The binding constant value 8.6 M-1 is on the similar order of that of Km1 (2.9 M-1), and the first order rate constant (k = 7.3×10-4 s-1) is smaller than that of EuDO2A(OH) (kp = 3.1×10-3 s-1), roughly consistent with what is expected.
Comparisons of various EuDO2A-BNPP reaction models and rates and with other systems. The above analyses were achieved by fitting experimental pH 9.35 data to three different models (Schemes 2, 3, and 4). Except the simple monomer reaction model, the other three models seem all to be acceptable if no further information is available. However, the monomer-dimer saturation model (Scheme 3) seems to be the most possible, due to the very possible formation of the hydroxo-bridged dimeric species, [Eu(DO2A)(OH)]2. Comparing the Scheme 3 fitting data (at pH 9.35) with those reported by others for the BNPP hydrolysis5,8-10,15-21, (Table s1), it is observed that our km1 and km2
values are in the order of 10-3-10-2 s-1, which are about similar or 10 times greater than those reported by others (i.e. 10-4-10-3 s-1). In general, the binding constants of the transition metal complexes with BNPP are greater than those of the lanthanide complexes, e.g. the BNPP binding constant is ~102 M-1 for the mononuclear
CuII-bipyridine complex derivatives15 and ~106 for dimeric CuII-triaminocyclohexane
species16. The strong binding may retard the leaving of the reacted substrates and make the catalyst poison. The half-lives of cobalt(III) complex systems for BNPP hydrolysis were found to be less than a couple hundred seconds19; however, the binding with BNPP was also too strong to be repeatedly used.
On the other hand, EuDO2A(OH)-BNPP binding constant is around 101, and that of the dimer-BNPP is around 102. This is due to the fact that at higher pH, the formation of EuDO2A(OH) results in zero net charge that diminishes the extent of binding with the negatively charged BNPP. The greater coordination number for lanthanide ions also reduces its overall Lewis acidity after ligand complexation.
Worth mentioning is the system studied by Martell, et al18, the dinuclear
Ln-macrocyclic complex is in the ratio of 3:1 to hydrolyze BNPP. At pH 8, the fourth order rate constant was determined to be k = 4×108 M-3s-1. The half-life for 1 mM dimer- BNPP reaction was 1.7 second, which is closer to those of natural nucleases (< 1 second).
Such a fast rate is attributed to a simultaneous six-metal nuclear reaction. On the other hand, our rate constants (second order rate constants ~ 0.4 - 4.0 M-1s-1) are lower than those of Martell’s but similar or slightly greater than those of Yatsimirsky’s (second order rate constants ~ 0.1 - 1.0 M-1s-1)10.
Effects of equilibration time after the preparation of Eu(DO2A)+ solutions on the BNPP hydrolysis rates. The data presented before this point were obtained using carefully and freshly prepared Eu(DO2A)+ solutions, i.e. within 30 minutes after complex solution preparation. When the mother EuDO2A+ solution was prepared at pH 6.0, the solution was allowed enough time (i.e. > 10 hours) for equilibration, and more than 99%
of the complexes was predicted to be in the monomeric form using a stability constant log Kf =12.99.6 However, if the Eu(DO2A)+ solutions after pH adjustment were allowed to equilibrate for 3 hours and 1 week, the obtained BNPP hydrolysis rate constants were found to be lower as shown in Figure 4, particularly at higher pH. The freshly prepared solutions showed the fastest rates (Figure 4, 30 min. curve). It was also found that the longer the equilibration time for higher pH EuDO2A+ solutions, the slower the resulting promoted BNPP hydrolysis rates (Figure 4, 3 hr. and 1 week curves).
pH
Figure 4. The plots of experimentally observed and calculated BNPP hydrolysis rate constants promoted by EuDO2A+ after different complex equilibration time vs.
pH. The calculated curves were obtained as discussed at the end of this paper (vide infra). The experimental and calculated data are listed in Table 3.
In addition, besides the inflection point shown in 30 min. curve at pH 8.1~8.4, all three curves show 2 more common inflection (i.e. rate jump) points at roughly pH 9.0 and pH 10.1. The rate jump beyond pH 8.1~8.4 may indicate that other more reactive,
hydroxide-coordinated species are formed. However, the fact that these observed rates decrease with time seems to indicate that these reactive species are transformed into other less reactive and/or inactive lanthanide complex species, particularly at higher pH.
Possible evidence of polynuclear EuDO2A+ species formation observed during pH titration. The formation of new and/or inactive EuDO2A+ species corroborates with the pH titration data obtained after various equilibration time (Figure s3, supporting information). Using the data after 30-minute equilibration time, the calculated EuDO2A+ stability constant is log Kf = 13.06, similar to what we reported previously6. The stability constant calculated after 10-hour equilibration time is log Kf = 16.78. If the “out of cell”
method is used with an equilibration time of 3 weeks for each data point, the calculated stability constant is log Kf = 17.62, which is still 1.8 log K units lower than that of
GdDO2A+ (log Kf = 19.4) reported by Sherry, et al.22 Thus, complex formation between Eu3+ and DO2A is a very slow reaction which may last for weeks and affect the
determination of stability constants and speciation. This is not necessarily only the formation of monomeric EuDO2A+ complex per se, but the formations of new species such as dimeric and polynuclear species. It is noted that, this dimer and polynuclear species formation was not considered when the stability constants were determined.)
Thus, the observed results seem to indicate that a kinetic effect is present. During the reaction of BNPP with EuDO2A+, the monomeric EuDO2A+ complexes form the more reactive dimeric species, which exist in solution with only finite concentrations and
continue to form less reactive or inactive polynuclear species, such as the tetrameric species. This might explain why the dimer formation constant is only 11.8 based on the kinetic models (vide supra).
Possible evidence of polynuclear CeDO2A+ species formation from ultraviolet spectroscopic studies. Because EuDO2A+ does not have absorption in the 250-300 nm ultraviolet region, we have studied the CeDO2A+ absorption spectral properties in the pH range 6-10.8, in the hope that the data may shed additional lights on what we have observed for EuDO2A+ system. As shown in Figure 5, free Ce3+ ion at pH 6.0 shows two absorption maxima at 252 nm and 298 nm, and the former peak has much greater intensity. When the Ce3+ ion is complexed by DO2A at pH 6.0, the peak intensity at 252 nm is decreased and the peak intensity at 298 nm is increased. The final spectral intensities remain unchanged at pH 6.0 even after 10 hours. However, when the pH of the CeDO2A+ solution is adjusted to pH 7, the peak at 252 nm disappears and a peak at 272 nm arises, and the peak at 298 nm is still present. The intensities of the two peaks continue to increase with time. The basic initial spectral profile remains similar but with increased intensity as the pH value is further increased to higher pH, i.e. pH 8 to 10.8 (Figure 5). If the 298 nm peak is chosen and the absorption intensity is monitored with time for the CeDO2A+ solutions at various pH (i.e. pH 7.0-10.8), it is observed that the 298 nm absorption intensities continue to grow even up to 3000 second observation time (Figure s4, supporting information). The rate of 298 nm peak intensity growth increases with increasing pH. The absorbances for all solutions grow beyond 3 after 24 hours and still have no sign of reaching equilibrium.
w a v e le n g th ( n m )
1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0
Absorbance
0 1
}
p H 7 , 8 , 9 , 1 0 , 1 0 . 8 C e3 + o n lyD O 2 A o n ly p H 6
Figure 5. The spectra of 1.0 mM CeDO2A+ at 25℃, pH = 6, 7, 8, 9, 10, and 10.8. The Ce3+ and DO2A spectra were measured at [Ce3+] = 1.0 mM and [DO2A]
=1.02 mM, respectively.
The above-mentioned phenomena are quite complicated and require further systematic studies. However, the macrocyclic system reported by Martell18, et al
indicated that their compound disintegrated at pH > 10 and no data was shown after pH >
10. Yatsimirsky, et al also reported that the rate data for the hydrolysis of BNPP by Ln-BTP system were sometimes difficult to reproduce10. All these seem to indicate that lanthanide ions and complexes could form polynuclear species at high pH, consistent with what have been reported by Yan, Zheng, et al.23-26 The following scheme 7 is therefore proposed as tentative hypothesis for what we have discussed thus far:
Scheme 7. Proposed dimereization, deprotonation, and polynuclear species formations of the EuDO2A+ complex.
In Scheme 7, EuDO2A+ complex is deprotonated with a pKa ~ 8.1-8.4. The deprotonated EuDO2A(H2O)2(OH) may form the hydroxo-bridged dimer,
L2Eu2(H2O)2(µ-OH)2 where L=DO2A, which could be deprotonated at higher pH to form species such as L2Eu2(H2O)(OH)(µ-OH)2 and L2Eu2(OH)2(µ-OH)2 with different BNPP hydrolysis reactivities. All these dimeric species could further form higher order polynuclear species slowly, such as the cubane-shaped tetranuclear species,
[EuDO2A(µ-OH)]4, which may have a [Eu4(µ-OH)4] core structure without inner-sphere coordinated water molecule and is inactive for BNPP hydrolysis23-26.
Tentative fitting of kobs vs. pH data as functions of equilibration time. Based on the proposed reaction mechanism for EuDO2A+ in Scheme 7, and assuming that the reactive species must contain coordinated hydroxide group(s) as well as coordination unsaturation, and that the formation of inactive species is negligible, the kobs for the
BNPP hydrolysis reaction can be tentatively described as follows (charge of each species is omitted):
kobs = k1[LEu(H2O)2(OH)] + k2[L2Eu2(H2O)2(µ-OH)2] + k3[L2Eu2(H2O)(OH)(µ-OH)2] + k4[L2Eu2(OH)2(µ-OH)2] (3)
Where k1, k2, k3, k4 are the respective rate constants for the LEu(H2O)2(OH),
L2Eu2(H2O)2(µ-OH)2, L2Eu2(H2O)(OH)(µ-OH)2, and L2Eu2(OH)2(µ-OH)2 species. Defining Kh1, Kh2, and Kh3 as the respective deprotonation (hydrolysis) constants for the
LEu(H2O)2(OH), L2Eu2(H2O)2(µ-OH)2, and L2Eu2(H2O)(OH)(µ-OH)2 species, the total concentration of the EuDO2A+ complex, [LEu]t, is:
[LEu]t = [LEu(H2O)3] + [LEu(H2O)2(OH)] + [L2Eu2(H2O)2(µ-OH)2]
+ [L2Eu2(H2O)(OH)(µ-OH)2] + [L2Eu2(OH)2(µ-OH)2] (4)
Using the Kh relationships and with the dimerization constant, Kf, equation 4 can be written as:
[LEu]t = [LEu(H2O)3] + Kh1[LEu(H2O)3]/[H+] + KfKh12[LEu(H2O)3]2/[H+]2
+ KfKh12Kh2 [LEu(H2O)3]2/[H+]3 + KfKh12 Kh2Kh3 [LEu(H2O)3]2/[H+]4 (5)
After rearrangement, equation 5 can be written as:
(KfKh12/[H+]2 + KfKh12Kh2/[H+]3 + KfKh12Kh2Kh3/[H+]4)[LEu(H2O)3]2 + (1 +
Kh1/[H+])[LEu(H2O)3] - [LEu]t = 0 (6)
Equation 6 is in the form of a quadratic equation, ax2 + bx + c = 0, where x is [LEu(H2O)3], a is KfKh12/[H+]2 + KfKh12Kh2/[H+]3 + KfKh12Kh2Kh3/[H+]4, and b is 1 + Kh1/[H+]. Using the values estimated previously, i.e. Kf = 11.8, pKh1 = 8.1, pKh2 = 9.0, and pKh3 = 10.1, one can solve for the [LEu(H2O)3] value at each pH listed in Table 3 for the 30 minutes data
set, and therefore, the [LEu(H2O)2(OH)], [L2Eu2(H2O)2(µ-OH)2],
[L2Eu2(H2O)(OH)(µ-OH)2], and [L2Eu2(OH)2(µ-OH)2] values. Figure 6 shows the “initial”
speciation plots of EuDO2A+ as functions of pH. The term “initial” is used because as equilibration time is increased, other inactive species are formed and the total effective EuDO2A+ concentration will be decreased (vide infra).
It is noted that the speciation plots are drawn based on the thermodynamic
equilibrium constants, i.e. Kf, Kh1, Kh2, and Kh3, obtained kinetically. Because the overall EuDO2A+ system was slow to reach equilibrium, the data collected were subjected to relatively larger uncertainties. Also, all these values are composites of multiple
pH-dependent equilibria8,9 and are at best, roughly estimated values. However, using these speciation concentration values and a least squares method, one can obtain the best fit k1, k2, k3, and k4 values and similarly, Kf, Kh1, Kh2, and Kh3 values. This can be done by initially estimating the k1, k2, k3, k4, Kf, Kh1, Kh2, and Kh3 values, calculating the kcalc values at several designated pH using equations 6, 5 and 3, and minimizing the sum of (kobs - kcalc)2 at these designated pH by changing the estimated k1, k2, k3, k4, Kf, Kh1, Kh2,
1.0 mM. The values were calculated using Kf = 11.8, pKh1 = 8.1, pKh2 = 9.0,
consistent with what expected, i.e. dimers are more reactive and specifically, a dimer with more coordinated water molecules is more reactive. Note that the k1 and k2 values, i.e.
3.08x10-2 M-1s-1 and 2.20 M-1s-1, compare reasonably well with those obtained with Scheme 2 at pH 9.35, i.e. k1 = 9.1×10-3 M-1s-1, k2 = 4.0 M-1s-1, and at pH 7.9, i.e. k1 = 7.4×10-3 M-1s-1, k2 = 0.41 M-1s-1. If the experimental uncertainties are assumed to be less important, the variations of both k1 and k2 values in these three sets of data are therefore due to the consideration of the other two reactive species, i.e. L2Eu2(H2O)(OH)(µ-OH)2
and L2Eu2(OH)2(µ-OH)2, in the present model but which were not considered previously in the Scheme 2 model.
The respective best fit Kf, Kh1, Kh2, and Kh3 values are Kf =11.9, pKh1 = 8.33, pKh2 = 8.97, and pKh3 = 10.09 which are in good agreements with what estimated previously.
As stated previously, the “initial” speciation plots will change with time. The total effective EuDO2A+ concentration, [LEu]t,eff, will decrease with time. Using the respective best fit k1, k2, k3, and k4 values, i.e. 3.08x10-2 M-1s-1, 2.20 M-1s-1, 1.05 M-1s-1, and 0.280 M-1s-1 as well as the Kf (11.9), pKh1 (8.33), pKh2 (8.97), and pKh3 (10.09) values obtained from the data set with 30 minutes equilibration time and by assuming that the
conversions of L2Eu2(H2O)2(µ-OH)2, L2Eu2(H2O)(OH)(µ-OH)2, L2Eu2(OH)2(µ-OH)2, and LEu(H2O)2(OH) to inactive species such as L4Eu4(µ-OH)4 take one simplified composite rate, the [LEu]t,eff values for the other two data sets (i.e. at 3 hour and 1 week
equilibration time, Table 3) can be estimated to be 0.51 mM and 0.23 mM, or 51% and 23% of the initial [LEu]t (=1.0 mM), respectively. This is done also by using a least square method: First, use an initial estimated [LEu]t,eff value, calculate the various speciation concentrations using equations 6 and 5. Then, using these speciation
concentrations and equation 3, calculate kcalc value at each specified pH and minimizing the sum of (kobs - kcalc)2 for all experimental pH by changing the estimated [LEu]t,eff
values.
From the [LEu]t,eff data, it is seen that the conversions of L2Eu2(H2O)2(µ-OH)2,
L2Eu2(H2O)(OH)(µ-OH)2, L2Eu2(OH)2(µ-OH)2, and LEu(H2O)2(OH) to inactive species are relatively faster initially and gradually slow down but continue even after 1-3 weeks as evidenced by the kinetic and thermodynamic data. The kobs values for the entire
processes are estimated (using 30 min. and 3 hr. data points) to be in the order of ~0.22 hr-1 in the beginning (first several hours after sample preparation) and slows down to
~0.11 d-1 or even less after 1 week (using 3 hr. and 1 week data points). This
information would be useful for further detailed studies of thermodynamics and kinetics of hydroxide-bridged trivalent lanthanide complex cluster formation.
Conclusions. Trivalent lanthanide ions are good Lewis acids for the promotion of BNPP hydrolysis. However, they need ligands to form complexes to prevent uncontrolled lanthanide hydroxide or oxide formation, i.e ligand-controlled hydrolysis. The properties of the resulting complexes are modified by the ligands, including charge, steric constraints, the number of inner-sphere coordinated water molecules, etc. In the present study, we found out that the dimeric {EuDO2A(µ-OH)}2 species are more reactive to promote BNPP hydrolysis. But the concentrations of the dimeric species exist in the solution could vary with time, probably reaching limited maximum concentrations and then decrease due to the formation of higher order polynuclear species at high pH. The resulting polynuclear species are inactive or less reactive toward BNPP hydrolysis. In particular, the relatively high rates of {EuDO2A(µ-OH)}2 promoted BNPP hydrolysis reaction are a kinetic event.
The freshly prepared solutions show the fastest rates. It is important to apply these discoveries for the design of better macrocyclic lanthanide complex reagents for phosphodiester bond hydrolysis and we are in the process of doing it.
Acknowledgment. The authors wish to thank the National Science Council of the
Republic of China (Taiwan) for financial support (grant number NSC-93-2113-M-009-004) of this work. A grant from the Atomic Energy Council is also acknowledged.
Supporting Information Available.:
Table s1. Examples of BNPP cleavage by selected metal complexes.
1.
1996, Kramer, et al. 2001, Planalp, et al. 2001, Gajda, et al. 1996, Burstyn, et al.
20℃, pH 6.6, The quickest, 0.01 M CoL
t1/2 = 167s 0.01 M CoL t1/2 = 15.1 s
1 mM FeMnL t1/2 = 4.77×103 s
8.
Schiff base macrocycle + 2La3+
9. 10.
Ln3+ only &
Eu3+ + ethylenediamine Eu3+ + propylendiamine
+ Ln3+
Eu3+ + Cyclen Eu3+ + Trpn
2000, Martell, et al. 2001, Yatsimirsky, et al. 1998, Schneider, et al.
35℃, [La3+]= 0.2-0.8 mM [L]=0.1-0.4 mM,
25℃, 2 mM Ln3+
+ 20mM BTP,
50℃, pH 7.0, 0-10 mM [Ln3+] or [LnL]
2La-L-2OH (quickest) R=k[2La-L-2OH]3[BNPP]
k= 4×108 M-3s-1
Dy-OH2+(quickest) R=k[Dy-OH2+][BNPP]
k= 0.81 M-1s-1
Er-BNPP(quickest) k = 8.6×10-4 s-1
K= 3.3×10-3 M 1 mM L-2La-2OH
t1/2 = 1.7 s
1 mM Dy-OH2+
t1/2 = 855 s
1 mM Er3+
t1/2 = 3.5×103 s
Figure s1. Plots of absorbance at 400 nm vs. time (s) for the EuDO2A+ promoted BNPP hydrolysis reaction. [EuDO2A+] = 1.0 mM, [BNPP] = 0.2-8.0 mM, 25℃, pH 7.90, [MPS] = 20 mM, µ = 0.10 M (CH3)4NCl
Time, s
0 1000 2000 3000 4000
Absorbance, 400 nm
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.2 mM 0.4 mM 0.8 mM 1.0 mM 2.0 mM 4.0 mM 8.0 mM
Figure s2. Examples of plots of absorbance change vs. time for the reactions of BNPP with EuDO2A+, 5 mM, pH 7.90 (○); EuDO2A+, 10 mM, pH 9.35 (▼); and EuHEDTA, 20 mM, pH 11.0 (●). [BNPP] = 0.10 mM, 25℃, µ = 0.10, (CH3)4NCl. The data were fitted to the equation: [4-Nitrophenolate] = [BNPP]0(1-e-kt). The final absorbances reach a limiting value of 1.87, indicating that the 0.10 mM BNPP is close to 100% reaction completion.
tim e, s
0 20000 40000 60000
Absorbance, 400 nm
0.0 0.5 1.0 1.5 2.0
Figure s3. Potentiometric EuDO2A+ titration curves with different equilibration time interval (i.e. 30 mins, 10 hrs and 3 weeks) for data acquisition. [Eu3+] = 1.0 mM, [DO2A] = 1.02 mM. μ=0.1, (CH3)4NCl.
0 2 4 6 8 10 12
0 1 2 3 4 5 6
mol of base/ mol of ligand pH
30 mins
10 hours 3 weeks
Figure s4. The observed absorbances at 298 nm vs. time for CeDO2A+, 1.0 mM, at various solution pH.
tim e (s )
0 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 2 5 0 0 0 3 0 0 0 0 3 5 0 0 0
Absorbance (298 nm)
0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8
p H 6 (0 .1 ) p H 7 (0 .4 )
p H 8 (0 .3 ) p H 9 (0 .3 ) p H 1 0 (0 .2 )
p H 1 0 .8 (0 .1 )
FIGURE CAPTIONS
Figure 1. Dependence of pseudo first order rate constant of BNPP hydrolysis on the concentration of EuDO2A+ at 25℃, pH 7.90, [MPS] = 20 mM, µ = 0.10 M (CH3)4NCl, [BNPP] = 0.10 mM. The line is calculated based on the best fit to the monomer-dimer reaction model in Scheme 1.
[ E u D O 2 A + ]
0 .0 0 0 0 .0 0 2 0 .0 0 4 0 .0 0 6 0 .0 0 8
kobs (s-1 )
0 .0 0 0 0 0 0 .0 0 0 0 2 0 .0 0 0 0 4 0 .0 0 0 0 6 0 .0 0 0 0 8 0 .0 0 0 1 0
Figure 2. Dependence of pseudo first order rate constant of BNPP hydrolysis on concentration of EuDO2A+; 25℃, pH 9.35, [BNPP] = 0.10 mM, µ = 0.10 M (CH3)4NCl. Solid line is the best fit to the monomer-dimmer saturation reaction model.
[ E u D O 2 A+] ( M )
0 .0 0 0 0 .0 0 5 0 .0 1 0 0 .0 1 5 0 .0 2 0 0 .0 2 5
kobs (s-1 )
0 .0 0 0 0 .0 0 2 0 .0 0 4 0 .0 0 6 0 .0 0 8
Figure 3. Dependence of pseudo first order rate constant on [EuHEDTA], [BNPP] =
0.10 mM, pH 11.0, 25℃, µ = 0.10 M (CH3)4NCl.
Figure 4. The plots of observed and calculated BNPP hydrolysis rate constants
promoted by EuDO2A+ after different complex equilibration time vs. pH. The calculated curves were obtained as discussed at the end of this paper (vide infra).
=1.02 mM, respectively.
w a v e le n g t h ( n m )
1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0
Absorbance
0 1
}
p H 7 , 8 , 9 , 1 0 , 1 0 . 8 C e3 + o n lyD O 2 A o n ly p H 6
SCHEME TITLES