pH is increased. Note that kinact values were not deter-
mined for FA and CA because the high KI values for these com-
pounds made such a determination impractical.
Although these data fit poorly to canonical pH versus rate
equations, the results of these studies demonstrated that the
plots of kinact versus pH plots are also bell-shaped (Figure 3),
with the groups contributing to the overall shape of the curve
possessing an average pKa of 7.5. As described above, these re-
sults further discount the simple SN2 mechanism. Ad-
ditionally, the drop in reactivity at higher pH values
indicates that general acid catalysis promotes
enzyme inactivation after the formation of the initial
enzyme·inactivator complex. These results also indi-
cate that the decrease in kinact is the major contribu-
tor to the observed effect on kinact/KI, thus indirectly
arguing against a pH effect on inactivator binding.
The observed effect on kinact is again consistent
with a role for general acid catalysis in enzyme in-
activation, specifically in the enzyme·inactivator com-
plex. Based on the proposed mechanism of catalysis
(Figure S3), the most likely residue is His471, which
serves to protonate the departing ammonia through
Figure 2. NMR titration curves: A) protons adjacent to the fluoride, B) protons on the d-
carbon.
ChemBioChem 2010, 11, 161 – 165
ꢀ 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chembiochem.org
163

the course of catalysis. Although we and others
have suggested that, for substrate turnover, proton
donation occurs during the collapse of the tetrahe-
dral intermediate,[1,14] it is equally plausible that pro-
tonation of the intermediate occurs during the for-
mation of this intermediate in either in a stepwise
fashion or concomitant with the change in hybridi-
zation that occurs upon thiolate attack on the guani-
dinium carbon. If either of the latter possibilities is
correct, the above-described inactivation data would
imply a role for this residue in stabilizing the tetra-
hedral intermediate formed during the inactivation
reaction (Scheme 2).
&
*
Figure 3. Rates of PAD4 inactivation by A) F-amidine in D2O ( ) and H2O ( ) and B) Cl-
amidine in H2O.
The pKa of His471 has been assigned as 7.3;[5] thus
at higher pH, this residue is unprotonated and
cannot donate a proton to stabilize the tetrahedral
intermediate formed by thiolate attack on the imini-
um carbon (3b; Scheme 2). Without this stabilization,
the equilibrium is greatly shifted towards form 1b. In
contrast, by stabilizing the tetrahedral intermediate,
the displacement of the halide (3a) would be fa-
vored. The protonation state of the intermediate (3)
is also likely influenced by the increasing pH. Based
on model compounds, the pKa of this intermediate is
expected to be 2 units lower than that of the parent
compound. Thus, at pH>8, a similar decline in reac-
tivity would be expected. These overlapping effects,
that is, loss of stabilization from the protonated histi-
Figure 4. Protonic inventories obtained for the F-amidine-induced inactivation of PAD4:
A) kinact and B) kinact/KI. The term n refers to the fraction of D2O in the reaction. Data were
obtained at pL=7.6.
dine (2) and deprotonation of intermediate (3), might account
for the sharp declines in the rates of inactivation that are ob-
served above pH 8.
thiolate. Consistent with this possibility is the fact that, while
the displacement of the pKa is expected to be ~0.4–0.6 pH
units higher in D2O than in H2O, the observed difference (~0.2)
is smaller; such smaller differences are highly suggestive of
ionization of a thiol to the thiolate. Also consistent with a
single ionization of an active site residue is the fact that the
proton inventory for kinact/KI is linear (Figure 4B; r2 =0.931).
In conclusion, the data strongly suggest that the inactivation
of PAD4 by F- and Cl-amidine proceeds by the multistep mech-
anism, that is, mechanism 2. Our data further suggest that pro-
tonation of the tetrahedral intermediate (3; Scheme 2) helps to
drive the halide-displacement to form the three-membered
sulfonium ring (4), which ultimately collapses to form the inac-
tivated enzyme (5). This finding—that protonation of the tetra-
hedral intermediate is important for enzyme inactivation—
might also suggest that, during catalysis, protonation of the
analogous intermediate is required for efficient substrate turn-
over.
Further evidence to support the proposed mechanism of in-
activation comes from measurements of the deuterium solvent
isotope effect (SIE). For these studies, we focused our efforts
on F-amidine, as opposed to CA or Cl-amidine, because this
compound can presumably only inactivate the enzyme
through the second mechanism, and the KI values are low
enough to facilitate the measurement of kinact values.
The average of two independent experiments indicates that
the SIE on kinact is normal (kHinact/kiDnact =2.17ꢁ0.94; Figures 3 and
4), whereas for kinact/KI, the SIE was inverted over the entire pL
range studied [(kinact/KHI )/(kinact/KID)=0.24ꢁ0.14; at the pL opti-
mum (Figures 1 and 4)]. The normal SIE on kinact is suggestive
of a proton in flight in the transition state. Such an effect is
consistent with the proposed mechanism of inactivation,
wherein proton donation to the tetrahedral intermediate
would be expected to yield a normal isotope effect. Consistent
with this possibility is the fact that proton inventory analyses
performed at the pL optimum are linear (r2 =0.947); this is
consistent with a single hydrogenic site in the isotope-sensitive
step of enzyme inactivation (Figure 4).
Experimental Section
Chemicals: Dithiothreitol (DTT), benzoyl l-arginine ethyl ester
(BAEE), and tris-(2-carboxyethyl)phosphine hydrochloride (TCEP)
were purchased from Sigma–Aldrich, F- and Cl-amidine were syn-
thesized as previously described,[7,8] 2-chloroacetamidine was ob-
tained from Oakwood Products (Columbia, SC), and protein argi-
nine deiminase 4 (PAD4) was purified as previously described.[5]
The large and inverse SIE observed for kinact/KI is consistent
with the inverse SIE obtained for substrate turnover;[5] this fur-
ther suggests that similarities exist between the mechanism of
substrate turnover and enzyme inactivation. As previously de-
scribed for substrate turnover,[5] this large inverse SIE could be
explained by pre-equilibrium ionization of the thiol to form the
Inactivation kinetics: Inactivation experiments with F-amidine, Cl-
amidine, and 2-fluoroacetamidine were performed and data were
164
www.chembiochem.org
ꢀ 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ChemBioChem 2010, 11, 161 – 165

fit to equations as previously described.[5] The inactivation of PAD4
by 2-chloroacetamidine has been described previously.[5] The inacti-
vation rates obtained for F-amidine, Cl-amidine, and 2-fluoroaceta-
midine from this analysis were plotted against pH. Given that the
dramatic decrease in activity at pH values >8 precluded fitting of
the data to standard equations, the curves for 2-fluoroacetamidine
and Cl-amidine were simply generated by using the line function
in GraFit (version 5.0.11).[15] The fit for the F-amidine data was
determined graphically.
Decomposition experiments: To investigate the effect of the reac-
tions conditions on Cl-amidine and F-amidine, these compounds
were subjected to the assay conditions in the absence of enzyme.
Briefly, each inhibitor was dissolved in assay buffers (pH 6.5, 7.0,
7.5, 8.0, and 8.5) and incubated at 378C. After 30 min, the samples
were flash frozen in liquid nitrogen. Each sample was analyzed by
reversed-phase (C18) analytical HPLC. The C18 column was pre-
equilibrated with ddH2O/0.05% TFA, and the reaction components
were separated by using a linear gradient of acetonitrile/0.05%
TFA.
Solvent isotope effects: These experiments were performed as
previously described,[5] except that the reaction was carried out in
>95% D2O. Data were fit to equations described previously.[5]
Acknowledgements
Proton inventory studies: Briefly, the experiments were performed
as described previously for the inactivation kinetics experiments.[5]
The only difference was that inactivation reactions were performed
in the presence of various D2O concentrations (0–95%). The data
collected were processed by using the methods described above.
kinact and kinact/KI values were obtained and plotted as a ratio of D2O
to H2O as a function of D2O concentration (n). The resulting plot
was fit by using the line function in GraFit (version 5.0.1.1).[15]
This work was supported by NIH grant GM079357 to P.R.T. and
by the Grayce B. Kerr Endowment to the University of Oklahoma
and to P.F.C. The authors thank Philip Cole for critical reading of
the manuscript.
Keywords: amidines · deiminases · inactivators · reaction
mechanisms · rheumatoid arthritis
Synthesis of 2-fluoroacetamidine: Ammonia (1.6 mL, 2m in
MeOH) was added to
a solution of 2-fluoro-ethylthioimidate
(250 mg, 1.6 mmol) in dry ethanol (10 mL) at 08C. The reaction
mixture was allowed to warm to RT. After 16 h of stirring, the vol-
atiles were removed under reduced pressure to afford a white
powder that contained both the title compound and ammonium
chloride. The final composition of this mixture was determined by
[1] P. R. Thompson, W. Fast, ACS Chem. Biol. 2006, 1, 433.
[2] E. R. Vossenaar, A. J. Zendman, W. J. van Venrooij, G. J. Pruijn, Bioessays
2003, 25, 1106.
[3] J. E. Jones, C. P. Causey, B. Knuckley, J. L. Slack-Noyes, P. R. Thompson,
Curr. Opin. Drug Discovery Dev. 2009, 12, 616.
[4] P. L. Kearney, M. Bhatia, N. G. Jones, Y. Luo, M. C. Glascock, K. L. Catch-
ings, M. Yamada, P. R. Thompson, Biochemistry 2005, 44, 10570.
[5] B. Knuckley, M. Bhatia, P. R. Thompson, Biochemistry 2007, 46, 6578.
[6] E. R. Vossenaar, W. J. Van Venrooij, Arthritis Res. Ther. 2004, 6, 107.
[7] Y. Luo, K. Arita, M. Bhatia, B. Knuckley, Y. H. Lee, M. R. Stallcup, P. R.
Thompson, Biochemistry 2006, 45, 11727.
[8] Y. Luo, B. Knuckley, Y. H. Lee, M. R. Stallcup, P. R. Thompson, J. Am.
Chem. Soc. 2006, 128, 1092.
[9] E. M. Stone, T. H. Schaller, H. Bianchi, M. D. Person, W. Fast, Biochemistry
2005, 44, 13744.
[10] J. C. Powers, J. L. Asgian, O. D. Ekici, K. E. James, Chem. Rev. 2002, 102,
4639.
[11] K. Kreutter, A. C. Steinmetz, T. C. Liang, M. Prorok, R. H. Abeles, D. Ringe,
Biochemistry 1994, 33, 13792.
1
NMR using an internal standard. H NMR (300 MHz, D2O): d=5.19
(d, JHꢀF =44.7 Hz, 2H); 13C NMR (100 MHz, D2O): d=166.12 (d, JCꢀF
=
19.9 Hz), 77.49 (d, JCꢀF =178.3 Hz); 19F NMR (379 MHz, D2O): d=
ꢀ233.67 (t, JHꢀF =44.8 Hz); HRMS-ESI (C2H6FN2+): calcd 77.0515,
obsd 77.0526.
NMR titration: NMR titrations were conducted on a 400 MHz spec-
trometer in H2O (5% D2O). Proton chemical shifts were measured
relative to 4,4-dimethyl-4-silapentane-1-sulfonic acid, and fluoride
chemical shifts were relative to trifluoroacetic acid (TFA; internal
tube). Upon dissolution of F-amidine, the pH was measured by
using a micro-pH meter, and the first spectra were taken. For sub-
sequent measurements, the sample was transferred to a clean vial,
where the pH was adjusted with NaOH (1m) before being trans-
ferred back to the NMR tube. Changes in chemical shift values
were plotted against pH. pKa values were determined by fitting the
data to Equation (1):
[12] J. Drenth, K. H. Kalk, H. M. Swen, Biochemistry 1976, 15, 3731.
[13] K. Arita, H. Hashimoto, T. Shimizu, K. Nakashima, M. Yamada, M. Sato,
Nat. Struct. Mol. Biol. 2004, 11, 777.
[14] E. M. Stone, A. L. Costello, D. L. Tierney, W. Fast, Biochemistry 2006, 45,
5618.
[15] R. J. Leatherbarrow, Erathicus Software, Staines, UK, 2004.
ðLim1 þ Lim2Þ10pHꢀpK
a
ð1Þ
y ¼
10pHꢀpK þ 1
a
using GraFit (version 5.0.11).[15] Lim1 is the minimum rate, and Lim2
Received: November 17, 2009
is the maximum rate.
Published online on December 11, 2009
ChemBioChem 2010, 11, 161 – 165
ꢀ 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chembiochem.org
165