Background

Introduction to protein fluorescence

Protein fluorescence
TRP Residue Proteins are the most extensively studied naturally fluorescent molecules. There are 3 emitting residues in proteins: tryptophan (Trp), tyrosine Tyr) and phenylalanine (Phe). The illumination of proteins at wavelengths 295-305 nm allows for the selective excitation of only Trp residues. The fluorescence parameters of tryptophan residues, in contrast to tyrosine and phenylalanine residues, are sensitive to the environment (environment-sensitive fluorophores). The main reason for this is the large redistribution of electron density in the asymmetric indole ring of the Trp residue (Figure 1) after the absorption of photons. There is no redistribution of electron density in Phe and practically no redistribution in Tyr residues because their side chains are symmetric rings (Teale and Weber, 1958; Teale, 1960; Weber, 1960; Konev, 1967; Longworth, 1971; Burstein, 1976, 1977; Lakowicz, 1983, 1999, 2006; Demchenko, 1986). The quantum-mechanical studies showed that much electron density is lost from Nε1 and Cγ atoms and is deposited at the Cε3, Cζ2, and Cδ2 atoms of the indole ring during excitation (10-15 sec) in the main fluorescent state 1La (Callis, 1997). This leads to a big increase in indole dipole moment in the excited 1La compared with the ground state (by up to >10 D in water) and creates a local non-equilibrium in the surrounding Trp environment (Konev, 1967; Burstein, 1976; Muiño and Callis, 1994; Pierce and Boxer, 1995; Callis, 1997). Depending on the physical and structural properties of the environment of tryptophan residues in proteins, various combinations of specific and universal interactions could occur during the lifetime of the excited state (nanoseconds), which affect the fluorescence properties.

Fluorescence spectra
The steady-state tryptophan fluorescence spectrum is one of the most widely used spectral properties for the study protein structure and conformation. This spectral parameter is easy to record on any spectrofluorometer. The shape and maximum position of the fluorescence spectrum (λmax) are energetic parameters that reflect the changes in the energetic gap between the excited (S1 or S1’) and ground (S0) states (Figure 2). The absorption of photons results in electron transition from the ground to the excited state (Terenin, 1967; Turro et al., 2004). The fluorescence is an electron transition from the excited state back to the ground state accompanied with the emission of photons. Depending on the environment of tryptophan fluorophores in proteins, different combination of specific and universal interactions can occur in the excited state, which leads to the changes in the level of the excited state, and as a result, changes in energetic gap between the excited and ground states. Therefore, the steady-state fluorescence spectrum should reflect the changes in environment of tryptophan fluorophores in proteins.

Mechanism of tryptophan spectral shift
TRP ResidueDepending on how polar and flexible the Trp environment is and what is its chemical nature, the environment would react differently to the redistribution of electron density in the indole ring. As a result, different interactions (universal or specific) might happen in the excited state, which would lead to different spectral response of the tryptophan fluorophores. Indeed, tryptophan residues can emit from 308 to 352 nm (Figure 3) depending on the environmental properties in the protein (Burstein et al., 1973; Burstein, 1977; 1983; Burstein et al., 2001; Lakowicz, 1999; 2006). A universal interaction is a dipole-dipole relaxation (reorientation) of protein groups or solvent molecules around a tryptophan fluorophore in response to the redistribution of electron density in the indole ring after photon absorption. The process occurs in nanosecond time scale or faster. These interactions play an essential role in the shift of the fluorescence spectra to longer wavelengths (Mataga et al., 1955, 1956; Lippert, 1957; Bilot and Kawski, 1962; Liptay, 1965; Mazurenko and Bakhshiev. 1970; Bakhshiev, 1972; Vincent et al., 1995, 1997; Toptygin and Brand, 2000, Lakowicz, 2000; Toptygin, 2003; Nilsson and Halle, 2005). The magnitude of the shift (Δν is the difference between wavenumber of the absorption and fluorescence) depends on several factors: i) the differences between dipole moment of the excited and ground states (Δμ=ΔE -ΔG); ii) dielectric constant (ε) and refractive index (n) of environment; and iii) time of dipole relaxation of Trp surrounding dielectric ( τR) in comparison with the lifetime of fluorescence ( τF), which is several nanoseconds. The fluorescence shift could be described by the modified Lippert equation:

Lippert Equation

As we mentioned above Tyr and Phe fluorescences are not sensitive for environment, since Δμ is about zero for these fluorophores and therefore, they are not informative to probe protein structure. So, the shift of position of the maximum of fluorescence spectrum would depend on how polar and flexible the Trp environment is. The biggest problem in the interpretation of protein fluorescence spectra lies in the anisotropic nature of proteins. The dielectric constant could vary in range from 80 (in water) to 5-10 inside protein matrix. Also the flexibility of the tryptophan environment in protein and water could be very different. For example, the time of dipole relaxation of water is of the order of femto-, pico-seconds, and therefore the tryptophan spectrum in water shifts to its final position (observed in steady-state measurements) during picoseconds (Shen and Knutson, 2001). However, the time of dipole relaxation of the residues inside a protein could be slower than nanoseconds (Nilsson and Halle, 2005; Xu et al., 2006).

The fluorescence shift cannot be explained only by solvent effect. When we say “solvent effect” we are considering the solvent as a medium with particular properties of electronic polarizability (refractive index) and molecular polarizability (dielectric constant). In fact, fluorophores could also have specific interactions with their local environment. These interactions can be due to the formation of weak hydrogen bonds in the excited state between fluorophore atoms and neighbor atoms or charge-transfer reactions (Lumry and Hershbergerg, 1978; Hershberger et al., 1981; Kavarnos and Turro. 1986; Lakowicz, 1999, 200, 2006; Maciejewski et al., 2003; Sengupta and Basu. 2004; Xie et al., 2005; Stalin and Rajendiran, 2005). In contrast to universal interactions, specific interactions are produced by just one or few groups interacting with fluorophores and also lead to the significant shift of emission spectra. For instance, in the nonpolar solvent cyclohexane, the indole displays a structured emission (Gryczynski et al., 1988). Addition of a small amount of ethanol (1-5%) results in a loss of the structured emission. This amount of ethanol is too small to change the solvent polarity significantly and cause a spectral shift due to general solvent effects (Gryczynski et al., 1988). The spectral shift seen in the presence of a small amount of ethanol is due to H-bonding of ethanol to the Nε1 atom of indole fluorophores. Such specific solvent effects occur for many fluorophores and should be considered when interpreting the emission spectra.

Time-resolved emission spectra
Depending on the environment, tryptophan residues exhibit various values of Stokes’ shift ranging from 15 to 50 nm. Time-dependent spectral shifts are usually studied by measuring of the time-resolved emission spectra (TRES), which are characterized by changes of center of gravity (Δcg) and spectral half-width (Δν) in time (Lakowicz, 1999; 2000; 2006). Examination of time dependent behavior of these two parameters could reveal the nature of the fluorescence shift (Easter et al., 1976; Badea and Brand, 1979; Vekshin et al., 1992; Vincent et al., 1997; Nanda and Brand, 2000; Peon et al., 2002). However, because of the rapid rates of spectral relaxation, it is difficult to measure protein TRES in aqueous solution at room temperature. Just a portion of tryptophan large Stokes’ shift in water could be observed in nanosecond dynamics (Shen and Knutson, 2001). Most of the shift is completed before the fastest photomultiplier tube (several picosecond) can detect it. These days the study of subpicosecond tryptophan dynamics (<100ps) has become a reality due to the great progress in the development of new ultrafast optical instruments. The use of ultrafast technique permits recording of time-resolved emission spectra in femto-pico second time interval (Peon et al., 2002; Xu et al., 2006).

Model of discrete states

Depending on the environment of tryptophan residues in proteins, the maximum position (λm) and quantum yield (q) of tryptophan fluorescence could vary widely - from 308 nm to 353 nm and from 0.4 to immeasurably low, respectively.

In 1967 Konev put forward the hypothesis of the existence of two main classes of tryptophan residues in proteins, which posses discrete values of fluorescent parameters λm and q (Konev, 1967; Volotovski and Konev, 1967). One of the classes included tryptophan fluorophores inside the protein in a low-polar hydrophobic environment with a shorter-wavelength position of fluorescent maximum (λm of ca. 330 nm) and rather low quantum yield (0.04 to 0.07). The second class consisted of exposed tryptophan residues in a high-polar aqueous environment with long-wavelength position of spectra (λm of ca. 350 nm) and quantum yield equal or higher than that of free aqueous tryptophan (about 0.13 to 0.17). This hypothesis had been based on the observation that protein spectrum shifts toward 350-353 nm upon denaturation by urea, and toward 330-332 nm upon addition of anionic detergents in acidic solutions. However, this model could not explain the existence of proteins with a high quantum yield (for example, 0.20-0.27 for serum albumins (Longworth, 1971)) and intermediate spectral maximum positions (341.5 nm) for some single-tryptophan containing proteins, such as human serum albumin (Ivkova et al., 1971).

In 1973 Burstein with co-workers revised and extended Konev’s hypothesis of discrete classes of tryptophan residues in proteins and suggested a new model using some additional spectral parameters and approaches (Burstein et al., 1973). The spectral bandwidth at the half-maximal amplitude Δλ was taken as an additional parameter. The linear relationship was found between the values of Δλ and the maximum position λm for tryptophan and other C-3-substituted indole derivatives in solvents of various polarities. These spectra could be regarded as a series of ‘elementary’ components representing the emission bands of individual tryptophan residues in proteins. Existence of a spectral shift accompanying the quenching of protein fluorescence by ionic solutes (NO3-, I-, Cs+) indicated on the multicomponent character of a protein emission spectrum. It was demonstrated that the spectra of proteins, which are shifted upon quenching, possess Δλ values exceeding those of ‘elementary’ components. The analysis of the differences between initial spectra of such proteins and those after 20%-quenching revealed that the best-quenched components have the longest-wavelength position at ca. 340 nm in native proteins, which is ca. 10 nm shorter than that postulated in the two-state model. However, the tryptophans in proteins denatured by urea or guanidinium chloride have a spectrum with λm of ca. 350 nm. These results allowed to develop an extended model of discrete states (classes) of tryptophan residues in proteins, which assumed the existence of five statistically most probable classes (Burstein et al., 1973; Burstein, 1977a; Burstein, 1983). According to the model, the following discrete classes of tryptophan residues were predicted to be most probable in proteins (Burstein, 1977b; 1983):

  1. class A (λm = 308 nm, structured spectra) - the fluorophores, which do not form hydrogen-bound complexes in the excited state (exciplexes) (Hershberger et al., 1981) with solvent or neighboring protein groups;
  2. class S (λm = 316 nm, structured spectra) includes the buried tryptophan residues that can form the exciplexes with 1:1 stoichiometry;
  3. class I (λm = 330-332 nm, Δλ = 48-50 nm) represents the buried fluorophores that can form the exciplexes with 2:1 stoichiometry;
  4. class II (λm = 340-342 nm, Δλ = 53-55 nm) represents the fluorophores exposed to the bound water possessing very long dipole relaxation time, which precludes the completing the relaxation-induced spectral shift during the excited state lifetime;
  5. class III (λm= 350-353 nm, Δλ = 59-61 nm) contains rather fully exposed fluorophores surrounded with highly mobile water completely relaxing during the excitation lifetime, which makes their spectra almost coinciding with those of free aqueous tryptophan;

At that time, there was constructed and used the calibrated diagram Δλ vs. λm for estimating the contributions of three most frequent model classes (I, II and III) of tryptophan residues in the fluorescence spectrum of a protein (Burstein et al., 1973). The application of this hypothesis was rather effective in the interpretation of protein tryptophan fluorescence data in various biophysical and molecular-biology studies. However, the idea of the existing of discrete classes of tryptophans in proteins was based on the analysis of very limited number of proteins. Later the hypothesis of discrete states was confirmed by analysis of spectral properties of proteins and structural parameters of environment of tryptophan residues.

Decomposition of fluorescence spectra

Complex nature of protein fluorescence spectra
The overwhelming majority of proteins contain more than one fluorophore and therefore exhibit smooth spectra that contain more than one component. The multicomponent nature of protein spectra makes their unequivocal interpretation difficult.

Decomposition algorithms
Here we would like to mention briefly two known methods for the decomposition of steady-state fluorescence spectra. The first approach implements the time- (Wahl and Auchet, 1972; Brochon et al., 1977; Knutson et al., 1982) or frequency-domain methods (Lakowicz and Cherek, 1981a, b; Wasylewski and Eftink, 1987) for the resolution of fluorescence spectra. The methods are based on lifetime measurements.

The other approach is based on an iterative non-linear-squares analysis of Stern-Volmer quenching plots (Stryjewski and Wasylewski, 1986; Wasylewski et al., 1988; Koloczek et al., 1991; Burstein, 1996). The method is based on the fact that the fluorescence of tryptophan residues can be quenched by external low molecular weight molecules, such as acrylamide, iodide and cesium ions (Lehrer, 1967, 1971, 1978, Eftink and Ghiron, 1977; Eftink, 1991). The probability of fluorescence quenching depends on the rate of collision of the quencher and fluorophore. In other words, the emission of tryptophan fluorophores located on the surface of the protein molecule is expected to be quenched more effectively than the fluorescence of the Trp residues buried in the protein matrix, where the quencher has limited access. The dependence of the emission intensity on the quencher concentration [c] is given by the well-known Stern-Volmer equation:

where F0, F is the fluorescence intensity and τ0, τis the lifetime in the absence and presence of the quencher, respectively; Ksv is a Stern-Volmer constant. The significant limitation of this method lies in the fact that it can only resolve a spectrum into two components, corresponding to two classes of tryptophan residues (exposed and buried).

Log-normal function for the describing of spectral curves
The decomposition methods described above do not employ any analytical descriptions of the spectral curves. There were many attempts to describe spectral components by using various mathematical functions, such as the Gauss or Lorentz distribution (Siano and Metzler, 1969; Morozov and Bazhulina, 1989; Metzler et al., 1991; Djikanovic et al., 2006). However, the quadriparametric maximal amplitude, Im, position of the maximum, νm, and positions of half-maximal amplitudes,ν- and ν+; Figure 4) log-normal function proposed by Siano and Metzler (1969), was the best one for describing the absorption spectra of complex molecules and was later successfully used to resolve multicomponent absorption spectra, including those of biological systems (Metzler et al. 1972; 1985; 1991; Morozov and Bazhulina, 1989). The log-normal function used in its mirror-symmetric form has been shown to accurately describe fluorescence spectra as well (Burstein and Emelyanenko, 1996), and can be written as:


where Im is the maximal intensity; ν is the current wavenumber; ρ is the band asymmetry parameter:

a is the function limiting point position:

Burstein and Emelyanenko (1996) have obtained a very important result, they have been able to find experimentaly the existence of linear relationships between the positions of maximal (νm) and two half-maximal amplitudes (ν- and ν+) for a large series of monocomponent spectra of small tryptophan derivatives in various solvents:

These relations allow to reduce the number of unknown parameters from four (Im, νm, ν-,ν+) to two (Im, ν-). Such a significant reduction in the number of parameters is known to make a decomposition analysis much more unambiguous (Antipova-Korotaeva and Kazanova, 1971). By integrating this additional information and using the log-normal function for the description of the spectral components, we have developed two mathematically different algorithms for the decomposition of fluorescence spectra.

Decomposition algorithms
Mathematically, the problem of the decomposition of the fluorescence spectrum into elementary components is an inverse ill-posed problem --- problems of this class are common in spectral and image analysis (Tikhonov, 1963, 1987; Craig and Brown, 1986; Schafer and Sternin, 1997; Henn and Witsch, 2000). It is necessary to determine the parameters of the spectral components from the overall experimental spectrum, where the components are indirectly manifested. In general, the solution of problems of this class is unstable against slight variations in the input data (noise). Since the real input data are known approximately (i.e., with some experimental error), this instability results in an inevitable ambiguity of the solutions within the given accuracy. Often a stable solution is found by integrating some additional information (constraints) that allows to effectively reduce the complexity of the problem (Tikhonov, 1963; Hansen, 1989, 1990).

The following constrains were used for the decomposition of fluorescence spectra, which allowed to reduce the complexity of the system and find a stable solution:

1) The spectrum of an elementary component on the frequency (wave number) scale is described by a biparametric (maximal amplitude and position of the maximum) log-normal function (Eq. 3 and 4) (Burstein and Emelyanenko, 1996).

2) The shape and position of tryptophan emission spectra remain unchanged by quenching of fluorescence by small water-soluble quenchers (Lehrer 1971; Lehrer and Leavis, 1978). Thus, a series of spectra measured at various quencher concentrations represents a sum of spectral components, position and shape of which are constant at all quencher concentrations, while the spectral relative contributions (intensities) are changed.

3) The change in the amplitudes of individual components with quenching obeys the Stern-Volmer law (Eq. 2) (Burstein, 1977; Lehrer 1971; Lehrer and Leavis, 1978).

4) The number of experimental points under analysis greatly exceeds the number of parameters sought. This approach attenuates the effect of occasional noise (Aksenenko et al., 1989).

Using this information we have developed two methods for a sufficiently stable decomposition of complex tryptophan fluorescence spectra with an error not exceeding the experimental one (Burstein et al., 2001). Here we outline the main ideas behind these algorithms. The input to the algorithms is constituted by the tryptophan fluorescence spectra measured at different concentrations c(i) of the external fluorescence quenchers (acrylamide or I-, or Cs+, or NO3-). Since, under the different concentrations of the quenchers, the position and shape of the spectral components remain unchanged, while the relative contributions of the components change, the experimental spectra can be written as:

where i= 1,..., N is the number of spectra corresponding to the i-th quencher concentration, c(i); j = 1,..., M is the number of current frequency (wavenumber), ν(j); k = 1,..., L is the number of component determined by the position of its spectral maximum, νm(j)(k); F(i, j) is the experimental intensity of fluorescence on the wavenumber scale in the i-th spectrum at the j-th frequency ν(j); φ(k, j) is the value of the log-normal function (equation 3, 4) with a position of the maximum at νm(k) at current frequency ν(j) with unit maximal amplitude (at given k and j, this value is the same for any of the N spectra); I(k, i) is the maximal amplitude of the k-th component in the i-th spectrum.

In order to decompose the spectra into components, it is necessary to find the positions νm(k) and the maximal intensities I(k, i) of the log-normal spectral components from the set of experimental spectra F(i,j). However, Eq. 6 cannot be solved analytically because the log-normal function φ(k, j) is transcendental with respect to the unknown νm(k) (see Eq. 3). An approximate solution can be only found by fitting the νm(k) values.

SIMS algorithm (SImple fitting procedure using the root-Mean-Square criterion)
At each step of this process, the φ(k, j) are computed for a given νm(k) value, and then the corresponding I(k, i) values are determined analytically by solving the set of linear equations. It is very important to emphasis that the I(k, i) values are not fitted, they are calculated.

The fact, that individual components in protein fluorescence spectra are very broad and mutually overlapped, poses the severe limitations on the procedure of searching for a functional minimum. Attempts to use modern fast fitting methods revealed a strong dependence of solutions on the initial conditions. Therefore, the exhaustive enumeration of νm values is used (with successively diminishing steps from ca. 8 nm down to 0.1 nm) to avoid “trapping” in the local minima of the functional and, thus, to find the global minimum. It is especially important in the presence of experimental noise. This procedure does not significantly increase computational time. Moreover, it obviates the need to set any arbitrary initial conditions, which often leads to an erroneous result when solving the inverse ill-posed problem (Tikhonov and Arsenin, 1986). This notwithstanding, the results of decomposition of experimental and simulated multicomponent spectra showed that the typical experimental noise of about 0.5-1.5% does not permit a sufficiently reliable decomposition for more than three spectral components. Therefore, we will consider this limiting case with L ≤ 3 in describing the algorithm. Uni-, bi- and tri-component solutions are searched independently, in turn, for the set of experimental spectra. The tri-component solution is considered as a more general case.

With fixed νm(1),νm(2) and νm(3) values at current wavenumber j at each fitting step, the solution can be found on the basis of the minimal least-square formalism, i.e. when the S is minimal :

The unknowns are I(k, i). The j(k, j) values are calculated from Eq. 3 at givennm(k) and n(j)values. The criterion S is minimal when .

These conditions allow the construction of N sets of three equations:

or, after opening the brackets,

Transposing the summation over k and j in the left part, we can write down the whole set:

Since all the sums over j are known, we obtain N non-uniform sets (i = 1,...,N) of linear equations, where each set contains three equations and can be solved independently; the main determinant being the same for all N sets. These canonical sets of linear equations are then solved (i.e., the I(k, i) amplitudes are evaluated) using the routine Gauss method (Cramer’s Rule). An analogous algorithm was developed for the decomposition of individual emission spectrum without quenchers (the program SIMS-MONO (PKM program)). In this case, the set of equations is constructed using an expanded set of points of a single spectrum.

Then, at each step the sum of absolute values (modules) of residuals S (differences between calculated and experimental intensities) is determined:

and the parameter D, which characterizes the quality of accordance of spectral components quenching with the Stern-Volmer law, i.e.:

Here Rsdis the relative root-mean-square residual between the values determined by solving the Eq. 6c and the Y(k,i) values calculated from the linear equation of Stern-Volmer low (Eq. 1) rewritten in the form:

where a(i) is an activity of ionic quenchers that is calculated using values of concentrations c(i) (Hodgman et al., 1955). The resulting combined minimization criterion (functional) is used in the form:

A set of components, i.e. the values of spectral maxima positions nm and maximal amplitudes Im, corresponding to the global minimum of S1 is considered as the solution of Eq. 10. The algorithm of three-component decomposition can be, in principle, expanded over an arbitrary number of components.

The procedure of searching for a sufficient number of components describing a series of experimental spectra of a protein is carried out as follows. The experimental series of spectra is consecutively decomposed into one, two and three components. Since the experimental spectra are measured with a constant wavelength increment, each value set i.e. νm(1), νm(2) and νm(3)) on the frequency scale (νm(cm-1) = 107/λm(nm) is determined by exhaustion in the wavelength range from 300 to 370 nm with consecutive three-times shortening steps from 8.1 to 0.1 nm. The intensities on the frequency (Fν) and the wavelength (Fλ) scales are related as Fν = Fλ . λ2; hence the spectra of individual components are converted onto the wavelength scale and the maximum position of components (νm(k)) are presented on the wavelength scale (λm(k)).

To estimate the quality of decomposition, the relative RMS residual of theoretical and experimental spectra is expressed as a percentage of maximal amplitude Fm of the spectrum, measured in the absence of quencher:

Where D is determined with Eq 12a and



In order to choose among one-, two- or three-component solutions as the most reliable one, we used the discriminant Ds values (goodness of fit) equal to the product of the functional Ts by the number of components searched for, i.e. the number of parameters (L) varied under fitting:

Also the procedure of smoothing of experimental spectra is incorporated into decomposition algorithms. The fluorescence spectra might contain some points distorted by the Raman line, scattered Hg lines from the light source and/or by random noise. After each decomposition cycle, the intensity values differing by more that 2% from the theoretical ones were changed to be equal to latter. The smoothing cycles are repeated while such differences disappear, but the number of iterations does not exceed 10 in order to avoid an eventual distortion of the spectral shape.

PHREQ algorithm (PHase-plot-based REsolution using Quenchers)
The algorithm PHREQ is an analytical realization of a graphical representation of two-component decomposition of a set of protein-tryptophan fluorescence spectra measured at various concentrations of quencher. The method uses a quasi-phase representation of parameters characterizing the shape of fluorescence spectra that was already successfully applied to the analysis of protein structural transitions (Kaplanas et al., 1975; Permyakov et al., 1980a, 1980b).

In the most general case, in order to use any physical parameter P either to characterize the shape of a transition curve A→B (Figure 6) or to estimate the proportion of components in the mixture of A and B components, this parameter (P) should be linearly related to either the extent of transition completing (α) or the contribution of a mixture component into the total concentration.

where CA and CB are concentrations of A and B. Then, the composite parameter p; for the system can be expressed as:

Therefore, p is a weighted mean of values PA and PB, which characterize the pure A and B components, respectively. The weight factors are β = 1 - α and α, respectively.

A two-state transition or a mixture can be characterized by two mutually independent physical parameters P1 and P2 linearly related to α:


It can be simply shown that at the same a value parameters, P1 and P2 are linearly related:

where k and m are factors expressed through the values of PA1, PA2, PB1and PB2, and the plane with coordinates (P1, P2) is a phase-plane. In such a plane the states A and B are represented by points (PA1, PA2) and (PB1, PB2), respectively (Figure 7). The transition between A and B is reflected by the totality of phase-points, which should be on the straight line between points A and B. At any intermediate point Z with coordinates located on this line, a is proportional to the ratio of lengths of the segments between the points Z and A and segment between points A and B, i.e. α= AZ/AB. These simple relationships graphically determine the contributions of components A and B at any step of the transitions in two-component mixtures. In the case of transitions measured by kinetics or equilibrium shift, the deviation from linearity of trajectory AB, suggests the existence of one or more intermediate states in the process.

In the case of decomposition of fluorescence spectra, the “physical” state is a position and shape of spectral component, which remains unchanged under different concentration of fluorescence quenchers. However, added quenchers perturb “spectral” state, i.e. change the ratios of component contributions. The role of parameters P1 and P2 for two-component fluorescence spectra plays the emission intensities F(ν1) and F(ν2) measured at different wavenumbers ν1 and ν2. The parameters F(ν1) and F(ν2) reflect the contributions of α and β of two components into the total emission spectrum. In order to obtain the trajectory on the quasi-phase plane [F(ν1), F(ν2)] it is necessary to measure the spectra at various concentrations of fluorescence quenchers. The quencher will change intensities of two components in different degrees depending on solvent accessibility of fluorophore(s) from which a component originates, but do not affect the shape and maximum positions of spectral components.

In the ideal imaginary case, when the quenching does not change the total emission quantum yield, the points obtained at several quencher concentrations should lie on straight line on the quasi-phase plane [F(ν1), F(ν2)]. This line connects points, which represent “pure” spectral forms (“νm(1)” and “νm(2)” on Figure 8). The total spectrum is a sum of these two “pure” spectral forms. In reality, the quenching alters the total quantum yield. Therefore, to exclude perverted effects of quenchers on total quantum yield it is necessary to normalize F(ν1) and F(ν2) values by either total surface area under the spectrum or by emission intensity at any third, constant wavenumber νn, F(νn). Since the precise measurement of the area under an experimental spectrum is almost impossible, we used normalizing with F(νn):

The F(ν1), F(ν2) and F(νn) can be represented as the combinations of normalized log-normal functions (φ(νn(i), νj)) at wavenumbers ν1, ν2 and νn with maxima at F(ν1) and F(ν2) according to Eq. 6, i.e.:


Thus, Pn1 and Pn2 could be presented as:


where and are values of log- normal functions with unite maximal amplitudes (see Eqs. 3 and 4) and maximum positions νm(i)at current wavenumber νj. In such a representation, αmeans the contribution of the component with the maximum position at νm(1) in the normalizing fluorescence intensity at νn, F(νn) .


As well as in the case of P1 = F(ν1) and P2 = F(ν2), Pn1 and Pn2 are mutually linearly related (the equation that is analogous to Eq. 20:



Therefore, the spectra measured at various quencher concentrations are represented by points on the linear track on the quasi phase-plane [Fr(ν1), Fr(ν2)] (Figure 8). Thus, the phase-plot can be used for estimating the main parameters of two-component spectrum, i.e. νm(1) and νm(2) and their relative contributions α and (1- α). In order to estimate the components maxima positions νm(1) and νm(2) we used the extrapolation of the linear track through the experimental points, obtained with various quencher concentrations, up to its intersection with the curve “pure” Log-N, which corresponds to the totality of all possible normalized log-normal functions. From the distances between the experimental point and the points of νm(1) and νm(2), which are d2 and d1, respectively, the contributions of components can be calculated:


and

The limitation of PHREQ algorithm is a possibility for the decomposition into only 2 components. If the solution is a 2-component one the results of the PHREQ analysis correlates with high accuracy with the results of the SIMS algorithm. However, if the SIMS algorithm gives the 1-component or 3-components solutions as the best one, the results of PHREQ analysis could be ignored.

Structural parameters of environment of tryptophan residues in proteins

Algorithm for the calculation of structural parameters of tryptophan environments in proteins The above methods of spectral analysis allow to extract the fluorescence properties of individual tryptophan residues, thus creating the opportunity to investigate the spectral-structural relationship. The algorithm for the calculation of structural properties of the environment of tryptophan residues from the atomic structures of proteins from PDB was created. The algorithm is designed to:

  1. characterize the environment of tryptophan fluorophores in terms of variety of structural properties;
  2. reveal possible partners for H-bond formation from all atoms around tryptophan residue in protein;
  3. identify clusters of tryptophan residues, where the probability of energy transfer could be significant;
  4. reveal all possible quenching groups among neighbor protein atoms

Spherical coordinate systems for indole ring atoms
Since each atom of indole fluorophore may contribute differently in universal or specific interactions with environment, we estimated environment characteristics for every indolic atom. The parameters of environment of nine indole atoms of tryptophan residue were then averaged or summed to characterize the environment of the given fluorophore as whole. In order to describe the surrounding of each of nine atoms of indole ring independently, the spherical systems of coordinates is introduced (Figure 9, where ρ is the distance, φ is the azimuth and θ is the elevation) centered at each atom. In the microenvironment of fluorophore all neighboring atoms of protein and structure-defined solvent located in near and far layers from 0 to 5.5 Å and from 5.5 to 7.5 Å from an indole atoms, respectively, are included. The program outputs the complete lists of distances ( ρ) and orientations (φ and θ) of “polar” (nitrogen, oxygen and sulfur) and carbon atoms located in each layer.

Potential hydrogen-bonding partners

The most probable mechanism of the exciplexes formation between excited fluorophore and surrounding atoms is hydrogen bonding (Lumry and Hershbergerg, 1978;Hershberger et al., 1981). The potential hydrogen bond donors and acceptors are revealed from the neighboring polar groups around indole atoms. It is now accepted that hydrogen bonds are strictly directional in nature (Legon and Millen, 1987). According to the geometric criteria of hydrogen bond, cos(θ) must be near to 1 for the potential donors (main-chain nitrogen atoms; Sγ of Cys; Nε2 and Nδ1 of His; Nζ of Lys; Nδ2 of Asn; Nε2 of Gln; Nε, Nη1 and Nη2 of Arg; Oγ of Ser; Oγ1 of Thr; Oη of Tyr, Sγ of Cys); and cos(θ) and cos(φ) must be near to 0 and 1, respectively, for the potential acceptors (main-chain carbonyl oxygen; Oδ1 and Oδ2 of Asp and Asn; Sγ of Cys; Oε1 and Oε2 Glu and Gln; Nδ1 of His; Sγ of Met; Oγ of Ser; Oγ of Thr; Oη of Tyr) (McDonald and Thronton, 1994). We considered all atoms listed above as potential partners for hydrogen bonding if they were located within a cone with angles differing by less than ca. 20° from the ideal geometry of H-bonds, i. e. |cos(θ)|>0.9 for possible donors in near and far layers, and |cos(θ)| < 0.35 and cos(φ)> 0.9 for possible acceptors in near and far layers.

Solvent accessibility and environment packing density
As we mentioned previously, the dipole reorientational relaxation in polar environment during excitation lifetime (the universal interactions) may play essential role in the shift of fluorescence spectra to longer wavelengths (Mataga et al., 1955, 1956; Lippert, 1957; Bilot and Kawski, 1962; Liptay, 1965; Bakhshiev, 1972; Vincent et al., 1995, 1997; Toptygin and Brand, 2000). Such a relaxation-induced spectral shift is may be much effective for tryptophan fluorescence due to a very big increase in indole dipole moment in excited 1La comparing with ground state (by up to >10 D) (Konev, 1967; Burstein, 1976; Lakowicz, 1983; Muiño and Callis, 1994; Pierce and Boxer, 1995; Callis, 1997). Recent quantum-mechanical studies showed that much electron density is lost from Nε1 and Cγ atoms and deposited at Cε3, Cζ2, Cδ2 atoms of indole ring during excitation in main fluorescent 1La state (Callis, 1997). Therefore, the emission band of tryptophan fluorophores that are accessible to bulk water, possessing the high density of large and fast-relaxing dipoles, is expected to be shifted maximally to longer wavelengths. We estimated relative accessibility of each atom of indole moieties (especially, Nε1 and Cζ2 atoms) and accessibility of indole ring as whole using modified algorithm based on the Lee and Richards approach (1971). The relative accessibility is expressed as the per cent ratio of the accessible area of an atom in a protein for the 1.4 Å spherical probe to that in free tryptophan. The solvent environment surrounding a protein is generally divided into two types: bulk (free) water that is fluid and not bound to the protein and water that is either partially or strongly bound to protein (Edsall and McKenzie, 1983; Otting et al., 1991; Levitt and Park, 1993). The program, therefore, presents the accessibility of indole ring to the solvent in absence and in presence of bound water molecules, which are included in atomic coordinates in PDB files.

The packing density

The packing density, i.e. the number of neighbor atoms within the layers up to 5.5 Å or up to 7.5 Å around indole ring, reflects the degree of burying of fluorophore into protein matrix and/or the presence of hollow crevices in the structure. In compact structure the packing density may serve as an inverse measure of the accessibility. An example of hollow cavity that surrounds the completely buried Trp48 in azurin was proposed by Turoverov et al. (1984, 1985). The packing density of Trp48 is rather low comparing with other buried tryptophan residues.

The measure of relative polarity of microenvironment

The relative polarity of fluorophore microenvironment in two surrounding layers we expressed as:

where S1 and S2 are per-cent portion of atoms of polar groups amongst all atoms in near and far layers, respectively. Acc – is the accessibility of indole ring of tryptophan residue. For buried tryptophan residues, when accessibility (Acc) is about zero, the parameters A1 and A2 become equal to S1 and S2, respectively, e.g. the relative polarity of environment is determined by only the “polar” atoms. However, in cases of partially or completely accessible fluorophores, the values of parameters A1 and A2 increase and reflect the quantity of highly polar water nearby them.

Temperature factor and “dynamic accessibility” measure

The occurrence of fluorescence spectral shift due to dipole relaxation in surrounding dielectric (Mataga et al., 1955, 1956; Lippert, 1957; Bilot and Kawski, 1962; Liptay, 1965; Bakhshiev, 1972) critically depends on the ratio of the medium relaxation time to the fluorophore fluorescence lifetime (see Eq. 1) (Mazurenko, 1973; Mazurenko and Udaltsov, 1978). The relaxation of the large dipoles of bulk water is very fast (a few hundreds of femtoseconds), while the relaxation time of dipoles of protein groups and bound water can be much longer and may reach many nanoseconds (Callis, 1997). Therefore, it was important to estimate the parameters, which could reflect a relative mobility of polar groups around fluorophores. Protein crystallography provides such a parameter as crystallographic temperature factor for individual atoms (Debye-Waller factor or B-factor). Although temperature B-factors in principle measure both static or dynamic disorder of atomic position, they are often indistinguishable from a measure genuine vibration of the atom around its mean position (Frauenfelder et al., 1979; Glusker et al., 1994; Carugo and Argos, 1997). Usually, temperature factors are considered in relative or normalized form (Carugo and Argos, 1997, 1998). We used the temperature B-factors of “polar” atoms as normalized to the mean B-factor value of all Ca atoms in crystal structure within both near (B1) and far (B2) layers around indole atoms.

Parameters R1 and R2

To account for a common effect of both mobility of neighbor polar atoms of protein and free water around indole ring we introduced parameters R1 and R2 that may be considered as a measure of “dynamic accessibility” for the bulk water:

All parameters calculated from atomic structures are static ones and only B-factors (B1, B2) and “dynamic accessibility” (R1, R2) are kind of dynamic characteristics of microenvironment.

Eventual intramolecular fluorescence quenching and efficiency of the energy homo-transfer

Fluorescence of individual tryptophan residues might be partially or totally quenched by some protein groups (Cowgill, 1970; Bushueva et al., 1974, 1975; Burstein, 1977a, 1983; Willaert and Engelborghs, 1991; Chen and Barkley, 1998; Yuan et al., 1998) or due to resonance energy homo-transfer to other indole fluorophore(s) (Konev, 1967; Burstein, 1976). A detailed analysis of the distance and orientation of potentially quenching groups (cystein SH and S-S groups, histidine imidazole or imidazolium, arginine guanidinium, hydrated amides etc.) nearby indole moiety allowed us to predict eventual quenchers of tryptophan fluorescence. The probability of excitation energy homo-transfer was estimated using Förster equation with parameters taken from Dale and Eisinger (Dale and Eisinger, 1974) and orientation factors calculated from mutual orientation of transition moments of donors in 1La state and of acceptors in either 1Laor 1Lb states from atomic structure in cases when the centers of their indolic rings in proteins were separated by less than 12 Å.

Five spectral-structural classes of tryptophan residues in proteins

The analysis of spectral and structural characteristics of tryptophan residues in proteins allowed to reveal a general correlation between the spectral and structural properties. The tryptophan residues in proteins can be grouped into five discrete classes based on their spectral parameters, and that these classes exhibit statistically significant correlation with classes revealed by analysis of six structural properties of the environment of tryptophan residues. The parameters which posses high discriminatory power and correlation between spectral and structural properties was revealed by applying of multivariate statistical analysis: cluster, discriminant and canonical (Reshetnyak et al., 2001). Thus, the previously-proposed model of discrete states was confirmed. According to this model, tryptophan fluorophores belonging to various classes have different environments in proteins

Table 1. The five spectral and structural classes.

Spectral and structural parameters Class A Class S Class I Class II Class III
The wavelengths of the most probable spectral positions (nm) revealed from an analysis of the fluorescence spectra of 160 proteins 308 321-325 330-333 341-344 346-350
Acc (averaged value of the relative solvent accessibility of the nine atoms of indole ring of the tryptophan fluorophore.) 1.9 0.81.4 6.0±3.6 14.8±7.5 55.3±15.9
Acc1-7 (averaged value of the relative solvent accessibility of 1 and 7 atoms of the tryptophan fluorophore) 0.0 1.0±2.2 11.2±8.5 26.7±19.1 71.1±19.5
Den (packing density: the number of neighbor atoms at a distance < 7.5 Å from the indole ring) 138.3 148.3±8.5 129.3±9.1 109.3±12.6 62.7±18.8
A (relative polarity of environment: portion of the atoms of the polar groups amongst all the atoms around the tryptophan residue at a distance < 7.5Å) 23.5 34.5±5.8 39.3±5.5 45.1±7.4 65.5±13.9
B (B-factor: crystallographic B-factors of the atoms of the polar groups normalized to the mean B-factor value of all the Ca atoms in the crystal structure) 0.61 0.89±0.17 1.11±0.20 1.23±0.32 1.54±0.55
(“Dynamic accessibility” [R = Acc.B], a dynamic characteristic of the microenvironment) 0.9 0.7±1.2 6.7±4.0 18.2±10.3 85.2±30.9

Class A contains tryptophan fluorophores deeply buried in protein matrix with non-polar and non-flexible environment consisting mostly of atoms that involved in stabilization of elements of secondary structure of protein. No partners for H-bonding revealed for tryptophan residue of this class. As a result the emission of tryptophan residues of this class is structured and has extremely short-wavelength position of maximum (308 nm) with zero accessibility of fluorophores to quenchers of tryptophan fluorescence. There are no specific or universal interactions in the excited state of tryptophan fluorophores of this class.

Class S Tryptophan residues have very similar to the fluorophores of class A structural properties of environment: fluorophores also are deeply buried inside protein. The major difference between the structural properties of tryptophans of class A and S is higher polarity and flexibility of the microenvironment. Also, there are evident free partners for hydrogen bond formation nearby the fluorophores of class S. The spectral properties of tryptophan residues of class S is long-wavelength shifted to 322.5±4.5 nm. Weak dipole-dipole interactions and exciplexes with 1:1 stoichiometry might be formed in the excited state of fluorophores of class S.

Class I represents the fluorophores with the averaged maximum position of fluorescence at 331.0±4.8 nm, the average width of spectrum Δλ = 48-50 nm and the relative Stern-Volmer constant values of about 10%. The Nε1 and Cζ2 atoms of indole ring (where the most redistribution of electron density is occurred after absorption of photon (29)) are in contact with water-structured molecules. These atoms of indole ring could be good candidates for the formation of H-bonds in the excited state in 2:1 stoichiometry with surrounding protein or water molecules. The environment of tryptophan residues of class I have lowered packing density that may result in an increase in frequency and/or amplitude of structural mobility of the environment favoring both hydrogen-bonded exciplex formation and dipole relaxation during the lifetime of fluorophore excited state. However, we assume that the environment of tryptophan residues of class I is less flexible than water molecules and, therefore, time of dipole relaxation of environment is higher than the lifetime of fluorescence (ns), which precludes the completing the relaxation-induced spectral shift during the excited state lifetime.

Class II contains the fluorophores with the averaged maximum position of fluorescence at 342.3±3.3 nm, the average width of spectrum Δλ = 53-55 nm and the relative Stern-Volmer constant of 44%. The main feature of environment of tryptophan residues of this class is presence of the structured-water molecule near to indole ring. The time of dipole relaxation of structured-water is less than fluorescence lifetime, which result in dipole-dipole relation and exciplex formation in the excited state.

Class III Fluorophores of this class has spectral properties similar to the free tryptophan in solution: the averaged maximum position of fluorescence at 347.0±3.1 nm, average width of spectrum Δλ = 59-61 nm and relative Stern-Volmer constant of about 76%. Tryptophan residues of this class are fully exposed to highly mobile water molecules that are enable to complete relaxation during the excitation lifetime. As a result, the spectra position of tryptophan residues of class III almost coincide with those of free aqueous tryptophan.

Statistical classification analysis

The statistical classification analysis is used for the assignment of tryptophan residues to one of five spectral-structural classes. Two different approaches of the assignment such as calculation of i) classification scores and ii) probabilities of assignment are applied. Both approaches are very sensitive to a training set, which is used as a model for assignment of a new object (tryptophan residue) to spectral-structural classes. For the training set we choose proteins containing no more than 4 tryptophan fluorophores for which the assignment of tryptophan residues to spectral components was obvious and straightforward. 42 tryptophan fluorophores of 24 proteins were taken in the training set (see Table 2 and Table 3).

Table 2. List of protein in the training set, their codes, PDB-entries code and resolution, tryptophan residue position in protein sequence and assignment of tryptophan residues to spectral components.

  Protein Protein codes PDB-entries (resolution, Å ) Trp residue position λ m, nm
1-Tryptophan containing proteins
1 Albumin (human serum), N-form ASH.N 1AO6 (2.5); 1BJ5 (2.5) W214 344.8
2 L-Asparaginase (E. coli B) ASP.N 3ECA (2.4) W66 323.9
3 Azurin (Pseudomonas aeruginosa) AZU 1JOI (2.05); 4AZU (1.9) W48 307.9
4 Glucagon GLG 1GCN (3.0) W25 350.8
5 Protein G, streptococcal GPS 1IGD (1.1) W48 342.5
6 Telokin KRP, myosin light-chain kinase (chicken gizzard) KRP 1TLK (2.8) W75 332.4
7 Monellin (Dioscoreophyllum cummensii) MON 1MON (1.7) W3 340.3
8 Parvalbumin II (cod Gadus morrhua) Ca-form PAC.CA Model by M.Laberge W102 326.5
9 Parvalbumin (whiting Gadus merlangus) PAM 1A75 (1.9) W102 317.9
10 Phospholipase A2 (bovine pancreas) PLB 1UNE (1.5); 2BPP (1.8) W3 352.3
11 Phospholipase A2 (porcine pancreas) PLS 1P2P (2.6); 4P2P (2.4) W3 349.4
12 RNAse T1 (Aspergillus oryzae) RNT 9RNT (1.5) W59 325.1
13 Vipoxin, protein A (Vipera ammodytes ammodyes); high ionic strength (dimers) VTA.HIS 3D model by B.Atanasov W30 323.6
14 Vipoxin, protein A (Vipera ammodytes ammodyes); low ionic strength (monomers) VTA.LIS 1VPI (1.76) W31 349.1
2-Tryptophan containing proteins
15 a 1-Antitrypsin (human) A1AT 2PSI (2.9); 7API (3.0); 8API (3.1); 9API (3.0) W194 W238 324.4 340.1
16 Neurotoxin II (cobra Naja naja oxiana venom) NO2 1NOR (NMR) W27 W28 344.4
17 HIV-1 protease PRH.LIS 1HHP (2.7) W6 W42 345.4
18 HIV-1 protease complex with pepstatin PRH.PST 5HVP (2.0) W6 W42 344.9
3-Tryptophan containing proteins
19 Agglutinin (wheat germ) AWG 7WGA (2.0); 9WGA (1.8) W41 (Quenched) W107 W150 (349.9) 349.1 349.1
20 Ovalbumin (hen egg white) OVH.LIS 1OVA (1.95) W160 W194 W275 336.9 325.8 336.9
21 Phosphatase alkalaine (Escherichia coli) PHA 1ALK (2.0) W109 W220 W268 322.8 345.8 345.8
22 Vipoxin, complex protein A & protein B (Vipera ammodytes ammodyes) VTC 1AOK (2.0) W31 W220 (Quenched) W231 334.2 (334.2) 334.2
4-Tryptophan containing proteins
23 G-Actin (rabbit skeletal muscule) ACR.G 1ATN (2.8) W79 (quenched) W86 W340 W356 (332.8) 320.9 320.9 332.8
24 a -Lactalbumin (cow milk) LAB 1HFZ (2.3) W26 W60 W104 W118 322.4 338.3 322.4 3338.3

Table 3. Six structural parameters of environment of tryptophan residues of proteins from the training set.

Protein Acc Acc1-7 Den B R A
Class A
AZU W48 0.001 0 167 0.61 0.00123.45
AZU W48* 0 0.0001 168 0.5 0 24
Class S
ASP.N W66 1.78 7.15 147 0.75 1.35 38.25
PAC.CA W102 0 0 141 0.875 0 21.9
RNT W59 0 0 154 1.01 0 33.9
AX6 W343 0 0 154 0.88 0 34.5
OVH,LIS W194 4.38 2.01 144.3 0.675 2.9 38
PHA W109 0.23 1.045 154.5 0.545 0.11 34.9
VTA.HIS W30 1.66 3.125 136.8 0.825 1.37 33.4
A1AT W194 0 0 139 0.925 0 34
ACR W86 0 0 130 0.71 0 30.15
AM W102 0.22 0 136 0.98 0.22 22
LAB W26 0 0 153 0.865 0 24.5
LAB W104 0.98 0 138 0.8 0.785 28.35
Class I
KRP W75 0.33 0 136 1.41 0.465 35.8
ACR.G W3563.69 12.185 133 1.04 3.85 34.25
VTC W231 8.85 10.4 133 1.17 10.305 43.8
VTC W31 5.39 17.85 136 0.945 5.095 36.15
LAB W118 11.5 22.65 123.5 0.835 9.04 42.8
LAB W60 2.66 8.925 121.8 1.02 2.665 31.35
Class II
OVH.LIS W160 10.8 25.65 115 0.995 10.7 48.4
OVH.LIS W275 1.07 2.6 112.8 1.565 1.605 31.15
A1AT W238 20.5 65.25 102.5 0.89 18.25 39.9
MON W3 31.4 52.85 83 1.36 42.9 62.4
PHA W220 22.4 38.25 77.5 1.745 40.65 50.45
PHA W268 17.8 44.4 115.5 0.855 14.9 42.8
ASH.N W214 31.1 42 98 0.685 21.75 38.35
GPS W48 6.39 18.435 143 2.315 14.75 44.55
Class III
NO2 W27 42 70.2 91 2.65 139.65 57.8
PRH.LIS W6 61.5 74.7 78 0.95 58.25 62.8
PRH.LIS W42 39.7 86.6 69 1.315 52.1 50.05
PRH.PST W6 60.3 75 57 1.035 62.55 84.95
PRH.PST W42 34.9 81.85 78.5 1.825 45.9 60.05
AX6 W192 86.2 97.9 22 1.195 103.05 71.95
VTA.LIS W31 86.5 100 37 0.875 76 92.5
PLS W3 53.7 50.3 55 0.665 35.85 67.45
PLB W3 56.9 44.8 63 1.345 77.3 64.35
GLG W25 74.8 98.2 43 1.01 75.45 57.5
AWG W107 63 68.9 51 1.31 82.05 85.95
AWG W150 37.7 37.65 84 1.51 56.9 68.2

*AZU listed 2 times with similar parameters, since more than one object should be included in one class

The discriminant analysis was performed with the tryptophan residues from the training set to find the classification functions (CFij), where i denotes the respective class (i=1,…,5) and j is the respective structural parameter (j=1,…,6) (Table 4), which allows the construction of classification scores (Si) for each class.

where Acc, Acc1-7, Den, B, R and A are 6 structural parameters (see Table 1). The classification scores are used to determine the most probable class to which a new object (tryptophan residue) belongs. A tryptophan residue belongs to the class for which it has the highest classification score.

Table 4.Classification functions (CFij) for five classes used for the calculation of classifications scores.

Class A Class S Class I Class II Class III
CFi1 (for Acc) 1.887529 1.665856 1.660745 1.648479 1.896667
CFi3 (for Den) 1.749734 1.50127 1.400457 1.270009 1.225099
CFi4 (for B) 6.21771 11.41912 17.7545 24.44695 28.8079
CFi5 (for R) -0.1984 -0.25385 -0.33244 -0.39137 -0.3135
CFi (constant) -155.733 -120.833 -115.328 -111.483 -133.413

To quantify the assignment of tryptophan residues to classes we introduced second classification approach that provides the values of the probabilities of the classification of new objects to 5 classes. The probability (Pi) is a function of three parameters: the Mahalanobis distances (MDi) between of the new object assigned to the ith class and various classes centroids, within-classes covariance matrices (Si) calculated from the training set, and a priori probabilities qi.

where

The Mahalanobis distance is a measure of distance in space, where variances-covariance within group is taken into account. The Mahalanobis distance (MDi) between the tryptophan residue, which is presented by a multivariate vector Xnew, and mean μi of one of the ith class of training set (i = 1, 2,.. 5) is defined as:

The Mahalanobis distances are calculated in a 2-dimensional space of roots (or canonical scores). First, we performed the discriminant and canonical analysis with the tryptophan residues from the training set to find the discriminant functions (DFij) (Table 5), where j is the respective structural parameter (j=1,…,6), which allow us to construct l number of canonical scores or roots (Rl), which are independent combinations of 6 structural parameters (the detailed description of the analysis see in Reshetnyak and Burstein, 2001):

Table 5. Discriminant functions (DFij) used for the calculation of two most significant roots (or canonical scores)

Root 1 Root 2
DFi1 (for Acc) 0.023049 -0.08415
DFi2 (for Acc1-7) 0.026581 0.0242
DFi3 (for Den) -0.03878 -0.05765
DFi4 (for B) 2.208221 1.856157
DFi5 (for R) -0.00819 -0.0484
DFi6 (for A) 0.026574 0.014981
DFi7 (constant) -0.4562 6.108798

Applying the sequential testing procedure (Reshetnyak et al., 2001) we found that 2 roots are the most significant ones, the rest are statistically non-significant and could be excluded from the consideration. The calculation of roots leads to the reduction of the space dimension, i.e. conversion of the 6-dimentional space of structural parameters into 2-dimentional space of roots. The roots are linear combinations of the structural parameters. Two roots were calculated for all tryptophan residues from the training using Eq. 34. The Mahalanobis distances between the object and the centroids of 5 classes are computed in the 2-dimentional space of roots. These distances are used for the calculation of probabilities of tryptophan assignment to class.

Table 6. Areas calculated for each of five Gauss functions used for the fitting of the distribution of occurrence of position of maximum of spectral components, the areas were used to calculate a priori probabilities (qi)

Class A Class S Class I Class II Class III Total
Area under the Gauss functions 1.4 29 25 33 25 113.4
A priori probabilities, qi 0.01 0.26 0.22 0.29 0.22 1.0

 

which represent the natural occurrence of tryptophan fluorophores emitting at particular wavelengths were derived from the spectral distribution constructed previously (Burstein and Reshetnyak, 2001). Figure 10 presents the distribution of the occurrences of the positions of the maxima of more than 350 spectral components obtained as a result of decomposition analysis of about 150 proteins. The distribution clearly indicates that tryptophan fluorophores of some classes are more frequent (the intensity is high for classes II and S) than other classes (class A). In other words the probability of finding of tryptophan residue in protein emitting at ~ 342 nm (class II) is higher than the probability of finding of tryptophan residue emitting at 308-310 nm (class A). To calculate a priori probabilities of the assignment of tryptophan fluorophores (objects) to five classes we fitted the distribution of the occurrence of the maximum position of the spectral components by sum of 5 Gauss functions, which represents each of the five classes. The best fit was found for Gauss functions with the position of maximum at 308.0, 325.7, 331.7, 344.0 and 350.0 nm. The area under the each Gauss functions was used to establish a priori probabilities taking into account that the sum of all probabilities should be equal to 1 (Table 6).

Application of spectral-structural analysis to study protein structure, dynamics and function

Here we present several examples of successful applications of spectral and structural algorithms in studies of structure-functional relations of various proteins.

The method of spectral analysis was applied for the study of folding kinetics and structure of membrane protein OEP16 and its single-tryptophan-containing mutants (Linke et al., 2004). Based on the spectral analysis it was predicted the environment properties of tryptophan residues. This work provided the strong evidence of correctness of decomposition algorithms, since the spectral components obtained as a result of spectral analysis were in excellent correlation with the experimental spectra of single-tryptophan-containing mutants of OEP16.

The spectral and structural analysis were used to study conformational changes of 20S proteasome of rat natural killer cells induced by mono and divalent cations (Reshetnyak et al., 2004). It was found that the emission of Trp13 (one of 19 tryptophan residues in protein) from a6 subunit located near the cluster of highly conserved proteasome residues is mostly sensitive to the activation of the enzyme. It was concluded that the expression of maximal chymotrypsin-like activity of 20S proteasome is associated with the conformational changes occur in this cluster that lead to the proteasome open conformation, allowing substrate access into the proteolytic chamber.

Analysis of fluorescence spectra of isoforms of recombinant rat nucleoside diphosphate kinase (NDPK), which catalyze the transfer of g -phosphate from nucleoside triphosphates to nucleoside diphosphates allowed us to reveal the origin of unusual fluorescence (extremely high quantum yield) in NDPK alpha. It was associated with the tyrosinate formation in active center of alpha enzyme, which was crucial for the activity of the protein (Orlov et al, 1997, 1999, 2003).

The spectral and structural analysis of skeletal myosin subfragment 1 (S1) allowed to find tryptophan residues emission of which are sensitive to the binding of ATP with S1, and as a result, propose the conformational changes in S1 structure associate with the nucleotide binding (Reshetnyak et al., 2000). First, the spectral and structural properties of S1 were analyzed in absence of ATP and spectral components were assigned to 5 tryptophan residues. Then, the changes of spectral components occurred during interaction of S1 with ATP (structure of S1 in presence of ATP is not available) were monitored. It was concluded that the emission of Trp440 and 510 are sensitive for ATP binding.

Decomposition analysis of emission spectra of Prodan and Acrylodan attached to G-, F-actin and myosin provided information about conformational changes in these proteins during process of polymerization of G-actin and interaction of myosin with actin (Emelyanenko et al., 2000).

Decomposition of emission spectra of wild type (WT) and Thr123Ile mutant of the lecithin:cholesterol acyltransferase (LCAT) in absence and presence of substrates allowed to reveal the conformation differences between WT and mutant forms of LCAT (Reshetnyak et al., 2006). The Thr123Ile mutation in LCAT leads to a conformation that is likely to be more rigid (less mobile/flexible) than that of the WT protein with a redistribution of charged residues around exposed tryptophan fluorophores. It was proposed that the redistribution of charged residues in mutant LCAT may be a major factor responsible for the dramatically reduced activity of protein with HDL and rHDL (containing apolipoprotein-AI).

 

The membrane disruption capacity of the Eosinophil Cationic Protein (ECP) and its single tryptophan containing mutants was studied by fluorescence decomposition analysis and structural analysis (Torrent et al., 2007). The fluorescence spectra of two tryptophan residues are very sensitive to the interaction of protein with liposomes. Based on the analysis of structural properties of tryptophan residues from atomic structures of the protein the spectral properties of individual tryptophan residues was predicted. Spectral analysis of single-tryptophan-containing mutants of ECP completely proved the prediction made on result of spectral and structural analysis .


PFAST interaction diagram

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