Electrostatic Coupling between DNA and Its Counterions Modulates

The measurements are relatively fast if the polarity of the electric field is reversed ... The anomalously high diffusion coefficients are due to elec...
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Electrostatic Coupling between DNA and Its Counterions Modulates the Observed Translational Diffusion Coefficients Earle Stellwagen and Nancy C. Stellwagen* Department of Biochemistry, University of Iowa, Iowa City, Iowa 52242, United States ABSTRACT: Free solution capillary electrophoresis (CE) is a useful technique for measuring the translational diffusion coefficients of charged analytes. The measurements are relatively fast if the polarity of the electric field is reversed to drive the analyte back and forth past the detection window during each run. We have tested the validity of the resulting diffusion coefficients using double-stranded DNA molecules ranging in size from 20 to 960 base pairs as the model system. The diffusion coefficients of small DNAs are equal to values in the literature measured by other techniques. However, the diffusion coefficients of DNA molecules larger than ∼30 base pairs are anomalously high and deviate increasingly from the literature values with increasing DNA molar mass. The anomalously high diffusion coefficients are due to electrostatic coupling between the DNA and its counterions. As a result, the measured diffusion coefficients vary with the diffusion coefficient of the counterion, as well as with cation concentration and electric field strength. These effects can be reduced or eliminated by measuring apparent diffusion coefficients of the DNA at several different electric field strengths and extrapolating the results to zero electric field.

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coefficients depend on the number of base pairs in the sample, the diffusion coefficient of the counterion, the concentration of the background electrolyte and the electric field strength, features that are consistent with electrostatic coupling between the DNA and its counterions.6 These coupling effects can be reduced or eliminated by extrapolating the observed diffusion coefficients to zero electric field.

ne of the fundamental properties of a macromolecule is the rate at which it moves through a solution in response to random Brownian motion, viscous drag, intermolecular interactions, and/or external forces. This intrinsic rate of movement, which is characterized by the translational diffusion coefficient, D, affects the interactions of DNA, RNA, and proteins with each other and with various small molecules in the cell. The translational diffusion coefficients of DNA have often been measured using dynamic light scattering and/or fluorescence correlation spectroscopy methods,1−6 although pulsed field gradient NMR,7 fluorescence recovery after photobleaching,8 and ultracentrifugation9have also been used. The various results are very consistent and indicate that the translational diffusion coefficients of double-stranded (ds) and single-stranded (ss) DNAs can be described by power laws that decrease with the increasing number of bases or base pairs in the molecule.10 Free solution capillary electrophoresis (CE) has also been used to measure DNA translational diffusion coefficients.11,12 CE is advantageous for such studies because the measurements are relatively straightforward and require only minute quantities of sample. In our previous studies, we found that the translational diffusion coefficients of small ss- and dsDNA oligomers were equal to those measured by other techniques;10−12 however, the diffusion coefficient of a 118-bp restriction fragment was ∼25% higher than expected.11 The present study was designed to identify the origin of the anomalously high diffusion coefficients observed for large DNA molecules by CE, using a more efficient measurement protocol to speed up the experiments. We find that DNA diffusion © 2015 American Chemical Society

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EXPERIMENTAL METHODS DNA Samples. Restriction fragments containing 79, 199, 442, and 960 bp were prepared by standard methods and characterized as described previously.12,13 A 20-bp oligomer with the sequence 5′-CGCAAAAACGCGCAAAAACG, called ds20 for brevity, was synthesized by IDT (Coralville, IA), purified by polyacrylamide gel electrophoresis, and annealed with its complement to form a duplex. DNA stock solutions were stored at −20 °C in T0.1E buffer (10 mM Tris-Cl buffer, 0.1 mM EDTA, pH 8.1) and diluted to ∼20 μM (20−75 ng/ μL) for the CE measurements. The mononucleotide 5′-ATP was also studied. Background Electrolytes (BGEs). Solutions of the desired concentration of Tris base and Bis-Tris base were brought to the desired pH by adding glacial acetic acid. The cation concentration in each buffer was calculated from the measured pH and the pKa of the buffering ion (Tris, pKa = 8.07; Bis-Tris, pKa = 6.27, both at 25 °C), using the Henderson-Hasselbach Received: June 12, 2015 Accepted: July 28, 2015 Published: July 28, 2015 9042

DOI: 10.1021/acs.analchem.5b02230 Anal. Chem. 2015, 87, 9042−9046

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Analytical Chemistry equation. Other BGEs contained 30 mM K, Na, Li, or tetrabutylammonium (TBA) acetate, added to 1 mM Tris acetate buffer. All BGEs are described in terms of the cation concentration in the solution, not the total buffer concentration. Capillary Electrophoresis. Capillary zone electrophoresis was carried out with a Beckman Coulter (Fullerton, CA) P/ACE MDQ Capillary Electrophoresis System operated in the reverse polarity mode (anode on the detector side) with UV detection at 254 nm, using methods described previously.13−15 The capillaries were internally coated with linear polyacrylamide (Polymicro Technologies, Phoenix, AZ) to minimize the electroosmotic flow (EOF) of the solvent. Previous studies have shown that internal polyacrylamide coatings do not affect the observed mobilities.14 The capillaries were 31.1 ± 0.2 cm in length (20.9 ± 0.1 cm to the detector) and 75 μm in internal diameter, mounted in a liquid-cooled cassette thermostated at 20 °C. The applied electric field ranged from 30 to 330 V/cm; the current was always 60 μA or less. Under such conditions, heating effects are negligible and the observed mobilities are independent of electric field strength.14 The DNA samples were injected hydrodynamically for 3 s at 0.5 psi (0.0035 MPa); the sample plug occupied ∼2.6% of the capillary length. Diffusion Measurements. Previous CE diffusion measurements in this laboratory have used the stopped migration method to measure DNA translational diffusion coefficients.11,12,14,15 Here, we have increased the efficiency of the measurements by using multiple stopping periods during a single run, with polarity reversal between each stop; similar protocols have been described by others.16−18 We call this method the reversing field method for brevity. Briefly, the DNA is injected into the capillary and electrophoresed past the optical window. The voltage is then turned off for a prescribed time. The same voltage but with the opposite polarity is then used to drive the peak past the window in the opposite direction. After a second stopping time, the voltage is reversed and the peak is driven past the window in the forward direction. This protocol is repeated multiple times to determine the dependence of the variance on the cumulative elapsed time (stopping times plus the time required to electrophorese the sample past the optical window in the forward and reverse directions). Time zero is defined as the time at which the electric field is applied after the sample is injected into the capillary. If the peaks in the electropherograms are approximately Gaussian in shape, the variance can be calculated from the peak width according to eq 1: σ 2 = 0.180(WhLd /t )2

D20, w =

D = σ 2/120t

⎞ ⎟⎟DT 293 ⎠

(3)

where T is the temperature of the measurement in K, ηT is the viscosity of water at temperature T, η293 is the viscosity of water at 20 °C, and DT is the diffusion coefficient measured at temperature T.21

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RESULTS Validation of the Reversing Field Method. A typical pulsing sequence used in this study is illustrated in Figure 1A.

Figure 1. Reversing field protocol. (A) The applied voltage, in kV, is plotted as a function of elapsed time, in min. (B) Dependence of the variance observed for ATP, in cm2, on the time elapsed after injection of the sample into the capillary, using the pulse sequence illustrated in (A). The BGE contained 75 mM Tris+; E = 136 V/cm. The line was drawn by linear regression (r2 = 0.985). From the slope of the line and eq 2, the diffusion coefficient of ATP at 20 °C is calculated to be 3.42 × 10−6 cm2 s−1.

(1)

where σ is the variance in cm , Wh is the full width of the peak at half height in min, Ld is the length of the capillary from the inlet to the optical window in cm, and t is the total elapsed time in min.19,20 The translational diffusion coefficient, D, in cm2 s−1 can be calculated from the values of σ2 measured at each elapsed time, using the Einstein equation, eq 2: 2

⎛ 293 ⎞⎛ ηT ⎜ ⎟⎜ ⎝ T ⎠⎜⎝ η

2

The analyte, ATP, in a BGE containing 75 mM Tris+ was first driven past the optical window by applying 4 kV of reverse polarity for 21 min. The voltage was then turned off for 6 min. At 27 min, 4 kV were applied for 4 min with normal polarity, driving ATP past the window again. At 31 min, the field was turned off for 6 min. At 37 min, 4 kV were again applied with reverse polarity for 4 min, after which the field was turned off for 6 min. This pulsing sequence was then repeated as many times as desired. Figure 1B illustrates the dependence of the variance, defined in eq 1, on the cumulative elapsed time after injection of the

(2)

However, the diffusion coefficients are more accurately calculated from the slopes of plots of the variance as a function of elapsed time, as described previously.11 Diffusion coefficients measured at temperatures other than 20 °C can be corrected to the standard condition of water at 20 °C using eq 3: 9043

DOI: 10.1021/acs.analchem.5b02230 Anal. Chem. 2015, 87, 9042−9046

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Analytical Chemistry sample into the capillary. The slope of the straight line corresponds to a diffusion coefficient of 3.42 × 10−6 cm2 s−1. This value is in good agreement with the diffusion coefficient of 3.3 × 10−6 cm2 s−1 calculated from the data of Bowen and Martin22 at similar cation concentrations, after correcting their results to 20 °C using eq 3. Additional experiments (not shown) indicate that the diffusion coefficients obtained by the reversing field method are independent of the number of reversing field pulses, the voltage used to drive the DNA through the capillary, and the length of the stopping time between pulses. Capillary Wall Effects. Although curved DNA molecules are known to interact with the polyacrylamide gel matrix and migrate anomalously slowly during gel electrophoresis,23 DNA mobilities measured in polyacrylamide-coated capillaries do not appear to be significantly affected by DNA−wall interactions. We have previously shown that the free solution mobility of DNA is independent of whether the wall coating is polyacrylamide, poly(N-acryloylaminoethoxyethanol) or poly(N-acryloylaminopropanol)].14 DNA mobilities in polyacrylamide-coated capillaries are independent of whether the capillary is 75 or 100 μm in diameter, again suggesting that DNA−wall interactions are not significant in these capillaries. If such interactions were to occur, one might expect that the diffusion coefficients measured by the reversing pulse method would depend on the number of reversing field pulses used in each experiment and/or the length of the stopping time between pulses. Since neither factor affected the observed results significantly, DNA−wall interactions do not appear to affect the longitudinal diffusion of DNA in the capillary. Never-theless, to allow for the possibility of unknown electrophoreticdependent effects on the observed results, the diffusion coefficients are described below as “apparent” diffusion coefficients. Comparison of the Apparent Diffusion Coefficients Measured for dsDNA with the Values Determined by Other Techniques. Apparent diffusion coefficients were measured for DNA molecules containing 20, 79, 199, 442, and 960 bp by the reversing field method, with the results shown in Figure 2A. The measured diffusion coefficients (DCE, ●) are compared with literature values (Dliterature, ○) obtained for various DNAs by dynamic light scattering and other methods.10 In agreement with previous studies,11,12 the apparent diffusion coefficient measured for the 20-bp oligomer by the reversing field method agreed with the literature values. However, the diffusion coefficients determined for larger DNA molecules became increasingly more divergent from the literature values with increasing DNA molar mass. This divergence can be seen more clearly in Figure 2B, where the DCE/DLiterature ratios are plotted as a function of DNA size. The DCE/Dliterature ratios increase progressively with increasing molar mass for DNA molecules larger than ∼30 bp. Dependence of the Variance on Electric Field Strength. The 199-bp DNA restriction fragment was chosen for further studies to determine the source of the anomalously high diffusion coefficients measured for large DNA molecules using CE methods. The variances observed for this DNA in 20 mM Tris+ increased linearly with increasing electric field strength, as shown in Figure 3. Since the slopes of the lines increased with increasing electric field strength, the diffusion coefficients of large DNA molecules also depend on the applied electric field strength.

Figure 2. Comparison of DNA diffusion coefficients measured by the reversing field method, DCE, with values in the literature obtained by other techniques, Dliterature. (A) Log−log plot of the dependence of (●), DCE; and (○), Dliterature on DNA molar mass, in base pairs. The BGE was 20 mM Tris+; E = 380 V/cm for ATP and the 20-bp DNA oligomer and 190 V/cm for the larger DNAs. The values of Dliterature were taken from refs 11 and 2. The straight line was drawn by linear regression (r2 = 0.997). (B) Dependence of the diffusion coefficient ratio, DCE/Dliterature, on the logarithm of DNA size in base pairs. Dliterature values for the DNAs studied here were interpolated from the straight line drawn through ○ in A.

Figure 3. Dependence of the variance of the 199-bp DNA restriction fragment, in cm2, on elapsed time, in min, in BGEs containing 20 mM Tris+. Three electric field strengths were used: (●), 117 V/cm; (▲), 65 V/cm; and (■), 33 V/cm (top to bottom). The lines were drawn by linear regression (r2 = 0.999, 0.997, and 0.984, top to bottom).

Dependence of Apparent DNA Diffusion Coefficients on the Diffusion Coefficient of the Counterion in the BGE. The results in Figure 3 indicate that the anomalously high 9044

DOI: 10.1021/acs.analchem.5b02230 Anal. Chem. 2015, 87, 9042−9046

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Analytical Chemistry diffusion coefficients observed for large DNA molecules by CE methods are determined in part by the applied electric field, which controls the velocity of the analyte in the capillary. Another factor that could be important is electrostatic coupling between DNA and its counterions, an effect that has been previously observed for DNA by dynamic light scattering.6,24 Because the diffusion coefficients of monovalent cations are higher than those of DNA, electrostatic coupling between the polyion and its counterions would increase the apparent diffusion coefficients measured for DNA.5,6,23 To determine whether electrostatic coupling contributes importantly to the anomalously high DNA diffusion coefficients measured by CE, apparent diffusion coefficients were measured for the 199-bp DNA fragment in BGEs containing 30 mM Li+, Na+, K+, TBA+, Tris+, or Bis-Tris+ as the only cation in the solution. The diffusion coefficients of the first four cations are available in the literature.25 We estimated the diffusion coefficients of Tris+ and Bis-Tris+ from the diffusion coefficients and radii of the tetraalkylammonium ions,25 which span the size range of Tris+ and Bis-Tris+. The radii of the tetraalkylammonium ions were calculated by Marcus25 from the van der Waals volumes of the functional groups given by Bondi.26 As shown in Figure 4, the diffusion coefficients of the tetraalkylammonium

Figure 5. Relationship between the apparent diffusion coefficient of the 199-bp DNA fragment and the diffusion coefficient of the counterion in the BGE. The diffusion coefficients are given in units of 106 cm2 s−1. In all cases, the cation concentration was 30 mM; the electric field strength was 117 V/cm. The straight line was drawn by linear regression (r2 = 0.866).

DNA diffusion coefficients are determined in part by the diffusion coefficient of the counterion in the BGE. Dependence of the Apparent Diffusion Coefficients on BGE Concentration. Diffusion coefficients were measured at various electric field strengths for the 199-bp fragment in Tris acetate buffers containing 20, 50, or 150 mM Tris+, with the results shown in Figure 6. At any given electric field

Figure 4. Dependence of the diffusion coefficients of the tetraalkylammonium ions (○) on cation radius, in picometers.24 From left to right, ○ correspond to the tetramethylammonium, tetraethylammonium, tetrapropylammonium, TBA, and tetrapentylammonium ions. The straight line was drawn by linear regression (r2 = 0.967). The arrows indicate the estimated diffusion coefficients of Tris and Bis-Tris, respectively (see text).

Figure 6. Dependence of the apparent diffusion coefficients observed for the 199-bp fragment on the square root of the electric field strength. Three different Tris+ concentrations were used: (⧫), 20 mM; (●), 50 mM; and (▲), 150 mM. The lines were drawn by linear regression; r2 = 0.990, 0.996, and 0.968 for BGEs containing 20, 50, and 150 mM Tris+, respectively.

ions decrease linearly with increasing cation radius. Since the radius of the Tris + ion is known to be 3.15 Å (315 pm) from X-ray diffraction studies,27 the Tris+ diffusion coefficient is estimated to be 10.65 × 10−6 cm2 s−1, as shown by the arrow in Figure 4. We estimated the radius of Bis-Tris+ from the molar volumes given by Bondi.26 When applied to Tris+, the molar volumes give an estimated radius of 3.01 Å (301 pm), close to the radius determined by crystallography. The corresponding radius of the Bis-Tris+ ion is estimated to be 361 pm, from which the diffusion coefficient is estimated to be 8.24 × 10−6 cm2 s−1 (Figure 4). Figure 5 illustrates the dependence of the apparent diffusion coefficient of the 199-bp DNA fragment on the diffusion coefficient of the cation. The apparent DNA diffusion coefficient increases approximately linearly with the increasing diffusion coefficient of the cation, as expected if the diffusion of DNA and its counterions are electrostatically coupled.6 Hence,

strength, the apparent diffusion coefficients decreased with increasing cation concentration. In addition, at any given cation concentration, the apparent diffusion coefficients increased with increasing electric field strength. The apparent diffusion coefficients observed in 20, 50, and 150 mM Tris+ at finite electric fields extrapolate to values of (0.175, 0.215, and 0.247) × 10−6 cm2 s−1, respectively, at zero electric field strength. The average value, (0.21 ± 0.03) × 10−6 cm2 s−1, is very close to the value expected10 from light scattering measurements, 0.22 × 10−6 cm2 s−1. Hence, the anomalously high diffusion coefficients observed for large DNA molecules at finite electric fields can be eliminated by extrapolating the results to zero electric field. In addition, 9045

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Analytical Chemistry

(2) Sorlie, S.; Pecora, R. Macromolecules 1990, 23, 487−497. (3) Eimer, W.; Williamson, J. R.; Boxer, S. G.; Pecora, R. Biochemistry 1990, 29, 799−811. (4) Eimer, W.; Pecora, R. J. Chem. Phys. 1991, 94, 2324−2329. (5) Liu, H.; Skibinska, L.; Gapinski, J.; Patkowski, A.; Fischer, E. W.; Pecora, R. J. Chem. Phys. 1998, 109, 7556−7566. (6) Liu, H.; Gapinski, J.; Skibinska, L.; Patkowski, A.; Pecora, R. J. Chem. Phys. 2000, 113, 6001−6010. (7) Lapham, J.; Rife, J. P.; Moore, P. B.; Crothers, D. M. J. Biomol. NMR 1997, 10, 255−262. (8) Nkodo, A. E.; Garnier, J. M.; Tinland, B.; Ren, H.; Desruisseaux, D.; McCormick, L. C.; Drouin, G.; Slater, G. W. Electrophoresis 2001, 22, 2424−2432. (9) Bonifacio, G. F.; Brown, T.; Conn, G. L.; Lane, A. N. Biophys. J. 1997, 73, 1532−1538. (10) Stellwagen, E.; Lu, Y.; Stellwagen, N. C. Biochemistry 2003, 42, 11745−11750. (11) Stellwagen, N. C.; Magnusdóttir, S.; Gelfi, C.; Righetti, P. G. Biopolymers 2001, 58, 390−397. (12) Stellwagen, E.; Stellwagen, N. C. Electrophoresis 2002, 23, 2794− 2803. (13) Stellwagen, E.; Lu, Y. J.; Stellwagen, N. C. Nucleic Acids Res. 2005, 33, 4425−4432. (14) Stellwagen, N. C.; Gelfi, C.; Righetti, P. G. Biopolymers 1997, 42, 687−703. (15) Dong, Q.; Stellwagen, E.; Dagle, J. M.; Stellwagen, N. C. Electrophoresis 2003, 24, 3323−3329. (16) Terabe, S.; Shibata, O.; Isemura, T. J. High Resolut. Chromatogr. 1991, 14, 52−55. (17) Tsuda, T.; Kitagawa, S.; Ono, T.; Maeda, M. J. Capillary Electrophor. 1997, 4, 113−116. (18) Musheev, M. U.; Javaherian, S.; Okhonin, V.; Krylov, S. N. Anal. Chem. 2008, 80, 6752−6757. (19) Huang, S.; Coleman, W. F.; Zare, R. N. J. Chromatogr. 1989, 480, 95−110. (20) Yao, Y. J.; Li, S. F. Y. J. Chromatogr. Sci. 1994, 32, 117−120. (21) Cantor, C. R.; Schimmel, P. R. Biophysical Chemistry, Part II; W. H. Freemen and Co.: San Francisco, 1980; pp 581−584. (22) Bowen, W. J.; Martin, H. L. Arch. Biochem. Biophys. 1964, 107, 30−36. (23) Stellwagen, N. C. Electrophoresis 1997, 18, 34−44. (24) Fulmer, A. W.; Benbasat, J. A.; Bloomfield, V. A. Biopolymers 1981, 20, 1147−1159. (25) Marcus, Y. Ion Properties; Marcel Dekker, Inc.: New York, 1997. (26) Bondi, A. J. Phys. Chem. 1964, 68, 441−451. (27) Rudman, R.; Eilerman, D.; La Placa, S. J. Science 1978, 200, 531−533. (28) Lin, S.-C.; Lee, W. I.; Schurr, J. M. Biopolymers 1978, 17, 1041− 1064.

Figure 6 shows that the anomalously high apparent diffusion coefficients become more normal in BGEs containing high cation concentrations, most likely because of the increased electrostatic shielding of the phosphate residues. Similar results have been observed by dynamic light scattering.6

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DISCUSSION Electrostatic coupling between a polyion and its counterions has been observed for many years. Early dynamic light scattering studies of poly-L-lysine28 and nucleosomal DNA24 showed that the diffusion coefficients of these polyions varied markedly with ionic strength because of electrostatic coupling between the polyion and its counterions. More recently, Pecora and co-workers2−6 have studied the diffusion of DNA molecules ranging from 20 to 2311 base pairs using a variety of dynamic light scattering and fluorescence correlation spectroscopy methods. In the ionic strength range relevant to CE (cation concentrations ranging from 10 to 200 mM), the DNA diffusion coefficients decreased with increasing ionic strength as observed here (Figure 6). The authors attributed the ionic strength dependence of the diffusion coefficients to the coupled diffusion of DNA and its counterions. Figure 5 provides a strong confirmation of electrostatic coupling between DNA and its counterions. Large cations that diffuse relatively slowly in solution would be expected to have a smaller effect on the measured diffusion coefficients than smaller cations that diffuse relatively rapidly. If electrostatic coupling were not present, DNA diffusion coefficients would be expected to be independent of cation size. The effect of different cations on apparent DNA diffusion coefficients has not been observed previously because almost all studies have been carried out in NaCl solutions. Electrostatic coupling between a polyion and its counterions appears to be an intrinsic property of the translational diffusion of polyions. We have used double-stranded DNA as our model system because monodisperse samples of any desired molar mass can be prepared, and the measured diffusion coefficients can be compared with extensive data in the literature. However, electrostatic coupling effects undoubtedly exist in other polyion-cation systems as well. The advantage of using CE for measuring diffusion coefficients is that the amounts of sample required are very small so that a variety of experimental conditions can be explored. In addition, the measurements are relatively rapid if the reversing field protocol is used.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by Grant GM061009 from the National Institute of General Medical Sciences and Grant CHE0748271 from the Analytical and Surface Chemistry Program of the National Science Foundation (to N.C.S.). Preliminary experiments with the reversing field protocol were carried out by Alexandar Zhivkov, with the support of NATO Collaborative Linkage Grant LST-CLG978851.

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REFERENCES

(1) Nicolai, T.; Mandel, M. Macromolecules 1989, 22, 2348−2356. 9046

DOI: 10.1021/acs.analchem.5b02230 Anal. Chem. 2015, 87, 9042−9046