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UNTERRICHT
Structural resolution in such studies is not necessarily restricted
by the use of nitroxide spin labels, if their conformational
distribution is taken into account 41,42 . Models can be
defi ned in terms of distance distributions that can be fi tted to
experimental data 20 . For example consider the highly-resolved
structure of the dimer of the sodium/proton antiporter NhaA
of Escherichia coli 40 , based on an x-ray structure of the monomer
and DEER measurements of nine spin-labelled mutants
(Figure 13A). The relative orientation and positioning of the
monomers in a homodimer are characterized by only four parameters,
two polar angles and a two-component translation vector
in the membrane plane. The distribution of the label position
was modelled by using a rotamer library of preferred spin label
conformations and computing Boltzmann statistics of these
conformations according to their interaction energy with the
protein. After determining the four free structural parameters
from the nine data sets, the structure was tested for integrity
by repeating the fi t with only seven out of the nine constraints
and noise added to the data sets. The family of 144 structures
obtained in this test had a root mean square deviation of only
0.6 Å from the best structure. Structural resolution is thus
limited by resolution of the x-ray structure of the monomer
of 3.45 Å and not by the SDSL/DEER approach. The derived
dimer structure has no clashes between the two monomers
and the interfacial domains fi t surprisingly well to a low-resolution
electron density map obtained by cryo-transmission electron
microscopy on two-dimensional crystals (Figure 13B).
IV. OUTLOOK
As indicated by the chosen examples, the recent technological
development of EMR has opened the way to explore basic questions
beyond the study of simple spin doublets. EMR can now
be applied for the study of high spin systems not only realized
in molecular magnets, but which are also abundant in catalytic
centers in biology and material sciences. Apart from the study
of permanent paramagnetic centers, pulsed EMR also allows
to follow chemical reactions on
FIG. 13: Highly resolved structural model of the dimer of the sodium/proton
antiporter NhaA of Escherichia coli obtained from an x-ray structure of the
monomer and SDSL EPR data 40 . (A) Side view of the model. Spin labelled residues
are marked red and die distances measured by DEER are indicated by
red lines. (B) Superposition of a top view of the structure with a low-resolution
electron density map obtained by cryo-TEM on a two-dimensional crystal.
The interfacial domain (marked blue) fits well, while the ion translocation
domain (marked red) appears to be rotated.
the microsecond scale, confi rming the importance of electronic
spins in controlling reaction pathways 43,44 . A booming application
area is given by diamagnetic biomacromolecules that have become
accessible to EMR by spin labeling. Within the next few
years we expect the development of systematic approaches for
deriving structural models from SDSL EPR data. We will also
108
see the application of EMR techniques for implementing pulse
sequences for quantum computing, a fi eld which highly benefi
ts from the vast knowledge base for the manipulation of density
matrices, accumulated over decades by the NMR community
45 . The reintroduction of electrical read-out of EMR signals
in this context is also a very promising task 46 . In the near future
we will probably also see applications of single molecule EMR,
a technique demonstrated to work in principle 47 .
V. BOX 1
ESR/EPR spectroscopy is related to the energy dependence of
the magnetic moment of an electron in a magnetic fi eld. The
Zeeman effect, which was originally detected via optical spectroscopy,
could be related to its total angular momentum, consisting
of orbital and spin contributions. In a condensed phase
orbital momenta are quite generally suppressed (“quenched“),
thus leaving the spin angular momentum as dominant part.
Because of the collinearity of angular momentum and magnetic
moment, on can defi ne a scalar proportionality constant, the
magnetogyric ratio γ leading to
μe = γS
γ = −gμe
H = μeBgS
The last equation is defi ning the effective spin Hamiltonian H,
allowing to calculate the energy levels and subsequently the
transition frequencies as function of an external magnetic fi eld
B. In general, coupling the two vector operators B and S necessitates
to express g as a 3x3 matrix. For the description of
spectra obtained under conditions of rapid isotropic averaging,
instead of a g matrix a scalar g value can be used, defi ned by
one third of the trace of the matrix elements. For the eigenvalues
we then fi nd
E = mSgμeB
(9)
(10)
The resulting solutions for a simple S = 1/2 spin system of an
isolated electron are plotted in Fig. 14 for a fi eld range, which is
accessible with recent superconducting magnet technology.
Energy (GHz)
400
200
0
-200
100 GHz
BUNSEN-MAGAZIN · 10. JAHRGANG · 3/2008
250 GHz
500 GHz
m S = +1/2
m S = -1/2
-400
0 5 10 15 20
magnetic field (T)
FIG. 14: Energy levels of a S = 1/2 spin in an external magnetic field B.
Resonance fields are indicated when using a specific microwave frequency.
“Standard“ X-band spectrometer with 9.5 GHz operating frequency usually
provide a field range of up to 1.5 T, easily generated with electromagnets.