Distance between paramagnetic centers

Exploiting different experimental approaches, EPR spectroscopy can access distances between paramagnetic centers in the range between 1 and 8 nm [1, 13, 47-54]. 

Distances between paramagnetic centers in the range 2-8 nm can be measured by specialized pulse techniques that record modulations due to the magnetic coupling between them. The coupling is of the same type as for the fine-structure in radical pairs. By measuring the fine-structure constant D the distance is obtained. This method has been used to obtain distances within spin-labelled proteins, where the spin labels are free radicals that have been attached to amino acids at two known positions. 

Einally, pulsed EPR experiments in solids allow determination of spin-lattice relaxation and phase memory times (Ti, Tm), whose dependence on temperature and nature of the environment can be analyzed to give information on the collective relaxation phenomena due to nuclear spin diffusion, electron-electron dipolar interaction, and instantaneous diffusion [9]. Note that the electron-electron dipolar interaction is also exploited in the DEER (PELDOR) technique for measuring the distance between paramagnetic centers. Instantaneous diffusion can give information on the microconcentration of radicals produced by high-energy irradiation in solids [e.g., 10]. 

Fig. 3 Distance measurements between paramagnetic centers by EPR spectroscopy. Below 0.5 nm. distance estimates are unreliable for 0.5

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

From Equations 11.1 and 11.2 we have seen that the strength of the dipole-dipole interaction decreases rapidly with increasing distance between two paramagnetic centers, and still we choose to call this a long-range interaction. The justification... 

The water proton NMRD profile of Cu(II) aqua ion at 298 K [108] (Fig. 5.36) is in excellent accordance with what expected from the dipole-dipole relaxation theory, as described by the Solomon equation (Eq. (3.16)). The best fitting procedure applied to a configuration of 12 water protons bound to the metal ion provides a distance between water protons and the paramagnetic center equal to 2.7 A, and a correlation time equal to 2.6 x 10 11 s, which defines the position of the cos dispersion. The correlation time is determined by rotation as expected from the Stokes-Einstein equation (Eq. (3.8)). The electron relaxation time is in fact expected to be one order of magnitude longer (see Table 5.6). This also ensures... 

In Eqs. (7-11), fi is the nuclear gyromagnetic ratio, g is the electron g factor, fiB is the Bohr magneton, rGdH is the electron spin - proton distance, co, and cos are the nuclear and electron Larmor frequencies, respectively (co=yB, where B is the magnetic field), and A/fl is the hyperfine or scalar coupling constant between the electron of the paramagnetic center and the proton of the coordinated water. The correlation times that are characteristic of the relaxation processes are depicted as ... 

Information about RNA structure and movement is critical for our understanding of how RNA is able to carry out its multifaceted functions. One spectroscopic technique that has shown great promise to study RNA, as well as other biopolymers, is electron paramagnetic resonance (EPR) spectroscopy, also named electron spin resonance (ESR) spectroscopy. EPR is a magnetic resonance technique that monitors the behaviors of unpaired electrons, and has long been used to study structure and dynamics of biomolecules (see recent reviews by Klug and Feix, 2008 Sowa and Qin, 2008). Structural information can be obtained by distance measurements, that is, by determination of distances between two spin-centers, and is the topic of another chapter in this volume (see Chapter 16 in this volume). 

The EPR technique allows to obtain information of three various kinds a) characterization of the nature of different paramagnetic centers (PCs) and their content in the sample b) relaxation and dynamic properties of PCs c) peculiarities of the spatial organization, local concentrations or mean distances between PCs in the system. The latter is usually connected with measurements of the energy of magnetic dipole-dipole interaction between electron spins. 

Apart from their short lifetimes, another important reason for not observing the O species is dipolar interaction. As explained later (Section IV), if the distance between one O species and another paramagnetic center (O or a metal ion) decreases, the linewidth may increase to the extent that the 0 species become EPR invisible. In this category of EPR invisible O species, there are not only the short-lived O produced according to Eq. (8), but also the long-lived O formed by heat pretreatment or adsorption, as discussed in the following section. 

In solving problems of enzyme catalysis, molecular biophysics of proteins, biomembranes and molecular biology it is necessary to know the spatial disposition of individual parts. One must also know the depth of immersion of paramagnetic centers in a biological matrix, i.e. the availability of enzyme sites to substrates, distance of electron tunneling between a donor and an acceptor group, position of a spin-label in a membrane and in a protein globule, distribution of the electrostatic field around the PC, etc. 

Distances between unpaired electrons ranging from 5 to 80 A and depth of immersion of a paramagnetic center up to 40 A can be measured by a combination of continuous wave (CW) and pulsed EPR techniques. 

Kulikov, A.V. (1976) Determination of distance between the nitroxide label and paramagnetic center in spin-labeled proteins from the parameters of the saturation curve of the ESR spectrum of the label at 77K. Molecul. Biol. (Moscow) 10, 109-116. 

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