**6. Two motion model for EPR spectra simulation of TEMPO radical in membranes**

The given approach can naturally be extended to membrane structures. On the Fig. 18, 19 calculated EPR spectra of TEMPO radical in DPPC in X- and W-bands, correspondingly, are shown. The experimental spectrum is taken from the excellent Smirnov's work (Smirnov et. al., 1995). The experimental part of this work is highly valuable, but the interpretation of EPR spectra, from our point of view, should be conducted differently. We propose model, according to which, TEMPO radical, being in lipid phase, subjects to fast anisotropic reorientation, simultaneously experiencing the slow dynamic process motion due to lateral heterogeneity of domain structure in lipid bilayer.

Figures 18 and 19 represent the first example when simulated EPR spectra precisely reproduce experimental EPR spectra both in X and W bands, with exactly the same magnetic and dynamic parameters. The only simulation parameter changed was the frequency of EPR device. This consistency of our approach with multifrequency EPR data strongly argues for approach described here for uniform interpretation of dynamical effects in EPR spectra of spin-labeled samples.

**Figure 19.** A. Experimental EPR spectrum of TEMPO radical in DPPC at 37.6°C (heavy line) and simulated spectrum (fine line) at W-band (microwave frequency 94.3 GHz), B0 = 33584 G, scan range is 60 G. B. The simulated EPR spectrum of TEMPO radical in lipid phase. Parameters are in Table 1. C. The simulated EPR spectrum of TEMPO radical in aqueous phase. Parameters are in Table 1.


**Table 1.** Parameters for simulation of EPR spectra (Fig. 18, 19) of TEMPO radical in DPPC to X and W bands.

*AX* 15.650 G *AY* 14.707 G *AZ* 16.743 G *τ* 0.007 ns 30 ns Line Width 0.8 G 1.0 G Fraction 0.55 0.45

### **7. Conclusion**

310 Nitroxides – Theory, Experiment and Applications

heterogeneity of domain structure in lipid bilayer.

in EPR spectra of spin-labeled samples.

**membranes** 

**6. Two motion model for EPR spectra simulation of TEMPO radical in** 

The given approach can naturally be extended to membrane structures. On the Fig. 18, 19 calculated EPR spectra of TEMPO radical in DPPC in X- and W-bands, correspondingly, are shown. The experimental spectrum is taken from the excellent Smirnov's work (Smirnov et. al., 1995). The experimental part of this work is highly valuable, but the interpretation of EPR spectra, from our point of view, should be conducted differently. We propose model, according to which, TEMPO radical, being in lipid phase, subjects to fast anisotropic reorientation, simultaneously experiencing the slow dynamic process motion due to lateral

Figures 18 and 19 represent the first example when simulated EPR spectra precisely reproduce experimental EPR spectra both in X and W bands, with exactly the same magnetic and dynamic parameters. The only simulation parameter changed was the frequency of EPR device. This consistency of our approach with multifrequency EPR data strongly argues for approach described here for uniform interpretation of dynamical effects

**Figure 19.** A. Experimental EPR spectrum of TEMPO radical in DPPC at 37.6°C (heavy line) and simulated spectrum (fine line) at W-band (microwave frequency 94.3 GHz), B0 = 33584 G, scan range is 60 G. B. The simulated EPR spectrum of TEMPO radical in lipid phase. Parameters are in Table 1. C. The simulated EPR spectrum of TEMPO radical in aqueous phase. Parameters are in Table 1.

In the conclusion, we presented a uniform approach to EPR spectra analysis based on twomotion model and temperature and viscosity dependence experiment. It was shown to be consistent with molecular dynamics simulations and multifrequency EPR. The present approach is, in principle, applicable to all kinds of spin-labeled macromolecules and polymers. Although TVD is not limited to X-band, this type of spectrometers is most common and especially easy to maintain. At X-band this method may be utilized to full power, as it allows separating rapid motion of spin label and slow Brownian tumbling of macromolecule in solution by simply changing the temperature and viscosity of solvent by adding sucrose. Where it is impossible to carry out such experiment, for example, in membrane structures with embedded spin probe, the two-motion model still remains applicable, and it is possible to follow the same spectra simulation approach as used in conjunction with temperature and viscosity dependence. The two-motion model for nitroxide spin label dynamics can applied successfully to interpretation EPR spectra of most systems involving covalently bound as well as non-bound spin probes (*eg,* TEMPO radical embedded in membrane). It should be noted, there is one weakness in the proposed method – relatively small (1-4 G) shifts of rather broad peaks has to be measured with sufficient degree of accuracy. Sometimes series of EPR spectra obtained at different conditions may appear very similar, but still they are distinguished by the position of broad outer peaks. With proposed method, it is possible to carry out purposefully the interpretation of EPR spectra of any spin-labeled biological object. Elucidation microscale dynamical features from its EPR spectra represents extremely difficult problem. This inverse problem of EPR spectroscopy still has no unequivocal solution. This is partially due to method limitations, but they may be partially overcome by using TVD approach, which extracts additional information from set of EPR spectra at different conditions. The detailed system dynamics may be obtained from MD simulations and verified against experimental EPR data by using order parameters, as it was shown here on example of Barstar-Barnase complex formation. The uniform method as described here is, therefore, considered to be a very big step forward for the resolution of inverse EPR problem for spin-labeled macromolecules and other biological nanoscale objects.

### **Author details**

Yaroslav Tkachev and Vladimir Timofeev *V.A. Engelhardt Institute of Molecular Biology/RAS, Moscow, Russia* 

### **8. References**


Lipari G., and Szabo A. (1982). Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. 1. Theory and range of validity. *J. Am. Chem. Soc.* 104, 4546-4559.

312 Nitroxides – Theory, Experiment and Applications

other biological nanoscale objects.

Yaroslav Tkachev and Vladimir Timofeev

*Molec. Graphics*, , vol. 14, pp. 33-38.

*Chem. B* , 112, 12095–12103.

*Letters.* 12, 103-106.

*V.A. Engelhardt Institute of Molecular Biology/RAS, Moscow, Russia* 

proteins and complex fluids. *J. Chem. Phys.* 131, 224507-224521.

Dudich I.V., Timofeev V.P., Volkenstein M.V., and Misharin A.Yu. (1977) Measurement of rotational correlation time of macromolecules by the ESR method in the case of a covalently bound spin label. *Molecular Biology (translated from Russian)*. 11, 531-538. Goldman S.A., Bruno G.V., Freed J.H. (1972). Estimating slow motional rotational correlation times for nitroxides by electron spin resonance. *J. Phys. Chem.* 76, 1858-1860. Halle B. (2009). The physical basis of model-free analysis of NMR relaxation data from

Humphrey, W., Dalke, A. and Schulten, K. (1996). "VMD - Visual Molecular Dynamics", *J.* 

Frederick K. K., Sharp K. A., Warischalk N., and Wand A.J. (2008). Re-evaluation of the model-free analysis of fast internal motion in proteins using NMR relaxation, *J. Phys.* 

Kuznetsov A.N., Wasserman A.M., Volkov A.Yu., Korst N.N. (1971). Determination of rotational correlation time of nitric oxide radicals in a viscous medium. *Chem. Phys.* 

**Author details** 

**8. References** 

applicable, and it is possible to follow the same spectra simulation approach as used in conjunction with temperature and viscosity dependence. The two-motion model for nitroxide spin label dynamics can applied successfully to interpretation EPR spectra of most systems involving covalently bound as well as non-bound spin probes (*eg,* TEMPO radical embedded in membrane). It should be noted, there is one weakness in the proposed method – relatively small (1-4 G) shifts of rather broad peaks has to be measured with sufficient degree of accuracy. Sometimes series of EPR spectra obtained at different conditions may appear very similar, but still they are distinguished by the position of broad outer peaks. With proposed method, it is possible to carry out purposefully the interpretation of EPR spectra of any spin-labeled biological object. Elucidation microscale dynamical features from its EPR spectra represents extremely difficult problem. This inverse problem of EPR spectroscopy still has no unequivocal solution. This is partially due to method limitations, but they may be partially overcome by using TVD approach, which extracts additional information from set of EPR spectra at different conditions. The detailed system dynamics may be obtained from MD simulations and verified against experimental EPR data by using order parameters, as it was shown here on example of Barstar-Barnase complex formation. The uniform method as described here is, therefore, considered to be a very big step forward for the resolution of inverse EPR problem for spin-labeled macromolecules and


**Section 3** 
