From the ESR spectra, it is possible to determine the valence of a paramagnetic ion and the symmetry of its environment, which, in combination with X-ray structural analysis data, makes it possible to determine the position of the paramagnetic ion in the crystal lattice. The value of the energy levels of a paramagnetic ion allows one to compare EPR results with optical spectra data and calculate the magnetic susceptibility of paramagnetic materials.
The EPR method makes it possible to determine the nature and localization of lattice defects, such as color centers. In metals and semiconductors, EPR is also possible, associated with a change in the orientation of the spins of conduction electrons. The EPR method is widely used in chemistry and biology, where in the process of chemical reactions or under the influence of ionizing radiation, molecules with an unfilled chemical bond - free radicals - can be formed. Their g-factor is usually close to , and the EPR linewidth 
small Because of these qualities, one of the most stable free radicals (), with g = 2.0036, is used as a standard in ESR measurements. In ER biology, enzymes, free radicals in biological systems and organometallic compounds are studied.
EPR in strong magnetic fields
The overwhelming majority of experimental studies of paramagnetic resonance have been carried out in magnetic fields whose strength is less than 20 ke. Meanwhile, the use of stronger static fields and alternating fields of higher frequencies would significantly expand the capabilities of the EPR method and increase the information it provides. In the near future, permanent magnetic fields up to 250 will become available ke and pulsed fields measured in tens of millions of oersteds. This means that Zeeman splittings in constant fields will reach approximately 25 
, and a in pulsed fields – values are two orders of magnitude greater. Lowe used a spectrometer with a superconducting magnet to measure EPR in fields H0
65
ke. Prokhorov and his colleagues observed EPR signals at the wavelength 
=1,21mm.
Strong magnetic fields should be of great benefit for the radiation of rare-earth ions in crystals, the intervals between the Stark sublevels of which are on the order of 10-100 
. The EPR effect in ordinary fields is often absent due to the fact that the main Stark level turns out to be a singlet, or because transitions between Zeeman sublevels of the main Kramers doublet are prohibited. The effect is, generally speaking, possible due to transitions between different Stark sublevels. Further, the crystal field in rare earth crystals is characterized by a large number of parameters, for determining which knowledge g- the tensor of the main Kramers doublet is not enough.
Strong magnetic fields can also be used to study iron group ions, in particular such as 
which have splittings of order 10 
100
.
When applied to exchange-coupled pairs, strong magnetic fields will allow, by observing the effect caused by transitions between levels with different values of the resulting spin S pairs with spectroscopic accuracy to measure the exchange interaction parameter J.
Paramagnetic resonance in strong magnetic fields will have a number of features. Magnetization saturation effects will occur at relatively high temperatures. At not very low temperatures, the polarization of ionic magnetic moments will be so great that, in addition to the external magnetic field, it will be necessary to introduce an internal field into the resonance conditions. A dependence of the resonance conditions on the shape of the sample will appear.
Phenomena electron paramagnetic resonance(EPR) and nuclear magnetic resonance(NMR) are widely used in modern physics, chemistry, biology and medicine in the study of processes occurring with the participation of paramagnetic molecules and nuclei. In addition, nuclear magnetic resonance is the physical basis of the most powerful modern method for obtaining images of human organs and tissues - magnetic resonance imaging(MRI).
The EPR method has gained great importance in chemistry and biology primarily due to its ability to detect and identify free radicals in chemical and biological systems. At the same time, not only the type and concentration of free radicals are determined with high accuracy, but also the kinetics of biochemical reactions that occur with the formation of free radicals in both intermediate and final stages of the reaction.
Free radicals in biological systems
It is known that, in accordance with the Pauli principle, each quantum state of a molecule can contain no more than two electrons, the spins of which must be oppositely oriented (compensated). Spin- this is an internal property of an electron, which manifests itself in the presence of its own mechanical torque J, i.e. the electron is like a “twisted” top. Stable molecules are usually characterized by an even number of electrons and each pair of electrons at any energy level has oppositely directed, or, as they say, compensated (paired) spins.
However, there are compounds in which the number of electrons is odd and then the spin of one of the valence electrons will not be compensated. The same situation arises if one electron is removed from a stable compound or, conversely, added to it. Then the spin of one of the electrons will also not be compensated.
A molecule or part of it that has an unpaired electron is called free radical.
From the point of view of chemistry, the presence of an unpaired electron in a molecule is nothing more than the presence of a free valence. Therefore, free radicals are very active chemically. They easily enter into chemical bonds with other molecules and chemical compounds, which affects the course of many processes in biological systems.
The following types of radicals play the most important role in biological systems (the radical is often indicated by a dot above the corresponding chemical group):
- free radicals of water: OH - hydroxyl, H0 2 - peroxide, 0 2 - superoxide;
- free radicals of organic molecules formed under the action of ionizing and ultraviolet radiation:
where e“ is the solvated electron, and the resulting radical is indicated by the dot above.
These free radicals play an important role in causing radiation damage to tissues and organs, as well as UV burns;
- quinone free radicals participate in redox reactions in the body;
- free radicals of lipids can be formed under certain conditions during the oxidation of their fatty acids. The presence of free radicals in the lipids of biological membranes leads to a disruption of their permeability to ions and other molecules, which leads to the development of one or another pathology in the body. An example of such pathologies is the development of UV erythema of the skin, light burns of the eyes, etc.
The main physical difference between free radicals and other molecules is that free radicals are paramagnetic, i.e. have their own magnetic moment, while stable molecules do not have it, i.e. they are diamagnetic. It is this difference in magnetic properties that makes it possible to detect free radicals among diamagnetic molecules.
The main physical method for studying free radicals in biological systems is electron paramagnetic resonance(EPR). The EPR method has become widespread in biology and medicine precisely because of its ability to determine the presence and type of free radicals in biological systems in vivo, study the kinetics of biochemical reactions with their participation, etc.
It is very important that this method is non-invasive, harmless and allows you to study the processes occurring in living organisms without making any changes to these processes.
Fundamentals of electron paramagnetic resonance and its application to the study of free radicals. Nuclear magnetic resonance. Chemical shift. Fundamentals of NMR tomography.
Magnetic resonance
Selective absorption of electromagnetic waves of a certain frequency by a substance in a constant magnetic field, caused by the reorientation of the magnetic moments of nuclei, is called nuclear magnetic resonance.
NMR can be observed when the condition ( h = g I I IN , Where g I - nuclear Lande multiplier) only for free atomic nuclei. Experimental values of the resonant frequencies of nuclei found in atoms and molecules do not correspond to the condition. In this case, a “chemical shift” occurs, which arises as a result of the influence of a local magnetic field created inside the atom by electron currents induced by an external magnetic field. As a result of this “diamagnetic effect,” an additional magnetic field arises, the induction of which is proportional to the induction of the external magnetic field, but is opposite to it in direction. Therefore, the total effective magnetic field acting on the nucleus is characterized by induction IN ef = (1 ) IN , where is the screening constant, the order of magnitude is equal to 10 -6 and depends on the electronic environment of the nuclei.
It follows that for a given type of nuclei located in different environments (different molecules or different, non-equivalent places of the same molecule), resonance is observed at different frequencies. This determines the chemical shift. It depends on the nature of the chemical bond, the electronic structure of the molecules, the concentration of the substance, the type of solvent, temperature, etc.
If two or more nuclei in a molecule are shielded differently, that is, the nuclei in the molecule occupy chemically non-equivalent positions, then they have a different chemical shift. The NMR spectrum of such a molecule contains as many resonance lines as there are chemically non-equivalent groups of nuclei of a given type in it. The intensity of each line is proportional to the number of nuclei in a given group.
There are two types of NMR spectra:lines according to their width. Spectra of solidsbodies have a large width, and this aboutThe field of application of NMR is called NMRwide lines. In liquids, observingthere are narrow lines and this is called NMRhigh resolution.
Based on the chemical shift, number and position of spectral lines, the structure of molecules can be determined.
Chemists and biochemists widely use the NMR method to study the structure of the simplest molecules of inorganic substances to the most complex molecules of living objects. One of the advantages of this analysis is that it does not destroy the objects of study.
Introscopy – visual observation of objects or processes inside optical opaque bodies, in opaque bodies, in opaque media (substances).
The advantage of the NMR tomography method is its high sensitivity in imaging soft tissues, as well as high resolution, down to fractions of a millimeter. Unlike X-ray tomography, NMR tomography allows you to obtain an image of the object under study in any section.
Magnetic resonance- selective absorption of electromagnetic waves by a substance placed in a magnetic field.
Depending on the type of particles - carriers of the magnetic moment - there are electron paramagnetic resonance (EPR) Andnuclear magnetic resonance (NMR) .
EPR occurs in substances containing paramagnetic particles: molecules, atoms, ions, radicals that have a magnetic moment due to electrons. The Zeeman phenomenon that arises in this case is explained by the splitting of electronic levels. The most common EPR is on particles with a purely spin magnetic moment .
Ucondition of resonant energy absorption:
Magnetic resonance is observed if a particle is simultaneously exposed to a constant induction field IN cut and electromagnetic field with frequency . Resonant absorption can be detected two ways: either, with a constant frequency, smoothly change the magnetic induction, or, with a constant magnetic induction, smoothly change the frequency. Technically, the first option turns out to be more convenient.
The shape and intensity of the spectral lines observed in EPR are determined by the interaction of the magnetic moments of electrons, in particular spin ones, with each other, with the lattice of a solid, etc.
During electron paramagnetic resonance, along with the absorption of energy and an increase in the population of the upper sublevels, the reverse process also occurs - non-radiative transitions to the lower sublevels, the energy of the particle is transferred to the lattice.
The process of transferring energy from particles to a lattice is called spin-regrid relaxation, it is characterized by time .
The modern technique for measuring EPR is based on determining the change in any parameter of the system that occurs when electromagnetic energy is absorbed.
The device used for this purpose is called EPR spectrometer. It consists of the following main parts (Fig. 25.5): 1 - an electromagnet that creates a strong uniform magnetic field, the induction of which can vary smoothly; 2 - generator of microwave radiation of an electromagnetic field; 3 - a special “absorbing cell”, which concentrates the incident microwave radiation on the sample and makes it possible to detect the absorption of energy by the sample (cavity resonator); 4 - an electronic circuit that provides observation or recording of EPR spectra; 5 - sample; 6 - oscilloscope.
Modern EPR spectrometers use a frequency of about 10 GHz
One of the biomedical applications of the EPR method is the detection and study of free radicals. ESR is widely used to study photochemical processes, in particular photosynthesis. The carcinogenic activity of certain substances is studied. For sanitary and hygienic purposes, the EPR method is used to determine the concentration of radicals in the air.
Electron paramagnetic resonance (EPR) is the phenomenon of resonant absorption of electromagnetic radiation by a paramagnetic substance placed in a constant magnetic field. Caused by quantum transitions between magnetic sublevels of paramagnetic atoms and ions (Zeeman effect). EPR spectra are observed mainly in the ultrahigh frequency (microwave) range.
The electron paramagnetic resonance method makes it possible to evaluate the effects that appear in EPR spectra due to the presence of local magnetic fields. In turn, local magnetic fields reflect the picture of magnetic interactions in the system under study. Thus, the EPR spectroscopy method allows one to study both the structure of paramagnetic particles and the interaction of paramagnetic particles with the environment.
The EPR spectrometer is designed for recording spectra and measuring the parameters of the spectra of samples of paramagnetic substances in the liquid, solid or powder phase. It is used in the implementation of existing and development of new methods for studying substances using the EPR method in various fields of science, technology and healthcare: for example, to study the functional characteristics of biological fluids based on the spectra of spin probes introduced into them in medicine; to detect radicals and determine their concentration; in the study of intramolecular mobility in materials; in agriculture; in geology.
The basic device of the analyzer is a spectrometric unit - an electron paramagnetic resonance spectrometer (EPR spectrometer).
The analyzer provides the ability to study samples:
- with temperature regulators - sample temperature control systems (including in the temperature range from -188 to +50 ºС and at liquid nitrogen temperature);
- in cuvettes, ampoules, capillaries and tubes using automatic sample changing and dosing systems.
Features of the EPR spectrometer
A paramagnetic sample in a special cell (ampoule or capillary) is placed inside a working resonator located between the poles of the spectrometer electromagnet. Electromagnetic microwave radiation of constant frequency enters the resonator. The resonance condition is achieved by linearly changing the magnetic field strength. To increase the sensitivity and resolution of the analyzer, high-frequency magnetic field modulation is used.
When the magnetic field induction reaches a value characteristic of a given sample, resonant absorption of the energy of these vibrations occurs. The converted radiation then enters the detector. After detection, the signal is processed and sent to a recording device. High-frequency modulation and phase-sensitive detection convert the EPR signal into the first derivative of the absorption curve, in the form of which electron paramagnetic resonance spectra are recorded. Under these conditions, the integral EPR absorption line is also recorded. An example of the recorded resonant absorption spectrum is shown in the figure below.
INTRODUCTION……………………………………………………………………………….2
1. PRINCIPLE OF THE EPR METHOD…………………………………………………..3
1.1. History of the discovery of the EPR method………………………………………………………..3
1.2. Mechanical and magnetic moments of an electron…………………………4
1.3. Zeeman effect………….................................................. ...................................6
1.4. Basic equation of resonance……………………………………………………………8
2. CHARACTERISTICS OF EPR SPECTRA ………………………………….10
2.1. Signal amplitude, line shape and line width…………………….10
2.2. Ultrafine structure of EPR spectra………………………………….16
……………………………………………………………..18
3. DEVICE OF EPR RADIO SPECTROMETER……………………...22
4. APPLICATION OF EPR IN MEDICAL AND BIOLOGICAL RESEARCH……………………………………………………………………………….24
4.1. EPR signals observed in biological systems………………..24
4.2. Spin label and probe method……………………………………………………26
4.3. Spin trap method……………………………………………...35
CONCLUSION……………………………………………………………...39
LIST OF SOURCES USED………………………..40
INTRODUCTION
Electron paramagnetic resonance(EPR, electron spin resonance), the phenomenon of resonant absorption of electromagnetic radiation by paramagnetic particles placed in a constant magnetic field, caused by quantum transitions between magnetic sublevels of paramagnetic atoms and ions (Zeeman effect). OpenZavoisky Evgeniy Konstantinovich V Kazan State University in 1944
In the absence of a constant magnetic field H, the magnetic moments of unpaired electrons are directed arbitrarily, the state of the system of such particles is degenerate in energy. When a field H is applied, the projections of magnetic moments onto the direction of the field take on certain values and the degeneracy is removed (Zeeman effect), i.e., the energy level splits electrons E 0 .
Since at the lower level the number electrons more in accordance with the Boltzmann distribution, then resonant absorption of the energy of the alternating magnetic field (its magnetic component) will predominantly occur.
For continuous observation of energy absorption, the resonance condition is not enough, because When exposed to electromagnetic radiation, the populations of sublevels will equalize (saturation effect). To maintain the Boltzmann distribution of populations of sublevels, relaxation processes are necessary.
The main parameters of EPR spectra are the intensity, shape and width of the resonance lines , g-factor, fine and hyperfine structure constants (HFS).
1. PRINCIPLE OF THE EPR METHOD
1.1.History of the discovery of the EPR method
Electron paramagnetic resonance method (EPR, EPRelectron paramagnetic resonance, ESR electron spin resonance ) is the main method for studyingparamagnetic particles. To paramagnetic particles having important biologicalmeaning there are two main types these are free radicals and metal complexesvariable valency (such as Fe, Cu, Co, Ni, Mn).
The electron paramagnetic resonance method was discovered in 1944 by E.K. Zavoisky when studying the interaction of electromagnetic radiation in the microwave range with metal salts. He noticed that a CuCl2 single crystal placed in a constant magnetic field of 40 Gauss (4 mT) could absorb radiation with a frequency of about 133 MHz.
The pioneers of the use of EPR in biological research in the USSR were L.A. Blumenfeld and A.E. Kalmanson, who began to study free radicals of proteins obtained under the influence of ionizing radiation.
Over time, the synthesis of stable nitroxyl radicals has significantly expanded the scope of application of the EPR method in biological and medical research. Today this method is one of the widely used methods of modern science.
1.2. Mechanical and magnetic moments of an electron
The EPR method is based on the absorption of electromagnetic radiation in the radio range by unpaired electrons located in a magnetic field.
It is well known that an electron in an atom participates in orbital and spin motion, which can be characterized by corresponding mechanical and magnetic moments. Thus, the orbital magnetic moment is related to the mechanical expression
(1)
where is the magnetic orbital moment, and is the mechanical orbital moment. In turn, the mechanical orbital momentum can be expressed in terms of the orbital quantum number
(2)
Substituting expression (1.2) into (1.1) we obtain that
The quantity is an elementary magnetic moment and is called the Bohr magneton for an electron. It is designated by the letter β and is equal to 9.27·1024 J/T.
For the spin magnetic moment we can write similar expressions
(4)
(5)
(6)
where is the spin magnetic moment, PS mechanical magnetic moment, and s spin quantum number. It is important to note that the proportionality coefficient between and PS (e/m ) twice as much as for and Pl(e/2m).
As a result, the total magnetic moment of the electron, which is a vector, will be equal to the sum of the vectors of the orbital and spin magnetic moments
(7)
Since the absolute values of and can differ greatly, for the convenience of taking into account the contribution of the orbital and spin magnetic moments to the total magnetic moment of the electron, a proportionality coefficient is introduced, showing the share of eachmoments in the total magnetic moment magnitude g or g-factor.
where Pj total mechanical moment of the electron, equal to Pl + Ps. g -Factor is equal to one at s = 0 (i.e. in the absence of spin motion) and is equal to two if the orbital momentum is zero ( l = 0). g -The factor is identical to the Lande spectroscopic splitting factor and can be expressed in terms of full quantum numbers S, P and J:
where (9)
Since in most cases electron orbitals are very different from spherical ones, the orbital magnetic moment makes a relatively small contribution to the total magnetic moment. To simplify calculations, this contribution can be neglected. In addition, if we replace the spin mechanical moment with its projection onto a selected direction (for example, the direction of the magnetic field), then we obtain the following expression:
(10)
where eh/4πm Bohr magneton, and magnetic quantum number, which is the projection of the spin magnetic moment onto the selected direction and equal to ±1/2.
1 .3. Zeeman effect
Figure 1 Orientation of electrons in an external magnetic field ( H).
In the absence of an external magnetic field, the magnetic moments of electrons are randomly oriented (Fig. 1 left), and their energy is practically the same from each other (E0). When an external magnetic field is applied, the magnetic moments of the electrons are oriented in the field depending on the magnitude of the spin magnetic moment (Fig. 1. right), and their energy level is split into two (Fig. 2).
Figure 2 Splitting of energy levels of single electrons in a magnetic field (Zeeman effect).
The energy of interaction between the magnetic moment of an electron and a magnetic field is expressed by the equation
(11)
where μ the total magnetic moment of the electron, N magnetic field strength, and cos(μH) cosine of the angle between vectors μ and H.
In our case, the energy of interaction of an electron with an external magnetic field will be equal to
(12)
and the difference in energy between the two levels will be
(13)
Thus, the energy levels of electrons placed in a magnetic field are split in this field depending on the magnitude of the spin magnetic moment and the intensity of the magnetic field ( Zeeman effect).
1.4.Basic resonance equation
The number of electrons in the system under study, having one or another energy, will be determined in accordance with the Boltzmann distribution, namely
(14)
where and is the number of electrons at a higher or lower energy level corresponding to the magnetic moment of an electron with spin +1/2 or 1/2.
If an electromagnetic wave falls on a system of electrons located in a magnetic field, then at certain values of the energy of the incident quanta transitions of electrons between levels will occur.
A necessary condition is the equality of the energy of the incident quantum (hν) and the energy difference between the levels of electrons with different spins (gβH).
ΔE = hν = gβH (15)
This equation expresses the basic condition for the absorption of energy by electrons and is calledbasic resonance equation. Under the influence of radiation, electrons at a higher energy level will emit energy and return to a lower level, this phenomenon is called stimulated emission. Electrons located at the lower level will absorb energy and move to a higher level
energy level, this phenomenon is calledresonant absorption. Since the probabilities of single transitions between energy levels are equal, and the total probability of transitions is proportional to the number of electrons located at a given energy level, the absorption of energy will prevail over its emission. This is due to the fact that, as follows from the Boltzmann distribution, the population of the lower energy level is higher than the population of the upper energy level.
It should be remembered that the difference in energy levels of an electron in a magnetic field (as well as other charged particles with spin, for example, protons) is associated with the presence of an electron’s own magnetic moment. Paired electrons have compensated magnetic moments, and they do not respond to an external magnetic field, so ordinary molecules do not produce EPR signals. Thus, EPR makes it possible to detect and study the propertiesfree radicals(having an unpaired electron in the outer orbitals) and complexes of metals of variable valence (in which the unpaired electron belongs to deeper electron shells). These two groups of paramagnetic particles are often called paramagnetic centers.
2. CHARACTERISTICS OF EPR SPECTRA
The EPR method allows us to study the properties of paramagnetic centers through the absorption spectra of electromagnetic radiation by these particles. Knowing the characteristics of the spectra, one can judge the properties of paramagnetic particles. The main characteristics of spectra include amplitude, line width, line shape, g -factor and hyperfine structure of spectra.
2.1. Signal amplitude, line shape and line width
Signal amplitude
The EPR signal is the first derivative of the absorption spectrum (Fig. 3). The area under the absorption line is proportional to the concentration of paramagnetic particles in the sample. Thus, the concentration of paramagnetic centers is proportional to the first integral under the absorption line or the second integral of the EPR spectrum. If two signals have the same width, then the concentrations of paramagnetic centers are related as the amplitudes of the signals in the absorption spectra.
Figure 3 - EPR signal. Left dependence of microwave absorption on magnetic field strength (H); on the right is the first derivative of this dependence. EPR spectrometers record curves of the second type.
To determine the concentration, the areas under the absorption curve are measured for a comparison sample with a known concentration of paramagnetic centers and for the measured sample, and the unknown concentration is found from the proportion, provided that both samples have the same volume:
(16)
where and are the concentrations of the measured sample and the reference sample, respectively, and S x and S 0 area under the absorption lines of the measured signal and the reference sample.
To determine the area under the absorption line of an unknown signal, you can use the technique of numerical integration
(17)
where f "(H ) first derivative of the absorption line (EPR spectrum), F(H ) absorption line function, and H magnetic field strength.
(18)
Given that F(H). H at points -∞ and ∞ is equal to zero and dF (H) is equal to f "(H) dH, we get
(19)
where f "(H ) first derivative of the absorption line, or EPR spectrum. It is easy to go from an integral to an integral sum, given that H = nΔH, we get
(20)
where ΔH step of magnetic field change, and n i step number. Thus, the area under the absorption curve will be equal to the product of the square of the magnetic field step size and the sum of the products of the EPR spectrum amplitude and the step number. From expression (20) it is easy to see that for large n (i.e., far from the center of the signal), the contribution of distant parts of the spectrum can be quite large even at small values of the signal amplitude.
Line shape
Although, according to the basic resonance equation, absorption occurs only when the energy of the incident quantum is equal to the energy difference between the levels of unpaired electrons, the EPR spectrum is continuous in a certain vicinity of the resonance point. The function describing the EPR signal is called the line shape function. In dilute solutions, when the interaction between paramagnetic particles can be neglected, the absorption curve is described by the Lorentz function:
(21)
where function of the absorption curve at the resonance point, the field value at the resonance point, signal width at half maximum. Similar notation is used for the absorption curve described by the Gaussian function.
(22)
The Gaussian function is the envelope of the EPR spectrum if there is interaction between paramagnetic particles. Taking into account the shape of the line is especially important when determining the area under the absorption curve. As can be seen from the above formulas, the Lorentz line has a slower decrease and, accordingly, wider wings, which can give a significant error when integrating the spectrum.
Line width
The width of the EPR spectrum depends on the interaction of the magnetic moment of the electron with the magnetic moments of the surrounding nuclei (lattice) (spin-lattice interaction) and electrons (spin-spin interaction). In the absence of these interactions, the energy absorbed by the electrons would lead to a decrease in the difference in the population of levels and the cessation of absorption.
However, in the experiment, no change in the population difference between the levels is observed due to the fact that there are processes in which the absorbed energy is transferred to the environment and the electrons return to the original level. Such processes are called relaxation processes; they maintain a constant difference in the population of energy levels. The relaxation mechanism consists of transferring the electromagnetic energy of a quantum to the lattice or surrounding electrons and returning the electron to
low energy level. The time during which an electron remains at a high-energy level is called relaxation time. Accordingly, there is a spin-lattice time ( T 1) and spin-spin ( T 2) relaxation.
One of the reasons for the broadening of absorption bands in EPR signals lies in the wave properties of elementary particles, which are manifested in the existence of the well-known Heisenberg uncertainty relation principle. According to this principle, the more accurately the observation time is specified (the smaller Δ t ), the greater the uncertainty in the particle energy (:
(23)
If we accept that Δ t it's relaxation time T, and Δ E corresponds to g βΔ H , then we get that
(24)
those. the uncertainty in the linewidth is inversely proportional to the relaxation time. The observed relaxation time is considered to be the sum of the spin-lattice and spin-spin relaxation times.
(25)
Free radicals in solutions have T1>> T 2, therefore the line width will depend mainly on T2.
The “natural” broadening of the EPR signal, which depends on the spin-lattice and spin-spin relaxation times, is not the only mechanism affecting the linewidth c signaled. Also play an important roledipole-dipole interaction; anisotropy g -factor a; dynamic line broadening and spin exchange.
At the core dipole-dipole interactionlies the interaction of the magnetic moment of an unpaired electron with the local magnetic field created by neighboring electrons and nuclei. The magnetic field strength at the point where the unpaired electron is located depends on the relative orientation of the magnetic moments of the unpaired electron and another electron or nucleus and the distance between these centers. The change in energy of an unpaired electron is given by the equation
(26)
where μ the magnetic moment of the electron, θ the angle between interacting magnetic moments R the distance between them.
Contribution g-factor anisotropyThe broadening of the EPR line is due to the fact that the orbital motion of the electron creates a magnetic field with which the spin magnetic moment interacts. This creates a shift in the external field strength at which resonance is observed, i.e. to a shift in the position of the maximum of the EPR signal. In turn, this manifests itself in an apparent deviation g -free electron factor from a value of 2.00. On the other hand, the influence of the orbital magnetic field on the electron
depends on the orientation of the molecule with respect to the external magnetic field, which leads to a broadening of the EPR signal when measured in a system consisting of many randomly oriented molecules.
The broadening of the EPR signal may also be associated with the mutual transformation of two paramagnetic particles. So, if each of the particles has its own EPR spectrum, then an increase in the rate of mutual transformation into each other will lead to broadening of the lines, because At the same time, the lifetime of the radical in each state decreases. Such a changesignal width is calleddynamic broadening signal.
Spin exchange is another reason for the broadening of the EPR signal. The mechanism of signal broadening during spin exchange is to change the direction of the spin magnetic moment of an electron to the opposite when it collides with another unpaired electron or another paramagnet. Since such a collision reduces the lifetime of the electron in a given state, the EPR signal again broadens. The most common case of broadening of the EPR line by the spin exchange mechanism is the broadening of the signal in the presence of oxygen or paramagnetic metal ions.
2.2 Hyperfine structure of EPR spectra
The splitting of a single EPR line into several is based on the phenomenonhyperfine interaction, i.e., the interaction of the magnetic moments of unpaired electrons () with the magnetic moments of neighboring nuclei (
Figure 4 provides an explanation of hyperfine interaction. The unpaired electron in the radical can be located close to the proton, for example, as in the ethanol radical (1). In the absence of influence from nearby protons, the electron has a signal in the form of a single line (2). However, the proton also has a magnetic moment, which is oriented in the external magnetic field ( H 0) in two directions (along the field or against the field) because, like an electron, it has a spin number S = ½. Being a small magnet, the proton creates a magnetic field, which at the location of the electron has certain values +Hp or Hp depending on the orientation of the proton (3). As a result, the total magnetic field applied to the unpaired electron (4) has a value slightly greater (+ Hp) or slightly less ( Hp) than in the absence of a proton (). Therefore, the EPR signal of the radical consists of two bands, the distance from which to the previous center of the band is equal to Hp (5).
Figure 4. Ultrafine splitting of the EPR signal in the ethanol radical.
1 ethanol radical. 2 EPR signal of an electron in an external field. 3 orientation of protons in an external magnetic field. 4 increase or decrease in the field acting on the electron as a result of the imposition of the magnetic field of the proton ( H p) to an external magnetic field. 5 ESR signal of a radical, in which the magnetic field of a proton is superimposed on an external magnetic field.
In the example we considered, the spin of the nucleus interacting with the unpaired electron was equal to ± 1/2, which ultimately gave us splitting into two lines. This spin value is characteristic of protons. The nuclei of nitrogen atoms (N14) have a spin integer . It can take values ±1 and 0. In this case, when an unpaired electron interacts with the nucleus of a nitrogen atom, splitting into three identical lines will be observed, corresponding to the spin values +1, 1 and 0. In the general case, the number
lines in the EPR spectrum is 2 m N+1. (see below, Fig. 10)
Naturally, the number of unpaired electrons and, accordingly, the area under the EPR absorption curve do not depend on the value of the nuclear spin and are constant values. Consequently, when a single EPR signal is split into two or three, the intensity of each component will be 2 or 3 times lower, respectively.
A very similar picture arises if an unpaired electron interacts not with one, but with several equivalent (with the same hyperfine interaction constant) nuclei that have a non-zero magnetic moment, for example, two protons. In this case, three states arise corresponding to the orientation of the proton spins: (a) both along the field, (b) both against the field, and (c) one along the field and one against the field. Option (c) is twice as likely as (a) or (b) because can be done in two ways. As a result of this distribution of unpaired electrons, a single line will split into three with an intensity ratio of 1:2:1. In general, for n equivalent nuclei with spin mN the number of lines is equal to n 2 m N +1.
2.3. Properties of atoms with magnetic nuclei, constants, HFC of an unpaired electron with a nucleus
|
Atom |
Mass number |
Nuclear spin |
a x 10- 4 T |
|
|
99,98 |
||||
|
7,52 |
54,29 |
|||
|
92,48 |
143,37 |
|||
|
316,11 |
||||
|
93,26 |
82,38 |
|||
|
72,15 |
361,07 |
|||
|
27,85 |
1219,25 |
|||
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819,84 |
IN -electronic systems (most organic free radicals)spin densityat the nuclear point is equal to zero (nodal point of the p-orbital) and two mechanisms for the occurrence of HFI (spin transfer) are realized: configuration interaction and the superconjugation effect. The mechanism of configuration interaction is illustrated by considering the CH fragment (Fig. 5). When an unpaired electron , its magnetic field interacts with a pair of electrons -C H bonds so that their partial pairing occurs (spin polarization), resulting in proton negative appearsspin density, since interaction energies spins and are different. The condition shown in Fig. 5, a, more sustainable, since for carbon atom , carrying unpaired electron , in accordance with Hund's rule the maximum is realizedmultiplicity. For systems of this type, there is a connection between the STI constant and proton and spin densityon the corresponding carbon atom , determined by the McConnell relation: where Q = -28 x 10 -4 T, - spin density on the carbon atom . Spin transfer through the mechanism of configuration interaction is realized for aromatic protons and -protons in organic free radicals.
Figure 5 - Possible spin configurations for-orbital bonding hydrogen atom in the C H fragment, and p-orbitals carbon atom with spin a - spins on the bonding -orbitals and p-orbitals carbon atom parallel, b - the same backs antiparallel.
The effect of superconjugation is to directly overlap orbitals of an unpaired electron and magnetic nuclei. In particular, in alkyl radicals, according to this mechanism, HFC appears on the nuclei-protons. For example, in the ethyl radical-protons HFC is determined by configuration interaction, and on-protons - superconjugation. Equivalence of STV with three protons the methyl group in the case under consideration is due to the rapid rotation of the CH group 3 relative to the C C bond. In the absence of free rotation (or in the case of hindered rotation), which is realized in the liquid phase for many systems with branched alkyl substituents or in single-crystal samples, the HFC constant with-protons is determined by the expression, Where - dihedral angle between 2p z-orbital of the -carbon atom and CH bond, B 0 4 x 10 -4 T determines the contribution of the spin polarization along the nuclear core (configuration interaction), B 2 45 x 10 -4 Tl. In the limit of rapid rotation a n = 2.65 x 10- 3 T. In spectroscopy EPR of triplet states (S=1), in addition to electron-nuclear interactions (ITI), it is necessary to take into account the interaction of unpaired electrons together. It is determined by the dipole-dipole interaction, averaged to zero in the liquid phase and described by the zero splitting parameters D and E, which depend on the distance between the unsaved electrons (radical pairs), as well asexchange interaction(isotropic), due to direct overlap orbitals of unpaired electrons (spin exchange), which is described by the exchange integral J exchange . For diradicals , in which each of the radical centers has one magnetic nucleus with the HFC constant on this nucleus a, in the case of fast (strong) exchange J exchange oh, and every unpaired electron biradical system interacts with the magnetic nuclei of both radical centers. With weak exchange (J exchange a) the EPR spectra of each radical center are recorded independently, that is, a “mono-radical” picture is recorded. Dependency J exchange from temperature and solvent allows one to obtain the dynamic characteristics of a diradical system (frequency and energy barrier of spin exchange).
- EPR RADIO SPECTROMETER DEVICE
The design of an EPR radiospectrometer only vaguely resembles that of a spectrophotometer for measuring optical absorption in the visible and ultraviolet parts of the spectrum (Fig. 6).
Figure 6 EPR spectrometer device.
The radiation source in the radio spectrometer is a klystron, which is a radio tube that produces monochromatic radiation in the centimeter wavelength range.
The role of a diaphragm in a radio spectrometer is played by an attenuator, which allows dosing the power incident on the sample. The sample cell in a radiospectrometer is located in a special block called a resonator. The resonator is a hollow parallelepiped made of metal, the cavity of which has a cylindrical or rectangular shape. It contains an absorbing sample. The dimensions of the resonator are such that the incoming radiation forms a standing electromagnetic wave in it. An element completely absent from an optical spectrometer is an electromagnet, which creates a constant magnetic field necessary to split the energy levels of electrons. The radiation that passes through the sample being measured hits the detector, then the detector signal is amplified and recorded on a recorder or computer. The unique design of the radio spectrometer lies in the fact that radio radiation is transmitted from the source to the sample and then to the detector using special rectangular tubes that serve as waveguides. The cross-sectional dimensions of the waveguides are determined by the wavelength of the transmitted radiation. This feature of the transmission of radio radiation through waveguides determines the fact that to record the EPR spectrum in a radio spectrometer, a constant radiation frequency is used, and the resonance condition is achieved by changing the magnetic field value.
Another important feature of the radio spectrometer is that this device does not measure absorption (A) of electromagnetic (microwave) waves, but the first derivative of absorption with respect to the magnetic field strength dA/dH. The fact is that to measure absorption, it is necessary to compare the intensities of transmitted radiation from the measured and control objects (say, an empty cuvette), but when measuring the first derivative, a control object is not needed. When the magnetic field changes, the intensity of microwave waves passing through empty space or a non-absorbing object does not change and the first derivative of absorption is zero. If microwave waves pass through an object with paramagnetic centers, then absorption occurs, and its magnitude depends on the strength of the magnetic field. We change the field and the absorption changes, which manifests itself in a change in the intensity of the measured microwave oscillation. It is this change in the intensity of the measured microwave with a slight modulation of the magnetic field around a given value that makes it possible to determine dA/dH at each point H, thereby obtaining spectra, or ESR signals.
- APPLICATION OF EPR IN MEDICAL AND BIOLOGICAL RESEARCH
- EPR signals observed in biological systems
The use of the EPR method in biological research is associated with the study of two main types of paramagnetic centers - free radicals and metal ions of variable valence. The study of free radicals in biological systems is associated with the difficulty of low concentrations of free radicals formed during cell activity. According to various sources, the concentration of radicals in normally metabolizing cells is approximately M, while modern radio spectrometers make it possible to measure the concentration of radicals M. The concentration of free radicals can be increased by inhibiting their death or increasing the rate of their formation. Under experimental conditions, education
radicals are most easily observed when biological objects are irradiated at very low temperatures (say 77K) during their irradiation with UV or ionizing radiation. The study of the structure of radicals of more or less complex biologically important molecules obtained under such conditions was one of the first areas of application of the EPR method in biological research (Fig. 7). The second direction of application of the EPR method in biological research was the study of metals of variable valence and/or their complexes that exist in vivo . Due to the short relaxation times, the EPR signals of metalloproteins can also only be observed at low temperatures, for example, the temperature of liquid nitrogen or even helium.
Figure 7 - ESR spectra of UV-irradiated cysteine at liquid nitrogen temperature (77 K) and ordinary temperature (300 K).
As an example in Fig. Figure 8 shows the EPR spectrum of a rat liver. On it you can see the signals of cytochrome P-450, which have g -factor 1.94 and 2.25, methemoglobin signal with g - factor 4.3 and free radical signal belonging to semiquinone radicals of ascorbic acid and flavins with g-factor 2.00.
Figure 8 - EPR spectrum of rat liver.
However, EPR signals of some radicals can also be observed at room temperature. Such signals include the EPR signals of many semiquinone or phenoxyl radicals, such as the semiquinone radical of ubiquinone, the phenoxyl and semiquinone radical of α-tocopherol (vitamin E), vitamin D, and many others (Fig. 9).
Figure 9 - EPR signals of semiquinone and phenoxyl radicals.
- Spin label and probe method
An important stage in the development of the use of the EPR method in biological research was the synthesis of stable free radicals. Among such radicals, nitroxyl radicals are the most popular.
The stability of nitroxyl radicals is due to the spatial screening of the NO group. , having an unpaired electron, four methyl groups that prevent the reaction involving free valence. However, such shielding is not absolute and the reaction of reduction of free valence can still occur. Ascorbic acid, for example, is a good reducer of nitroxyl radicals.
The EPR spectrum of nitroxyl radicals usually consists of three lines of equal intensity, due to the interaction of the unpaired electron with the nucleus of the nitrogen atom (Fig. 10).
Figure 10 - Formula and EPR spectrum of the nitroxide radical 2,2,6,6-
tetramethyl-piperidine-1-oxyl (TEMPO).
Let us leave aside the complicated theory that explains the dependence of the EPR signal shape on the mobility of the probe and limit ourselves to a very schematic presentation of what is observed in experiments. If the nitroxyl radical is in an aqueous solution, then its rotation is isotropic and quite fast, and an EPR signal consisting of three narrow symmetrical lines is observed (Fig. 11, top). As the rotation speed decreases, a broadening of the lines and a change in the amplitude of the spectrum components is observed (Fig. 11, middle). A further increase in the viscosity of the medium leads to an even greater change in the EPR signal of the spin probe (Fig. 11, bottom).
To quantitatively describe the rotational motion of a radical, the concept of rotational correlation time (τс) is used. It is equal to the time of rotation of the nitroxide radical through an angle π/2. Based on the analysis of the EPR signal, the correlation time can be estimated using the empirical equation
(27)
Where Δ is the bandwidth of the EPR spectrum at a low field value, and is the intensity of the high-field and low-field components of the EPR spectrum. This equation can be used for correlation times from 5 to s.
The synthesis of stable nitroxyl radicals of the TEMPO family was an important step in the use of the EPR method to study the internal viscosity of biological membranes and proteins to solve biomedical problems.
Figure 11 - ESR spectrum of TEMPO at different rotational correlation times τс (numbers to the left of the spectra).
However, TEMPO derivatives, unfortunately, have one significant drawback - due to their amphiphilicity, it is difficult to determine the localization of this probe and thus answer the question of where we, in fact, determine microviscosity. This problem was practically solved when so-called “fatty acid spin probes” appeared, i.e. compounds in which a nitroxide radical molecule has been covalently attached to a fatty acid molecule. In this case, the ESR spectrum undoubtedly reflects the properties of the hydrophobic (lipid) phase of the system under study, into which the probe is inserted. Figure 12 shows the schematic structure of the fatty acid spin probe molecule, 5-doxyl stearate, in which the nitroxyl radical (doxyl, a compound structurally related to TEMPO) is attached to the 5th carbon atom of the stearic acid molecule. The motion of such a probe is characterized by a quantity called the order parameter S , which characterizes the degree of asymmetry of the probe’s rotation relative to the longitudinal and transverse axes of its molecule. The order parameter can be found from the characteristics of the EPR spectrum using the empirical equation
(28)
where A|| and A⊥ parameters shown in the figure. Theoretically, the order parameter can vary from 0 to 1, with changes in the viscosity and structure of the membrane. With completely symmetrical rotation, when the rotation speed around three axes is the same (which is typical for spherical particles in an isotropic medium), the order parameter is zero. The ordering parameter is equal to 1 if the axis of rotation of the probe coincides with the normal to the membrane, and rotation relative to other axes is completely absent. At low temperatures or in membranes made of synthetic saturated phospholipids, the probe rotates predominantly around the long axis of the molecule, oriented across the membrane. In this case, the order parameter has high values. As the viscosity of the membrane decreases, the value of the order parameter decreases.
Figure 12 Chemical formula and ESR spectrum of 5 doxyl stearate.
A very valuable quality of spin probes containing a fatty acid is the ability to measure the order parameter at different distances from the membrane surface, the so-called order profile or viscosity profile. To do this, they use a set of spin probes, which are molecules of the same fatty acid that contain a nitroxyl moiety at different distances from the carboxyl group. For example, spin probes with a nitroxide radical at the 5, 7, 12 and 16 carbon atoms of stearic acid are used. A set of these connections makes it possible to measure the parameter S at distances of 3.5, 5, 8.5 and 10.5 angstroms from the membrane surface (Fig. 13).
Figure 13—Change in the EPR signal upon removal of the nitroxide radical from the polar carboxyl group of the fatty acid.
Typically, the EPR spectra of a spin probe embedded in a membrane and a probe located in the surrounding aqueous solution can differ significantly. This property has been exploited to create a new class of spin probes that can measure membrane interfacial potential (often called surface potential). To measure this potential, the water/membrane distribution coefficient of the neutral and charged probes is measured. Since a charged probe interacts with charges located on the surface of the membrane, its distribution coefficient will differ from that of a neutral probe. The ratio of the distribution coefficients serves as a measure of the surface potential of the membrane being studied. The chemical formula of the spin probe used to measure the surface potential is shown in Fig. 14.
Figure 14 - Chemical formula of a charged spin probe.
Another important application of the spin probe method is the measurement of pH in microvolumes, for example, inside lysosomes or phagosomes of cells. For these purposes, special pH-sensitive spin probes are used (Fig. 15). The pH measurement method using spin probes is based on the ability of the probe to produce different EPR spectra in
protonated and deprotonated forms. Thus, depending on the pK of the spin probe, there is a certain pH range in which its protonation occurs and the corresponding change in the EPR spectrum occurs (Fig. 16).
Figure 15 - Chemical formulas of a pH-sensitive spin probe.
Figure 16 - ESR spectra and the dependence of the concentration of a deprotonated pH-sensitive spin probe on pH
Everything that has been discussed so far in this section concernsspin probe method. However, no less interesting isspin label method. The spin label method is based on the same principle of changing the EPR spectrum of a nitroxide radical depending on the speed and isotropy of its rotation. The difference between the method is the fact that the spin label is covalently bonded to another more or less large
molecule.
One of the first and successful applications of the spin label method was to measure the number and accessibility of protein SH groups (Fig. 17). The chemical formula and EPR spectrum of the spin label interacting with sulfhydryl groups in the free state and after attachment to the protein are shown in Fig. 18.
Figure 17 - Scheme of interaction of a spin probe with the thiol group of a protein.
It can be seen from the figure that the EPR spectra of the spin label in the free and bound states are very different, which is due to the difference in the speed and direction of rotation. Naturally, a bound spin label has a significantly lower rotation speed than in a free form. Moreover, the number of associated spin labels and, accordingly, the intensity of the EPR signal are proportional to the number
sulfhydryl groups reacted with the spin label, which makes it possible to determine not only the mobility of the probe, but also its quantity.
Figure 18 - Chemical formula of the spin label for SH groups and EPR spectra of the immobilized (1), bound (2) and free (3) spin label.
Currently, there are many methodological techniques that make it possible to study the topography of a protein globule using spin labels. Since many metal ions of variable valency are paramagnetic and, in addition, can be located in the active center of the enzyme, the interaction of a spin label attached, for example, to a cysteine or histidine residue of a protein globule, with a metal ion will lead to a broadening of the ESR spectrum as a result of dipole-dipole interaction paramagnetic
- Spin trap method
The appearance of nitroxyl radicals turned out to be a decisive event in solving the problem of detecting and studying free radicals formed in living systems. The detection of radicals was made possible thanks to the advent of the method
spin traps. The essence of the method is that some compound that is not a nitroxyl radical, but has a structure close to the nitroxyl radical (spin trap), interacts with a free, short-lived radical and is converted into a long-lived nitroxyl radical ( spin adduct ), the ESR spectrum of which is unique for a given radical or family of radicals.
Based on their chemical nature, spin traps can be classified into two main classes: nitrones and nitroso compounds. Nitrones include the two most popular spin traps: C-phenyl-N-tert-butyl nitrone (PBN) and 5,5-dimethyl-pyrroline-1-oxyl (DMPO). The reaction between PBN and a radical is as follows:
Stability of the resulting nitroxyl radical FBN (spin adduct) is explained by the fact that the oxygen atom, on which the unpaired electron is localized, is spatially shielded by three methyl groups. The spin adduct of the radical has a unique EPR spectrum (see Fig. 19). In this case, the shape of the EPR spectra of spin adducts depends on the nature of the added free radical. Thus, it is possible to study free radical reactions in biological objects using the EPR method at physiological temperatures.
Figure 19 - EPR spectrum of a spin adduct and values of hyperfine splitting constants for some radicals.
aH and aN constants of hyperfine splitting on the proton and nitrogen atom, respectively
Figure 20 Scheme of the DMPO and OH radical trap reaction.
In Fig. Figure 20 shows the reaction of another spin trap, DMPO, with a hydroxyl radical and the formation of a spin adduct of this radical. Again, by measuring the hyperfine splitting constants of the spin adduct spectrum, a short-lived radical can be identified.
The spin trap method occupies one of the most important places in biomedical research, because allows you to detect and identify radicals formed in living cells and tissues. Among such radicals, superoxide and hydroxyl radicals, as well as nitric oxide, should be noted. In addition, the use of the spin trap method makes it possible to study the antioxidant properties of substances and the amount of antioxidant reserve.
CONCLUSION
The electron paramagnetic resonance (EPR) method is based on the interaction of a substance with a magnetic field. As the name of the method suggests, it is used to study paramagnetic particles.
It is known that when paramagnetic materials are placed in a magnetic field, the paramagnetic material is drawn into this field. This is due to the presence of magnetic moments in paramagnetic materials. Magnetic moments are created by unpaired electrons.
Examples of paramagnetic particles of interest to biologists are free radicals, which are intermediate products of biochemical reactions, and metal ions of variable valence, such as iron, copper, manganese, etc.
The manifestation of a magnetic moment in an electron is due to the fact that the electron is a charged particle, and when the electron rotates around its axis (spin motion), a magnetic field appears directed along the axis of rotation. When a paramagnetic sample is placed in a magnetic field, the magnetic moments of unpaired electrons are oriented in this
field, similar to what happens with magnetic needles.
The magnetic moment of an unpaired electron in an external magnetic field can be oriented in two ways - along the field and against the field. Thus, if there are unpaired electrons in the system under study, the application of an external magnetic field leads to the separation of electrons into groups: the magnetic moments of some electrons are oriented along the field, while others are oriented against it.
LIST OF SOURCES USED
- D. Ingram Electron paramagnetic resonance in biology [Text]. Publishing house "Mir", 1972.
- Free radicals in biological systems [Text]. vol.1, art.88-175, 178-226. Publishing house "Mir", 1979.
3. J. Wertz and J. Bolton, Theory and practical applications of the EPR method [Text], Moscow: Mir, 1975.
4. Modern methods of biophysical research [Text]. Workshop on biophysics, edited by A.B. Rubina, Moscow: Higher School, 1988.
5. Spin label method [Text]. Theory and application, edited by L. Berliner, Moscow: Mir, 1979.
6. A.N. Kuznetsov, Spin probe method, Moscow [Text]: Nauka, 1976.
7. V.E. Zubarev, Spin trap method, Moscow [Text]: Moscow State University Publishing House, 1984.
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