Counting the monomers in nanometer-sized oligomers by pulsed electron-electron double resonance

Article abstract of DOI:10.1021/ja065787t

In a lot of cases active biomolecules are complexes of higher order, thus methods capable of counting the number of building blocks and elucidating their geometric arrangement are needed. Therefore, we experimentally validate here spin-counting via 4-puls

Full text of DOI:10.1021/ja065787t

Published on Web 05/08/2007
Counting the Monomers in Nanometer-Sized Oligomers by
Pulsed Electron-Electron Double Resonance
Bela E. Bode,† Dominik Margraf,† Jo¨rn Plackmeyer,† Gerd Du¨rner,‡
Thomas F. Prisner,† and Olav Schiemann*,†
Contribution from the Institute of Physical and Theoretical Chemistry, Center for Biomolecular
Magnetic Resonance, and Institute of Organic Chemistry and Chemical Biology,
Max-Von-Laue-Strasse 7, J. W. Goethe-UniVersity, 60438 Frankfurt am Main, Germany
Received August 9, 2006; E-mail: olav.schiemann@prisner.de
Abstract: In a lot of cases active biomolecules are complexes of higher order, thus methods capable of
counting the number of building blocks and elucidating their geometric arrangement are needed. Therefore,
we experimentally validate here spin-counting via 4-pulse electron-electron double resonance (PELDOR)
on well-defined test samples. Two biradicals, a symmetric and an asymmetric triradical, and a tetraradical
were synthesized in a convergent reaction scheme via palladium-catalyzed cross-coupling reactions.
PELDOR was then used to obtain geometric information and the number of spin centers per molecule in
a single experiment. The measurement yielded the expected distances (2.2-3.8 nm) and showed that
different spin-spin distances in one molecule can be resolved even if the difference amounts to only 5 Å.
The number of spins n has been determined to be 2.1 in both biradicals, to 3.1 and 3.0 in the symmetric
and asymmetric triradicals, respectively, and to 3.9 in the tetraradical. The overall error of PELDOR spin-
counting was found to be 5% for up to four spins. Thus, this method is a valuable tool to determine the
number of constituting spin-bearing monomers in biologically relevant homo- and heterooligomers and
how their oligomerization state and geometric arrangement changes during function.
Introduction
that depends on the binding of several proteins during the
catalytic cycle is the RNA processing spliceosome.6 The number
There is a growing interest in the study of large protein-
protein complexes in membranes. For example, it is known from
crystal structures that ion-channels and transporters,1 like the
the ClC chloride channel, potassium channels, or glutamate
transporters, are complexes comprising two or more monomeric
protein units.2 For other ion-channels or transporters, like the
polypeptide antibiotic Antiamobin,3 the number of constituting
monomers have been proposed on the basis of molecular
modeling but not verified experimentally. Furthermore, several
signal-transduction proteins like the fumarate sensor DcuS4 are
only active in membranes, where it is proposed to form a
specific homo-oligomer. The number of constituting monomers
is, however, unknown. Another highly debated topic is the
question whether membrane-bound electron-transfer proteins of
the respiratory chain form super complexes5 to enable fast and
reliable interprotein electron transport. Also, a huge machinery
and type of interacting partners change from state to state
through the process of RNA cleavage and ligation. For several
of these functional states it is not fully understood how many
and which proteins are involved.
One method that can be employed to investigate the number
of monomers in a oligomer is X-ray crystallography. However,
it is still demanding to obtain suitable single crystals of large
complexes, and it has not yet been possible to crystallize them
within membranes. Therefore, complementary biophysical
methods capable of measuring the number of interacting
monomers in the presence or absence of a membrane, like cryo-
electron microscopy,7 are needed. In solution, electrospray
ionization mass spectrometry is a well-established method for
the determination of such noncovalent interactions.8 Two other
methods also enabling extraction of the number of constituting
units in solution are confocal time correlated fluorescence
spectroscopy9 and, as shown recently, fluorescence resonance
energy transfer (FRET).10 In addition, dynamic light scattering
can be employed to monitor soluble aggregates and oligomers
† Institute of Physical and Theoretical Chemistry, Center for Biomolecular
Magnetic Resonance.
‡ Institute of Organic Chemistry and Chemical Biology.
(1) (a) MacKinnon, R. Angew. Chem., Int. Ed. 2004, 43, 4265. (b) Gouaux,
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J. AM. CHEM. SOC. 2007, 129, 6736-6745
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Counting Monomers in Nanometer-Sized Oligomers
A R T I C L E S
by their hydrodynamic properties.11 First approaches in liquid-
12
and solid-state13 nuclear magnetic resonance (NMR) are
published. In this study, we show experimentally that also pulsed
electron-electron double resonance (PELDOR)14 can be used
to count the number of interacting monomers in a complex.
PELDOR is a reliable method to measure interspin distances
in the nanometer range15 between nitroxide spin labels16 or
native spin centers in biomolecules.17 Milov, Tsvetkov, et al.
proposed in 1984 that PELDOR can not only be used to measure
spin-spin distances but, in addition, to count the number of
coupled spins from the modulation depth18 and used this to
postulate the aggregation state of small peptides.19 However,
up to now there is no report on the experimental verification of
spin-counting by PELDOR using fully characterized test
systems. Therefore, we describe herein the synthesis of suitable
model systems mimicking different geometries and aggregation
states of biomolecules and use the model systems to evaluate
the method with respect to accuracy and limitations for
biological applications.
Figure 1. Pulse sequences for 4-pulse ELDOR.
meter detector 410 on Macherey-Nagel Nucleosil 50-10 columns.
Elemental analysis was performed on a Foss-Heraeus CHN-O-Rapid.
PELDOR Methodology. All following spin-counting experi-
ments were done with the 4-pulse ELDOR pulse sequence shown in
Figure 1.
The pulses at the detection frequency νA create an echo from the
spins on resonance, named in the following as A spins. Introduction
of an inversion pulse at the pump frequency νB flips spins resonant
with this second frequency, here defined as B spins. Thus, a coupling
ωAB between A and B spins causes a shift in the Lamor frequency of
the A spins by ωAB and therefore a change in the echo signal V(t). The
resulting PELDOR signal (V(t)) can be considered as a product of two
contributions:
Methods and Materials
Synthesis. Coupling reactions and deprotection steps were carried
out applying standard Schlenk techniques under argon atmosphere. All
explicit synthesis procedures are given in the Supporting Information.
Dry toluene was degassed by several freeze-thaw cycles. Benzene was
distilled from sodium metal, and amines were distilled from CaH2 both
under argon atmosphere. Dry DMF was degassed with argon.
Analytic relied on elemental analysis and mass spectrometry such
as EI, ESI, and MALDI. EI mass spectra were recorded on a CH7A
spectrometer from MAT. ESI mass spectra were acquired on a LCQ
Classic spectrometer from Thermo Electron and MALDI mass spectra
on a Voyager DE-Pro or STR spectrometer from Applied Biosystems.
Proton nuclear magnetic resonance spectra of diamagnetic molecules
were acquired at 250 MHz on a Bruker AM-250 spectrometer and
calibrated using residual nondeuterated solvents as internal standard
(δ CHCl3 ) 7.240). IR spectra were recorded on a Jasco FTIR 420
spectrometer using KBr pellets. Analytical HPLC was carried out with
a Waters 590 pump, a Waters UV detector 440, and Waters refracto-
V(t) ) VintraVinter
(1)
V
intra describes all spins coupled in one spin cluster, whereas Vinter takes
into account the signal decay caused by a homogeneous distribution
of the clusters in the sample. Assuming that the spin-orientations are
not changed because of spin diffusion or spin-lattice relaxation, Vintra
can be described by eq 2.18
n
n
1
V(t)intra
)
(1 - λB(1 - cos(ωABt)))
(2)
∑ ∏
A)1 B)1
B*A
n
with
and
ωAB ) ωdd + 2πJAB
(3)
(4)
(9) (a) Heinze, K. G.; Jahnz, M.; Schwille, P. Biophys. J. 2004, 86, 506. (b)
Becker, C. F. W.; Seidel, R.; Jahnz, M.; Bacia, K.; Niederhausen, T.;
Alexandrov, K.; Schwille, P.; Goody, R. S.; Engelhard, M. Chem. Bio.
Chem. 2006, 7, 891.
µ0p γAγB
3 (3 cos2 θ - 1)
ωdd ) -
4π
rAB
(10) (a) Liu, J.; Lu, Y. J. Am. Chem. Soc. 2002, 124, 15208. (b) Watrob, H.
M.; Pan, C.-P.; Barkley, M. D. J. Am. Chem. Soc. 2003, 125, 7336.
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Chugh, J.; Chatterjee, A.; Kumar, A.; Mishra, R. K.; Mittal, R.; Hosur, R.
V. FEBS J. 2006, 273, 388. (c) Cramer, J.; Jaeger, J.; Restle, T. Biochemistry
2006, 45, 3610.
where n is the number of radicals per cluster, λB is the fraction of B
spins inverted by the pump pulse, t is the time delay of the pump pulse,
ωdd is the full dipole-dipole splitting, µ0 is the vacuum permeability,
γ are the magnetogyric ratios of the spins, p is the Planck constant
divided by 2π, rAB is the distance between the spins, θ is the angle
between rAB and the external magnetic field, JAB is the exchange
(12) Krishnan, V. V. J. Magn. Reson. 1997, 124, 468.
(13) Luo, W.; Hong, M. J. Am. Chem. Soc. 2006, 128, 7242.
(14) Milov, A. D.; Salikov, K. M.; Shirov, M. D. Fiz. TVerd. Tela 1981, 23,
975.
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R. E.; Pannier, M.; Diederich, F.; Gramlich, V.; Hubrich, M.; Spiess, H.
W. Angew. Chem., Int. Ed. 1998, 37, 2833.
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O.; Weber, A.; Edwards, T. E.; Prisner, T. F.; Sigurdsson, S. T. J. Am.
Chem. Soc. 2003, 125, 3434. (c) Schiemann, O.; Piton, N.; Mu, Y.; Stock,
G.; Engels, J. W.; Prisner, T. F. J. Am. Chem. Soc. 2004, 126, 5722. (d)
Zhou, Z.; DeSensi, S. C.; Stein, R. A.; Brandon, S.; Dixit, M.; McArdle,
E. J.; Warren, E. M.; Kroh, H. K.; Song, L.; Cobb, C. E.; Hustedt, E. J.;
Beth, A. E. Biochemistry 2005, 44, 15115.
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Borbat, P. J. Am. Chem. Soc. 2005, 127, 15014. (b) Kay, C. W. M.; Elsa¨sser,
C.; Bittl, R.; Farell, S. R.; Thorpe, C. J. Am. Chem. Soc. 2006, 128, 76. (c)
Elsa¨sser, C.; Brecht, M.; Bittl, R. J. Am. Chem. Soc. 2002, 124, 12606. (d)
Hara, H.; Kawamori, A.; Astashkin, A. V.; Ono, T.-A. Biochim. Biophys.
Acta 1996, 1276, 140.
coupling in units of Hz, and ... is the averaging over values of rAB
AB, and θ. We assume JAB to be negligible versus ωdd and also that
the radical centers in a cluster do not bear any angular correlation.
,
J
Considering a random distribution of clusters and neglecting excluded
volumes, Vinter can be written as eq 5.20
2πγAγBµ
V(t)inter ) exp -
0cλBt
(5)
(
)
x
3p
9
Here c is the radical concentration in m-3
.
Thus, the coupling between spins can be deduced parameter-free
from the time domain signal by division of V(t) by Vinter and cosine
Fourier transformation. In disordered samples a broad distribution of
(18) (a) Milov, A. D.; Ponomarev, A. B.; Tsvetkov, Y. D. Chem. Phys. Lett.
1984, 110, 67. (b) Milov, A. D.; Maryasov, A. G.; Tsvetkov, Y. D. Appl.
Magn. Reson. 1998, 15, 107.
(19) Milov, A. D.; Tsvetkov, Y. D.; Formaggio, F.; Crisma, M.; Toniolo, C.;
Raap, J. J. Am. Chem. Soc. 2000, 122, 3843.
(20) Mims, W. B. In Electron Paramagnetic Resonance; Geschwind, S., Ed.;
Plenum: New York, 1972; pp 263.
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J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007 6737

A R T I C L E S
Bode et al.
ω
AB values exists. Therefore, the cos(ωABt) terms in eq 2 will interfere
3-pulse sequence as for the detection sequence in the PELDOR
measurements (for details see Supporting Information). Tikhonov
regularizations were performed on spectra with τ2 of 6-8 µs with time
increments ∆t of 8-12 ns to increase the resolution of the distance
transformations. All spectra for quantification of the modulation depth
were divided by a monoexponential decay and normalized to the point
t ) 0. These preprocessed datasets were also taken for cosine Fourier
transformation. λΒ was calibrated using standard biradicals; it was
determined to be 0.43 and 0.12 for a 12 and a 92 ns inversion pulse,
respectively.
Simulation of PELDOR Time Domain Data. Simulations were
performed based on eq 2-5, with detection and pumping efficiencies
explicitly calculated for each orientation and nitrogen hyperfine
state. The respective resonance positions are computed based on
the g and hyperfine tensor of the monomeric nitroxide spin label
from literature21 and the experimental values for pulse lengths and
microwave frequency. Full rotational freedom about the acetylene
linkers and backbone bending of (10° weighted with a cos2 profile
was assumed and 10 000 structures generated. Excitation profiles
were calculated with the analytic expression for rectangular pulses.
Powder averages are performed with 12 300 equally distributed points
on the half sphere.
to zero for times t . ωAB-1, and Vintra will tend to its limit Vλ, which
is the value of Vintra when all modulation is damped. Assuming that all
B spins are of similar nature, Vλ can be written in the form of
Vλ ) (1 - λB)(n-1)
(6)
Thus, Vλ values factorize under the conditions given above, for example,
a triradical can be described as the square of a biradical and a
tetraradical as the cube of a biradical. This approximation will not be
valid if the coupling spins belong to radicals with different spectral
widths. In that case the different λB values have to be taken into account
explicitly.
From eq 6 follows that the number of radicals in a cluster is
ln Vλ
n )
+ 1
(7)
ln(1 - λB)
If λ , 1, then eq 6 can be approximated linearly to eq 8:18a
Vλ ) 1 - λB(n - 1)
(8)
The only free parameter in the calculation of n is λΒ, which can be
determined experimentally using a standard biradical. In case of strong
angular correlations different λΒ values for each A-B pair in eq 2 have
to be explicitly taken into account. The extent of such effects will be
discussed in the results section.
Results and Discussion
Synthesis of Model Systems. Suitable model systems for
PELDOR spin-counting should be chemically stable and rigid
and have a spin-spin distance that is well within the limit of
the method (15-80 Å).16a,22 The polynitroxide radicals 1-5
(Scheme 1) containing fairly rigid ethynyl substituted aromatic
spacers fulfill these requirements. In addition, the use of these
spacers allowed us to synthesize molecules 1-5 from a small
pool of building blocks.
The nitroxide 3-ethynyl-1-oxyl-2,2,5,5-tetramethylpyrroline
6, which is commonly used as a spin label for RNA or
DNA,16c,23 was employed as the spin-bearing group. It was
prepared from 2,2,6,6-tetramethyl-4-oxopiperidine24 in slight
modification to to the procedure described by Hideg et al.25
Molecule 6 was converted to the polyradical precursor 9 via
the coupling and protection sequence shown in Scheme 2. We
decided to first attach a protected acetylene to 4,4′-diiodobi-
phenyl and add the nitroxide spin-label 6 in a second step for
reasons of synthesis economy, as 6 has to be synthesized in
eight steps. Because the nitroxyl moiety is easily reduced or
oxidized,26 a protective group strategy for acetylene units and
cleavage conditions not interfering with the nitroxyl functionality
had to be applied. Here, we chose the polar protecting group
2-hydroxypropyl, because it facilitates separation via column
chromatography in contrast to unpolar protecting groups as
trimethylsilane.27 We favored the 2-hydroxypropyl group over
Pulse EPR Measurements. All samples were prepared from
solutions of radicals 1-6 in d8-toluene (100 µM in spins, 80 µL). The
samples were saturated with argon prior to rapid freezing and storage
in liquid nitrogen. Mixtures of radicals were obtained by combining
d8-toluene solutions of the pure substances after determination of their
concentrations by cw-EPR. All PELDOR spectra were recorded on a
Bruker ELEXSYS E580 pulsed X-band EPR spectrometer with a
standard flex-line probe head housing a dielectric ring resonator (MD5
W1) equipped with a continuous flow helium cryostat (CF935) and
temperature control system (ITC 502) both from Oxford instruments.
The second microwave frequency was coupled into the microwave
bridge by a commercially available setup (E580-400U) from Bruker.
All pulses were amplified via a pulsed travelling wave tube (TWT)
amplifier (117X) from Applied Systems Engineering. The resonator
was over-coupled to a quality factor Q of about 50. Four-pulse ELDOR
experiments were performed with the pulse sequence π/2(νA)-τ1-π-
(νA)-(τ1 + t)-π(νB)-(τ2 - t)-π(νA)-τ2-echo. The pump pulse (νB) was
set to 12 ns at the resonance frequency of the resonator and applied to
the maximum of the nitroxide spectrum, where it selects the central mI
) 0 transition of Azz together with the mI ) 0, (1 transitions of Axx
and Ayy. The pulse amplitude was optimized on maximum inversion of
a Hahn-echo on the pump frequency. Detection pulses (νA) were set to
32 ns and applied at 70 MHz higher frequency. The amplitude was
chosen to optimize the refocused echo. The π/2-pulse was phase-cycled
to eliminate receiver offsets. All spectra were recorded at 40 K with
an experiment repetition time of 5 ms, a video amplifier bandwidth of
25 MHz and an amplifier gain of 60 dB. For quantitative measurements
of the modulation depth τ1 was set to 400 ns and τ2 to 5200 ns. Usually
1000 scans were accumulated with 272 data points and time increments
∆t of 20 ns giving an approximate measurement time of 1 h. All spectra
were acquired using the same experimental parameters as quality factor
of the resonator, pulse amplitudes, and timings. Spectra for low λΒ
were measured using the same conditions but with an inversion pulse
of 92 ns and a τ2 of 4400 ns. Suppression of proton modulation by the
addition of 8 spectra of variable τ1 with ∆t1 of 8 ns was done for
comparative reasons. (These data are only shown in the Supporting
Information.) Transverse relaxation times and the corresponding scaling
factors for 1-6 were estimated by comparing the Hahn echo and
refocused echo amplitudes (40960 averages each) using the same
(21) Fritscher, J.; Beyer, M.; Schiemann, O. Chem. Phys. Lett. 2002, 364, 393.
(22) Jeschke, G. Chem. Phys. Chem. 2002, 3, 927.
(23) (a) Spaltenstein, A.; Robinson, B. H.; Hopkins, P. B. J. Am. Chem. Soc.
1988, 110, 1299. (b) Piton, N.; Schiemann, O.; Mu, Y.; Stock, G.; Prisner,
T. F.; Engels, J. W. Nucleosides Nucleotides Nucl. 2005, 24, 771. (c) Piton,
N.; Mu, Y.; Stock, G.; Prisner, T. F.; Schiemann, O.; Engels, J. W. Nucleic
Acids Res. 2007, doi:10.1093/nar/gkm169.
(24) (a) Pauly, H. Justus Liebigs Ann. Chem. 1902, 322, 77. (b) Rozantsev, E.
G. In Free Nitroxyl Radicals; Ulrich, H., Ed.; Plenum Press: New York,
1970; pp 203.
(25) (a) Ka´lai, T.; Balog, M.; Jeko¨, J.; Hideg, K. Synthesis 1999, 973. (b)
Schiemann, O.; Piton, N.; Plackmeyer, J.; Bode, B. E.; Prisner, T. F.; Engels,
J. W. Nat. Protoc. 2007, 2, 904.
(26) (a) Schwartz, M. A.; Parce, J. W.; McConnell, H. M. J. Am. Chem. Soc.
1979, 101, 3592. (b) Brackmann, W.; Gaazbeek, C. J. Rec. TraV. Chim.
1966, 85, 221.
(27) (a) Ito, H.; Arimoto, K.; Senusui, H.-O.; Rosomi, A. Tetrahedron Lett.
1997, 38, 3977. (b) Ley, K. D.; Li, Y.; Johnson, J. V.; Powell, D. H.;
Schanze, K. Chem. Commun. 1999, 1749.
9
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Counting Monomers in Nanometer-Sized Oligomers
A R T I C L E S
Scheme 1. Overview of Synthesized Polyradical PELDOR Model Systems
hydroxymethyl because of the lower toxicity of the reagent.28
Purification of 7 is readily performed, and a 43% yield was
obtained.
nonconjugated terminal acetylenes.32 Here, the protected precur-
sor 8 was obtained in 74% yield. Molecule 8 was converted to
the deprotected33 precursor 9 in 93% yield by reacting 8 and
Nitroxide 6 can be attached to the halogeno-substituted sp2-
carbon atom in 7 by means of transition metal-catalyzed cross
coupling reactions such as the Sonogashira coupling.29 Nitrox-
ides can usually be coupled in high yields (84%)30 under mild
conditions.31 However, Sonogashira couplings involving 1,3-
enynes such as 6 are up to 17% lower in yield than those using
(29) (a) Khan, S. I.; Grinstaff, M. W. J. Am. Chem. Soc. 1999, 121, 4704. (b)
Takahashi, S.; Kuroyama, Y.; Sonogashira, K.; Hagihara, N. Synthesis 1980,
627. (c) Ka´lai, T.; Balog, M.; Jeko¨, J.; Hubbell, W. L.; Hideg, K. Synthesis
2002, 2365. (d) Kirchner, J. J.; Hustedt, E. J.; Robinson, B. H.; Hopkins,
P. B. Tetrahedron Lett. 1990, 31, 593.
(30) Romero, F. M.; Ziessel, R. Tetrahedron Lett. 1999, 40, 1895.
(31) Sonogashira, K. In Handbook of organopalladium chemistry for organic
synthesis; Nigishi, E., de Meijere, A., Eds.; Wiley: New York, 2002; Vol.
1, pp 493.
(32) (a) Miller, M. W.; Johnson, C. R. J. Org. Chem. 1997, 62, 1582. (b)
Fritscher, J.; Beyer, M.; Schiemann, O. Chem. Phys. Lett. 2002, 364, 393.
(28) (a) Bumagin, N. A.; Ponomaryov, A. B.; Beletskaya, I. P. Synthesis 1984,
728. (b) Kukula, H.; Veit, S.; Godt, A. Eur. J. Org. Chem. 1999, 277.
9
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A R T I C L E S
Bode et al.
Scheme 2. Synthesis of Polyradical Precursor 9a
product could not be isolated as a pure substance. Synthesizing
the corresponding non-iodo substituted biradical 2 from 1,3-
diiodobenzene also did not succeed again because of problems
in purification. We address these purification problems to the
dimerization of 9 to the homo-coupling product 1 and further
uncharacterized byproducts. The formation of 1 could not be
avoided in any Sonogashira coupling using precursor 9. It can
be isolated in a yield of up to 15% following the synthesis of
3-5 given in Scheme 3. To overcome these problems, we chose
to synthesize 1,3-diethynylbenzene 1339 and attach this to the
iodo-substitued radical 14 (Scheme 4). In that manner the
formation of 1 is excluded and 14 was obtained in 45% yield.
The homocoupling products of 13 were readily separated off
via column chromatography. (Note: The colorless oil 13 is
known to explode upon attempts of Vacuum distillation. 13
should only be distilled at high Vacuum and temperatures of
less than 60 °C in well-shielded equipment. Only limited
quantities should be stored or manipulated as pure, undiluted
material). Molecules 3 and 5 were not prepared using the
strategy shown in Scheme 4 because of the increasing reactive
character of higher polyethynyl compounds such as 1,2,4,5-
tetraethynylbenzene.40
Hence, convenient routes to rigid, shape persistent polyradical
systems have been established by means of Sonogashira
couplings and a corresponding polar protective group strategy.
This route is easily extendable to a variety of iodo substituted
arylic compounds. In comparison to a synthesis strategy where
a spin label bearing an acid functionality is attached via
esterification in the final step of the synthesis,41 less coupling
and deprotection steps are needed here. The overall yields are
comparable for both strategies.
a Conditions: (a) HNEt2, benzene, CuI, PdCl2(PPh3)2, 2-methyl-3-butyn-
2-ol, 43%; (b) NEt3, piperidine, DMF, CuI, PdCl2(C6H5CN)2, spin-label 6,
74%; (c) KOH, toluene, 93%.
KOH in toluene at 110 °C.34 Compound 9 was used without
further purification.
PELDOR Distance Measurements. The 4-pulse ELDOR
time traces of model systems 1-5 and the corresponding
distances obtained from Tikhonov regularizations42 are shown
in Figure 2. The obtained distances agree well with the predicted
ones and are summarized in Table 1. To ensure the reproduc-
ibility and significance, the regularization was also performed
on longer time traces with higher resolution than shown in
Figure 2. No changes in the dominant peaks in the distance
domain were observed. Cosine Fourier transformation as an
alternative method to extract distances from the time-domain
data did not resolve all individual dipolar frequencies in traces
d and e as strong peaks (see Supporting Information). Especially
in trace e, the full set of three predicted distances could only
be recovered by Tikhonov regularization. Provided a high signal-
to-noise ratio is obtained and modulations are observed, this
procedure is a valuable tool to extract distances. In 4 and 5 all
different distances within the molecules could be disentangled
even though two distances in 5 differ by 5 Å only.
The terminal acetylene 9 was then reacted with either 1,3,5-
triiodobenzene 1035,36 or 1,2,4,5-tetraiodobenzene 1137 leading
to the symmetric polyradical molecules 3 and 5, respectively.
The asymmetric triradical 4 was obtained by coupling 12, the
reaction product of 6 with 10, to precursor 9. Molecules 3, 4,
and 5 were yielded in 14%, 66%, and 18%, respectively. The
low yields upon coupling of more than one acetylene unit to an
aromatic system are commonly observed for phenylacetylene
systems.38 Yields of Sonogashira couplings involving nitroxides
6 and 9 could be raised by up to 18% using bis(benzonitrile)-
palladium(II)chloride as a catalyst and either triethylamine or
a 1:5 mixture of piperidine and triethylamine instead of bis-
(triphenylphosphine)palladium(II)chloride in triethyl- or diethyl-
amine (Scheme 3).
The initial attempt to couple 9 two times to 10 to obtain a
biradical from the given pool of building blocks failed, as the
(33) (a) Harris, S. J.; Walton, D. R. M. Tetrahedron 1978, 34, 1037. (b) Havens,
S. J.; Mergenrother, P. M. J. Org. Chem. 1985, 50, 1763. (c) Swindell, C.
S.; Fan, W.; Klimko, P. G. Tetrahedron Lett. 1994, 35, 4959. (d) Rodriquez,
J. G.; Martin-Villamil, R.; Cano, F. H.; Fonesca, I. J. Chem. Soc., Perkin
Trans. I 1997, 709.
(34) Ley, K. D.; Li, Y.; Johnson, J. V.; Powell, D. H.; Schanze, K. Chem.
Commun. 1999, 1749.
(35) Crystal structure of 1,3,5-triiodobenzene: Margraf, D.; Bats, J. W. Acta
Cryst. 2006, E62, 502.
(36) Preparation of 1,3,5-triiodobenzene: Scho¨berl, U.; Magnera, T. F.; Harrison,
R. M.; Fleischer, F.; Pflug, J. L.; Schwab, P. F. H.; Meng, X.; Lipiak, D.;
Noll, B. C.; Allured, V. S.; Rudalevige, T.; Lee, S.; Michl, J. J. Am. Chem.
Soc. 1997, 119, 3907.
(37) Preparation of 1,2,4,5- tetraiodobenzene: Mattern, D. L. J. Org. Chem.
1984, 49, 3051.
(38) Jones, C. S.; O’Connor, M. J.; Haley, M. M. In Acetylene Chemistry;
Diederich, F., Stang, P. J., Tykwinski, R. R., Eds.; Wiley: Weinberg,
Germany, 2005; pp 303.
The linear biradical 1 (trace a) exhibits the largest number
of visible oscillations leading to a narrow peak in the distance
transformation. In contrast, the bent, meta-substituted molecules
(39) Neenan, T. X.; Whitesides, G. M. J. Org. Chem. 1988, 53, 2489.
(40) Berris, B. C.; Hovakeemian, G. H.; Lai, Y.-H.; Mestdagh, H.; Vollhardt,
K. P. C. J. Am. Chem. Soc. 1985, 107, 5670.
(41) Godt, A.; Franzen, C.; Veit, S.; Enkelmann, V.; Pannier, M.; Jeschke, G.
J. Org. Chem. 2000, 65, 7575.
(42) (a) Jeschke, G.; Koch, A.; Jonas, U.; Godt, A. J. Magn. Reson. 2002, 155,
72. (b) Bowman, M. K.; Maryasov, A. G.; Kim, N.; DeRose, V. J. Appl.
Magn. Reson. 2004, 26, 23. (c) Chiang, Y.-W.; Borbat, P. P.; Freed, J. H.
J. Magn. Reson. 2005, 172, 279. The program used for data inversion was
obtained from the following: Distance Measurements on Nanoscopic
Lengthscales by Pulse EPR. http://www.mpip-mainz.mpg.de/∼jeschke/
distance.html.
9
6740 J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007

Counting Monomers in Nanometer-Sized Oligomers
A R T I C L E S
Scheme 3. Synthesis of Polyradical Systemsa
a Conditions: (a) NEt3, DMF, CuI, PdCl2(C6H5CN)2, 12, 66%; (b) HNEt2, C6H6, CuI, PdCl2(PPh3)2, 10, 14%; (c) NEt3, piperidine, DMF, CuI,
PdCl2(C6H5CN)2, 11, 18%; (d) NEt3, piperidine, DMF, CuI, PdCl2(C6H5CN)2, spin-label 6, 32%.
Scheme 4. Synthesis of Biradical 4a
structure than in a linear structure based on simple geometric
considerations. Consequently, the asymmetric triradical 4 shows
peaks of approximately the same widths as for radicals 2 and
3. The faster damping of the modulation of 4 is due to the
interfering dipolar frequencies. The approximately 2-fold higher
intensity of the peak at 2.5 nm in the distance domain of
asymmetric triradical 4 may also be rationalized by the
molecular geometry, the shorter distance can be extracted two
times, the longer distance only once. However, tetraradical 5
does not show this correlation. According to structural symmetry
all three distances appear two times, but the intensities of the
peaks differ. On the other hand the decreasing widths of the
peaks at 2.2 (ortho), 3.4 (meta), and 3.8 (para) nm are in
agreement with the above considerations about molecular
a Conditions: a) NEt3, piperidine, DMF, CuI, PdCl2(C6H5CN)2, trim-
structure and bending motions. Consequently, Tikhonov regu-
ethylsilylethyne; (b) TBAF, THF; (c) NEt3, piperidine, DMF, CuI,
PdCl2(C6H5CN)2, 13, 11%.
larization nicely yields the mean distances, but a quantitative
analysis of the distance distribution should be treated with care.
The reason is that in current state-of-the-art software imple-
2 and 3 display faster damping of the oscillations and conse-
mentations the time domain data is only simulated as a sum of
quently broader peaks in the distance domain. The different
pairs and not as a sum of products of triples or quadruples.
widths of the peaks in the distance domain can be qualitatively
Therefore, cross-terms of higher order in λB arising from the
simultaneous pumping of several B spins in tri- and tetraradicals
are not properly treated.42b Especially, in tetraradical 5 the
probability of multiple, coherent B-spin flips is fairly high
(∼35%), which might cause the observed regularization artifact
and improper amplitudes in the distance distribution.
related to the molecular structure. In a linear, stretched structure
as in 1, the spin-spin distance can only be reduced by molecular
bending motions. Whereas, in bent structures as in 2 and 3
bending motions can increase and decrease the end-to-end
distance around the equilibrium structure. Furthermore, the same
angular deviations lead to larger distance deviations in a bent
9
J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007 6741

A R T I C L E S
Bode et al.
Figure 2. PELDOR trace of model systems 1, 2, 3, 4, 5 in panels a, b, c, d, e, respectively. Distance transformations from Tikhonov regularizations are
shown as inset. The peak marked with an asterisk (/) in the distance domain of panel e is an artifact from the regularization, which is not significant within
the signal-to-noise ratio (see Supporting Information).
Table 1. Distances r [nm] from Modeling and Tikhonov
Regularization
derived for geometrically uncorrelated radical centers. On the
basis of the considerations of Milov, Tsvetkov et al.18 (see also
modelled r
[nm]b
PELDOR r
[nm]c
Methods and Materials section) the spectra in Figure 2 were
corrected for the intermolecular contributions to the echo decay
by division by a monoexponential decay and normalized to t )
0. The processed spectra are shown in Figure 3.
moleculea
1
2
3
3.4
3.4
3.4
2.5
3.4
2.0
3.4
3.9
3.4(0.1)
3.3(0.4)
3.3(0.4)
2.5(0.4)
3.3(0.4)
2.2(0.5)
3.3(0.4)
3.8(0.3)
4 [1,3/1,5]
4 [3,5]
5 [ortho]
5 [meta]
5 [para]
Figure 3 clearly demonstrates that the modulation depth
increases from a mono- to a tetraradical. Reading off the
modulation depth Vλ at the end of the respective time traces
and substituting the value into eq 7 allows direct determination
of the number of spins n. The spin-counting results are compared
to the actual number of spins in the corresponding molecules
in Table 2. Obviously, the experimental spin-counting nicely
reproduces the nominal number of spin centers in the model
systems. The accuracy in n is determined by the error in the
modulation depths Vλ. The observed experimental reproducibility
of the individual Vλ values is within 0.02 leading to an error in
a The numbers in square brackets give the positions at the benzene ring
to which the nitroxide bearing moieties are linked to. b The values are the
distances between the centers of the N-O bonds. c The number in brackets
is the full width at half-maximum of the corresponding peak.
PELDOR Spin-Counting. We then used molecules 1-6 to
prove that the number n of coupled nitroxides can be determined
from the PELDOR time traces, using the analytical expressions
9
6742 J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007

Counting Monomers in Nanometer-Sized Oligomers
A R T I C L E S
Figure 3. Corrected time domain signals for determination of n in 1-6.
Vλ is read off as the echo amplitude at t ) 5000 ns.
Figure 4. Modulation depths can be described as factorized by the number
of coupling spins.
Table 2. Number of Spins n from Processed Time Domain Data
a
molecule
n
Vλ
nfound
1
2
3
4
5
2
2
3
3
4
0.54
0.53
0.30
0.32
0.20
2.1(1)
2.1(1)
3.1(2)
3.0(2)
3.9(2)
a The number in brackets is the error in the last digit, determined from
a ∆Vλ of 0.02.
n of about 5%. Important for this accuracy is a high signal-to-
noise ratio (here >100:1) and a precise value for λΒ. In this
study λΒ was calibrated with standard biradicals.43 Phase cycling
of the π/2-pulse is mandatory to eliminate receiver offsets,
because the applied deconvolution of intra- and intermolecular
contributions to the echo decay implies that the experimental
trace is zero at infinity. In addition, the measured number of
spins was independent of the sample concentration and τ-mod-
ulation averaging (see Supporting Information). Under these
conditions monomers, dimers, trimers, and tetramers can be
readily distinguished. Within these limits a pentamer can still
be identified, but for n > 5 we expect a strong decrease in
accuracy, since Vλ will come closer to zero, which lowers the
signal-to-noise ratio, and the differences in Vλ decrease with
the potency of n.
Figure 5. Experimental PELDOR data and simulations for 1 and 3.
simulations were obtained by explicit calculation of λB for each
structure and random orientation with respect to the external
magnetic field. The result depicted in Figure 5 shows that
especially the modulation depth parameters λB of the experi-
mental data are reproduced very well. Thus, estimating equal
λB values is feasible. However, we do not exclude that weak
angular correlations might be present, but they are not observed
within the error of the experiment. Recent work by Jeschke and
co-workers44 on similar biradical model systems exhibited high
flexibility and also weak correlations in label orientations. In
biological systems spin labels are usually even more flexible
than in this study, so their angular correlation will be even
weaker. Thus, it is possible to count the number of monomers
in samples of pure oligomeric states, using eq 7.
As mentioned in the Methods and Materials section, Vλ is
described as a product of the contributions of all coupled spins
(eq 6). Figure 4 shows the applicability of eq 6. The cube root
of tetraradical 5 and the square roots of triradicals 3 and 4 give
within the error the same Vλ as biradicals 1 and 2.
In this work we approximated λB to be identical in radicals
1-6, which will be valid if the orientations of the nitroxide
labels within one molecule, and thus their respective hyperfine
and g-tensor orientations, are not correlated with each other. If
this assumption was not fulfilled, λB would depend on the
relative orientation. To verify our assumption of negligible
angular correlation, we performed numerical simulations of the
time domain signals of linear biradical 1 and bent triradical 3
exhibiting different geometries. Assuming some degree of
backbone bending ((10°) and full rotational freedom about the
acetylene linkers a set of 10 000 structures was generated. The
To verify the linear approximation, leading to eq 8, we
increased the inversion pulse length to 92 ns, decreasing λΒ to
about 0.12. This pulse is still not long enough to yield a λB
fulfilling the linear approximation. In addition, data obtained
with the 92 ns pump pulse do not meet the accuracy of the 12
ns pulse, even within the factorization approach (eq 7) (see
Supporting Information). This longer, more selective inversion
pulse introduces several problems: First, its small excitation
bandwidth leads to an orientation selectivity of the pumped
species causing the absolute error in λΒ to increase as compared
(43) Weber, A.; Schiemann, O.; Bode, B.; Prisner, T. F. J. Magn. Reson. 2002,
157, 277.
(44) Godt, A.; Schulte, M.; Zimmermann, H.; Jeschke, G. Angew. Chem., Int.
Ed. 2006, 45, 7560.
9
J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007 6743

A R T I C L E S
Bode et al.
Table 3. Mixtures and the Corresponding Measured and
Calculated Vλ
Column 4 in Table 3 shows the results for the six mixtures
according to eq 10. The calculated values are now in agreement
with the experimental data, indicating the importance of
relaxation for mixtures.
In samples of unknown composition this analysis becomes
more demanding, because the fraction of each oligomer and its
mixturea
V
λ measuredb
V
λ calculatedc
V
λ calculatedd
1+6 (1)
3+6 (2)
4+6 (2)
5+6 (3)
1+3 (1)
1+5 (2)
0.77(2)
0.69(2)
0.75(2)
0.76(2)
0.43(2)
0.43(2)
0.77
0.65
0.65
0.61
0.42
0.37
0.79
0.68
0.74
0.74
0.42
0.41
respective dipolar relaxation enhancement are unknown. In this
18a,46
case, studying Vλ as a function of λB
might allow an
a The number in brackets gives the difference in n between the two
molecules. b The number in brackets gives the error in the last digit. c These
numbers are calculated with eq 9. d These numbers are calculated with eq
10.
extraction of the constituents of the mixture, assuming a high
enough signal-to-noise ratio. Furthermore, extraction of Vλ as
a function of the observation time window τ2 might allow
extrapolation of the dipolar relaxation scaling factors of the
different oligomers. Therefore, with a series of measurements,
the dependencies of Vλ on λB and τ2 might be determined and
the composition of unknown mixtures derived.
Prior to this experimental validation of spin-counting, the
method had already been applied to biological systems of known
oligomerization states,47 but the data did in neither case
reproduce the oligomeric states found in crystal structures or
by biochemical methods. These discrepancies might be attributed
to experimental noise, incomplete spin labeling, and/or mixtures
of oligomeric states.
to the short pulse by amplification of the effects of small angular
correlations. Second, the differences in Vλ become smaller with
decreasing λΒ, which raises the overall uncertainty in n. Finally,
in the case of different dipolar coupling strengths, as present in
our model systems, λΒ will show a dependence on the
coupling.45 This dependence can be neglected only if the
microwave field strength B1 is much larger than the dipolar
coupling, which is here fulfilled better for the 12 ns pulse as
compared to the 92 ns pulse. However, a long inversion pulse
might be useful for aggregates with a large number of spin-
bearing centers.46
Comparison with Other Methods. Another EPR based
method for nanometer distance measurements is the excitation
of double quantum coherences (DQC).48 However, this method
is technically more demanding, because the full EPR-spectra
have to be excited and the nature of the experiment does not
allow counting the number of spins in a cluster easily.
In comparison to high-resolution NMR, dynamic light scat-
tering, fluorescence spectroscopy, or ESI that can all be
performed in solution under native conditions, PELDOR
measurements need to be performed in immobilized samples,
usually glassy frozen solutions. On the other hand, PELDOR
is not restricted in system size; measurements can be performed
in membranes and yield in the same experiment not only the
number of constituting monomers but also precise information
about their geometric arrangement. The method is comparable
to spin-spin distance measurements in solid-state NMR, for
example, REDOR; however, owing to the higher magnetic
moment of electron spins, distances of up to 80 Å are accessible
by PELDOR.
Since biological systems may exhibit an equilibrium between
monomers, dimers, and higher oligomers, we prepared various
mixtures of mono-, bi-, tri-, and tetraradicals equimolar in spin
concentrations and measured the resulting PELDOR spectra
(Table 3, Figure S4 in Supporting Information).
The analysis of these data is complicated, because n in eq 7
cannot simply be substituted by the average number of spins nj
(see also Supporting Information Table S4). The substitution
with nj would only be valid, if the linear approximation leading
to eq 8 was fulfilled. Instead the resulting signal is the sum of
responses of different species and eq 6 transforms to eq 9, where
xi is the fraction of spins in the respective oligomer giving the
signal Vλi.
V ) x V
i λi
(9)
∑
λ
i
In column 3 of Table 3 the Vλ of each mixture is calculated
using eq 9, which are the weighted sums of the signals of the
pure substances. Comparison with the experimental results
shows that the data are not reproduced for mixtures with large
differences in the number of coupled spins per molecule. We
attribute this to different transversal relaxation induced by the
dipolar couplings within the oligomers. Therefore, the proper
weighting factors also have to contain the contribution of each
oligomer to the refocused echo intensity. This difference in
transversal relaxation is taken explicitly into account by the
scaling factor si yielding eq 10 (for details see Supporting
Information).
Conclusion
We have shown on a variety of newly synthesized polyradi-
cals that a single PELDOR data set yields not only distances,
and thereby precise geometric information on the nanometer
scale, but also the number of spins n in a molecule. The method
has an overall error of ∼5% in n for up to four spins, provided
that the spin-labeling is complete and that the error of the
excitation probability factor λΒ does not exceed 0.02, which
can be readily achieved. In complexes with more than five spins,
with incomplete labeling, or in the presence of mixtures of
oligomeric states this accuracy strongly decreases. Mixtures of
s x V
i λi
∑
i
i
(47) (a) Jeschke, G.; Bender, A.; Schweikardt, T.; Panek, G.; Decker, H.; Paulsen,
H. J. Biol. Chem. 2005, 280, 18623. (b) Hilger, D.; Jung, H.; Padan, E.;
Wegener, C.; Vogel, K.-P.; Steinhoff, H.-J.; Jeschke, G. Biophys. J. 2005,
89, 1328. (c) Banham, J. E.; Timmel, C. R.; Abbott, R. J. M.; Lea, S. M.;
Jeschke, G. Angew. Chem., Int. Ed. 2006, 45, 1058.
Vλ )
(10)
s x
∑
i
i
i
(48) (a) Borbat, P. P.; Mchaourab, H. S.; Freed, J. H. J. Am. Chem. Soc. 2002,
124, 5304. (b) Borbat, P. P.; Davis, J. H.; Butcher, S. E.; Freed, J. H. J.
Am. Chem. Soc. 2004, 126, 7746. (c) Dzikovski, B. G.; Borbat, P. P.; Freed,
J. H. Biophys. J. 2004, 87, 3504. (d) Pornsuwan, S.; Bird, G.; Schafmeister,
C. E.; Saxena, S. J. Am. Chem. Soc. 2006, 128, 3876.
(45) Jeschke, G.; Chechik, V.; Ionita, P.; Godt, A.; Zimmermann, H.; Banham,
J.; Timmel, C. R.; Hilger, D.; Jung, H. Appl. Mag. Reson. 2006, 30, 473.
(46) Bowman, M. K.; Becker, D.; Sevilla, M. D.; Zimbrick, J. D. Radiat. Res.
2005, 163, 447.
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6744 J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007

Counting Monomers in Nanometer-Sized Oligomers
A R T I C L E S
oligomeric states could be analyzed by measuring Vλ as a
function of λB, with the limitations described herein. Thus,
PELDOR is a method by which the oligomeric state of
biologically relevant complexes can be evaluated down to
concentrations of ∼50 µM at a volume of 80 µL, given that the
monomers carry a spin center, and that the spin-spin distances
are within the PELDOR limit (15-80 Å).
applicability and limitations of the analytical expressions used.
This work has been supported by the Center for Biomolecular
Magnetic Resonance Frankfurt and the Deutsche Forschungs-
gemeinschaft (SFB 579 (“RNA - ligand interactions”) and SCHI
531-5/2). D.M. is grateful for a CMP fellowship.
Supporting Information Available: Detailed experimental
procedures, all Fourier transformed PELDOR spectra, spectra
with proton modulation suppression, spectra of mixtures,
PELDOR data with a low λΒ pump pulse, and concentration
dependence. This material is available free of charge via the
Internet at http://pubs.acs.org.
Acknowledgment. We acknowledge Prof. Dr. Christoph
Elschenbroich, Philipps-University Marburg, for recording EI
mass spectra, Dr. Ute Bahr, Johann Wolfgang Goethe-
University, for recording ESI and MALDI mass spectra and
Prof. Dr. Snorri Th. Sigurdsson for discussion. We thank
reviewer 2 and reviewer 4 for helpful discussions about
JA065787T
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J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007 6745