**6. Nonlinear fluorescence spectroscopy of proteins**

#### **6.1 Determination of photophysical parameters of single- and double-tryptophancontaining proteins**

The emission spectra at several values of photon flux density *F* are shown in Fig. 6(a, b). In the figures, the band with a maximum value of *F* (4×1025 cm–2s–1) corresponds to the maximum value of the Raman scattering signal from water molecules. One can see that the maximum of the human serum albumin (HSA) fluorescence band does not change its position when *F* is changed. This is due to the fact that HSA contains one saturating fluorophore. However, the bovine serum albumin (BSA) fluorescence band is blue shifted (from 340 to 335 nm) when *F* is increased, owing to the fact that BSA contains two fluorophores in different environments (therefore, with different spectral properties), which exhibit different degrees (factors) of saturation. Taking into account the blue shift of the HSA fluorescence spectrum (in comparison with the BSA fluorescence spectrum) and the

which attributed to the chromophore of G form. The spectral characteristics of the proteins

Note that the presence of the three protein forms can be qualitatively seen in the absorption spectrum (Fig. 5). However, as is described in (Banishev et al., 2009), the quantitative determination of the individual photophysical parameters of their chromophore with the help of only conventional methods are problematic. This is explained by the fact that the preparative separation of the forms is rather difficult and, as a result, it is hard to find their partial concentrations. At that rate, for example, for calculating the molar extinction coefficient (or absorption cross section) of chromophore from absorption spectra, the total protein concentration (total concentration of all forms) is used. As a result, the extinction coefficients are artificially underestimated (Kredel at al., 2008). At present, the only method that used for determining the individual extinction coefficient of chromophore of each spectral form can be found in (Ward, 2005). However, as it was pointed out in (Kredel et al., 2008), the values measured by the method are inaccurate in case of red FPs. Although, the procedure which enables to reduce the experimental errors has been proposed by (Kredel et

form

mRFP1 Glutamine (Gln) 503 584 584 607 mRFP1/Q66S Serine (Ser) 506 562 561 579 mRFP1/Q66C Cysteine (Cys) 505 568 568 588 mRFP1/Q66N Asparagine (Asn) 525 570 570 604 mRFP1/Q66H Histidine (His) 504 588 588 618 mRFP1/Q66A Alanine (Ala) 500 582 578 605 mRFP1/Q66L Leucine (Leu) 500 582 577 613 mRFP1/Q66F Phenylalanine(Phe) 507 591 595 624 Table 1. The position (nm) of the maximum of the absorption, fluorescence excitation and

**6.1 Determination of photophysical parameters of single- and double-tryptophan-**

The emission spectra at several values of photon flux density *F* are shown in Fig. 6(a, b). In the figures, the band with a maximum value of *F* (4×1025 cm–2s–1) corresponds to the maximum value of the Raman scattering signal from water molecules. One can see that the maximum of the human serum albumin (HSA) fluorescence band does not change its position when *F* is changed. This is due to the fact that HSA contains one saturating fluorophore. However, the bovine serum albumin (BSA) fluorescence band is blue shifted (from 340 to 335 nm) when *F* is increased, owing to the fact that BSA contains two fluorophores in different environments (therefore, with different spectral properties), which exhibit different degrees (factors) of saturation. Taking into account the blue shift of the HSA fluorescence spectrum (in comparison with the BSA fluorescence spectrum) and the

Red form

maxabs maxabs maxex maxem

are presented in the Table 1.

al., 2008), the problem remains still topical.

emission spectra of the proteins.

**containing proteins** 

Protein Residue at 66 Green (G)

**6. Nonlinear fluorescence spectroscopy of proteins** 

similarity of the properties of Trp-214 in HSA and Trp-212 in BSA (see Section 5.1), one can assume that, in the system of two tryptophans of BSA, Trp-212 serves as the donor of the energy (the energy transfer occurs via Forster mechanism), and Trp-214 is the acceptor (i.e., its fluorescence spectrum is presumably shifted towards long wavelengths).

Fig. 6. (a) HSA and (b) BSA emission spectra at several values of photon flux density (see text); (1) is fluorescence and (2) is water Raman scattering band. (c) Saturation and (d) kinetic curves for BSA; fluorescence was registered at 390 (squares) and 310 (circles) nm. Lines are plotted using model (1b) and Eqs. (2b, c) for parameters from the Table 2.

The kinetic curves (see Eq. 6) and the fluorescence saturation curves of BSA are shown in Fig. 6(c, d). For BSA, the saturation curves depend on the registration wavelength in the wavelength range 310–390 nm. This is due to the fact that the BSA fluorescence band is a superposition of the bands of two tryptophans possessing different spectral properties. A similar difference in the curves for HSA is negligible. For the determination of the photophysical parameters of HSA fluorophore from fluorescence saturation and kinetic curves, the model (1a) and Eq. (2a) have been used. The same calculation procedure was done for BSA experimental curves, but with using the model (1b) and Eqs. (2b,c); the fluorescence signal was measured at 310 nm (when registered the fluorescence saturation and kinetic curves of the donor) and 390 nm (for similar curves of the acceptor). The resulting values of the parameters of protein fluorophores are presented in the Table 2.

As one can see from the Table 2 that the values of photophysical parameters *σ* and *τ* of Trp-214 in HSA and Trp-212 in BSA are similar. This result should have been expected based on a comparison of the structures of these proteins. The rates of energy transfer in BSA from excited donor to unexcited acceptor (*KDA*) and to excited acceptor (*KSS*) are small in comparison with the rate of intramolecular relaxation (*-1*). This can be due to following reasons: (i) in BSA, the tryptophan residues in the D–A pair are located at a distance that is

Laser Fluorescence Spectroscopy:


*A*, 

of the donor and acceptor (from the unit of volume) are:

(immediately after the excitation pulse is over); *A=[D\*]0*

excited donor molecules concentration at a time point *t=*0*;* 

given above.

a result, the lifetimes

tryptophan to the chromophore.

Application in Determining the Individual Photophysical Parameters of Proteins 199

As a preliminary step in determination of the full set of the mRFP1 photopysical parameters, the analysis of fluorescence decay at picoseconds excitation has been done. The excitation wavelength was 266 nm in order to match the acceptor (tryptophan) absorption band. The acceptor fluorescence decay under excitation of an ensemble of donor-acceptor pairs by

 IA(t)~Bexp(-t/A)-Aexp(-t/D+A) (4) where, *B=A+[A\*]0*, *[A\*]0* is the excited acceptor molecules concentration at a time point *t=*0

fluorescence lifetime of the donor in the presence of the acceptor; other designations are

The fluorescence decay signal was measured at picoseconds time-resolved fluorimeter described in Section 3.2. The excitation wavelength was 266 nm and the signal registration was done in the range of the R form chromophore fluorescence (the chromophores of others forms are non-fluorescent). The experimental time dependence was fitted by function (4), as

fluorescence decay curve were obtained. The *КDA* cannot be determined only from the fluorescence decay curve, because in this case it would be necessary to remove the acceptor and measure the fluorescence lifetime of the donor (in the absence of the acceptor). As it will be shown below, the nonlinear fluorimetry method makes it possible to resolve this problem for the native protein without any preparative action. The processing of the fluorescence decay curve of the mRFP1 allowed us to determine the lifetime values, *τA=*1.6 ns and *τD+A=*0.24 ns. The values of *B* and *A* in (4) were found to be practically equal. It is indicative of the absence of the direct excitation of the acceptor; therefore, in the equation system (1b) one can assume *σA=*0 (under excitation at 266 nm) and for this reason, the acceptor fluorescence (under this wavelength excitation) is a result of the energy transfer from the

The next step was to measure and analyse the fluorescence saturation curves with excitation at the wavelength of 266 nm. To improve the stability of the inverse problem solution, the process of singlet-singlet annihilation from the model (1b) was excluded. At pH 7.4 (the acidity at which the protein was initially produced), the mRFP1 solution is represented as a sum of three subensembles of molecules, each having its own set of photophysical parameters, and the dynamics of the populations of the collective states is described by its own system of equations similar to (1b). The number of the photons of the tryptophan fluorescence is calculated from Eq. (2b), where the sum under the integral is the population of the collective states *n2* and *n4* for all three forms. The fluorescence of the R form is calculated from Eq. (2c), where the populations of the collective states *n3* and *n4* of this form are present. It is difficult to resolve the inverse problem of nonlinear fluorimetry in such a situation, because the number of unknown parameters is too large. But, as was mentioned in Section 4.2, there are the techniques that allow reducing the number of the simultaneously present forms to two. In that case if the portion of the concentration of the R form is *cR* and that of the second form (for example, G) is *cG*, then the numbers of the fluorescence photons

*KDA/(1/D+A-1/*

*D+A*, and the partial contributions of *B* and *A* components of the

*D+A=(1/*

*A)*; *[D\*]0* is the

*D+KDA)-1* is the

insufficient for a noticeable energy transfer between them. According to the data on the BSA structure (Peters, 1996), the distance between two tryptophans in the molecule is about 3.5 nm. For comparison, the Forster radius for the energy transfer between free tryptophans ranges from 0.6 to 1.2 nm (depending on the solvent). (ii) perhaps, the mutual orientation of the transition dipoles of fluorophores impedes the energy transfer (Lakowicz, 1999).


Table 2. Photophysical parameters of fluorophores (tryptophan residues) in HSA and BSA.

It is significant that the values of the absorption cross section determined using the method of nonlinear fluorimetry are true values for fluorophores and they are obtained without *a priori* information about the contribution of other groups into absorption at a specific wavelength and about the concentration of fluorophores. This is a unique feature of nonlinear fluorimetry. As mentioned above, there are three absorption groups in proteins (tryptophan, tyrosine and phenylalanine) and the absorption spectra of these three amino acids are overlapping. In that situation it is hard to separate the contribution of each amino acid group from total protein absorption without any preparative action on a molecule. For that reason, the absorption cross section of the tryptophan residue in protein is assumed to be equal to the absorption cross section of free tryptophan in solution (Pace et al., 1995), because it is supposed that this parameter is weakly dependent on the environment. However, a comparison of the equimolar solution and protein solution absorption spectra (Fig. 4) shows that these spectra do not coincide for HSA and BSA. Therefore, it is clear that such an assumption is just estimation and for diagnostics of the state of a protein it is necessary to be able to determine the true photophysical parameters of tryptophan merged in protein matrix. That has been done in this Section. The absorption cross section for tryptophan in aqueous solution is equal to 1.6×10−17 cm2 (Banishev et al., 2008a) (at 266 nm); now, it can be compared with the true values of the absorption cross section of tryptophan residues in native proteins (see Table 2). The abilities of the approach are not limited by albumins.

#### **6.2 Determination of photophysical parameters of mRFP1 protein under UV excitation**

According to three-dimensional structure (PDB ID1g7k) of the mRFP1, there is a tryptophan at a distance of about 15Å from the protein chromophore, which could be a potential partner (the donor) for inductive FRET to the protein chromophore. Thereby, the tryptophan and the chromophore form a LDA pair inside a molecule of the FP.

insufficient for a noticeable energy transfer between them. According to the data on the BSA structure (Peters, 1996), the distance between two tryptophans in the molecule is about 3.5 nm. For comparison, the Forster radius for the energy transfer between free tryptophans ranges from 0.6 to 1.2 nm (depending on the solvent). (ii) perhaps, the mutual orientation of

> 6.20.5 (30.3)×10-17 <10-7 <10-7

Table 2. Photophysical parameters of fluorophores (tryptophan residues) in HSA and BSA.

It is significant that the values of the absorption cross section determined using the method of nonlinear fluorimetry are true values for fluorophores and they are obtained without *a priori* information about the contribution of other groups into absorption at a specific wavelength and about the concentration of fluorophores. This is a unique feature of nonlinear fluorimetry. As mentioned above, there are three absorption groups in proteins (tryptophan, tyrosine and phenylalanine) and the absorption spectra of these three amino acids are overlapping. In that situation it is hard to separate the contribution of each amino acid group from total protein absorption without any preparative action on a molecule. For that reason, the absorption cross section of the tryptophan residue in protein is assumed to be equal to the absorption cross section of free tryptophan in solution (Pace et al., 1995), because it is supposed that this parameter is weakly dependent on the environment. However, a comparison of the equimolar solution and protein solution absorption spectra (Fig. 4) shows that these spectra do not coincide for HSA and BSA. Therefore, it is clear that such an assumption is just estimation and for diagnostics of the state of a protein it is necessary to be able to determine the true photophysical parameters of tryptophan merged in protein matrix. That has been done in this Section. The absorption cross section for tryptophan in aqueous solution is equal to 1.6×10−17 cm2 (Banishev et al., 2008a) (at 266 nm); now, it can be compared with the true values of the absorption cross section of tryptophan residues in native proteins (see Table 2). The abilities of the approach are not limited by

**6.2 Determination of photophysical parameters of mRFP1 protein under UV excitation**  According to three-dimensional structure (PDB ID1g7k) of the mRFP1, there is a tryptophan at a distance of about 15Å from the protein chromophore, which could be a potential partner (the donor) for inductive FRET to the protein chromophore. Thereby, the tryptophan and

the chromophore form a LDA pair inside a molecule of the FP.

*Trp-214* 4.5 0.5 (1.30.1)×10-17 <10-7

*Trp-134 (donor) Trp-212 (acceptor)* 

50.5 (10.1)×10-17 <10-7 <10-7

the transition dipoles of fluorophores impedes the energy transfer (Lakowicz, 1999).

Protein Parameters Tryptophan residues

HSA

BSA

albumins.

, ns 

, ns 

*K'32*, s-1

*KDA*, s-1 *KSS*, s-1

(ex=266), cm2

(ex=266), cm2

As a preliminary step in determination of the full set of the mRFP1 photopysical parameters, the analysis of fluorescence decay at picoseconds excitation has been done. The excitation wavelength was 266 nm in order to match the acceptor (tryptophan) absorption band. The acceptor fluorescence decay under excitation of an ensemble of donor-acceptor pairs by -pulse is described (Valeur, 2002) as:

$$\mathbf{I\_{A}(t)} \sim \mathbf{B} \cdot \exp(\mathbf{-t}/\tau\_{\mathrm{A}}) \cdot \mathbf{A} \cdot \exp(\mathbf{-t}/\tau\_{\mathrm{D} \ast \mathrm{A}}) \tag{4}$$

where, *B=A+[A\*]0*, *[A\*]0* is the excited acceptor molecules concentration at a time point *t=*0 (immediately after the excitation pulse is over); *A=[D\*]0KDA/(1/D+A-1/A)*; *[D\*]0* is the excited donor molecules concentration at a time point *t=*0*; D+A=(1/D+KDA)-1* is the fluorescence lifetime of the donor in the presence of the acceptor; other designations are given above.

The fluorescence decay signal was measured at picoseconds time-resolved fluorimeter described in Section 3.2. The excitation wavelength was 266 nm and the signal registration was done in the range of the R form chromophore fluorescence (the chromophores of others forms are non-fluorescent). The experimental time dependence was fitted by function (4), as a result, the lifetimes *A*, *D+A*, and the partial contributions of *B* and *A* components of the fluorescence decay curve were obtained. The *КDA* cannot be determined only from the fluorescence decay curve, because in this case it would be necessary to remove the acceptor and measure the fluorescence lifetime of the donor (in the absence of the acceptor). As it will be shown below, the nonlinear fluorimetry method makes it possible to resolve this problem for the native protein without any preparative action. The processing of the fluorescence decay curve of the mRFP1 allowed us to determine the lifetime values, *τA=*1.6 ns and *τD+A=*0.24 ns. The values of *B* and *A* in (4) were found to be practically equal. It is indicative of the absence of the direct excitation of the acceptor; therefore, in the equation system (1b) one can assume *σA=*0 (under excitation at 266 nm) and for this reason, the acceptor fluorescence (under this wavelength excitation) is a result of the energy transfer from the tryptophan to the chromophore.

The next step was to measure and analyse the fluorescence saturation curves with excitation at the wavelength of 266 nm. To improve the stability of the inverse problem solution, the process of singlet-singlet annihilation from the model (1b) was excluded. At pH 7.4 (the acidity at which the protein was initially produced), the mRFP1 solution is represented as a sum of three subensembles of molecules, each having its own set of photophysical parameters, and the dynamics of the populations of the collective states is described by its own system of equations similar to (1b). The number of the photons of the tryptophan fluorescence is calculated from Eq. (2b), where the sum under the integral is the population of the collective states *n2* and *n4* for all three forms. The fluorescence of the R form is calculated from Eq. (2c), where the populations of the collective states *n3* and *n4* of this form are present. It is difficult to resolve the inverse problem of nonlinear fluorimetry in such a situation, because the number of unknown parameters is too large. But, as was mentioned in Section 4.2, there are the techniques that allow reducing the number of the simultaneously present forms to two. In that case if the portion of the concentration of the R form is *cR* and that of the second form (for example, G) is *cG*, then the numbers of the fluorescence photons of the donor and acceptor (from the unit of volume) are:

Laser Fluorescence Spectroscopy:

et al., 2001; Truong & Ikura, 2001).

*ex=266)* and

absence of the acceptor) and the acceptor.

*A(*

> *D* and

**parameters of the fluorescent form of the mRFP1 protein** 

table: (1)

*E* *D(*

the unexcited acceptor; (3)

(Banishev et al., 2009).

determined. The

lifetime

Application in Determining the Individual Photophysical Parameters of Proteins 201

efficiency in LDA pairs by conventional methods (Valuer, 2002)). For mRFP1, this value can be compared with ones for the free tryptophan (*τD=*2.8 ns (Banishev et al., 2008a)), HSA (*τD=*4.5 ns) and BSA (*τD=*5 and *τA=*6.2 ns). Simultaneously, the excited state lifetime values of the chromophores of the GH and G form have been obtained (*τA* in the Table 3), although the chromophores of these forms are non-fluorescent. The obtained results show that the high volume (*E=*0.89) of the energy transfer efficiency from the tryptophan to the chromophores in all three forms of the protein is of special scientific and practical interest. This permits employing mRFP1 as a promising fluorescence indicator that makes use of its own inner LDA pair (an alternative is the preparation of such pairs of two proteins (Srinivas

Parameter Values for R form Values for GH form Values for G form

*ex=266)* are the absorption cross section of the donor

and *K'32*, defined in Section 2, have been determined from fluorescence

*<sup>A</sup>* are the excited state lifetimes of the donor (in the

D(ex=266), cm2 (10.2)10-16 (10.2)10-16 (10.2)10-16 A(ex=266), cm2 0 not defined not defined KDA, s-1 (3.70.7)109 (7.81)109 (2.50.7)109 E 0.89 0.94 0.84 A, ns 30.15 1.90.4 1.70.4 D, ns 2.10.5 2.10.5 2.10.5 Table 3. The photophysical parameters of the LDA pairs in mRFP1 by UV excitation. In the

(tryptophan) and the acceptor (chromophore) at the wavelength of 266 nm; (2) *KDA* and

**6.3 Influence of a single amino-acid substitution on the individual photophysical** 

In this Section, the influence of a single amino acid substitution in mRFP1 at position 66 on optical characteristics of the chromophore of fluorescent spectral form (R form) is performed. For that purpose, the method of nonlinear laser fluorimetry was realized in the version when the protein fluorescence is excited by the wavelength of 532 nm (i.e. the only protein chromophore was excited). All technical details of the procedure can be found in

At first, the photophysical parameters of R form chromophore of the proteins were

saturation curve for each of the eight protein samples. Because the solution of each of the eight proteins contains mature (red) and immature (green) form, the only fluorescence in the red spectral range (from 550 nm) was detected (to obtain the parameters only for R form chromophore). The typical view of the measured fluorescence saturation curves can be found in (Banishev et al., 2009). To simplify the inverse problem solution, the fluorescence

532 nm). It was found that for all protein samples the fluorescence decay best fit by a singleexponential dependence (Banishev et al., 2009). Solving the inverse problem of nonlinear

was measured independently with the picosecond laser fluorimeter (excitation at

*KDA/(KDA+1/τD)* are the rate and efficiency of the energy transfer from the excited donor to

$$N\_{\rm H}^{\rm D}(\lambda) = \tau\_{\rm D}^{-1} \cdot \eta\_{\rm D} \cdot \int\_{-\phi}^{+\phi} [c\_{\rm R} \cdot (n\_2^{\rm R}(t, r) + n\_4^{\rm R}(t, r) \text{ )} + c\_{\rm G} \cdot (n\_2^{\rm G}(t, r) + n\_4^{\rm G}(t, r) \text{ )}] dt \tag{5a}$$

$$N\_{\rm FI}^{A}(\lambda) = \boldsymbol{\tau}\_{A}^{-1} \cdot \boldsymbol{\eta}\_{A} \cdot \int\_{-\infty}^{+\infty} \boldsymbol{c}\_{R} [\boldsymbol{n}\_{3}^{\rm R}(t, r) + \boldsymbol{n}\_{4}^{\rm R}(t, r)] \, dt \tag{5b}$$

where the symbols R and G denote the R and G form molecules; *n2*, *n3*, and *n4* are the collective states (see (1b)); *ηD* and *ηA* are the fluorescence quantum yields (see (2b,c)); and *c* is the relative concentration of the forms in total molecules concentration. The amount of the R form molecules *cR* can be found from the algorithm that described in the next Section.

In this connection, the following procedure has been realized:


The experimental dependences *Φ−<sup>1</sup> D(F)* and *Φ−<sup>1</sup> A(F)* for case (a) can be found in (Shirshin et al., 2009). When measured the saturation curves *Φ−1D(F)* and *Φ−<sup>1</sup> A(F)*, the intensity in the spectra of the first and second orders of the RS valence band of water molecules (the wavelengths are 291 and 582 nm, correspondingly) were used as a reference signal; the excitation was at 266 nm. Having performed this procedure, the photophysical parameters of FP mRFP1 under UV excitation (266 nm) have been determined (see Table 3).

Let us discuss the main results of this Section. First of all, it is interesting to compare the true value of the absorption cross section obtained for tryptophan in the FP mRFP1 with the values for tryptophan in an aqueous solution (1.6×10−17 cm2 (Banishev et al., 2008)), human serum albumin (1.3×10−17 cm2), and bovine serum albumin (*σD=*1×10−17 cm2 and *σA=*3×10−<sup>17</sup> cm2), which were determined in previous Section. One can see that the values for tryptophans in proteins are different and do not equal to the value for a free tryptophan, as is often assumed. I want to emphasize that the lifetime of the excited state of the donor (tryptophan) *τD* in the absence of the acceptor (chromophore) has been obtained without the removal of the acceptor (as it is often supposed when determine the energy transfer

24 2 4 ( ) [ ( ( , ) ( , ) ) ( ( , ) ( , ) )] *D R <sup>R</sup> <sup>G</sup> <sup>G</sup> N c Fl D D R <sup>n</sup> <sup>G</sup>*

3 4 ( ) [ ( , ) ( , )] *A R <sup>R</sup> N c Fl A A R*

where the symbols R and G denote the R and G form molecules; *n2*, *n3*, and *n4* are the collective states (see (1b)); *ηD* and *ηA* are the fluorescence quantum yields (see (2b,c)); and *c* is the relative concentration of the forms in total molecules concentration. The amount of the R form molecules *cR* can be found from the algorithm that described in the next Section.

a. The value of the protein solution pH was set near 9; in this situation, the protein solution contains only protein molecules of the R and G forms. After that, two saturation curves were taken under excitation at the wavelength of 266 nm and fluorescence registration at 330nm (the fluorescence saturation curve of the donor, i.e., the molecules of the tryptophan contained in the protein matrix of the R and G forms) and at 607nm (the fluorescence saturation curve of the acceptor, i.e., the chromophore only in the protein molecules of the R form). Resolving the inverse problem, in which fluorescence response formation is described by two systems of the kind of (1b) for the populations of the collective states of the LDA pairs in macromolecules of R and G forms, and the values of the parameters *τD+A*, *τA*, *σA=*0 for the R form of the protein are considered to be known (see above), the values of *KDA* (for the R and G forms) and *τ<sup>A</sup>*

b. The protein sample was irradiated with the Ar laser at a wavelength of 488 nm (the pH value is near to a neutral one) and made only the R and GH forms present in the solution. After that, I used the same procedure of measurement and calculation of the saturation curves and determined the following parameters: *KDA* (for R and GH forms of protein) and *τA* (for the GH form of the protein). The values of the *KDA* for the R form

The experimental dependences *Φ−1D(F)* and *Φ−1A(F)* for case (a) can be found in (Shirshin et al., 2009). When measured the saturation curves *Φ−1D(F)* and *Φ−1A(F)*, the intensity in the spectra of the first and second orders of the RS valence band of water molecules (the wavelengths are 291 and 582 nm, correspondingly) were used as a reference signal; the excitation was at 266 nm. Having performed this procedure, the photophysical parameters

Let us discuss the main results of this Section. First of all, it is interesting to compare the true value of the absorption cross section obtained for tryptophan in the FP mRFP1 with the values for tryptophan in an aqueous solution (1.6×10−17 cm2 (Banishev et al., 2008)), human serum albumin (1.3×10−17 cm2), and bovine serum albumin (*σD=*1×10−17 cm2 and *σA=*3×10−<sup>17</sup> cm2), which were determined in previous Section. One can see that the values for tryptophans in proteins are different and do not equal to the value for a free tryptophan, as is often assumed. I want to emphasize that the lifetime of the excited state of the donor (tryptophan) *τD* in the absence of the acceptor (chromophore) has been obtained without the removal of the acceptor (as it is often supposed when determine the energy transfer

of FP mRFP1 under UV excitation (266 nm) have been determined (see Table 3).

*t r n t r c n t r n t r dt*

*n t r n t r dt*

(5a)

(5b)

1

1

In this connection, the following procedure has been realized:

(for the G form) have been determined.

in both cases coincided in error limits of the experiment.

efficiency in LDA pairs by conventional methods (Valuer, 2002)). For mRFP1, this value can be compared with ones for the free tryptophan (*τD=*2.8 ns (Banishev et al., 2008a)), HSA (*τD=*4.5 ns) and BSA (*τD=*5 and *τA=*6.2 ns). Simultaneously, the excited state lifetime values of the chromophores of the GH and G form have been obtained (*τA* in the Table 3), although the chromophores of these forms are non-fluorescent. The obtained results show that the high volume (*E=*0.89) of the energy transfer efficiency from the tryptophan to the chromophores in all three forms of the protein is of special scientific and practical interest. This permits employing mRFP1 as a promising fluorescence indicator that makes use of its own inner LDA pair (an alternative is the preparation of such pairs of two proteins (Srinivas et al., 2001; Truong & Ikura, 2001).


Table 3. The photophysical parameters of the LDA pairs in mRFP1 by UV excitation. In the table: (1) *D(ex=266)* and *A(ex=266)* are the absorption cross section of the donor (tryptophan) and the acceptor (chromophore) at the wavelength of 266 nm; (2) *KDA* and *EKDA/(KDA+1/τD)* are the rate and efficiency of the energy transfer from the excited donor to the unexcited acceptor; (3) *D* and *<sup>A</sup>* are the excited state lifetimes of the donor (in the absence of the acceptor) and the acceptor.

### **6.3 Influence of a single amino-acid substitution on the individual photophysical parameters of the fluorescent form of the mRFP1 protein**

In this Section, the influence of a single amino acid substitution in mRFP1 at position 66 on optical characteristics of the chromophore of fluorescent spectral form (R form) is performed. For that purpose, the method of nonlinear laser fluorimetry was realized in the version when the protein fluorescence is excited by the wavelength of 532 nm (i.e. the only protein chromophore was excited). All technical details of the procedure can be found in (Banishev et al., 2009).

At first, the photophysical parameters of R form chromophore of the proteins were determined. The and *K'32*, defined in Section 2, have been determined from fluorescence saturation curve for each of the eight protein samples. Because the solution of each of the eight proteins contains mature (red) and immature (green) form, the only fluorescence in the red spectral range (from 550 nm) was detected (to obtain the parameters only for R form chromophore). The typical view of the measured fluorescence saturation curves can be found in (Banishev et al., 2009). To simplify the inverse problem solution, the fluorescence lifetime was measured independently with the picosecond laser fluorimeter (excitation at 532 nm). It was found that for all protein samples the fluorescence decay best fit by a singleexponential dependence (Banishev et al., 2009). Solving the inverse problem of nonlinear

Laser Fluorescence Spectroscopy:

Protein

sample. Note:

*,*  and 

determined by solving system of Eqs. (6).

Application in Determining the Individual Photophysical Parameters of Proteins 203

One can see from the Table 4 that at the absorption maximum of the R form of the mRFP1

*<sup>R</sup>(max)*=(21540) mM-1cm-1, which is drastically (four times) larger than the value published in (Campbell et al., 2002). This difference is due to the fact that the (Campbell et al., 2002) calculated the extinction coefficient using the total protein concentration (and, therefore, found the integral extinction coefficient) rather than the partial concentration (as in our case). As a result, the determination of the partial concentration of fluorescent molecules allowed us to find the individual extinction coefficient of the chromophore of the R form.

\*\*, %

*<sup>T</sup>* are the fluorescence lifetime, fluorescence quantum yield and

 *T\**

*<sup>R</sup>(max)* (mM-1cm-1) *CR/C0*

mRFP1 21540 266 0.240.03 0.010.01 mRFP1/Q66S 8513 346 0.200.04 0.050.02 mRFP1/Q66C 13520 176 0.190.04 0.010.01 mRFP1/Q66N 13315 94 0.170.03 0.020.02 mRFP1/Q66H 23027 84 0.130.03 0.070.02 mRFP1/Q66A 17116 22 0.190.04 0.050.02 mRFP1/Q66L 24040 22 0.120.03 0.060.02 mRFP1/Q66F 14218 22 0.040.03 0.120.03 Table 4. Individual photophysical parameters of the R form and its fraction in the protein

quantum yield to the triplet state (converted from *K'32*), respectively. Other parameters are defined after the system of Eqs. (6). \* Determined from the fluorescence saturation curve; \*\*

In the general case, the determination of photophysical parameters of FPs with the help of integral characteristics of the sample is incorrect, which can be proved by several examples. By using the dynamic difference method, (Kredel et al., 2008) obtained the individual extinction coefficient 143 mM-1cm-1 for the chromophore of the R form of mPlum, which is also drastically larger than other published values ranging from 22 to 41 mM-1cm-1 (Shcherbo et al., 2007) for this protein. It is interesting to note that (Gross et al., 2000) have earlier reported a similar value of 150 mM-1cm-1 for the R form chromophore of red FP DsRed (the table value for this protein is assumed to be 75 mM-1cm-1). In their approach, the amount of immature species was deduced from mass spectroscopic analysis. Another example can be found in (Strack et al., 2010). Using the method described in (Ward, 2005), (Strack et al., 2010) got an assessed value of 123 mM-1cm-1 for DsRed.T7, which is close to that obtained by (Kredel et al., 2008). From these examples one can see that the values of the individual extinction coefficients of the R form chromophore are close, as it is expected to be, because the chromophores of these proteins are considered to be chemically identical. One can assume a minor disagreement due to chromophore orientation change relative to protein matrix or composition of its closest environment (this can explain the difference in the extinction values for mPlum, DsRed and DsRed.T7 determined by (Kredel et al., 2008; Gross et al., 2000) and (Strack et al., 2010)). However, the published values of the extinction of red FPs with the same chromophore drastically vary depending on the protein: 75 mM-1cm-1 per a polypeptide chain for the DsRed, 120 mM-1cm-1 per a polypeptide chain for tdimer2(12) (Campbell at al., 2002), 22 mM-1cm-1 for mPlum (Shcherbo et al., 2007), 50 mM-1cm-1 for mRFP1 (Campbell at al., 2002) and 90 mM-1cm-1 for mStrawberry (Shu et al., 2006). Discrepancies follow directly from the content of immature form in the protein samples.

fluorimetry for each saturation curve at given , the and *K'32* for each protein sample have been defined. Note that in this scheme of nonlinear laser fluorimetry the 532-nm laser pulses were used for exciting fluorescence, and, hence, is the absorption cross section of the protein R form at 532 nm, i.e., *<sup>R</sup>(532).* 

At the second stage, the partial concentration of the mature and immature species in the resultant solution of each mutant has been determined. As was said above, the equilibrium between the GH and G forms of FPs can be shifted under the action of external factors. Using this property of red FPs, it is possible to find the ratio of concentrations of all forms. However, the only the red fluorescence of R form is useful for practical application (Piatkevich et al., 2010). The green form is the by-products of maturation and supposed to be absent in ideal case. For that reason the measurement procedure has been simplified and the concentration of the R form and the total concentration of the GH and G forms were determined.

Indeed, given above-mentioned assumptions, one can write the following system of equations:

$$\begin{aligned} \frac{\Phi\_0^{(570)} \cdot \sigma\_{\rm KS}^{(570)} \cdot \sigma\_{\rm KS}^{(570)}}{\Phi\_0^{(532)} \cdot \sigma\_{\rm KS}^{(532)} &= \frac{\sigma\_R^{(570)}}{\sigma\_R^{(532)}}\\ \mathbf{C}\_R \cdot \sigma\_R^{(570)} &= 2.3D^{(570)}I^{-1} \\ \mathbf{C}\_R \cdot \sigma\_R^{(532)} + \mathbf{C}\_G \cdot \sigma\_G^{(532)} &= 2.3D^{(532)}I^{-1} \\ \mathbf{C}\_R + \mathbf{C}\_G &= \mathbf{C}\_{0'} \end{aligned} \tag{6}$$

where *CR*, *CG* are the concentrations of the R form and the total concentration of the G and GH forms in the solution (in cm-3); *C0* is the total concentration of protein molecules determined by conventional methods (McCluskey, 2003); *R(570)* and *<sup>R</sup>(532)* are the individual absorption cross section of the chromophore of fluorescent form at 570 and 532 nm; *<sup>R</sup>(570)* is integral absorption cross section of the chromophore of green form; *D(570)*, *D(532)*and *RS(570)*, *RS(532)* are the optical density of the protein solution and Raman scattering cross section of water (Filipova et al., 2001) at 570 and 532 nm, respectively.

The first equality in system (6) reflects the fact that the quantum yields (expressed in terms of the fluorescence parameter *<sup>0</sup>* (Filipova et al., 2001)) upon excitation of the protein solution at 532 and 570 nm are the same. The second and third equalities are the optical density (determined from the absorption spectrum of the proteins) written in terms of the concentration of protein molecules absorbing light at 570 and 532 nm and in terms of their absorption cross section. The wavelengths of 570 and 532 nm were chosen for reason mentioned in (Banishev et al., 2009). In system (6) the sought-for quantities are *CR*, *CG*, *R(570), G(532),* while experimentally measured values are *0(570)/0(532)*, *D(570), D(532), l, C0, <sup>R</sup>(532)* (the latter found by means of nonlinear laser fluorimetry). After the *<sup>R</sup>(570)* was found, one can find the maximum value of the individual absorption cross section *<sup>R</sup>(max)* of the R form chomophore, or the extinction coefficient *R(max)*, which is more convenient for comparison with data from literature. This value can be calculated using the absorption spectrum and relation *D(max)/D(570)=R(max)/<sup>R</sup>(570)*, where *D(max)* is the optical density at the maximum of the absorption band of the R form. The results for the eight samples are given in the Table 4.

, the 

been defined. Note that in this scheme of nonlinear laser fluorimetry the 532-nm laser pulses

At the second stage, the partial concentration of the mature and immature species in the resultant solution of each mutant has been determined. As was said above, the equilibrium between the GH and G forms of FPs can be shifted under the action of external factors. Using this property of red FPs, it is possible to find the ratio of concentrations of all forms. However, the only the red fluorescence of R form is useful for practical application (Piatkevich et al., 2010). The green form is the by-products of maturation and supposed to be absent in ideal case. For that reason the measurement procedure has been simplified and the concentration of the R form and the total concentration of the GH and G forms were

Indeed, given above-mentioned assumptions, one can write the following system of

 

(532) (532) (532) 1

2.3

*R(570)* and

*<sup>0</sup>* (Filipova et al., 2001)) upon excitation of the protein

*0(532)*, *D(570), D(532), l, C0,* 

*<sup>R</sup>(570)*, where *D(max)* is the optical density at the maximum of the

*R(max)*, which is more convenient for comparison

(570) (570) (570)

(532) (532) (532)

0

*R G R G*

*C Dl*

,

absorption cross section of the chromophore of fluorescent form at 570 and 532 nm;

integral absorption cross section of the chromophore of green form; *D(570)*, *D(532)*and

(570) (570) 1

*C C Dl*

where *CR*, *CG* are the concentrations of the R form and the total concentration of the G and GH forms in the solution (in cm-3); *C0* is the total concentration of protein molecules

*RS(532)* are the optical density of the protein solution and Raman scattering cross section of

The first equality in system (6) reflects the fact that the quantum yields (expressed in terms

solution at 532 and 570 nm are the same. The second and third equalities are the optical density (determined from the absorption spectrum of the proteins) written in terms of the concentration of protein molecules absorbing light at 570 and 532 nm and in terms of their absorption cross section. The wavelengths of 570 and 532 nm were chosen for reason mentioned in (Banishev et al., 2009). In system (6) the sought-for quantities are *CR*, *CG*,

absorption band of the R form. The results for the eight samples are given in the Table 4.

with data from literature. This value can be calculated using the absorption spectrum and

*0(570)/*

 

*RS R RS R*

2.3

and *K'32* for each protein sample have

is the absorption cross section of the

(6)

*<sup>R</sup>(532)* are the individual

*<sup>R</sup>(570)* is

> *RS(570)*,

> > *R(570),*

*<sup>R</sup>(532)* (the

*<sup>R</sup>(max)* of the R form

*<sup>R</sup>(570)* was found, one can

fluorimetry for each saturation curve at given

protein R form at 532 nm, i.e.,

determined.

equations:

were used for exciting fluorescence, and, hence,

*<sup>R</sup>(532).* 

0

0

*R R*

*R G*

determined by conventional methods (McCluskey, 2003);

water (Filipova et al., 2001) at 570 and 532 nm, respectively.

*G(532),* while experimentally measured values are

chomophore, or the extinction coefficient

*R(max)/*

relation *D(max)/D(570)=*

latter found by means of nonlinear laser fluorimetry). After the

find the maximum value of the individual absorption cross section

of the fluorescence parameter

*CCC*

One can see from the Table 4 that at the absorption maximum of the R form of the mRFP1 *<sup>R</sup>(max)*=(21540) mM-1cm-1, which is drastically (four times) larger than the value published in (Campbell et al., 2002). This difference is due to the fact that the (Campbell et al., 2002) calculated the extinction coefficient using the total protein concentration (and, therefore, found the integral extinction coefficient) rather than the partial concentration (as in our case). As a result, the determination of the partial concentration of fluorescent molecules allowed us to find the individual extinction coefficient of the chromophore of the R form.


Table 4. Individual photophysical parameters of the R form and its fraction in the protein sample. Note: *,*  and *<sup>T</sup>* are the fluorescence lifetime, fluorescence quantum yield and quantum yield to the triplet state (converted from *K'32*), respectively. Other parameters are defined after the system of Eqs. (6). \* Determined from the fluorescence saturation curve; \*\* determined by solving system of Eqs. (6).

In the general case, the determination of photophysical parameters of FPs with the help of integral characteristics of the sample is incorrect, which can be proved by several examples. By using the dynamic difference method, (Kredel et al., 2008) obtained the individual extinction coefficient 143 mM-1cm-1 for the chromophore of the R form of mPlum, which is also drastically larger than other published values ranging from 22 to 41 mM-1cm-1 (Shcherbo et al., 2007) for this protein. It is interesting to note that (Gross et al., 2000) have earlier reported a similar value of 150 mM-1cm-1 for the R form chromophore of red FP DsRed (the table value for this protein is assumed to be 75 mM-1cm-1). In their approach, the amount of immature species was deduced from mass spectroscopic analysis. Another example can be found in (Strack et al., 2010). Using the method described in (Ward, 2005), (Strack et al., 2010) got an assessed value of 123 mM-1cm-1 for DsRed.T7, which is close to that obtained by (Kredel et al., 2008). From these examples one can see that the values of the individual extinction coefficients of the R form chromophore are close, as it is expected to be, because the chromophores of these proteins are considered to be chemically identical. One can assume a minor disagreement due to chromophore orientation change relative to protein matrix or composition of its closest environment (this can explain the difference in the extinction values for mPlum, DsRed and DsRed.T7 determined by (Kredel et al., 2008; Gross et al., 2000) and (Strack et al., 2010)). However, the published values of the extinction of red FPs with the same chromophore drastically vary depending on the protein: 75 mM-1cm-1 per a polypeptide chain for the DsRed, 120 mM-1cm-1 per a polypeptide chain for tdimer2(12) (Campbell at al., 2002), 22 mM-1cm-1 for mPlum (Shcherbo et al., 2007), 50 mM-1cm-1 for mRFP1 (Campbell at al., 2002) and 90 mM-1cm-1 for mStrawberry (Shu et al., 2006). Discrepancies follow directly from the content of immature form in the protein samples.

Laser Fluorescence Spectroscopy:

simulations performed by (Khrameeva et al., 2008).

Application in Determining the Individual Photophysical Parameters of Proteins 205

directly connected with the optical properties (the steady-state spectra positions, fluorescence quantum yield, etc.) of red FPs. The deviations from chromophore coplanarity are responsible for the changes in the optical characteristics for mCherry and mStrawberry (Shu et al., 2006). The interrelation between the optical properties of the monomeric red FPs and the geometry of their chromophores was also confirmed by the molecular dynamics simulations conducted for mRFP1 mutants with single polar amino acid substitutions at position 66 (Khrameeva et al., 2008). The simulations have shown that the substitutions have an influence on the torsion angles in the phenolic and imidazolidine rings of the chromophore as well as on the torsion angles in the regions of connection between these rings and chromophore attachment to β-barrel. It was predicted that the volume of the amino acid residue at position 66 can correlate with the optical characteristics of the mutants. The experimental results presented in this Section are consistent with the results of

Fig. 7. The dependence of the (a) extinction coefficient, (b) position of absorption/ excitation (squares) and fluorescence emission (triangles) maximum of the protein R form on the volume of 66th amino acid residue. The solid and hollow scatters are polar and non-polar amino acids, respectively. (c) and (d) are schematic diagrams of chrmophore environment, showing the residues location at positions 213, 42 and 213 , 215, respectively. Hydrogen bonds are shown in dashed lines, labeled with lengths in angstroms. Glu is glutamate.

For the mutants with non-polar groups at residue 66 (alanine, leucine and phenylalanine) there is no correlation effect. The non-polar substitutions lead to breakage of hydrogen bonds between the 66th residue of the chromophore and glutamine-42 and glutamine-213. Formation of a new bond between the chromophore and the glutamate-215 is unlikely

In the measurements I obtained 215 mM-1cm-1 for mRFP1, which is larger than the value for DsRed and mPlum. However, it should be noted that I did not take into account the photochemical processes (photoionisation, photobleaching, etc. (Banishev et al., 2008a) in the model of fluorescence response generation (1a). The efficiency of these processes in the protein samples under study may be different. When efficient enough, the photochemical processes may contribute noticeably to fluorescence saturation. In this case their emission can result in the saturation curve giving an overstated value of the absorption cross section and, therefore, overstated quantity of *<sup>R</sup>(max)*. On the other hand, as it was mentioned in Section 5.2, the method applied by (Kredel et al., 2008) for determining the individual extinction coefficient of mPlum is not accurate enough in the case of red FPs (the method is well adapted only for GFP-like FPs). Therefore, the obtained value of 143 mM-1cm-1 can be underestimated and the precise value of the chromophore extinction is greater.

As it was shown earlier (Banishev et al., 2009), for the R form of the proteins mRFP1, mRFP1/Q66S and mRFP1/Q66C, the position of the maximum of absorption, fluorescence excitation and emission bands depends on the substituted amino-acid residue at position 66 and positively correlates with the volume of this residue: the maximum moves to the red range with increasing the volume of the residue. A similar correlation was described for the individual extinction coefficient of the R form chromophore, i.e. a higher extinction coefficient corresponds to a larger volume of the residue. The results for the new mutants mRFP1/Q66N, mRFP1/Q66H, mRFP1/Q66A, mRFP1/Q66L and mRFP1/Q66F are presented in Fig. 7(a, b). In the same figure the results obtained in (Banishev et al., 2009) for mRFP1, mRFP1/Q66S and mRFP1/Q66C are plotted. The values of the amino acids volume were taken from (Zamyatin, 1972). One can see that the dependence of the position of steady-state spectra (at maximum) of two new mutants (mRFP1/Q66N and mRFP1/Q66H) on the volume of amino-acid residue at position 66 has the same trend as described in (Banishev et al., 2009). The same can be observed for the individual extinction coefficient (but not for the integral one). There are no such dependences for characteristics of the proteins mRFP1/Q66A, mRFP1/Q66L and mRFP1/Q66F.

The results can be explained in the following way. It is known that formation of R form chromophore of red FPs goes through formation of a double bond between the Cα and N atoms of the 66th amino acid residue. Since dehydrogenation of a bond between Cα and N atoms involves the carbonaceous framework of the 66th amino acid residue in the system of conjugation, then the changes in the side radical of this residue can lead to the changes in the spectral and photophysical properties of the new mutants.

In the case of a polar amino acid at position 66 (serine, cysteine, asparagines and histidine), its side radical can form hydrogen bonds with the side radicals of glutamine-42, glutamine-213 and glutamate-215 (see Fig. 7 (c, d)). These radicals, in turn, belong to the protein shell (the β-barrel) and are rather rigidly bonded to it (Khrameeva et al., 2008). A change in the geometry of the side radical at position 66 will in this case cause a change in the geometry of the chromophore imidazolidine ring, because the interaction of the chromophore with the glutamine-42 and glutamine-213 through the hydrogen bond network can be distorted and a new bond with glutamate-215 can be formed. As a result, the chromophore tilt- and twistangles (the pictures with the explanation of the angles can be found in (Piatkevich et al., 2010)) will change and the chromophore coplanarity will be distorted. In (Piatkevich et al., 2010) it was shown on the basis on x-ray diffraction data that the chromophore planarity is

In the measurements I obtained 215 mM-1cm-1 for mRFP1, which is larger than the value for DsRed and mPlum. However, it should be noted that I did not take into account the photochemical processes (photoionisation, photobleaching, etc. (Banishev et al., 2008a) in the model of fluorescence response generation (1a). The efficiency of these processes in the protein samples under study may be different. When efficient enough, the photochemical processes may contribute noticeably to fluorescence saturation. In this case their emission can result in the saturation curve giving an overstated value of the absorption cross section

Section 5.2, the method applied by (Kredel et al., 2008) for determining the individual extinction coefficient of mPlum is not accurate enough in the case of red FPs (the method is well adapted only for GFP-like FPs). Therefore, the obtained value of 143 mM-1cm-1 can be

As it was shown earlier (Banishev et al., 2009), for the R form of the proteins mRFP1, mRFP1/Q66S and mRFP1/Q66C, the position of the maximum of absorption, fluorescence excitation and emission bands depends on the substituted amino-acid residue at position 66 and positively correlates with the volume of this residue: the maximum moves to the red range with increasing the volume of the residue. A similar correlation was described for the individual extinction coefficient of the R form chromophore, i.e. a higher extinction coefficient corresponds to a larger volume of the residue. The results for the new mutants mRFP1/Q66N, mRFP1/Q66H, mRFP1/Q66A, mRFP1/Q66L and mRFP1/Q66F are presented in Fig. 7(a, b). In the same figure the results obtained in (Banishev et al., 2009) for mRFP1, mRFP1/Q66S and mRFP1/Q66C are plotted. The values of the amino acids volume were taken from (Zamyatin, 1972). One can see that the dependence of the position of steady-state spectra (at maximum) of two new mutants (mRFP1/Q66N and mRFP1/Q66H) on the volume of amino-acid residue at position 66 has the same trend as described in (Banishev et al., 2009). The same can be observed for the individual extinction coefficient (but not for the integral one). There are no such dependences for characteristics of the

The results can be explained in the following way. It is known that formation of R form chromophore of red FPs goes through formation of a double bond between the Cα and N atoms of the 66th amino acid residue. Since dehydrogenation of a bond between Cα and N atoms involves the carbonaceous framework of the 66th amino acid residue in the system of conjugation, then the changes in the side radical of this residue can lead to the changes in

In the case of a polar amino acid at position 66 (serine, cysteine, asparagines and histidine), its side radical can form hydrogen bonds with the side radicals of glutamine-42, glutamine-213 and glutamate-215 (see Fig. 7 (c, d)). These radicals, in turn, belong to the protein shell (the β-barrel) and are rather rigidly bonded to it (Khrameeva et al., 2008). A change in the geometry of the side radical at position 66 will in this case cause a change in the geometry of the chromophore imidazolidine ring, because the interaction of the chromophore with the glutamine-42 and glutamine-213 through the hydrogen bond network can be distorted and a new bond with glutamate-215 can be formed. As a result, the chromophore tilt- and twistangles (the pictures with the explanation of the angles can be found in (Piatkevich et al., 2010)) will change and the chromophore coplanarity will be distorted. In (Piatkevich et al., 2010) it was shown on the basis on x-ray diffraction data that the chromophore planarity is

*<sup>R</sup>(max)*. On the other hand, as it was mentioned in

underestimated and the precise value of the chromophore extinction is greater.

proteins mRFP1/Q66A, mRFP1/Q66L and mRFP1/Q66F.

the spectral and photophysical properties of the new mutants.

and, therefore, overstated quantity of

directly connected with the optical properties (the steady-state spectra positions, fluorescence quantum yield, etc.) of red FPs. The deviations from chromophore coplanarity are responsible for the changes in the optical characteristics for mCherry and mStrawberry (Shu et al., 2006). The interrelation between the optical properties of the monomeric red FPs and the geometry of their chromophores was also confirmed by the molecular dynamics simulations conducted for mRFP1 mutants with single polar amino acid substitutions at position 66 (Khrameeva et al., 2008). The simulations have shown that the substitutions have an influence on the torsion angles in the phenolic and imidazolidine rings of the chromophore as well as on the torsion angles in the regions of connection between these rings and chromophore attachment to β-barrel. It was predicted that the volume of the amino acid residue at position 66 can correlate with the optical characteristics of the mutants. The experimental results presented in this Section are consistent with the results of simulations performed by (Khrameeva et al., 2008).

Fig. 7. The dependence of the (a) extinction coefficient, (b) position of absorption/ excitation (squares) and fluorescence emission (triangles) maximum of the protein R form on the volume of 66th amino acid residue. The solid and hollow scatters are polar and non-polar amino acids, respectively. (c) and (d) are schematic diagrams of chrmophore environment, showing the residues location at positions 213, 42 and 213 , 215, respectively. Hydrogen bonds are shown in dashed lines, labeled with lengths in angstroms. Glu is glutamate.

For the mutants with non-polar groups at residue 66 (alanine, leucine and phenylalanine) there is no correlation effect. The non-polar substitutions lead to breakage of hydrogen bonds between the 66th residue of the chromophore and glutamine-42 and glutamine-213. Formation of a new bond between the chromophore and the glutamate-215 is unlikely

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because of non-polarity of substituted residues. Therefore, there is no defined correlation between the chromophore geometry (consequently, the volume of the substituted amino acid residue) and the optical properties of the proteins.

At the present time the red FPs whose molecules are monomers are of particular interest (Piatkevich et al., 2010) as fluorescent markers. Attempts to find new variants of red FPs in order to improve their properties (higher brightness, photo and pH stability, etc.) are performed. However, the interrelation between optical or photophysical parameters and structural properties of FPs, which is necessary for development of these studies, is rather unclear. A method for prediction of properties of FPs based on their structure is still not developed. This problem might be solved by analysis of properties of mutant proteins with point mutations. Therefore, the results obtained in this Section can be used to tackle the general problem of the development of an algorithm, which could provide the prediction of the spectral properties of FPs based on their structures. The data will also be useful for revealing promising positions for directed mutagenesis.
