**1. Introduction**

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Spin labeling method crossed its 47-th anniversary. It was invented in 1965 by Harden McConnel. He was the first who reported EPR spectra of bovine serum albumin and poly- (L-lysine) with stable nitroxide radicals chemically bound, and attempted to interpret them (Stone et al., 1965). As it stands today, we must conclude that there is little consensus between different scientists on the problem of such EPR spectra interpretation. When stepped into area of studying much more sophisticated biological objects comparing to these McConnel used, spin labeling methods this problem appeared to be very difficult. Its difficulty arises not only from the objects complexity, but also from method limitations, which relies on the solution of EPR reverse problem. Even with all of extensive developments done since 1965, such as availability of new microwave frequencies and pulsed EPR techniques, which, in fact, grew into separate method, the problem remains. It originates from large discrepancy between the information content of EPR spectrum and underlying object's behavior. Systems studies modern life science is interested in displays such a large degree of versatility that simply does not fit into single spectrum. This work summarizes our attempts to address this issue during the past 30 years.

The key for interpreting EPR spectra uniquely is to use as much of experimental data as possible. The most of informational content is found in spectra containing broad outer peaks (BOPs), as otherwise strongly narrowed spectra are highly degenerate, and attempting to solve reverse problem from them with underlying model which is slightly more complex than trivial is prone to non-uniqueness. Our method is primarily based on spectra with BOPs, to extract the most of useful information. In spectra of liquid solutions, their position is strongly affected by the mobility of nitroxide, and it is modulated by nitroxide

© 2012 Tkachev and Timofeev, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Tkachev and Timofeev, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

environment and macromolecule Brownian motion. These are two main contributions into EPR lineshape the method is capable to resolve with most objects being studied.

We have previously suggested that monitoring the position of the broad outer peaks (BOPs) in EPR spectra of spin-labeled macromolecules unravels the system dynamics to the maximum extent conventional EPR can deliver. This may be achieved by studying of socalled temperature and viscosity dependencies, or TVDs, for short. In many cases, they provide a key to the interpretation of EPR spectra of spin-labeled macromolecules, by eliminating the large degree of non-uniqueness arising from different kinds of molecular motion. Similar approach is applicable to the non-covalent spin probe EPR studies of membranes. From these dependencies one can experimentally determine two very important quantities: the rotational correlation time (*τ*) of the protein molecule, and McConnell's order parameter (*S*) of rapid spin-label motion. Possibility of immediate use of these parameters for computational simulation of the EPR spectra significantly contributes to unique interpretation.

McConnell pioneered the use of the BOPs position in EPR spectra depending on the value of correlation time of a nitroxide radical motion. He conducted theoretical (McCalley et al., 1972), using Bloch equation, and experimental (Shimshick & McConnell, 1972) studies of the spin labeled alpha-chymotrypsin. Kuznetsov (Kuznetsov et al., 1971) theoretically showed the dependence of low-field BOP shift on the value of nitroxide molecular motion correlation time. J. Freed (Goldman et al., 1972) theoretically derived the expression for separation between BOPs depending on the value of *τ* for nitroxide radical.

We in parallel worked with the same problem, but for some reasons our first work has been published only in 1977 (Dudich et al., 1977). In this work it was emphasized for the first time that it is necessary to consider partial averaging of nitroxide magnetic tensors due to the fast reorientation of spin label relative to the macromolecule. This fast motion effectively changes the values of nitroxide magnetic tensors components. Most of the studies mentioned above were focusing on influence of polarity of an immediate NO• moiety environment. Although this influence is not challenged, the polarity effects from nearby amino acid residues are very object-specific, as the surface charge of protein is. It is also pHdependent, making it very difficult to follow. Additionally, in many practical cases the nitroxide moiety of attached label is significantly exposed to solvent, reducing polarity change effects. The fast motion is still ubiquitous, as neither label-to-protein linkage, nor the local protein structure at labeling site is perfectly rigid. In J. Freed's work (Mason and Freed, 1974) this fast motion relative to the carrier (molecular unit label is bound to) was considered as very rapid motion with respect to one of the molecular axes, while setting the diffusion tensor components in perpendicular plane to very slow motion, with an artificial introduction of tilt between the diffusion tensor principal axes relative to magnetic tensors ones.

The method based on averaging and is similar to known Model Free (MF) approach widely accepted in NMR (Lipari and Szabo, 1982). In this method, fast motion is considered to be independent of overall tumbling. The complicated Slowly Relaxing Local Structure (SRLS) model developed by Freed (Meirovitch et al., 2007) is claimed to benefit from including the coupling between these motions. It is achieved by substitution of composite diffusion operator into stochastic Liouville equation. This point was recently shown to be challengeable (Halle B., 2009). With simplified two-dimensional SRLS model Halle showed that attempting to exploit an advantage over MF it takes from motions coupling, lead to rather unphysical conditions. The contention was that complication introduced in SRLS probably does not worth its theoretical benefits.

286 Nitroxides – Theory, Experiment and Applications

to unique interpretation.

environment and macromolecule Brownian motion. These are two main contributions into

We have previously suggested that monitoring the position of the broad outer peaks (BOPs) in EPR spectra of spin-labeled macromolecules unravels the system dynamics to the maximum extent conventional EPR can deliver. This may be achieved by studying of socalled temperature and viscosity dependencies, or TVDs, for short. In many cases, they provide a key to the interpretation of EPR spectra of spin-labeled macromolecules, by eliminating the large degree of non-uniqueness arising from different kinds of molecular motion. Similar approach is applicable to the non-covalent spin probe EPR studies of membranes. From these dependencies one can experimentally determine two very important quantities: the rotational correlation time (*τ*) of the protein molecule, and McConnell's order parameter (*S*) of rapid spin-label motion. Possibility of immediate use of these parameters for computational simulation of the EPR spectra significantly contributes

McConnell pioneered the use of the BOPs position in EPR spectra depending on the value of correlation time of a nitroxide radical motion. He conducted theoretical (McCalley et al., 1972), using Bloch equation, and experimental (Shimshick & McConnell, 1972) studies of the spin labeled alpha-chymotrypsin. Kuznetsov (Kuznetsov et al., 1971) theoretically showed the dependence of low-field BOP shift on the value of nitroxide molecular motion correlation time. J. Freed (Goldman et al., 1972) theoretically derived the expression for

We in parallel worked with the same problem, but for some reasons our first work has been published only in 1977 (Dudich et al., 1977). In this work it was emphasized for the first time that it is necessary to consider partial averaging of nitroxide magnetic tensors due to the fast reorientation of spin label relative to the macromolecule. This fast motion effectively changes the values of nitroxide magnetic tensors components. Most of the studies mentioned above were focusing on influence of polarity of an immediate NO• moiety environment. Although this influence is not challenged, the polarity effects from nearby amino acid residues are very object-specific, as the surface charge of protein is. It is also pHdependent, making it very difficult to follow. Additionally, in many practical cases the nitroxide moiety of attached label is significantly exposed to solvent, reducing polarity change effects. The fast motion is still ubiquitous, as neither label-to-protein linkage, nor the local protein structure at labeling site is perfectly rigid. In J. Freed's work (Mason and Freed, 1974) this fast motion relative to the carrier (molecular unit label is bound to) was considered as very rapid motion with respect to one of the molecular axes, while setting the diffusion tensor components in perpendicular plane to very slow motion, with an artificial introduction

separation between BOPs depending on the value of *τ* for nitroxide radical.

of tilt between the diffusion tensor principal axes relative to magnetic tensors ones.

The method based on averaging and is similar to known Model Free (MF) approach widely accepted in NMR (Lipari and Szabo, 1982). In this method, fast motion is considered to be independent of overall tumbling. The complicated Slowly Relaxing Local Structure (SRLS) model developed by Freed (Meirovitch et al., 2007) is claimed to benefit from including the

EPR lineshape the method is capable to resolve with most objects being studied.

Here we will present a clear algorithm suitable for correct and unequivocal interpretation of EPR spectra according to two independent motions (TwIM) model. As an example we will present an EPR study of spin-labeled Barstar in solution as well as attached to sepharose adsorbent to eliminate slow tumbling. Parameters measured from temperature and viscosity dependencies will be fed into the EPR spectra simulation program, and resulting spectra compared to experimental ones. We also show how the given approach may be naturally extended to membrane structures. Joint use of this method, together with Molecular Dynamics simulations, allows deeper investigation of the object's nature.
