Second, the CE method indicates that 20 protein structures have similar fold as structure of 1ATP-E. However, the PFSA has capability further to distinguish the dissimilarity between 20 structures of cAMP dependent protein kinases. According to CE method, if Z Score is larger than 3.5, the compared proteins have similar fold in structure. The values of Z Score of 20 structures of cAMP are from 3.9 to 7.9, so they all have similar fold structure as 1ATP-E. The values of PFSA-S for 20 structures are distributed in the wide range of 0.9145 - 0.0565. According to PFSA approach, the value of PFSA-S is near one when two structures have high similarity, and on the contrary, the value of PFSA-S is near zero when two structures with less similarity. The PFSA-S value 0.0565 is for comparison between 1ATP-E and No. 20 of structure. PFSA-S near zero indicates that the pair of structures is dissimilar. It is noted that the sequence length of structures 20 is 94. To compare with 1ATP-E, two structures have big difference in length and the alignment generates 228 gaps which give the lower value of PFSA-S. Therefore, the PFSA has ability to distinguish the structural deference in more detail.

#### **4.2.3 PFSA vs. other methods**

A set of 10 pairs of proteins with lower structural similarity was recognized as difficult structures for comparison, and was evaluated by VAST (Madej et al., 1995; Gibrat et al., 1996), DALI (Holm & Sander, 1993; Holm & Park, 2000), CE (Shindyalov & Bourne, 1998), Prosup (Lackner et al., 2000) and LGA (Zemla, 2003) methods respectively. The structural similarity was evaluated by two optimistic parameters, i.e. lower RMSD and larger number of equivalent residues. It is apparently, in Table 10, that various methods gave comparative results for each pair of proteins. The results from various methods provide complementary information for protein structural comparison. Overall, the ProSup and LGA methods provided consistent results with restriction of RMSD less than 3.0. The PFSA, however, offers new observation for assessment of similarity of protein structures. First, the similarity is able to be evaluated by a single value of the PFSA-S. In order to compare with other methods, information of (sum of number of identical and analogous shapes) / (number of gaps) / (PFSA-S) is listed in Table 10. The similarity score of PFSA-S is determined by number of identical shapes, number of analogous shapes and number of gaps. Second, the value of score PFSA-S may judge the similarity crossing isolated comparisons, i.e. the values of score PFSA-S from unrelated comparisons can be used to assess the protein homologous degree. Each pair of proteins in Table 10 is a lonely comparison without common reference structure, but the value of PFSA-S may indicate which pair of structures has higher similarity. In Table 10, the results of each pair of comparison are sorted according the values of PFSA-S descendingly. For example, the pair of comparison of 1CEW-I and 1MOL-A has the PFSA-S = 0.564 and the pair of comparison of 1CID and 2RHE has the PFSA-S = 0.384. A conclusion may be obtained that the pair of 1CEW-I and 1MOL-A has higher structural similarity than the pair of 1CID and 2RHE. Third, relative size of compared proteins makes the contribution to structural similarity in PFSA approach. With various methods, the value of RMSD is often used to make judgment of structural similarity. For example, the pair of comparison of 1CEW-I and 1MOL-A have the RMSD (VAST: 2.0, DALI: 2.3, CE: 2.3, ProSup: 1.9and LGA: 2.0); the pair of comparison of 1TEN and 3HHR-B have the RMSD (VAST: 1.6, DALI: 1.9, CE: 1.9, ProSup: 1.7 and LGA: 1.9). Both pairs have lower RMSD than other

Second, the CE method indicates that 20 protein structures have similar fold as structure of 1ATP-E. However, the PFSA has capability further to distinguish the dissimilarity between 20 structures of cAMP dependent protein kinases. According to CE method, if Z Score is larger than 3.5, the compared proteins have similar fold in structure. The values of Z Score of 20 structures of cAMP are from 3.9 to 7.9, so they all have similar fold structure as 1ATP-E. The values of PFSA-S for 20 structures are distributed in the wide range of 0.9145 - 0.0565. According to PFSA approach, the value of PFSA-S is near one when two structures have high similarity, and on the contrary, the value of PFSA-S is near zero when two structures with less similarity. The PFSA-S value 0.0565 is for comparison between 1ATP-E and No. 20 of structure. PFSA-S near zero indicates that the pair of structures is dissimilar. It is noted that the sequence length of structures 20 is 94. To compare with 1ATP-E, two structures have big difference in length and the alignment generates 228 gaps which give the lower value of PFSA-S. Therefore, the PFSA has ability to distinguish the structural deference in

A set of 10 pairs of proteins with lower structural similarity was recognized as difficult structures for comparison, and was evaluated by VAST (Madej et al., 1995; Gibrat et al., 1996), DALI (Holm & Sander, 1993; Holm & Park, 2000), CE (Shindyalov & Bourne, 1998), Prosup (Lackner et al., 2000) and LGA (Zemla, 2003) methods respectively. The structural similarity was evaluated by two optimistic parameters, i.e. lower RMSD and larger number of equivalent residues. It is apparently, in Table 10, that various methods gave comparative results for each pair of proteins. The results from various methods provide complementary information for protein structural comparison. Overall, the ProSup and LGA methods provided consistent results with restriction of RMSD less than 3.0. The PFSA, however, offers new observation for assessment of similarity of protein structures. First, the similarity is able to be evaluated by a single value of the PFSA-S. In order to compare with other methods, information of (sum of number of identical and analogous shapes) / (number of gaps) / (PFSA-S) is listed in Table 10. The similarity score of PFSA-S is determined by number of identical shapes, number of analogous shapes and number of gaps. Second, the value of score PFSA-S may judge the similarity crossing isolated comparisons, i.e. the values of score PFSA-S from unrelated comparisons can be used to assess the protein homologous degree. Each pair of proteins in Table 10 is a lonely comparison without common reference structure, but the value of PFSA-S may indicate which pair of structures has higher similarity. In Table 10, the results of each pair of comparison are sorted according the values of PFSA-S descendingly. For example, the pair of comparison of 1CEW-I and 1MOL-A has the PFSA-S = 0.564 and the pair of comparison of 1CID and 2RHE has the PFSA-S = 0.384. A conclusion may be obtained that the pair of 1CEW-I and 1MOL-A has higher structural similarity than the pair of 1CID and 2RHE. Third, relative size of compared proteins makes the contribution to structural similarity in PFSA approach. With various methods, the value of RMSD is often used to make judgment of structural similarity. For example, the pair of comparison of 1CEW-I and 1MOL-A have the RMSD (VAST: 2.0, DALI: 2.3, CE: 2.3, ProSup: 1.9and LGA: 2.0); the pair of comparison of 1TEN and 3HHR-B have the RMSD (VAST: 1.6, DALI: 1.9, CE: 1.9, ProSup: 1.7 and LGA: 1.9). Both pairs have lower RMSD than other

more detail.

**4.2.3 PFSA vs. other methods**

remaining pairs and have overall agreement with various methods. However, PFSA approach distinguishes these two pairs by PFSA-S. With PFSA-S = 0.456, the pair of 1TEN and 3HHR-B is ranked below other five pairs, including the pair of 1CEW-I and 1MOL-A with PFSA-A = 0.564. The separation is explained by a factor that the pair of 1CEW-I and 1MOL-A has comparable length of sequence (108 : 94), but the pair of 1TEN and 3HHR-B has larger different in length (99 : 195). The contribution of relative difference of size is counted in PFSA approach. Therefore, with normalization of PFSA-S, for separated comparisons, the similarity degree still can be evaluated without common reference protein.

Table 10. Comparison of 10 pairs of proteins with lower structural similarity using various methods. N1 and N2 are the lengths of proteins. For methods of VAST, DALL, CE, ProSup and LGA, the results are presented as (Number of identical residues) / (RMSD). For PFSA approach, results are presented as (sum of number of identical and analogous shapes) / (number of gaps) / (PFSA-S). The results of each pair of comparison are sorted according values of PFSA-S descendingly.

### **5. Conclusion**

The PFSA approach adopts the vector of folding shape of five residues as element, and the geometric feature of folding shape is embedded by alphabets as representation. With application of alphabets, the alignment of protein structures is straightforward and steady. This study demonstrates two advantages in PFSA approach. First, 27 PFSC vectors are able to cover all possible folding shapes of five successive C atoms in protein. This is fundamental important because it offers a complete description of folding conformation for any protein with given 3D structure. Second, with consistent procedure, the PFSA approach generates unique score for similarity and detail information in alignment table, which provides new observation for the protein structure comparison.

#### **6. Acknowledgments**

This work was supported in part by a grant from the Indiana Spinal Cord and Brain Injury Research Fund (2009-2011). The algorithms of PFSC and PFSA have been coded with Java (J2SE v.1.5.0\_07) computer language. Requests for additional information will be accepted via e-mail to<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>or via Website: http://www.proteinshape.com.

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## **Theoretical Analyses of Photoinduced Electron Transfer from Aromatic Amino Acids to the Excited Flavins in Some Flavoproteins**

Kiattisak Lugsanangarm1, Nadtanet Nunthaboot2, Somsak Pianwanit1,3,\*, Sirirat Kokpol1,3 and Fumio Tanaka1,4,\* *1Department of Chemistry, Faculty of Science, Chulalongkorn University, 2Department of Chemistry, Faculty of Science, Mahasarakham University, Mahasarakham, 3Center of Excellence for Petroleum, Petrochemicals, and Advanced Materials, Chulalongkorn University, Bangkok, 4Laser Biochemistry Division, Institute for Laser Technology, Osaka, 1,2,3Thailand 4Japan*

#### **1. Introduction**

Electron transfer phenomena have been an important subjects in the fields of physics (Jortner & Bixon, 1999), chemistry (Mataga et al., 2005a, 2005b; Vogler et al., 2011) and biology (Marcus & Sutin, 1985; Gray & Winkler, 1996; Bendal, 1996). Photoinduced electron transfer (PET) plays an essential role in photosynthetic systems (Blankenship, 2002). In the last decade a number of new flavin photoreceptors have been found. Among six families of the photoreceptors, phototropins (Crosson & Moffat, 2001), cryptochromes (Giovani et al., 2003) and BLUF (blue-light sensing using flavin) contain flavins as the reaction center (Masuda & Bauer, 2002). The PET from Tyr to the excited isoalloxazine (Iso\*) is considered as an initial step of the photo-regulation for photosynthesis in AppA (Masuda & Bauer, 2002; Laan et al., 2003) and pili-dependent cell motility in TePixD (Kita et al., 2005) and in Slr1694 (Masuda et al., 2004) photoactive bacteria.

Flavoproteins contain flavin mononucleotide (FMN), flavin adenine dinucleotide, and riboflavin as a cofactor and are ubiquitously distributed in various microorganisms, in leafy vegetables and specific tissues of other multicellular plants, and in the milk, brain, kidney, liver and heart of mammals, where they play an essential role in many redox reactions (Frago et al., 2008).

The fluorescence of flavins was first reported by Weber (1950), along with the fluorescence quenching of flavins by various substances, including aromatic amino acids. Since then many researchers have studied the photochemistry of flavins and flavoproteins (Silva &

<sup>\*</sup> Corresponding Authors

Edward, 2006). The quenching of flavin fluorescence by an indole ring was reported with isoalloxazine-(CH2)n-indole dyads by McCormick (1977). Time-resolved fluorescence spectroscopy of flavins and flavoproteins has been reviewed by Berg and Visser (2001). However, a number of flavoproteins are practically non-fluorescent, but rather they emit fluorescence with very short lifetimes (sub-picoseconds) upon excitation with an ultra-short laser pulse (Mataga et al., 1998, 2000, 2002; Tanaka et al. 2007; Chosrowjan et al., 2007, 2008, 2010). In these flavoproteins tryptophan (Trp) and/or tyrosine (Tyr) residues always exist near the isoalloxazine ring (Iso). The remarkably fast fluorescence quenching in these flavoproteins was demonstrated to be caused by PET from Trp and/or Tyr to the excited state Iso (Iso\*), by means of picosecond (Karen et al., 1983, 1987) and femtosecond (Zhong & Zewail, 2001) transient absorption spectroscopy. The PET phenomena in these flavoproteins are similar to the flavin photo-receptors (Crosson & Moffat, 2001; Masuda & Bauer, 2002), but had been discovered before the flavin photoreceptors.

Since the seminal works on electron transfer theory by Marcus (1956a, 1956b, 1964), several researchers have further developed the electron transfer theory (Hush, 1961; Sumi & Marcus, 1986; Bixon & Jortner, 1991, 1993; Bixon et al., 1994; Kakitani & Mataga, 1985; Kakitani et al., 1991, 1992). However, they have been modeled for PET in bulk solution and it is not clear whether these theories can be applicable to PET in proteins. Therefore, it is required to establish a method to quantitatively analyze PET in proteins.

In any electron transfer theories there are several parameters that are difficult to determine experimentally. The PET rates in flavoproteins have been analyzed experimentally with ultrafast fluorescence dynamics and theoretically by an electron transfer theory using the atomic coordinates obtained by molecular dynamics (MD) simulation. The procedure to determine the unknown PET parameters is as follows (Nunthaboot et al., 2008a, 2009a): (1) the time-dependent atomic coordinates of flavoproteins are obtained by MD simulation, (2) the PET rates are then calculated using a PET theory and the atomic coordinates with a set of trial PET parameters, (3) the parameters are then varied until the best-fit between the calculated and observed fluorescence decays is obtained, according to a non-linear least squares method.

In this review article we describe the results of quantitative analyses of PET in wild type (WT) flavodoxin and FMN binding proteins from *Desulfovibrio vulgaris*, Miyazaki F, and three relevant flavodoxin amino acid substitution mutants (isoforms) and two relevant FMN binding protein amino acid substitution mutants, respectively, and discuss the characteristics of the PET mechanism in flavoproteins.

Note that for brevity, unless stated otherwise, reference to flavodoxin and FMN binding proteins in this article refers to those from *Desulfovibrio vulgaris*, Miyazaki F.

#### **2. Method of analysis of Photoinduced Electron Transfer (PET) in flavoproteins**

#### **2.1 Electron transfer theory in flavoproteins**

All of the original PET theories were modeled for a system in solution. Here, we describe the PET theories that have been used for the flavoproteins. Electrostatic (ES) energy was first introduced by Nunthaboot et al. (2009a).

#### **2.1.1 Marcus-Hush theory**

160 Protein Structure

Edward, 2006). The quenching of flavin fluorescence by an indole ring was reported with isoalloxazine-(CH2)n-indole dyads by McCormick (1977). Time-resolved fluorescence spectroscopy of flavins and flavoproteins has been reviewed by Berg and Visser (2001). However, a number of flavoproteins are practically non-fluorescent, but rather they emit fluorescence with very short lifetimes (sub-picoseconds) upon excitation with an ultra-short laser pulse (Mataga et al., 1998, 2000, 2002; Tanaka et al. 2007; Chosrowjan et al., 2007, 2008, 2010). In these flavoproteins tryptophan (Trp) and/or tyrosine (Tyr) residues always exist near the isoalloxazine ring (Iso). The remarkably fast fluorescence quenching in these flavoproteins was demonstrated to be caused by PET from Trp and/or Tyr to the excited state Iso (Iso\*), by means of picosecond (Karen et al., 1983, 1987) and femtosecond (Zhong & Zewail, 2001) transient absorption spectroscopy. The PET phenomena in these flavoproteins are similar to the flavin photo-receptors (Crosson & Moffat, 2001; Masuda & Bauer, 2002),

Since the seminal works on electron transfer theory by Marcus (1956a, 1956b, 1964), several researchers have further developed the electron transfer theory (Hush, 1961; Sumi & Marcus, 1986; Bixon & Jortner, 1991, 1993; Bixon et al., 1994; Kakitani & Mataga, 1985; Kakitani et al., 1991, 1992). However, they have been modeled for PET in bulk solution and it is not clear whether these theories can be applicable to PET in proteins. Therefore, it is

In any electron transfer theories there are several parameters that are difficult to determine experimentally. The PET rates in flavoproteins have been analyzed experimentally with ultrafast fluorescence dynamics and theoretically by an electron transfer theory using the atomic coordinates obtained by molecular dynamics (MD) simulation. The procedure to determine the unknown PET parameters is as follows (Nunthaboot et al., 2008a, 2009a): (1) the time-dependent atomic coordinates of flavoproteins are obtained by MD simulation, (2) the PET rates are then calculated using a PET theory and the atomic coordinates with a set of trial PET parameters, (3) the parameters are then varied until the best-fit between the calculated and observed fluorescence decays is obtained, according to a non-linear least squares method. In this review article we describe the results of quantitative analyses of PET in wild type (WT) flavodoxin and FMN binding proteins from *Desulfovibrio vulgaris*, Miyazaki F, and three relevant flavodoxin amino acid substitution mutants (isoforms) and two relevant FMN binding protein amino acid substitution mutants, respectively, and discuss the

Note that for brevity, unless stated otherwise, reference to flavodoxin and FMN binding

All of the original PET theories were modeled for a system in solution. Here, we describe the PET theories that have been used for the flavoproteins. Electrostatic (ES) energy was first

proteins in this article refers to those from *Desulfovibrio vulgaris*, Miyazaki F.

**2. Method of analysis of Photoinduced Electron Transfer (PET) in**

but had been discovered before the flavin photoreceptors.

characteristics of the PET mechanism in flavoproteins.

**2.1 Electron transfer theory in flavoproteins**

introduced by Nunthaboot et al. (2009a).

**flavoproteins**

required to establish a method to quantitatively analyze PET in proteins.

When the *jth* flavoprotein contains several PET donors, the PET rate from the *kth* Trp and/or Tyr near Iso to Iso\* by Marcus theory as modified by Hush (1961) (MH theory) is expressed by Eq. (1), and the energy diagram for MH theory is shown in Figure 1.

Fig. 1. Energy diagram for Marcus-Hush PET theory

$$k\_{\rm MH}^{\rm ik} = \frac{2\pi}{\hbar} \frac{H\_q^2}{\sqrt{4\pi \mathcal{L}\_\rm S}^{\rm k}} \exp\left[-\frac{\left\{\Delta G\_q^0 - \varepsilon^2 \;/\ \varepsilon\_{\rm DA} R\_{\rm jk} + \mathcal{\lambda}\_\rm S^{\rm ik} + ES\_j(k)\right\}^2}{4\mathcal{L}\_\rm S^{\rm k} k\_B T}\right] \tag{1}$$

In Eq. (1), *Hq* is the electronic interaction energy between Iso\* and Trp (*q* = Trp) or Tyr (*q* = Tyr). *Rjk* is the center to center (Rc) distance between Iso and the ET donor *k* in the *j*th flavoprotein. , *Bk* , *T* and *e* are the reduced Planck constant, Boltzmann constant, temperature and electron charge, respectively. *DA* is the static dielectric constant of medium between the PET donors and acceptor. ( ) *ES k <sup>j</sup>* is the net ES energy between the *kth* aromatic ionic species and all other ionic groups in the *j*th flavoprotein, as described below. *jk S* is the solvent reorganization energy of the Iso\* and the *kth* donor in the *j*th flavoprotein, as shown by Eq. (2);

$$\lambda\_s^{\prime k} = e^2 \left( \frac{1}{2a\_{\rm ho}} + \frac{1}{2a\_q} - \frac{1}{R\_{\beta k}} \right) \left( \frac{1}{\varepsilon\_o} - \frac{1}{\varepsilon\_{\rm DA}} \right) \tag{2}$$

Here, *Iso a* and *<sup>q</sup> a* are the radii of Iso and the donor *q* (Trp or Tyr), assuming these reactants are spherical, and is the optical dielectric constant (a value of 2 being used). *DA* is the static dielectric constant between Iso and a donor. The radii of Iso, Trp and Tyr were determined according to the following procedure. (1) The three dimensional sizes of lumiflavin for Iso, 3-methylindole for Trp, and p-methylphenol for Tyr were obtained by a semi-empirical molecular orbital method (PM3). (2) The volumes of these molecules were determined as asymmetric rotors. (3) The radii of the spheres having the same volumes of the asymmetric rotors are obtained. The obtained radii by this procedure are *Iso a* = 0.224 nm, *Trp a* = 0.196 nm and *Tyr a* = 0.173 nm.

The standard free energy gap ( <sup>0</sup> *Gq* ) was expressed with the ionization potential ( *<sup>q</sup> EIP* ) of the PET donor *q* (Trp or Tyr), as shown in Eq. (3).

$$
\Delta \mathbf{G}\_q^0 = \mathbf{E}\_{I\!\!\!P}^0 - \mathbf{G}\_{I\!\!\!so}^0 \tag{3}
$$

where <sup>0</sup> *GIso* is the standard Gibbs energy related to the electron affinity of Iso\*. The values of *<sup>q</sup> EIP* for Trp and Tyr were 7.2 eV and 8.0 eV, respectively (Vorsa et al., 1999).

#### **2.1.2 Kakitani-Mataga (KM) theory**

The PET rate by Kakitani & Mataga (KM theory) is expressed as Eq. (4), which describes the PET rate for both adiabatic and non-adiabatic processes, whilst the MH and Bixon-Jortner (BJ) theories (see below) describe only adiabatic processes.

$$k\_{\rm KM}^{\rm jk} = \frac{\nu\_0^q}{1 + \exp\left\{\mathcal{J}^q(R\_{\parallel k} - R\_0^q)\right\}} \sqrt{\frac{k\_B T}{4\pi \lambda\_\odot^{\rm k}}} \exp\left[-\frac{\left\{\Delta G\_q^0 - e^2 \;/\ \varepsilon\_{\rm DA} R\_{\parallel k} + \mathcal{A}\_\mathcal{S}^{\rm k} + ES\_\mathcal{J}(\mathbf{k})\right\}^2}{4\lambda\_\odot^{\rm k} k\_B T}\right] \tag{4}$$

Here 0 *q* is an adiabatic frequency, *<sup>q</sup>* is the PET process coefficient, and <sup>0</sup> *<sup>q</sup> R* is a critical distance between the adiabatic and non-adiabatic PET processes. These quantities depend only on *q* (Trp or Tyr). When 0 *<sup>q</sup> R R jk* the ET process is adiabatic, whereas when 0 *<sup>q</sup> R R jk* it is non-adiabatic. The other quantities are the same as those in the MH theory (section 2.1.1).

#### **2.1.3 Bixon-Jortner (BJ) theory**

The BJ theory describes the PET rates from various vibronic states, as shown in Eq. (5), while the MH and KM theories only describe the PET from the lowest vibrational state.

$$k\_{\rm B}^{\vec{k}} = \frac{2\pi}{\hbar} H\_q^2 \frac{\exp\left\{-\beta(\mathcal{R}\_{\vec{\mathcal{R}}} - \sigma\_q) - S\right\}}{\sqrt{2\pi\mathcal{A}\_S^{\vec{k}}}} \sum\_{i=0}^n \frac{S^i}{i!} \exp\left[-\frac{\left\{\Delta G\_q^0 - \varepsilon^2 \;/\ \mathcal{E}\_{\rm DA} \mathcal{R}\_{\vec{\mathcal{R}}} + \lambda\_S^{\vec{k}} + i\hbar \{\boldsymbol{\alpha}\} + \mathcal{E} S\_j(\boldsymbol{k})\right\}^2}{4\mathcal{A}\_S^{\vec{k}} k\_B T}\right] (5)$$

*S <sup>V</sup>* / is the vibronic coupling constant, where *<sup>V</sup>* is the reorganization energy associated with the average frequency , *n* is the number of vibrational modes in the donor and *<sup>q</sup>* is the van der Waals contact and is given by Eq. (6).

$$
\sigma\_q = a\_{lso} + a\_q \tag{6}
$$

The meanings of all the other notations are the same as that given in the MH theory (section 2.1.1).

determined as asymmetric rotors. (3) The radii of the spheres having the same volumes of the asymmetric rotors are obtained. The obtained radii by this procedure are *Iso a* = 0.224 nm,

The standard free energy gap ( <sup>0</sup> *Gq* ) was expressed with the ionization potential ( *<sup>q</sup> EIP* ) of

where <sup>0</sup> *GIso* is the standard Gibbs energy related to the electron affinity of Iso\*. The values of

The PET rate by Kakitani & Mataga (KM theory) is expressed as Eq. (4), which describes the PET rate for both adiabatic and non-adiabatic processes, whilst the MH and Bixon-Jortner

exp

*jk S S B*

*R R k T*

distance between the adiabatic and non-adiabatic PET processes. These quantities depend

it is non-adiabatic. The other quantities are the same as those in the MH theory (section

The BJ theory describes the PET rates from various vibronic states, as shown in Eq. (5), while

exp ( ) / ( ) 2 exp 2 ! 4 *jk <sup>n</sup> <sup>i</sup> jk q q DA jk <sup>S</sup> <sup>j</sup> jk*

*R S G e R i ES k <sup>S</sup> k H*

The meanings of all the other notations are the same as that given in the MH theory (section

<sup>2</sup> 0 2

(5)

*i k T*

, *n* is the number of vibrational modes in the

*<sup>q</sup> Iso <sup>q</sup> a a* (6)

*<sup>V</sup>* is the reorganization energy

the MH and KM theories only describe the PET from the lowest vibrational state.

0

*<sup>q</sup>* is the van der Waals contact and is given by Eq. (6).

*BJ <sup>q</sup> jk jk <sup>i</sup> <sup>S</sup> <sup>B</sup> <sup>S</sup>*

is the vibronic coupling constant, where

*jk <sup>q</sup> q DA jk <sup>S</sup> <sup>j</sup> jk <sup>B</sup>*

*G e R ES k k T <sup>k</sup>*

*<sup>q</sup> EIP* for Trp and Tyr were 7.2 eV and 8.0 eV, respectively (Vorsa et al., 1999).

0 0 *<sup>q</sup> GE G <sup>q</sup> IP Iso* (3)

<sup>2</sup> 0 2

is the PET process coefficient, and <sup>0</sup>

*<sup>q</sup> R R jk* the ET process is adiabatic, whereas when 0

/ ( )

(4)

*<sup>q</sup> R* is a critical

*<sup>q</sup> R R jk*

*Trp a* = 0.196 nm and *Tyr a* = 0.173 nm.

**2.1.2 Kakitani-Mataga (KM) theory**

Here 0 *q*

2.1.1).

*S <sup>V</sup>* /

donor and

2.1.1).

the PET donor *q* (Trp or Tyr), as shown in Eq. (3).

(BJ) theories (see below) describe only adiabatic processes.

0

1 exp ( ) 4 4

*KM q q jk jk*

0

is an adiabatic frequency, *<sup>q</sup>*

only on *q* (Trp or Tyr). When 0

**2.1.3 Bixon-Jortner (BJ) theory**

associated with the average frequency

2

 #### **2.2 Electrostatic (ES) energy between the photoproducts and ionic groups in a protein**

Proteins, including flavoproteins, contain many ionic groups, which may influence the PET rate. The cofactor in the relevant flavoproteins is FMN, which has two negative charges at the phosphate. The ES energy between the Iso anion or donor *kth* cation, and all the other ionic groups in the *jth* flavoprotein is expressed by Eq. (7):

$$E\_j(k) = \sum\_{i=1}^{n\_k} \frac{\mathbf{C}\_k \cdot \mathbf{C}\_{Glu}}{\varepsilon\_0^j R\_k \{Glu - i\}} + \sum\_{i=1}^{n\_k} \frac{\mathbf{C}\_k \cdot \mathbf{C}\_{Asp}}{\varepsilon\_0^j R\_k \{Asp - i\}}$$

$$+ \sum\_{i=1}^{n\_k} \frac{\mathbf{C}\_k \cdot \mathbf{C}\_{Lys}}{\varepsilon\_0^j R\_k \{Lys - i\}} + \sum\_{i=1}^{n\_k} \frac{\mathbf{C}\_k \cdot \mathbf{C}\_{Arg}}{\varepsilon\_0^j R\_k \{Arg - i\}} + \sum\_{i=1}^2 \frac{\mathbf{C}\_k \cdot \mathbf{C}\_P}{\varepsilon\_0^j R\_k (P - i)}\tag{7}$$

where *nE* , *nB* , *nK* and *nR* are the numbers of Glu, Asp, Lys and Arg residues, respectively, in the flavoprotein. Here, *k* = 0 for the Iso anion, and *k* > 0 for the donor cations. 0 *j* is the static dielectric constant inside the entire *jth* flavoprotein, which should be different from *DA* . *Ck* is the charge of the aromatic ionic species *k*, and is -*e* for *k* = 0 (Iso anion), +*e* for *k* > 1. *CGlu* (= - *e*), *CAsp* (= - *e*), *CLys* (= + *e*), *CArg* (= + *e*) and *CP* (= - *e*) are the charges of Glu, Asp, Lys, Arg and phosphate anions, respectively. It was assumed that these groups are all in an ionic state in solution. The pKa values of the ionic amino acids in water are 4.3 in Glu, 3.9 in Asp, 10.5 in Lys and 12.5 in Arg. However, as residues within proteins these pKa values may be modified in the range of ± 0.3. His displays a pKa of 6.0 in water. All fluorescence measurements were performed in 0.1 M phosphate buffer at pH 7.0, where His should be neutral. Distances between the aromatic ionic species *k* and the *i*th Glu are denoted as ( ) *R Glu i <sup>k</sup>* , those between *k* and the *i*th Asp are denoted as ( ) *R Asp i <sup>k</sup>* , and so on. ( ) *ES k <sup>j</sup>* is expressed in Eq. (8);

$$ES\_j(k) = E\_j(0) + E\_j(k)\tag{8}$$

#### **2.3 Observed ultrafast fluorescence dynamics of flavodoxins and FMN binding proteins**

Ultrafast fluorescence dynamics of flavodoxins and FMN binding proteins have been measured by means of a fluorescence up-conversion method (Mataga et al., 2002; Chosrowjan et al., 2007, 2008, 2010). The fluorescence decay functions of the WT flavodoxin, the two single substitution isoforms, Y97F and W59F, and the double substitution, Y97F/W59F (DM), are represented by Eq. (9), whilst the fluorescence decays of the WT FMN binding protein and the four single substitution isoforms, E13T, E13Q, W32Y and W32A, are represented by Eq. (10).

$$F\_{\rm FD}^{j}(\mathbf{t}) = \sum\_{i=1}^{n} \alpha\_{\rm FDi}^{j} \exp(-\mathbf{t} \mid \tau\_{\rm FDi}^{j}) \quad \text{ (j = 1, WT; j = 2, Y97F; j = 3, W59F; j = 4, Y97F/W59F)} \quad \text{(9)}$$

$$F\_{\rm FBP}^{\rm j}(\mathbf{t}) = \sum\_{i=1}^{n} \alpha\_{\rm FBP}^{\rm j} \exp(-\mathbf{t} \,/\ \pi\_{\rm FBP}^{\rm j}) \,\mathrm{(j=1, W7; j=2, E13T; j=3, E13Q; j=4, W32Y; j=5, W32A)} \quad \text{(10)}$$

In Eq. (9), *n* = 1 or 2, and in Eq. (10) *n* = 1 to 3, depending on the protein system, *j*. The decay parameters are listed in Table 1. The experimental decay of the WT flavodoxin contains an additional lifetime component with 500 ps. However, it was interpreted to be free FMN dissociated from the protein. The average lifetime values, *<sup>k</sup> AV* , were obtained from 1 *<sup>n</sup> j jj AV ii i* and are listed in the last line of Table 1. The decays with *n* greater than 1 display non-exponential function.

aThe observed flavodoxin and FMN binding protein decay functions are expressed in Eqs. (9) and (10), respectively.

bData were taken from the work by Mataga et al. (2002).

cData were taken from the works by Chosrowjan et al. (2007, 2008, 2010).

dDM denotes the Y97F/W59F double mutant.

eAveraged lifetimes were obtained by 1 *<sup>n</sup> j jj AV ii i* .

Table 1. Fluorescence decay parameters of the flavodoxin and FMN binding protein isoforms from *Desulfovibrio vulgaris*, Miyazaki F a

#### **2.4 Determination of the PET parameters**

The calculated decay function in the *jth* protein system is expressed by Eq. (11).

$$F\_{calc}^{j}(t) = \left\langle \exp\left\{-\sum\_{k=1}^{m} k\_{ET}^{jk}(t')t\right\} \right\rangle\_{AV} \tag{11}$$

... *AV* means the averaging procedure of the exponential function in Eq. (11) over *t'*. In Eq. (11) we assumed that the decay function at every instant of time, *t*', during the MD simulation time range can always be expressed by an exponential function, and thus the MD simulation time range must be much longer than experimental decay time range. In Eq. (11) *m* is the total number of PET donors in the *jth* flavoprotein. In MH theory, the unknown PET parameters were *Hq* (*q* = Trp and Tyr), <sup>0</sup> *GIso* , *DA* and 0 *j* , whilst in KM theory they are 0 *q* , *q* , and 0 *<sup>q</sup> <sup>R</sup>* for Trp and Tyr, <sup>0</sup> *GIso* , *DA* and 0 *j* , and in BJ theory they are *Hq* (*q* = Trp or Tyr), , *<sup>V</sup>* , , <sup>0</sup> *GIso* , *DA* and 0 *j* . These parameters were determined so as to obtain the minimum value of <sup>2</sup> , as defined by Eq. (12), by means of a non-linear least squares method, according to the Marquardt algorithm.

$$\mathcal{X}^2 = \frac{1}{N\_j N\_F} \sum\_{j=1}^{N\_j} \sum\_{i=1}^{N\_F} \frac{\left\{ F\_{\text{calc}}^j(t\_i) - F\_{\text{obs}}^j(t\_i) \right\}^2}{F\_{\text{calc}}^j(t\_i)} \tag{12}$$

Here, *NF* denotes the number of time intervals in the fluorescence decay, and *Nj* is the total number of flavoproteins for simultaneous analysis.

### **3. Flavodoxins from** *Desulfovibrio vulgaris***, Miyazaki F**

#### **3.1 Homology modeling**

164 Protein Structure

In Eq. (9), *n* = 1 or 2, and in Eq. (10) *n* = 1 to 3, depending on the protein system, *j*. The decay parameters are listed in Table 1. The experimental decay of the WT flavodoxin contains an additional lifetime component with 500 ps. However, it was interpreted to be

(ps) 0.157 0.254 0.322 18 0.167 0.107 0.134 3.4 30.1

) (1.0) (0.85) (0.83) (1.0) (0.96) (0.86) (0.85) (0.23) (1.0)

(ps) - 4.0 5.5 - 1.5 1.5 0.746 18.2 -

) - (0.15) (0.17) - (0.04) (0.12) (0.12) (0.74) -

(ps) - - - - - 30 30 96 -

) - - - - - (0.02) (0.03) (0.03) -

e (ps) 0.157 0.816 1.20 18 0.22 0.872 1.10 17.1 30.1

aThe observed flavodoxin and FMN binding protein decay functions are expressed in Eqs. (9) and (10),

1 *<sup>n</sup> j jj AV ii i*

 .

Table 1. Fluorescence decay parameters of the flavodoxin and FMN binding protein

The calculated decay function in the *jth* protein system is expressed by Eq. (11).

*F t k tt*

1 ( ) exp ( ') *<sup>m</sup> <sup>j</sup> jk calc ET*

... *AV* means the averaging procedure of the exponential function in Eq. (11) over *t'*. In Eq. (11) we assumed that the decay function at every instant of time, *t*', during the MD simulation time range can always be expressed by an exponential function, and thus the MD

*k AV*

(11)

and are listed in the last line of Table 1. The decays with *n* greater than 1

Flavodoxinb FMN binding proteinc WT Y97F W59F DMd WT E13T E13Q W32Y W32A

*AV*

, were obtained

free FMN dissociated from the protein. The average lifetime values, *<sup>k</sup>*

from

1 *j*

( <sup>1</sup> *j*

2 *j*

( <sup>2</sup> *j*

3 *j*

( <sup>3</sup> *j*

*k AV*

respectively.

bData were taken from the work by Mataga et al. (2002).

isoforms from *Desulfovibrio vulgaris*, Miyazaki F a

**2.4 Determination of the PET parameters**

dDM denotes the Y97F/W59F double mutant.

eAveraged lifetimes were obtained by

cData were taken from the works by Chosrowjan et al. (2007, 2008, 2010).

Decay parameter

1 *<sup>n</sup> j jj AV ii i*

display non-exponential function.

Flavodoxins are small flavoproteins with a molecular weight of 15 - 23 kDa that have been isolated from a variety of microorganisms. Flavodoxins are considered to function as electron-transport proteins in various metabolic pathways (Sancho, 2006). They contain one molecule of non covalently-bound FMN (see Chart 1) as a cofactor, and exhibit a highly negative reduction potential for the semiquinone / hydroquinone couple of FMN, and accordingly the semiquinone state is stable. The redox properties of FMN in flavodoxins are considerably different from those of the free FMN.

The biochemical properties of flavodoxin from *Desulfovibrio vulgaris*, strain Miyazaki F were first characterized by Kitamura et al. (1998). The dissociation constant of FMN is 0.38 nM, which is ~1.6-fold higher than that in the related flavodoxin from Desulfovibrio vulgaris Hildenborough (0.24 nM). The redox potential of these two closely related flavodoxins is also slightly different, being E1 = -434 and -440 mV for the Miyazaki and Hildenborough forms, respectively, for the oxidized-semiquinone reaction of flavodoxin, and E2 = -151 and -143 mV for the semiquinone-2-electron reduced reaction, respectively (Kitamura et al., 1998). Recently, the three-dimensional structures of numerous flavodoxins have been determined, including Desulfovibrio vulgaris Hildenborough (Watenpauph, 1973) and the flavodoxins from Anacystis nidulans (Drennan et al., 1999), Clostridium beijerinckii (Ludwig et al., 1997), Escherichia coli (Hoover & Ludwig, 1997), Anabaena 7120 (Burkhart et al., 1995) a red algae (Fukuyama et al., 1992) Chondrus crispu (Fukuyama et al., 1990) and H. pylori (Freigang et al., 2002) by X-ray crystallography. The structure of flavodoxin, however, has not yet been determined, although the primary structure is known (Kitamura et al., 1998).

The ultrafast fluorescence dynamics of flavodoxins (Mataga et al., 2002) have been extensively investigated in the WT and the Y97F, W59F and W59F/Y97F (DM) substitution isoforms, as described above.

Chart 1. Chemical structure of FMN and its atom notations.

#### **3.2 Three-dimensional structures of four flavodoxin isoforms**

The protein structures of the WT, single amino acid substitution (Y97F and W59F) and the double amino acid substitution (W59F/Y97F; DM) isoforms have been determined by homology modeling method with the Modeler Module of the Discovery Studio 2.0 software package (http://www.discoverystudios.com) using the flavodoxin *Desulfo*v*ibrio* v*ulgaris*, strain Hildenborough structure (PDB code: 1J8Q) as the template. This protein displays 66% amino acid sequence identity and 79% similarity to the WT flavodoxin of Miyazaki reviewed herein. The validities of the structures were examined with a Verified3D analysis (visit for the method, www.proteinstructures.com by Prof. Salam Al-Karadaghi). Verify3D assigns each residue a structural class based on its location and environment (alpha, beta, loop, polar, apolar etc). Then, a database generated from good structures is used to obtain a score for each of the 20 amino acids in this structural class. Figure 2 shows the Verified3D scores at each amino acid residue, where the quality of the structures is satisfactory.

MD simulations were performed for 10 ns in order to investigate the dynamic properties of the proteins and the important interactions that are involved in the binding of the FMN cofactor to the proteins. Figure 3 shows the three-dimensional structures in water that were obtained by MD simulation.

Chart 1. Chemical structure of FMN and its atom notations.

obtained by MD simulation.

**3.2 Three-dimensional structures of four flavodoxin isoforms**

The protein structures of the WT, single amino acid substitution (Y97F and W59F) and the double amino acid substitution (W59F/Y97F; DM) isoforms have been determined by homology modeling method with the Modeler Module of the Discovery Studio 2.0 software package (http://www.discoverystudios.com) using the flavodoxin *Desulfo*v*ibrio* v*ulgaris*, strain Hildenborough structure (PDB code: 1J8Q) as the template. This protein displays 66% amino acid sequence identity and 79% similarity to the WT flavodoxin of Miyazaki reviewed herein. The validities of the structures were examined with a Verified3D analysis (visit for the method, www.proteinstructures.com by Prof. Salam Al-Karadaghi). Verify3D assigns each residue a structural class based on its location and environment (alpha, beta, loop, polar, apolar etc). Then, a database generated from good structures is used to obtain a score for each of the 20 amino acids in this structural class. Figure 2 shows the Verified3D

scores at each amino acid residue, where the quality of the structures is satisfactory.

MD simulations were performed for 10 ns in order to investigate the dynamic properties of the proteins and the important interactions that are involved in the binding of the FMN cofactor to the proteins. Figure 3 shows the three-dimensional structures in water that were

Fig. 2. Verifyed-3D analysis of the template (1J8Q), and the four isoforms of *Desulfobivrio vulgaris*, strain Miyazaki F., that were constructed by the homology modeling. The compatibilities of amino acids in their environments are indicated by the positive scores. Data taken from Lugsanangarm et al. (2011a).

Fig. 3. Structures of four flavodoxin isomers. In the WT isoform, Trp59, Tyr97, Tyr99 and Trp16 are potential PET donors to Iso\*, whilst these are Trp59, Tyr99 and Trp16 in the Y97F isomer and Tyr97, Tyr99 and Trp16 in the W59F isomer. In the DM, Tyr99 and Trp16 are the potential PET donors. Data were taken from Lugsanangarm et al. (2011a).

#### **3.3 Decomposition free energy analysis of amino acid residues at the FMN binding site**

In order to evaluate the important amino acid residues for FMN binding, the decomposition free energy per amino acid residue has been obtained. Figure 4 shows the decomposition energy of FMN from FMN-apoflavodoxin complexes. The amino acids near FMN are categorized into three groups, the 10-loop, 60-loop and 90-loop regions (see Figure 4). The decomposition energy is highest in the amino acids in the 10-loop regions (Ser9, Thr10, Thr11, Gly12 and Asn13 and Thr14) in all isoforms (Figure 4). All amino acids in the 10-loop region form hydrogen bonds with the FMN side chain viz: Ser9OH with O3P, Thr10NH(peptide) with O1P, Thr11OH with O2P, Thr11NH(peptide) with O2P and O1P, Gly12NH(peptide) with O2P, Asn13NH(peptide) with O2P, Thr14OH with O3P and Thr14NH(peptide) with O3P (see Chart 1 for atom notations). These hydrogen bond interactions are considered to contribute the largest proportion of the decomposition free energy. Among the four flavodoxin isoforms, the decomposition energy is highest in Y97F (-9.30 kcal/mol), followed by W59F (-9.25 kcal/mol), DM (-8.60 kcal/mol) and is lowest in the WT (-8.54 kcal/mol).

Fig. 4. Decomposition free energy of amino acid residues at the FMN binding site of the four flavodoxin isoforms. The energies are shown with green bars for WT, red bars for W59F, deep blue bars for Y97F and light blue bars for DM. Data were taken from Lugsanangarm et al. (2011a).

#### **3.4 Structural dynamics of flavodoxins**

168 Protein Structure

In order to evaluate the important amino acid residues for FMN binding, the decomposition free energy per amino acid residue has been obtained. Figure 4 shows the decomposition energy of FMN from FMN-apoflavodoxin complexes. The amino acids near FMN are categorized into three groups, the 10-loop, 60-loop and 90-loop regions (see Figure 4). The decomposition energy is highest in the amino acids in the 10-loop regions (Ser9, Thr10, Thr11, Gly12 and Asn13 and Thr14) in all isoforms (Figure 4). All amino acids in the 10-loop region form hydrogen bonds with the FMN side chain viz: Ser9OH with O3P, Thr10NH(peptide) with O1P, Thr11OH with O2P, Thr11NH(peptide) with O2P and O1P, Gly12NH(peptide) with O2P, Asn13NH(peptide) with O2P, Thr14OH with O3P and Thr14NH(peptide) with O3P (see Chart 1 for atom notations). These hydrogen bond interactions are considered to contribute the largest proportion of the decomposition free energy. Among the four flavodoxin isoforms, the decomposition energy is highest in Y97F (-9.30 kcal/mol), followed by W59F (-9.25 kcal/mol), DM (-8.60 kcal/mol) and is

Fig. 4. Decomposition free energy of amino acid residues at the FMN binding site of the four flavodoxin isoforms. The energies are shown with green bars for WT, red bars for W59F, deep blue bars for Y97F and light blue bars for DM. Data were taken from Lugsanangarm et

**3.3 Decomposition free energy analysis of amino acid residues at the FMN binding**

**site**

al. (2011a).

lowest in the WT (-8.54 kcal/mol).

Potential PET donors in the WT flavodoxin are Trp59, Tyr97 and Tyr99 and Trp16. The protein dynamics of these flavodoxin isoforms have been examined by viewing the timedependent changes in the Rc distances and the inter-planar angles between Iso and these donors. Figure 5 shows the time-evolutions of Rc in the four different flavodoxin isoforms, where the Rc distances clearly fluctuate rapidly but are mostly within ± 10% of the mean values. In the DM the Rc values of Tyr99 and Trp16 vary with long periods in addition to the rapid fluctuation. Since the bulky Tyr97 and Trp59 residues are both replaced by the smaller Phe residue in the DM then the space around Iso may be increased compared to that in the WT, and so may account for the marked fluctuation in the Rc distances of Tyr99 and Trp16. Figure 6 shows the time-evolutions of the inter-planar angles in the WT flavodoxin, where the variation of the inter-planar angles is about ± 30 deg around the mean. The derived mean Rc and edge-to-edge (Re) distances and inter-planar angles over the MD time range are listed in Table 2. The Rc distance was shortest in Tyr97 and then Trp59 in all four flavodoxin isoforms, whilst Tyr99 and Trp16 are quite far from Iso. The inter-planar angle of Trp 59 in the WT is -43 deg, while it is 73 deg in Y97F.

Fig. 5. Time evolution of the Rc distance between Iso and the indicated potential PET donor in the (A) WT, (B) Y97F, (C) W59F and (D) DM (Y97F/W59F) flavodoxin isoforms. Figure 5A was taken from Lugsanangarm et al. 2011b. Figures 5B, 5C and 5D were taken from Lugsanangarm et al. 2011c.

Fig. 6. Time evolution of the inter-planar angle between Iso and the four potential PET donors in the WT flavodoxin. Data were taken from Lugsanangarm et al. (2011b).

a The means values are listed, which were obtained by taking the average over the MD simulation time (2 ns with 0.1 ps time intervals). Data are taken from Lugsanangarm et al. (2011c).

b Center to center and c edge to edge distances between Iso and the aromatic amino acids.

d Inter-planar angles between Iso and the aromatic amino acids.

e The data are taken from Lugsanangarm et al. (2011b).

f Tyr97 is replaced by Phe.

g Trp59 is replaced by Phe.

h Both Tyr97 and Trp59 are replaced by Phe

Table 2. Geometrical factors in the four flavodoxin isoformsa. Data were taken from Lugsanangarm et al. (2011c).

#### **3.5 The PET mechanism in flavodoxins**

#### **3.5.1 Analysis of PET with crystal structures of flavoproteins**

The PET analysis in flavoproteins first starts with their crystal structures (Tanaka et al., 2007, 2008). The logarithms of the averaged PET rate (inverse of the averaged lifetimes) in ten flavoprotein systems are plotted against the Re and Rc distances. The logarithms of the PET

Fig. 6. Time evolution of the inter-planar angle between Iso and the four potential PET donors in the WT flavodoxin. Data were taken from Lugsanangarm et al. (2011b).

Protein Donor *R*cb *R*ec Angled

WTe Trp59 0.642 0.247 -42.8

Y97Ff Trp59 0.858 0.264 73.1

W59Fg Tyr97 0.577 0.259 14

DMh Tyr99 1.35 0.496 -28.6

a The means values are listed, which were obtained by taking the average over the MD simulation time

Table 2. Geometrical factors in the four flavodoxin isoformsa. Data were taken from

The PET analysis in flavoproteins first starts with their crystal structures (Tanaka et al., 2007, 2008). The logarithms of the averaged PET rate (inverse of the averaged lifetimes) in ten flavoprotein systems are plotted against the Re and Rc distances. The logarithms of the PET

(2 ns with 0.1 ps time intervals). Data are taken from Lugsanangarm et al. (2011c). b Center to center and c edge to edge distances between Iso and the aromatic amino acids.

d Inter-planar angles between Iso and the aromatic amino acids.

**3.5.1 Analysis of PET with crystal structures of flavoproteins**

e The data are taken from Lugsanangarm et al. (2011b).

h Both Tyr97 and Trp59 are replaced by Phe

**3.5 The PET mechanism in flavodoxins**

f Tyr97 is replaced by Phe. g Trp59 is replaced by Phe.

Lugsanangarm et al. (2011c).

Tyr97 0.536 0.301 14 Tyr99 1.28 0.533 23.5 Trp16 1.72 1.18 -18.1

Tyr99 1.12 0.329 55.7 Trp16 2.1 1.51 53

Tyr99 1.34 0.513 28.9 Trp16 1.85 1.42 -24.5

Trp16 2.02 1.44 30.9

(nm) (nm) (deg)

rates can be expressed with two straight lines when Rc instead of Re is used (see Figure 7). At longer distances the PET rate rapidly decreases with increasing Rc distances, while at shorter distances it decreases slowly with the same sized increments in the Rc value. When Re is used in place of Rc as the distance measure, no such clear distance-dependence is observed in the flavoprotein systems. According to Moser et al. (1992), the logarithm of the PET rate in photosynthesis systems linearly decreases with increasing Re. However, the time domain of the PET rates in their work is much longer than the one in the flavoprotein systems. It is conceivable then that the logarithm of the PET rate in photosynthesis systems increases more slowly with Rc when the distances become shorter.

The PET in the fast phase with low slope was interpreted to be "Coherent PET", where the PET takes place to the Franck-Condon state of Iso\* from Trp or Tyr (Mataga et al., 2002).

Of the ten flavoproteins evaluated, the PET donors with a Rc distance of less than 1 nm were all Trp residues, except for Tyr97 in flavodoxin with an exceptionally low PET rate at an Rc value of 0.57 nm. The low rate in Tyr97 was elucidated by the higher ionization potential of Tyr compared to Trp (Tanaka et al., 2007, 2008). Moreover, the agreement between ln *obs ET k* and ln *calc ET k* were the highest with KM theory (Figure 7) compared to that MH theory (Sumi & Marcus, 1986) or BJ theories (not shown).

Fig. 7. ln *ET k* vs. Rc plot for the observed and KM theory calculated PET rates of 10 flavoprotein systems. Y and YC represent ln *obs ET k* and ln *calc ET k* , respectively, where *obs ET k* and *calc ET k* are the observed and KM theory calculated PET rates, respectively. Data are taken from Tanaka et al. (2008).

#### **3.5.2 PET analysis with MD snapshots of four flavodoxin isoforms**

The PET analysis from ultrafast fluorescence dynamics was first conducted by Nunthaboot et al. (2008a, 2009a). Time-dependent PET rates in FMN binding proteins were evaluated from the atomic coordinates of the protein as obtained by MD simulation. All PET theories contain several PET parameters that cannot be experimentally determined. Rather these parameters are numerically determined by a non-linear least-square method, as described in Section 2.4.

Fluorescence decay functions of four flavodoxin isoforms (WT, Y97F, W59F and DM) were simultaneously analyzed, with the atomic coordinates of these proteins obtained by MD simulation and KM theory, by Lugsanangarm et al. (2011b, 2011c). The PET parameters common among these flavodoxin systems are listed in Table 3. Ultrafast decay functions of the flavodoxins are expressed by Eq. (9) using the decay parameters listed in Table 1. It is noted that the values of 0 and are quite different between Trp and Tyr, which is related to the electron coupling terms in the KM theory. The quantum basis for the difference is described by Nunthaboot et al. (2008b). In these works it is assumed that the static dielectric constant varies with the protein systems. Table 4 lists the static dielectric constants inside each protein. The dielectric constant of the WT flavodoxin is greatest among the four systems, and that of the DM is the lowest. This is reasonable because Iso in the WT flavodoxin is sandwiched between the polar Trp59 and Tyr97 residues, while both of them are replaced by the non-polar Phe in the DM. Thus, in the DM isoform Iso should be in a relatively non-polar environment, whilst in the Y97F and W59F isoforms the Iso residue may be in a moderately polar environment.

aPhysical meanings of the PET parameters are described at Section 3.1. The PET parameters in the Table are common among the four isoforms of flavodoxin (WT, W59F, Y97F and DM), and were obtained according to the procedure described at Section 3.4.

bFor flavodoxins, the four isoforms (WT, Y97F, W59F, DM) were simultaneously analyzed. Data are taken from Lugsanangarm et al. (2011b, 2011c).

cFor the FMN binding proteins, the five isoforms (WT, E13T, E13Q, W32Y and W32A) were simultaneously analyzed.

a Dielectric constants, <sup>0</sup> *j* , are determined according to the procedure described at Section **3.4**

b The WT, Y97F, W59F and DM (Y97F/W59F) flavodoxin isoforms were simultaneously analyzed. Data are taken from Lugsanangarm, et al. (2011b, 2011c)

c The WT, E13T, E13Q, W32Y, W32A FMN binding protein isoforms were simultaneously analyzed.

Table 4. Dielectric constant inside the protein a Data taken from Lugsanangarm et al. (2011c) for Flavodoxin, and Nunthaboot et al. (2011).

#### **3.5.3 Dynamics of the PET Rate and related physical quantities in flavodoxins**

Time-dependent changes in the PET rates of the four flavodoxin isoforms are shown in Figure 8. n the WT and Y97F isoforms, the PET rates from Trp59 are the fastest even though

Fluorescence decay functions of four flavodoxin isoforms (WT, Y97F, W59F and DM) were simultaneously analyzed, with the atomic coordinates of these proteins obtained by MD simulation and KM theory, by Lugsanangarm et al. (2011b, 2011c). The PET parameters common among these flavodoxin systems are listed in Table 3. Ultrafast decay functions of the flavodoxins are expressed by Eq. (9) using the decay parameters listed in Table 1. It is

to the electron coupling terms in the KM theory. The quantum basis for the difference is described by Nunthaboot et al. (2008b). In these works it is assumed that the static dielectric constant varies with the protein systems. Table 4 lists the static dielectric constants inside each protein. The dielectric constant of the WT flavodoxin is greatest among the four systems, and that of the DM is the lowest. This is reasonable because Iso in the WT flavodoxin is sandwiched between the polar Trp59 and Tyr97 residues, while both of them are replaced by the non-polar Phe in the DM. Thus, in the DM isoform Iso should be in a relatively non-polar environment, whilst in the Y97F and W59F isoforms the Iso residue

(nm-1)

Trp Tyr Trp Tyr Trp Tyr Flavodoxinb 3090 2460 55.6 9.64 0.772 0.676 7.60 - FMN binding proteinc 1016 197 21.0 6.25 0.663 0.499 6.71 2.19 aPhysical meanings of the PET parameters are described at Section 3.1. The PET parameters in the Table are common among the four isoforms of flavodoxin (WT, W59F, Y97F and DM), and were obtained

bFor flavodoxins, the four isoforms (WT, Y97F, W59F, DM) were simultaneously analyzed. Data are

Table 3. The best-fit PET parametersa . Data are taken from Nunthaboot et al. (2008a, 2009a,

Flavodoxin b FMN binding protein c Variant WT Y97F W59F DM WT E13T E13Q W32Y W32A

5.85 4.78 4.04 2.28 14.8 5.99 6.69 5.89 6.29

b The WT, Y97F, W59F and DM (Y97F/W59F) flavodoxin isoforms were simultaneously analyzed. Data

Time-dependent changes in the PET rates of the four flavodoxin isoforms are shown in Figure 8. n the WT and Y97F isoforms, the PET rates from Trp59 are the fastest even though

c The WT, E13T, E13Q, W32Y, W32A FMN binding protein isoforms were simultaneously analyzed. Table 4. Dielectric constant inside the protein a Data taken from Lugsanangarm et al. (2011c)

**3.5.3 Dynamics of the PET Rate and related physical quantities in flavodoxins**

, are determined according to the procedure described at Section **3.4**

cFor the FMN binding proteins, the five isoforms (WT, E13T, E13Q, W32Y and W32A) were

are quite different between Trp and Tyr, which is related

*R*0 (nm)

<sup>0</sup> *GIso*

(eV) *DA*

noted that the values of

System

simultaneously analyzed.

a Dielectric constants, <sup>0</sup>

2011).

 0 *j*  0 and

may be in a moderately polar environment.

according to the procedure described at Section 3.4.

taken from Lugsanangarm et al. (2011b, 2011c).

*j*

are taken from Lugsanangarm, et al. (2011b, 2011c)

for Flavodoxin, and Nunthaboot et al. (2011).

 0 (ps-1) the Rc distance between Iso and Tyr97 in the WT is shorter (see Table 2). The mean PET rates over the MD time range (2 ns with 0.1 ps intervals) are listed in Table 5 along with the other mean physical quantities. The mean PET rate is fastest from Trp59 in WT and then in Y97F, as mentioned above, and is then followed by Tyr97 in the W59F isoform. The PET rates from Trp16 and Tyr99 are always negligibly slow.

The net ES energy, ( ) *ES k <sup>j</sup>* , markedly varied from -0.00159 eV in Trp59 (Y97F) to 3.42 eV in Tyr99 (W59F), while *jk S* varied from 0.377 eV in Trp16 (DM) to 2.06 eV in Tyr99 (WT), and the ES energy between the donor and acceptor, <sup>2</sup> / <sup>0</sup> *j jk e R* , varied from -0.652 eV in Tyr97 (W59F) to -0.142 eV in Trp16 (Y97F). The amount of the variation is largest in the net ES energies. The dielectric constant between the Iso anion and the donor cation, *DA* , is not introduced in the PET analysis for flavodoxins.

Fig. 8. The PET rates from Trp and/or Tyr to Iso\* in four flavodoxin isoforms. Figure for WT was taken from Lugsanangarm (2011b). Figures for W59F, Y97F and DM were taken from Lugsanangarm (2011c).

Table 5A. Mean physical quantities related to the PET in the WT and W59Fa flavodoxin isoformsa. Data were taken from Lugsanangarm et al. (2011c).

aPhysical quantities were obtained with the PET parameters listed in Table 3. Mean values are from over the MD time range (2 ns with 0.1 ps intervals).

bKM evaluated PET rates are given by Eq. (4).

cSolvent reorganization energy, as given by Eq. (2).

dNet ES energy, as given by Eq. (8).

eStandard free energy gap, as given by Eq. (3). f

ES energy between the Iso anion and the donor cation.

gTotal free energy gap, as given by Eq. (12).

Table 5B. Mean physical quantities related to the PET in the Y97F and DM flavodoxin isoformsa. Lugsanangarm et al. (2011c)

#### **4. Protein dynamics of FMN binding proteins**

The FMN binding protein from *Desulfo*v*ibrio* v*ulgaris* (Miyazaki F) is considered to play an important role in the electron transport process in the bacterium, but the whole picture of the electron flow and coupling of the redox proteins is not yet clear (Kitamura et al., 1998). Three-dimensional structures of the FMN binding protein from *D.* V*ulgaris* (Miyazaki F) were determined by X-ray crystallography (Suto et al., 2000) and NMR spectroscopy (Liepinsh et al., 1997). According to these structures, Trp32 is the closest residue to Iso

 (eV)c 1.53 1.54 1.99 2.06 1.20 1.54 1.59 ( ) *ES k <sup>j</sup>* (eV)d −0.0172 −0.0942 2.73 2.71 −0.219 0.984 3.42 <sup>0</sup> *Gq* (eV)e −0.467 0.333 −0.467 0.333 0.333 −0.467 0.333

<sup>0</sup> ( ) *GT jk* (eV)g 0.868 0.221 −2.12 −2.86 0.583 −0.321 −3.49

Table 5A. Mean physical quantities related to the PET in the WT and W59Fa flavodoxin

*jk kKM* (ps-1)b 4.95 - - - 7.43 x 10-2 ln *jk kKM* 1.60 −96.5 −134 −95.0 −2.60

 (eV)c 1.47 1.81 1.74 0.377 0.385 ( ) *ES k <sup>j</sup>* (eV)d −0.00159 1.20 3.26 2.13 0.0131 <sup>0</sup> *Gq* (eV)e −0.467 −0.467 0.333 −0.467 0.333

<sup>0</sup> ( ) *GT jk* (eV)g 0.855 −0.594 −3.31 −1.35 0.124

Table 5B. Mean physical quantities related to the PET in the Y97F and DM flavodoxin

The FMN binding protein from *Desulfo*v*ibrio* v*ulgaris* (Miyazaki F) is considered to play an important role in the electron transport process in the bacterium, but the whole picture of the electron flow and coupling of the redox proteins is not yet clear (Kitamura et al., 1998). Three-dimensional structures of the FMN binding protein from *D.* V*ulgaris* (Miyazaki F) were determined by X-ray crystallography (Suto et al., 2000) and NMR spectroscopy (Liepinsh et al., 1997). According to these structures, Trp32 is the closest residue to Iso

(eV)f −0.386 −0.142 −0.289 −0.313 −0.470

aPhysical quantities were obtained with the PET parameters listed in Table 3. Mean values are from over

Physical quantity Y97F DM

isoformsa. Data were taken from Lugsanangarm et al. (2011c).

(eV)f −0.384 −0.460 −0.144 −0.193 −0.652 −0.196 −0.263

Trp59 Trp16 Tyr99 Trp16 Tyr99

*jk kKM* (ps-1)b 7.10 1.26 x 10-3 - - 3.13 - ln *jk kKM* 1.96 −6.68 −125 −115 1.14 −69.10 −<sup>156</sup>

WT W59F

Trp59 Tyr97 Trp16 Tyr99 Tyr97 Trp16 Tyr99

Physical quantity

*jk S*

<sup>2</sup> / <sup>0</sup> *j jk e R*

*jk S*

<sup>2</sup> / <sup>0</sup> *j jk e R*

the MD time range (2 ns with 0.1 ps intervals). bKM evaluated PET rates are given by Eq. (4). cSolvent reorganization energy, as given by Eq. (2).

eStandard free energy gap, as given by Eq. (3). f ES energy between the Iso anion and the donor cation.

gTotal free energy gap, as given by Eq. (12).

isoformsa. Lugsanangarm et al. (2011c)

**4. Protein dynamics of FMN binding proteins**

dNet ES energy, as given by Eq. (8).

followed by Tyr35 and then Trp106. To examine the effect of Trp32 on the PET rate in the FMN binding protein, Trp32 was replaced by Tyr (W32Y) or Ala (W32A), and further the single negative charge at residue 13, glutamate 13 (E13) was replaced by either Thr (E13T) or Gln (E13Q). The crystal structures of E13T and E13Q were determined by X-ray crystallography (Chosrowjan et al. 2010). The dynamic behavior of these FMN binding protein isoforms were studied by MD simulation (Nunthaboot et al., 2008a, 2009a, 2011), and Figure 9 shows snapshots of the WT, E13T, E13Q, W32Y and W32A FMN binding protein isoforms.

Fig. 9. Protein structures near Iso in the five FMN binding protein isoforms. Trp32, Tyr35 and Trp106 are potential PET donors in the FMN binding protein. Trp32 is replaced by Tyr in W32Y and Ala in W32A. Amino acids at residue position 13 are also shown in the Figures. These structures were obtained by MD simulation.Data were taken from Nunthaboot et al. (2011). (Reproduced by permission of the PCCP Owner Societies).

Mean the donor-acceptor distances over MD time range are summarized in Table 6A, 6B. The WT displays great variations in the Rc distances with long periods, in addition to the instantaneous fluctuations. The mean values of the geometrical factors over the entire MD time range (2 ns with 0.1 ps time intervals) are listed in Table 6. The Rc distance is shortest in Trp32 among the three different aromatic amino acid residue positions (Trp/tyr32, Tyr 35 and Trp106) with mean distances of Trp32 of 0.70, 0.72 and 0.75 nm in the WT, E13T and E13Q isoforms, respectively. The distance between Iso and Tyr32 in W32Y is shorter than that between Iso and Trp32 in the WT. The inter-planar angle between Iso and Trp32 varies from -52 deg in the WT to -38 deg in the E13Q isoform, while that between Iso and Tyr35 varies from 43 deg in W32A to 93 deg in the WT.

#### **4.1 Amino acid at position 13 of the FMN binding proteins**

The WT FMN binding protein contains Glu13, with a negative charge at neutral pH, whilst in the E13T and E13Q substitution isoforms the amino acids at this position are Thr13 and Gln13 with neutral charges. The distances between the PET donors or acceptor and amino acid residue 13 of the five FMN binding protein isomers are listed in Table 7. The distances between Iso and side chain of amino acid 13 do not significantly vary between the five FMN binding protein isoforms (range 1.5 – 1.6 nm), nor does that between Trp32 (0.9 – 1.0 nm), Tyr35 (1.0 – 1.2 nm) and Trp106 (1.7 – 1.97 nm) excepting that of Trp106 in the W32Y isoform that was further away (2.13 nm).

aMean values of factors between Iso and the nearby indicated aromatic amino acids are listed. The mean

values were obtained by taking an average over the entire MD time range. bCenter-to-center distance (Rc) and edge-to-edge (Re) distance. cRelative standard deviation (RSD), obtained from SD/mean value.

Table 6A. Geometrical factor of Iso and the indicated nearby aromatic amino acids of the FMN binding protein isomersa. Data were taken from Nunthaboot et al. (2011). (Reproduced by permission of the PCCP Owner Societies).

time range (2 ns with 0.1 ps time intervals) are listed in Table 6. The Rc distance is shortest in Trp32 among the three different aromatic amino acid residue positions (Trp/tyr32, Tyr 35 and Trp106) with mean distances of Trp32 of 0.70, 0.72 and 0.75 nm in the WT, E13T and E13Q isoforms, respectively. The distance between Iso and Tyr32 in W32Y is shorter than that between Iso and Trp32 in the WT. The inter-planar angle between Iso and Trp32 varies from -52 deg in the WT to -38 deg in the E13Q isoform, while that between Iso and Tyr35

The WT FMN binding protein contains Glu13, with a negative charge at neutral pH, whilst in the E13T and E13Q substitution isoforms the amino acids at this position are Thr13 and Gln13 with neutral charges. The distances between the PET donors or acceptor and amino acid residue 13 of the five FMN binding protein isomers are listed in Table 7. The distances between Iso and side chain of amino acid 13 do not significantly vary between the five FMN binding protein isoforms (range 1.5 – 1.6 nm), nor does that between Trp32 (0.9 – 1.0 nm), Tyr35 (1.0 – 1.2 nm) and Trp106 (1.7 – 1.97 nm) excepting that of Trp106 in the W32Y

> Rc (nm)b Re (nm)b Trp32 Tyr32 Tyr35 Trp106 Trp32 Tyr32 Tyr35 Trp106

WT 0.703 -- 1.016 1.052 0.261 -- 0.425 0.314 (RSDc) -0.072 -- -0.097 -0.088 -0.086 -- -0.292 -0.29 E13T 0.724 -- 0.872 0.913 0.269 -- 0.331 0.269 (RSDc) -0.048 -- -0.069 -0.038 -0.079 -- -0.181 -0.111 E13Q 0.748 -- 0.854 0.939 0.265 -- 0.287 0.294 (RSDc) -0.044 -- -0.053 -0.043 -0.095 -- -0.123 -0.131 W32Y -- 0.654 0.826 0.907 -- 0.276 0.284 0.251 (RSDc) -- -0.05 -0.075 -0.036 -- -0.091 -0.167 -0.11 W32A -- -- 0.769 0.895 -- -- 0.29 0.277 (RSDc) -- -- -0.082 -0.05 -- -- -0.226 -0.139

aMean values of factors between Iso and the nearby indicated aromatic amino acids are listed. The mean

Table 6A. Geometrical factor of Iso and the indicated nearby aromatic amino acids of the FMN binding protein isomersa. Data were taken from Nunthaboot et al. (2011). (Reproduced

values were obtained by taking an average over the entire MD time range. bCenter-to-center distance (Rc) and edge-to-edge (Re) distance. cRelative standard deviation (RSD), obtained from SD/mean value.

by permission of the PCCP Owner Societies).

varies from 43 deg in W32A to 93 deg in the WT.

isoform that was further away (2.13 nm).

Protein system

**4.1 Amino acid at position 13 of the FMN binding proteins**

Table 6B. Inter-planar angle factor between Iso and the indicated nearby aromatic amino acids of the FMN binding protein isomersa Data were taken from Nunthaboot et al. (2011). (Reproduced by permission of the PCCP Owner Societies).

aMean distances (+ 1 standard deviation), averaged over the MDS time range, are shown in units of nm. bDistances were obtained taking the average over all distances between atoms in the aromatic ring and the center of the two oxygen atoms in the side chain of Glu13.

cObtained by taking the average over all distances between the atoms in the aromatic ring and the oxygen atom of the Thr13 (E13T) or Gln13 (E13Q) side chain.

Table 7. Geometry of the amino acid residue at position 13 in the five FMN binding protein isoformsa. Data were taken from Nunthaboot et al. (2011). (Reproduced by permission of the PCCP Owner Societies).

#### **4.2 The PET rates and related physical quantities in FMN binding proteins**

The common parameters among the five FMN binding protein isoforms are listed in Table 3, where 0 = 1016 (ps-1) for Trp and 197 (ps-1) for Tyr, = 21.0 (nm-1) for Trp and 6.25 (nm-1) for Tyr, *R*0 = 0.663 (nm) for Trp and 0.499 (nm) for Tyr. <sup>0</sup> *GIso* = 6.71 (eV) and *DA* = 2.19.

These values are quite different from those of the flavodoxins. The time-evolutions of the PET rates in the five different FMN binding protein isoforms over the MD time course are shown in Figure 10. Fluctuations of the PET rate are always marked in Tyr35, but not so much in Trp32. In the WT isoform the PET rates vary with rather long periods in addition to the instantaneous fluctuations, which is in accord with the time-evolution of Rc distances in the WT. The mean PET rate and physical quantities related to the PET rates are listed in Table 8, where the PET rate is observed to always be fastest from Trp32, and then from Trp106 whilst that from Tyr35 is always slow (see also Figure 10). Among the WT, E13T and

a Mean (± SD) values, taken over the MD time range (2 ns with 0.1 ps intervals), are listed. The PET rate is obtained by KM theory.

b The PET rate is given by Eq. (4).

178 Protein Structure

Quantity Donor WT E13T E13Q W32Y W32A

Tyr32 -- -- -- 1.6 ±

Tyr32 -- -- -- 0.217

Tyr32 -- -- -- 0.123

Tyr32 -- -- -- 0.197

Tyr32 -- -- -- -1.009

17.22 14.76

6.4 400 x10-21

0.003 0.003

0.206 0.004

0.240 0.005

0.223 0.003

0.335 0.043

0.472 0.050

0.312 0.027

0.449 0.041

7 200 x10-17

0.018 0.011

0.208

0.229 0.004

0.225 0.003

0.021 0.028

0.269

0.391 0.041

0.290

0.412 0.035

10.43 -- --

30 x10-7

3.7 200 x10-14

0.192 0.350

0.004 -- --

0.236 0.006

0.223 0.002

0.074 0.030

0.032 -- --

0.033

0.256 0.052

0.141 0.039

0.021 -- --

0.330 0.046

0.215 0.034

0.045 -- --

0.020 --

0.049 --

0.005 --

5 130 x 10-13

0.176 0.599

0.231 0.006

0.222 0.003

0.079 0.026

0.242 0.052

0.230 0.054

0.321 0.043

0.309 0.042

Trp32 7.10

Trp32 0.202

Iso 0.071

Trp32 0.076

Trp32 -0.949

Tyr35 4 <sup>95</sup>

Trp106 0.082

Tyr35 0.249

Trp106 0.232

Trp32 0.005

Tyr35 0.080

Trp106 -0.140

Tyr35 0.150

Trp106 -0.069

Tyr35 -0.660

3.08

x 10-14

0.110

0.005

0.006

0.005

0.013

0.017

0.025

0.007

0.010

0.022

0.017

0.055

0.070

*jk KM k* <sup>b</sup> (ps-1)

*jk <sup>S</sup>* <sup>c</sup> (eV)

( ) *Ej k* <sup>d</sup> (eV)

( ) *ES k <sup>j</sup>* <sup>e</sup> (eV)

2 <sup>0</sup> / *DA jk e R* f

(eV)

c Solvent reorganization energy is given by Eq. (2).

d ES energy of the Iso anion or the donor cation and other ionic groups, as given by Eq. (7).

e Net ES energy, as given by Eq. (8).

f ES energy between the Iso anion and a donor cation.

g Total standard free energy, as given by Eq. (12).

Table 8. Mean PET rate and its related physical quantities in five FMN binding protein isoforms a. Data were taken from Nunthaboot et al. (2011). (Reproduced by permission of the PCCP Owner Societies).

E13Q isoforms, the PET rate from Trp32 was fastest in E13T. The values of *jk S* do not vary significantly with the donor and protein system (range 0.202 – 0.231 eV). Likewise the ES energies between the Iso anion and the donor cations, <sup>2</sup> / *DA jk e R* , did not vary much among the donors (range -0.949 eV to -0.627 eV) (Table 8 and Figure 11). In contrast, the net ES energies, ( ) *ES k <sup>j</sup>* , varied from -0.069 eV in Trp106 (WT) to 0.449 eV in Tyr35 (E13T). This remarkable variation in ( ) *ES k <sup>j</sup>* compared to the other physical quantities is also seen in the flavodoxin isoforms.

#### **4.3 Effect of changing the negative charge of amino acid residue 13 on the PET rate**

The PET rate of Trp32 was fastest in all five FMN binding protein isoforms. The ES energies between the Iso anion and ionic groups in the proteins, ( ) *E k <sup>j</sup>* , fell from 0.071 eV in the WT (and similar values in W32Y and W32A) to -0.023 eV and 0.021 eV in E13T and E13Q, respectively (Table 8; Figure 11), suggesting a potential affect of the charge neutralization at residue position 13. In addition, the ES energies between the Trp32 cation and the ionic groups in the proteins increased dramatically from 0.005 eV in the WT, to 0.335 eV and 0.269 eV in the E13T and E13Q isoforms, respectively. In the WT the ES energy between the negative charge of Glu and Trp32 cation should be negative, which contributes to reduce the value of ( ) *E k <sup>j</sup>* . In the neutral charged (at residue 13) E13T and E13Q isoforms the stabilizing energy found in the WT disappears, again supporting the potential importance of the negative charge at residue 13. It is noted that the absolute values of the net ES energies are quite low in the WT, while they are much higher in the other isoforms. Net ES energies of Trp32, from which the PET rate is fastest, are always positive, while those for Trp106 are negative in the WT, E13T and E13Q isoforms.

Fig. 10. Time-evolution of the PET rate in the five FMN binding protein isoforms. Data were taken from Nunthaboot et al. (2011). (Reproduced by permission of the PCCP Owner Societies).

#### **5. Energy gap law in flavodoxin and FMN binding protein systems**

The total free energy gap of the *kth* donor in the *jth* flavoprotein is expressed by Eq. (12);

$$-\Delta G\_T^0(jk) \propto -ES\_j(k) + e^2 \ne \varepsilon\_{DA} R\_{jk} - \Delta G\_q^0 \tag{12}$$

When *jk S* varies with <sup>0</sup> ( ) *GT jk* , the normal energy gap law is modified, as in Eq. (13);

$$\left[1\,\mathrm{m}\,k\_{\mathrm{KM}}^{\mathrm{jk}}\,/\,\lambda\_{\mathrm{S}}^{\mathrm{jk}}\,\mathrm{ox}\,-\right]\left[\left(1+\Delta G\_{\mathrm{T}}^{\mathrm{0}}(jk)\,/\,\lambda\_{\mathrm{S}}^{\mathrm{jk}}\right)^{2}\right]\tag{13}$$

Fig. 10. Time-evolution of the PET rate in the five FMN binding protein isoforms. Data were taken from Nunthaboot et al. (2011). (Reproduced by permission of the PCCP Owner

**5. Energy gap law in flavodoxin and FMN binding protein systems**

The total free energy gap of the *kth* donor in the *jth* flavoprotein is expressed by Eq. (12);

0 20 *GT* ( ) () / *<sup>j</sup> DA jk <sup>q</sup> jk ES k e R G*

<sup>2</sup> <sup>0</sup> ln / 1 ( ) / *jk jk jk KM S S <sup>T</sup> k G*

varies with <sup>0</sup> ( ) *GT jk* , the normal energy gap law is modified, as in Eq. (13);

*jk*

  (12)

(13)

Societies).

When *jk S*

Fig. 11. Net ES energy in the five FMN binding protein isoforms. Data were taken from Nunthaboot et al. (2011). (Reproduced by permission of the PCCP Owner Societies).

Here ( ) *ES k <sup>j</sup>* is given by Eq. (8), and <sup>0</sup> *Gq* by Eq. (3). The values of <sup>0</sup> ( ) *GT jk* are listed in the bottom lines of Table 5 for flavodoxins and Table 8 for FMN binding proteins. Figure 12 shows the modified energy gap law in flavodoxins and FMN binding proteins, as expressed by Eq. (13). The inserts in Figure 12 represent the approximate parabola functions. In the both systems, the PET takes place in the normal region.

#### **6. Concluding remarks on the PET mechanism in flavoproteins**

Quantitative analyses of the PET in proteins have been difficult, because all of the current PET theories contain several unknown parameters which cannot be determined experimentally. In the earlier works the PET rate was qualitatively analyzed from the following two aspects.

1. The donor-acceptor distance-dependence of the PET rate (Dutton law).

Hopfield (1974) described biological electron transfer rate in the ground state of a donor in terms of the electron tunneling model. In this model, the rate drops off exponentially with increasing donor-acceptor distance. Hopfield estimated the slope of the logarithm of the rate against the distance to be 14 nm -1 for biological electron transfer reactions. Indeed, Moser et al. (1992) have experimentally demonstrated that logarithms of PET rates linearly decrease with the Re distance between PET donors and acceptors in photosynthetic proteins. In accord, the slope of the logarithm of the PET rate against the free energy gap was also around 14 nm-1. Gray & Winkler (1996) have reviewed the experimental works on PET rates in ground state donors from various aspects.

Fig. 12. Modified energy gap law in (A) flavodoxins and (B) FMN binding proteins. Inserts indicate the approximate parabola functions, Y ln / *jk jk KM <sup>S</sup> k* , and X <sup>0</sup> ( )/ *jk G jk <sup>T</sup> <sup>S</sup>* . Formally, the value of ln / *jk jk KM <sup>S</sup> k* should be maximal when <sup>0</sup> ( ) *GT jk* = *jk S* . Data were taken from Lugsanangarm et al. (2011c) for Figure 12A and Nunthaboot et al. (2011) for Figure 12B. (Reproduced by permission of the PCCP Owner Societies).

2. The free energy gap dependence of PET rate (Energy gap law).

The characteristics of the Marcus theory (1956a, 1956b, 1964) is that the logarithm of the PET rate is a parabolic function of the reorganization energy and the free energy gap (see Eq. (1)), which is common with the other theories (see Eqs. (4) and (5)). As a test for the Marcus theory many researchers have examined the dependence of the logarithmic values of the PET rates on the free energy gap. Rehm & Weller (1969; 1970) first examined the energy gap law with the donor-acceptor systems in organic solvents, but could not find the predicted parabolic dependence. Later Closs et al. (1986) and Mataga et al. (2003) found evidence of the PET processes in the so-called "Inverted region". Interested readers should consult Mataga et al. (2005), who have precisely reviewed the current knowledge of PET in solution.

Quantitative analyses of the PET in proteins have been difficult, because all of the current PET theories contain several unknown parameters which cannot be determined experimentally. In the earlier works the PET rate was qualitatively analyzed from the

Hopfield (1974) described biological electron transfer rate in the ground state of a donor in terms of the electron tunneling model. In this model, the rate drops off exponentially with increasing donor-acceptor distance. Hopfield estimated the slope of the logarithm of the rate against the distance to be 14 nm -1 for biological electron transfer reactions. Indeed, Moser et al. (1992) have experimentally demonstrated that logarithms of PET rates linearly decrease with the Re distance between PET donors and acceptors in photosynthetic proteins. In accord, the slope of the logarithm of the PET rate against the free energy gap was also around 14 nm-1. Gray & Winkler (1996) have reviewed the experimental works on PET rates

Fig. 12. Modified energy gap law in (A) flavodoxins and (B) FMN binding proteins. Inserts

taken from Lugsanangarm et al. (2011c) for Figure 12A and Nunthaboot et al. (2011) for

should be maximal when

The characteristics of the Marcus theory (1956a, 1956b, 1964) is that the logarithm of the PET rate is a parabolic function of the reorganization energy and the free energy gap (see Eq. (1)), which is common with the other theories (see Eqs. (4) and (5)). As a test for the Marcus theory many researchers have examined the dependence of the logarithmic values of the PET rates on the free energy gap. Rehm & Weller (1969; 1970) first examined the energy gap law with the donor-acceptor systems in organic solvents, but could not find the predicted parabolic dependence. Later Closs et al. (1986) and Mataga et al. (2003) found evidence of the PET processes in the so-called "Inverted region". Interested readers should consult Mataga et al. (2005), who have precisely reviewed the current knowledge of PET in solution.

*KM <sup>S</sup> k*

, and X

<sup>0</sup> ( ) *GT jk*

<sup>0</sup> ( )/ *jk G jk <sup>T</sup> <sup>S</sup>*

 = *jk S*

.

. Data were

**6. Concluding remarks on the PET mechanism in flavoproteins**

1. The donor-acceptor distance-dependence of the PET rate (Dutton law).

following two aspects.

in ground state donors from various aspects.

indicate the approximate parabola functions, Y ln / *jk jk*

A B

*KM <sup>S</sup> k*

Figure 12B. (Reproduced by permission of the PCCP Owner Societies).

2. The free energy gap dependence of PET rate (Energy gap law).

Formally, the value of ln / *jk jk*

The energy gap law in proteins was first experimentally demonstrated in the reaction center of the purple bacterium*, Rhodobacter sphaeroides*, by Gunner & Dutton (1989), and in both the plant photosystem I and reaction center of the purple bacterium by Iwaki *et al*. (1996). In these systems, the PET takes place in the normal regions, as in the flavoproteins described above.

We have been trying to quantitatively analyze PET in flavoproteins (Nunthaboot et al., 2008a, 2008b, 2009a, 2009b, 2010, 2011; Lugsanangarm et al., 2011b, 2011c), using the experimental and theoretical approaches of evaluating the ultrafast fluorescence dynamics of Iso in the flavoproteins and using MD simulation based approaches, respectively.The following conclusions have been derived on the mechanisms of PET in the flavoproteins.

#### **7. Perspective of the quantitative PET analyses**

Method of homology modeling has been useful for the determinations of protein structures, which have been experimentally unable (www.proteinstructures.com). The present method for the quantitative analysis of the PET mechanism may be also applicable to photosynthetic systems and flavin photoreceptors, such as AppA (Nunthaboot et al., 2009b; 2010). Most of the flavoproteins function in the electron transport and electron transfer from a substrate to Iso without light. A number of researchers have been working on the mechanisms of the dark electron transfer in proteins (Grey & Winkler, 1996; Beratan et al., 1991; 2008). These works, however, have mostly focused on the electron coupling term, and not discussed much on the nuclear term. ES energy which is in the nuclear term, should also play an important role on the dark electron transfer rates, and redox potentials of Iso in flavoproteins. Determination of all physical quantities contained in both electronic and nuclear terms of an electron transfer theory could explore a new aspect of the mechanisms of PET and dark electron transfer phenomena in proteins.

#### **8. Acknowledgments**

The Royal Golden Jubilee Ph.D. Program (3.C.CU/50/S.1), from Chulalongkorn University and The Thailand Research Fund (TRF) and The Ratchadaphiseksomphot Endowment Fund from Chulalongkorn University are acknowledged for financial support. N. N. (Grant No. MRG5380255) acknowledges the funding for New Research from the Thailand Research Fund. We thank Computational Chemistry Unit Cell, Chulalongkorn University and the National Electronics and Computer Technology Center (NECTEC) for computing facilities. The Thai Government Stimulus Package 2 (TKK2555) under the Project for Establishment of Comprehensive Center for Innovative Food, Health Products and Agriculture and The Higher Education Research Promotion is acknowledged.

#### **9. References**

dark electron transfer in proteins (Grey & Winkler, 1996; Beratan et al., 1991; 2008). These works, however, have mostly focused on the electron coupling term, and not discussed much on the nuclear term. ES energy which is in the nuclear term, should also play an important role on the dark electron transfer rates, and redox potentials of Iso in flavoproteins. Determination of all physical quantities contained in both electronic and nuclear terms of an electron transfer theory could explore a new aspect of the mechanisms

The Royal Golden Jubilee Ph.D. Program (3.C.CU/50/S.1), from Chulalongkorn University and The Thailand Research Fund (TRF) and The Ratchadaphiseksomphot Endowment Fund from Chulalongkorn University are acknowledged for financial support. N. N. (Grant No. MRG5380255) acknowledges the funding for New Research from the Thailand Research Fund. We thank Computational Chemistry Unit Cell, Chulalongkorn University and the National Electronics and Computer Technology Center (NECTEC) for computing facilities. The Thai Government Stimulus Package 2 (TKK2555) under the Project for Establishment of Comprehensive Center for Innovative Food, Health Products and Agriculture and The

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### **Estimating Hydrogen Bond Energy in Integral Membrane Chromoproteins by High Hydrostatic Pressure Optical Spectroscopy**

Liina Kangur1, John D. Olsen2, C. Neil Hunter2 and Arvi Freiberg1 *1University of Tartu, 2University of Sheffield 1Estonia, 2United Kingdom*

#### **1. Introduction**

190 Protein Structure

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> Proteins are biological macromolecules that participate in virtually every process in live organisms. By nature they are divided into three categories: globular, membrane, and fibrous proteins. The globular proteins are present in the cytosol of cells and in body fluids such as blood; the membrane proteins are "solubilized" in two-dimensional lipid membranes that organize the macroscopic body space; the, usually, large fibrous proteins reinforce membranes and maintain the structure of cells and tissues. In the cell the membrane proteins are responsible for structural, catalytic, transport, signalling, control, and other crucial life-supporting functions (Palazzo 2006). Protein function is defined by its folded structure (Rose and Wolfenden 1993) and the self-assembly into the folded structure is largely governed by a manifold of generally weak, spatially oriented hydrogen (H) bonds that also confer distinct quantum properties (Li, Walker et al. 2011). Multiple H-bond interactions are responsible for binding the strands of RNA, DNA, and other biopolymers together, as well as for elasticity of skeletal and cardiac muscles. Cooperativity of the Hbond interactions appears to be a defining feature at all levels of biomolecular folding and function (Lu, Isralewitz et al. 1998; Finkelstein and Ptitsyn 2002; Lin, Mohammed et al. 2011). Proteins are only functional if associated with water, but unlike the dynamic network of H-bonds in the bulk solvent, the interactions with biomolecules are short-range, affecting only one or two layers of waters (Ball 2008). Although there is no doubt that H-bonds are extremely important structural elements of proteins, their role in stabilizing proteins is still a matter of debate. Studying H-bonds within proteins, particularly membrane bound proteins, therefore, permits insights into fundamental biological phenomena, indeed all of life on earth.

> Hydrogen bond energies in simple model compounds and small peptides have been investigated in great detail (Sheu, Yang et al. 2003; Wendler, Thar et al. 2010). Hydrogen bonds in folded globular proteins, and especially in membrane proteins, are, however, much more difficult to characterize. The most frequently used methods are scanning calorimetry

and titration with chemical denaturants such as urea. Both these methods probe unfolding of the whole protein and provide integrated rather than bond-specific information. Moreover, changing the temperature at constant pressure causes simultaneous changes of the system's kinetic energy and its volume/potential energy that are difficult to separate. In this work we show that in certain cases the use of pressure, another fundamental thermodynamic variable, offers attractive advantages. Continuous and reversible tuning of the protein density can be achieved over a wide range without changing its primary structure and chemical potential of the solute. Hydrogen bonds are controversially reported to be either widely insensitive to pressure (Phelps and Hesterberg 2007) or promoted by it (Boonyaratanakornkit, Park et al. 2002). We use native protein co-factors as intrinsic probes and optical spectroscopy as a sensitive tool for identifying specific H-bonds that undergo major changes under external compression as well as for studying the energetics of these bonds.

The light harvesting (LH) antenna pigment-protein complexes of purple photosynthetic bacteria are one of the best-characterized membrane chromoproteins (Blankenship, Madigan et al. 1995; Hunter, Daldal et al. 2008). They absorb solar photons and transfer the resulting excitations to the reaction center (RC) special pair sites, where the excitation energy is transformed into potential chemical energy. In the wild type (wt) purple bacterium *Rhodobacter (Rb.) sphaeroides* the photosynthetic apparatus is organized into spherical chromatophore vesicles of ~50 nm diameter (Hu, Ritz et al. 2002; Cogdell, Gall et al. 2006; Sener, Olsen et al. 2007; Sener, Strümpfer et al. 2010). The reaction center light-harvesting 1 core complex and peripheral light-harvesting 2 protein complexes (RC-LH1 and LH2, respectively) form the majority of the proteins in these vesicles, where the self-assembled photosystems of LH complexes are reminiscent of ordered two-dimensional crystals. Low resolution electron microscope and full atomic resolution crystal structures of the protein complexes have also been known for some time for a number of species (Karrasch, Bullough et al. 1995; McDermott, Prince et al. 1995; Koepke, Hu et al. 1996; Roszak, Howard et al. 2003; Qian, Hunter et al. 2005). The basic building block of these antenna structures is a heterodimer of a-helical polypeptides designated a and b (coloured yellow and magenta in Fig. 1), each non-covalently binding either two (LH1) or three (LH2) bacteriochlorophyll *a* (Bchl) chromophore co-factors along with carotenoid molecules. The number of hetrodimers in the structures of bacterial core complexes vary from 15 in the bacterium *Rhodopseudomonas palustris* (Roszak, Howard et al. 2003) or 16 in *Rhodospirillum rubrum* (Karrasch, Bullough et al. 1995) to 28 in the dimeric core complex of *Rb. sphaeroides* (Qian, Hunter et al. 2005; Bullough, Qian et al. 2009). In contrast, only two forms of the peripheral antenna complex are known, including 8 (as in *Rhodospirillum molichianum* (Koepke, Hu et al. 1996)) or 9 heterodimers (*Rb. sphaeroides*, *Rhodopseudomonas (Rps.) acidophila*, and *Rubrivivax gelatinosus* (McDermott, Prince et al. 1995; Walz, Jamieson et al. 1998; Ranck, Ruiz et al. 2001)). In LH2 from *Rb. sphaeroides* each polypeptide pair binds two Bchl molecules at the outer membrane surface and one molecule on its cytoplasmic side, forming two concentric pigment circles (B850 and B800, respectively) with *C*9 symmetry, see Fig. 1.

The spectroscopic properties of LH1 and LH2 chromoproteins have been extensively studied (Van Amerongen, Valkunas et al. 2000; Hu, Ritz et al. 2002; Cogdell, Gall et al. 2006). While free in organic solvents, the lowest singlet (*Q*y) electronic transition of Bchl is located in the near infrared region at ~775 nm (Grimm, Porra et al. 2006; Rätsep, Cai et al. 2011).

and titration with chemical denaturants such as urea. Both these methods probe unfolding of the whole protein and provide integrated rather than bond-specific information. Moreover, changing the temperature at constant pressure causes simultaneous changes of the system's kinetic energy and its volume/potential energy that are difficult to separate. In this work we show that in certain cases the use of pressure, another fundamental thermodynamic variable, offers attractive advantages. Continuous and reversible tuning of the protein density can be achieved over a wide range without changing its primary structure and chemical potential of the solute. Hydrogen bonds are controversially reported to be either widely insensitive to pressure (Phelps and Hesterberg 2007) or promoted by it (Boonyaratanakornkit, Park et al. 2002). We use native protein co-factors as intrinsic probes and optical spectroscopy as a sensitive tool for identifying specific H-bonds that undergo major changes under external compression as well as for studying the energetics of these

The light harvesting (LH) antenna pigment-protein complexes of purple photosynthetic bacteria are one of the best-characterized membrane chromoproteins (Blankenship, Madigan et al. 1995; Hunter, Daldal et al. 2008). They absorb solar photons and transfer the resulting excitations to the reaction center (RC) special pair sites, where the excitation energy is transformed into potential chemical energy. In the wild type (wt) purple bacterium *Rhodobacter (Rb.) sphaeroides* the photosynthetic apparatus is organized into spherical chromatophore vesicles of ~50 nm diameter (Hu, Ritz et al. 2002; Cogdell, Gall et al. 2006; Sener, Olsen et al. 2007; Sener, Strümpfer et al. 2010). The reaction center light-harvesting 1 core complex and peripheral light-harvesting 2 protein complexes (RC-LH1 and LH2, respectively) form the majority of the proteins in these vesicles, where the self-assembled photosystems of LH complexes are reminiscent of ordered two-dimensional crystals. Low resolution electron microscope and full atomic resolution crystal structures of the protein complexes have also been known for some time for a number of species (Karrasch, Bullough et al. 1995; McDermott, Prince et al. 1995; Koepke, Hu et al. 1996; Roszak, Howard et al. 2003; Qian, Hunter et al. 2005). The basic building block of these antenna structures is a heterodimer of a-helical polypeptides designated a and b (coloured yellow and magenta in Fig. 1), each non-covalently binding either two (LH1) or three (LH2) bacteriochlorophyll *a* (Bchl) chromophore co-factors along with carotenoid molecules. The number of hetrodimers in the structures of bacterial core complexes vary from 15 in the bacterium *Rhodopseudomonas palustris* (Roszak, Howard et al. 2003) or 16 in *Rhodospirillum rubrum* (Karrasch, Bullough et al. 1995) to 28 in the dimeric core complex of *Rb. sphaeroides* (Qian, Hunter et al. 2005; Bullough, Qian et al. 2009). In contrast, only two forms of the peripheral antenna complex are known, including 8 (as in *Rhodospirillum molichianum* (Koepke, Hu et al. 1996)) or 9 heterodimers (*Rb. sphaeroides*, *Rhodopseudomonas (Rps.) acidophila*, and *Rubrivivax gelatinosus* (McDermott, Prince et al. 1995; Walz, Jamieson et al. 1998; Ranck, Ruiz et al. 2001)). In LH2 from *Rb. sphaeroides* each polypeptide pair binds two Bchl molecules at the outer membrane surface and one molecule on its cytoplasmic side, forming two concentric pigment circles (B850 and B800, respectively) with *C*9 symmetry, see Fig. 1.

The spectroscopic properties of LH1 and LH2 chromoproteins have been extensively studied (Van Amerongen, Valkunas et al. 2000; Hu, Ritz et al. 2002; Cogdell, Gall et al. 2006). While free in organic solvents, the lowest singlet (*Q*y) electronic transition of Bchl is located in the near infrared region at ~775 nm (Grimm, Porra et al. 2006; Rätsep, Cai et al. 2011).

bonds.

Significant red shifts of this transition are observed in the antenna systems, for example, the major absorption band in the LH2 complex from *Rb. sphaeroides* peaks at 850 nm (B850 band, see Fig. 2) (Van Dorssen, Hunter et al. 1988; Freiberg, Rätsep et al. 2011), while the spectroscopic equivalent of the ab-(Bchl)2 heterodimer subunit called B820, obtained by breaking down the LH1 complex, has a maximum at 820 nm (Loach and Parkes-Loach 2008). These large spectral shifts are primarily related to unique arrangements of the Bchls in the LH proteins, promoting strong inter-pigment (exciton) interactions. The B850 absorption band is the product of the 18 tightly packed and overlapping Bchl molecules on the periplasmic side of the complex, in a waterwheel arrangement, having intermolecular distances of less than 1 nm. The 9 monomeric Bchls of the other ring on the cytoplasmic side of the complex, which are widely separated (~2 nm), give rise to an absorption band at around 800 nm (B800 band). The B800 band shift from the molecular 775-nm absorption is mainly determined by interactions between the chromophores and the surrounding protein. Universal dispersion interactions aside, the factors that contribute most to the solvent/protein shifts are H-bonds to the *C*3-acetyl carbonyl of the Bchl chromophores (Fowler, Sockalingum et al. 1994; He, Sundstrom et al. 2002; Uyeda, Williams et al. 2010) and various conformational interactions (Gudowska-Nowak, Newton et al. 1990).

The absorption spectra of Bchl molecules, being sensitive to even minor structural rearrangements in the LH complexes, have been taken advantage of in the present work. According to Lesch et al. (Lesch, Schlichter et al. 2004) the integrity of protein complexes can be monitored with sub-nanometer spatial resolution by the so-called molecular probe method.

Fig. 1. Different representations of the LH2 pigment-protein complex using the same colour code for structural elements. The space fill model on the right clearly shows how densely packed the molecule actually is; the ribbon representation on left allows easy reference to the individual pigment cofactors; placed in the middle is an overlapped pair. The lipid bilayer covering hydrophobic parts of the complex is also schematically presented. The green B850 and blue B800 Bchl cofactors are sandwiched between the inner yellow ring of αpolypeptides and the outer magenta ring of β- polypeptides. The carotenoid molecules closely attached to the B850 and B800 Bchl rings are omitted for clarity.

To date mostly only water-soluble globular proteins have been studied under high pressures, with the result that functional protein structures cover just a narrow region in the pressure-temperature phase diagram close to physiological temperatures (Silva and Weber 1993; Boonyaratanakornkit, Park et al. 2002; Scharnagl, Reif et al. 2005; Meersman, Dobson et al. 2006). The photosynthetic LH membrane complexes were first investigated under high pressure in (Freiberg, Ellervee et al. 1993). This and subsequent studies (Sturgis, Gall et al. 1998; Gall, Ellervee et al. 2001; Timpmann, Ellervee et al. 2001; Gall, Ellervee et al. 2003) have shown that increasing the pressure at laboratory temperatures causes a smooth red (i.e., lower-energy) shift and broadening of the near-infrared absorption bands of Bchl. In the wt LH2 complexes from *Rb. sphaeroides* and *Rps. acidophila* extracted with mild detergents into a detergent-buffer environment a non-monotonic behaviour was observed (Kangur, Timpmann et al. 2008). With reference to genetic engineering results (Fowler, Visschers et al. 1992; Fowler, Sockalingum et al. 1994) this observation was qualitatively interpreted as due to rupture of the H-bonds at the binding sites of the excitonically coupled B850 chromophores (Kangur, Leiger et al. 2008).

In this chapter, we shall concentrate on a quantitative evaluation of H-bond energies that stabilize the strongly coupled Bchl co-factors in the B850 ring of the peripheral LH2 complex from *Rb. sphaeroides* by means of high-pressure optical spectroscopy. The availability of different genetically-modified preparations is an important advantage of this bacterium, besides its known spatial structure (Walz, Jamieson et al. 1998). The mutants constructed to support and widen our findings on wt complexes include a LH2 complex with a modified carotenoid background (neurosporene instead of a mixture of spheroidene and spheroidenone in the wt complex) and two B850-only LH complexes devoid of the B800 ring of Bchl molecules, one with wt carotenoids and another with neurosporene. To confirm that studies of purified membrane proteins have relevance to the intact membrane, the measurements have been performed both on detergent-isolated and native membranebound complexes. As a result, not only pressure-induced breakage of the H-bonds to the B850 chromophores have been demonstrated in all the samples, confirming the previous results on wt complexes (Kangur, Leiger et al. 2008; Kangur, Timpmann et al. 2008), but also their energies have been determined for the first time. The breakage appears to be a cooperative, "all-or-none" type transition, apparently triggered by the rupture of the weakest bond. Furthermore, the energies derived for the membrane-embedded and detergent-isolated complexes match each other within experimental uncertainty.

#### **2. Thermodynamic aspects of protein stability against pressure**

The phenomenological basis of protein stability against pressure is well established (Silva and Weber 1993; Boonyaratanakornkit, Park et al. 2002; Scharnagl, Reif et al. 2005; Meersman, Dobson et al. 2006). In a minimalist version of thermodynamic modelling just two global protein states, native (*N*) and denatured (*D*), are assumed. The equilibrium constant of the two-state denaturation reaction is given by Eq. (1), where [*N*] and [*D*] indicate the equilibrium concentrations of native and denatured protein, respectively, *R* is the universal gas constant, *T* is the thermodynamic temperature, and *P* is the pressure.

$$\mathbf{K}(P) = \begin{bmatrix} D \end{bmatrix} / \begin{bmatrix} N \\ \end{bmatrix} = \exp\left[-\Lambda \mathbf{G} \left(P\right) / RT\right] \tag{1}$$

The pressure dependence of the free energy change associated with protein denaturation, in the lowest (linear) order of approximation, can be represented as

$$
\Delta G\left(P\right) = \Delta G^0 + \Delta V^0 P\right.\tag{2}
$$

pressure in (Freiberg, Ellervee et al. 1993). This and subsequent studies (Sturgis, Gall et al. 1998; Gall, Ellervee et al. 2001; Timpmann, Ellervee et al. 2001; Gall, Ellervee et al. 2003) have shown that increasing the pressure at laboratory temperatures causes a smooth red (i.e., lower-energy) shift and broadening of the near-infrared absorption bands of Bchl. In the wt LH2 complexes from *Rb. sphaeroides* and *Rps. acidophila* extracted with mild detergents into a detergent-buffer environment a non-monotonic behaviour was observed (Kangur, Timpmann et al. 2008). With reference to genetic engineering results (Fowler, Visschers et al. 1992; Fowler, Sockalingum et al. 1994) this observation was qualitatively interpreted as due to rupture of the H-bonds at the binding sites of the excitonically coupled B850

In this chapter, we shall concentrate on a quantitative evaluation of H-bond energies that stabilize the strongly coupled Bchl co-factors in the B850 ring of the peripheral LH2 complex from *Rb. sphaeroides* by means of high-pressure optical spectroscopy. The availability of different genetically-modified preparations is an important advantage of this bacterium, besides its known spatial structure (Walz, Jamieson et al. 1998). The mutants constructed to support and widen our findings on wt complexes include a LH2 complex with a modified carotenoid background (neurosporene instead of a mixture of spheroidene and spheroidenone in the wt complex) and two B850-only LH complexes devoid of the B800 ring of Bchl molecules, one with wt carotenoids and another with neurosporene. To confirm that studies of purified membrane proteins have relevance to the intact membrane, the measurements have been performed both on detergent-isolated and native membranebound complexes. As a result, not only pressure-induced breakage of the H-bonds to the B850 chromophores have been demonstrated in all the samples, confirming the previous results on wt complexes (Kangur, Leiger et al. 2008; Kangur, Timpmann et al. 2008), but also their energies have been determined for the first time. The breakage appears to be a cooperative, "all-or-none" type transition, apparently triggered by the rupture of the weakest bond. Furthermore, the energies derived for the membrane-embedded and

detergent-isolated complexes match each other within experimental uncertainty.

The phenomenological basis of protein stability against pressure is well established (Silva and Weber 1993; Boonyaratanakornkit, Park et al. 2002; Scharnagl, Reif et al. 2005; Meersman, Dobson et al. 2006). In a minimalist version of thermodynamic modelling just two global protein states, native (*N*) and denatured (*D*), are assumed. The equilibrium constant of the two-state denaturation reaction is given by Eq. (1), where [*N*] and [*D*] indicate the equilibrium concentrations of native and denatured protein, respectively, *R* is the universal gas constant, *T* is the thermodynamic temperature, and *P* is the pressure.

The pressure dependence of the free energy change associated with protein denaturation, in

*K P D N G P RT* / exp / (1)

0 0 *GP G VP* , (2)

**2. Thermodynamic aspects of protein stability against pressure**

the lowest (linear) order of approximation, can be represented as

chromophores (Kangur, Leiger et al. 2008).

 where <sup>000</sup> *GGG D N* is the standard free energy difference between the denatured and the native state and <sup>0</sup> *VVV D N* is the partial molar volume change in going from the native to the denatured state measured at standard conditions. <sup>0</sup> *G* has to be positive in order for the protein to be stable at standard conditions. If the volume of the denatured state is smaller than the volume of the native state (i.e., <sup>0</sup> *V* is negative), the free energy change decreases as pressure is increased. The phase boundary (midpoint) pressure is determined as 0 0 *P GV* 1/2 / . At pressure *P*1/2 , native and denatured structures have equal probabilities of existence. Past this pressure, the denatured state has lower free energy and is stabilized against the native state.

#### **3. Absorption spectra of LH2 complexes under ambient conditions**

Figure 2 presents the overview optical absorption spectra of the LH2 complexes in the spectral range from 240 nm to 1000 nm, recorded at ambient temperature and pressure. For solubilization and purification of the complexes from their native membrane environment the detergent dodecyl-dimetyl-amine oxide, commonly known as LDAO, was used. As seen, the spectra of the detergent-isolated and native membrane-bound complexes are similar. Peak positions of the key bands observed in the spectra are presented in Table 1.

Fig. 2. Absorption spectra of the wt and mutant LH2 complexes studied, recorded at ambient temperature and pressure. The spectra of detergent-isolated (drawn with coloured lines) and native membrane-embedded (black lines) complexes are normalized relative to the B850 absorption band peak. The reference spectrum of Bchl in diethyl ether is shown in magenta. Neuro designates the mutant containing neurosporene, while B850-only+neuro is the double mutant with no B800 molecules and containing neurosporene carotenoids.

Table 1. Peak positions in nanometers (±0.5 nm) in the absorption spectra of the membranebound (m) and detergent-isolated (i) LH2 complexes recorded at ambient conditions. The bands are classified according to the related Bchl transitions as described in the text.

A comparison with the spectrum of Bchl in diethyl ether implies that the bands of the cofactor chromophores peaking around 850 (B850 band), 800 (B800 band), 590, and 380 nm are related to, respectively, the *Q*y, *Q*x, and Soret electronic transitions of the Bchl molecule. The bands evident between the *Q*x and Soret transitions are from carotenoid molecules, being a mixture of spheroidene and spheroidenone in wt and neurosporene in mutant complexes. Compared with the structure-less spectrum of the native mixture, the neurosporene spectrum is clear-cut and blue shifted, showing three sharp peaks between 430 and 490 nm. Replacement of the wt carotenoids with neurosporene does not significantly influence the electronic states of the Bchl co-factors. The blue-shifted position of the neurosporene spectrum allows easier observation of the *Q*x transitions of the protein-bound Bchls. The ultraviolet part of the spectrum, including the peak at 270 nm, is characteristic of the bulk protein scaffold.

The *Q*y transitions of LH2 Bchls, which give rise to the B800 and B850 bands, are shifted toward longer (red) wavelengths and are associated with strongly excitonically coupled Bchls in the case of B850. In contrast, the *Q*x transitions of the Bchl molecules belonging to the B800 and B850 arrangements apparently overlap. This can be interpreted as arising from the relatively weak oscillator strength of the *Q*x transitions, leaving the transitions in all participating molecules almost localized. The stronger B850 exciton coupling compared with B800 clarifies not only the splitting between these bands but also the larger width of the B850 band (Freiberg, Timpmann et al. 1999). A peculiar triple structure in the Soret range of the complexes suggests considerable interactions between the respective strong molecular transitions and related large splitting of the bands. A greater red shift of the B850 band in the B850-only mutant as compared with the wt complex has been noted. It was explained by a somewhat enhanced exciton coupling in this complex, presumably because the missing B800 molecules allow more compact packing of the protein (Timpmann, Trinkunas et al. 2004). A weak shoulder around 795 nm in the spectrum of the B850-only mutant is most probably due to overlapping transitions of the B850 (vibronic) excitons and possibly the presence of some "free" Bchl molecules rather than residual B800 molecules (Rätsep, Hunter et al. 2005). More details about spectral properties of the LH2 complexes and their temperature dependencies can be found in (Freiberg, Rätsep et al. 2011).

In the following sections we shall mainly focus on the lowest-energy B850 absorption band. The particular interest toward this absorption feature is explained by the central role the respective transitions play in native photosynthesis by mediating excitation energy funnelling into the RC. Since Bchl molecules from both the B850 and B800 rings contribute to the *Q*x band at 590 nm, we shall briefly characterize the influence of pressure on this band too. The detailed behaviour of the quasi-monomeric B800 band under high pressure will be described elsewhere.

#### **4. Variations of the B850 absorption spectra induced by externally applied high hydrostatic pressure**

#### **4.1 Detergent-isolated complexes**

196 Protein Structure

wt

neuro

B850-only+neuro

protein scaffold.

Sample *Q*<sup>y</sup> *<sup>Q</sup>*x Soret Car B850 B800

m 851.1 801.1 591.3 378.0

i 849.4 800.7 590.7 373.3

m 852.4 - 594.7 377.6

i 852.0 - 594.0 378.7

B850-only m 850.2 - 590.9 378.5 497.2

Table 1. Peak positions in nanometers (±0.5 nm) in the absorption spectra of the membranebound (m) and detergent-isolated (i) LH2 complexes recorded at ambient conditions. The bands are classified according to the related Bchl transitions as described in the text.

A comparison with the spectrum of Bchl in diethyl ether implies that the bands of the cofactor chromophores peaking around 850 (B850 band), 800 (B800 band), 590, and 380 nm are related to, respectively, the *Q*y, *Q*x, and Soret electronic transitions of the Bchl molecule. The bands evident between the *Q*x and Soret transitions are from carotenoid molecules, being a mixture of spheroidene and spheroidenone in wt and neurosporene in mutant complexes. Compared with the structure-less spectrum of the native mixture, the neurosporene spectrum is clear-cut and blue shifted, showing three sharp peaks between 430 and 490 nm. Replacement of the wt carotenoids with neurosporene does not significantly influence the electronic states of the Bchl co-factors. The blue-shifted position of the neurosporene spectrum allows easier observation of the *Q*x transitions of the protein-bound Bchls. The ultraviolet part of the spectrum, including the peak at 270 nm, is characteristic of the bulk

The *Q*y transitions of LH2 Bchls, which give rise to the B800 and B850 bands, are shifted toward longer (red) wavelengths and are associated with strongly excitonically coupled Bchls in the case of B850. In contrast, the *Q*x transitions of the Bchl molecules belonging to the B800 and B850 arrangements apparently overlap. This can be interpreted as arising from the relatively weak oscillator strength of the *Q*x transitions, leaving the transitions in all participating molecules almost localized. The stronger B850 exciton coupling compared with B800 clarifies not only the splitting between these bands but also the larger width of the B850 band (Freiberg, Timpmann et al. 1999). A peculiar triple structure in the Soret range of the complexes suggests considerable interactions between the respective strong molecular transitions and related large splitting of the bands. A greater red shift of the B850 band in the B850-only mutant as compared with the wt complex has been noted. It was explained by

m 849.4 800.8 587.5 377.4 496.9 i 847.8 800.8 588.4 376.8 503.1

i 849.6 - 591.8 377.5 498.9

492.8 460.9 432.8

492.9 461.1 434.3

489.4 457.2 427.5

490.1 458.8 430.8