**Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods**

Xuejing Hou and Harvey J.M. Hou

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/2615

## **1. Introduction**

482 Thermodynamics – Fundamentals and Its Application in Science

microarrays. Nucleic Acids Research. 30(16):e86.1 – e86.8

Unexpected Behavior Patterns. Biophysical Journal. 89:2950 – 2959

[24] Dai H, Meyer M, Stepaniants S, Ziman M, Stoughton R (2002) Use of hybridization kinetics for differentiating specific from non-specific binding to oligonucleotide

[25] Zhang Y, Hammer D A, Graves D J (2005) Competitive Hybridization Kinetics Reveals

[26] Diaz F, Malutan R, Gomez P, Martinez R, Stetter B, Fe Paz M, Garcia E, Pelaez J (2006) Estimating Oligonucleotide Microarray Expression by Hybridization Process Modelling. Proc. of IEEE/NLM Life Science Systems and Applications Workshop. 1 – 2

> Thermodynamics of a chemical reaction is a fundamental and vital issue for complete understanding of the reaction at the molecular level and involves the elucidation of the energy level of reactant and products, direction of reaction, and driving force or spontaneity of the reaction (Tadashi, 2011). Most the chemical reactions are enthalpy driven and are determined by chemical bonding energy of the reactants and products. However, some of the chemical reaction or process is entropy driven and are largely due the probability or disorder of the system during the reaction. Protein denaturation and dissolution of potassium iodide in water are such examples. In chemistry and biology, especially electron transfer reaction, the entropy changes are often assumes small and negligible. The understanding of thermodynamics of electron transfer reactions is relatively limited (Mauzerall, 2006).

> To study the thermodynamics of reaction in chemistry and biology, photosynthetic reaction is an excellent model system. The photosynthesis involves multiple electron transfer reaction driven by sunlight under room temperature and neutral pH (Blankenship, 2002; Diner and Rappaport, 2002; Golbeck, 2006). The understanding of light-induced electron transfer reaction in photosynthesis will provide fundamental knowledge of chemical reactions and guide the design and fabrication in artificial photosynthetic system in address the global energy and environmental crisis in the 21st century (Lewis and Nocera, 2006). In particular the solar energy storage of solar energy using water splitting reaction mimicking photosynthesis might solved energy and pure water problems at the same time (Kanan and Nocera, 2008; Cook et al., 2010; Hou, 2010, 2011). The electron transfer reactions in photosynthesis involves four major chlorophyll binding protein complexes: Photosystem II, cytochrome b6f, photosystem I, and ATP synthase (Figure 1). Photosystem I and photosystem II are belong to two types of different reaction centers in nature, respectively. Type I reaction centers incorporate a phylloquinone or menaquinone as secondary electron

© 2012 Hou and Hou, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

acceptor, A1, and three tertiary iron-sulfur cluster electron acceptors, FA, FB, and FX. Type II centers use two quinone acceptors: QA undergoes one-electron reduction, and QB undergoes a two-electron reduction with concomitant protonation.

Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods 485

**Figure 2.** X-ray crystallographic structure (upper panel) and the arrangment of the cofactors (lower pahnel) in photosystem I from cyanobacterium *Synechococcus* elongatus (Jordan et al., 2001)

A quinone molecule is a perfect electron transfer cofactor due to its reversible electrochemical redox properties and plays a key role in photosynthetic electron transfer process. For example, both type I and type II reaction centers contain a quinone that operates as an intermediate electron acceptor and as a one-electron carrier. However, the local protein environment and chemical properties of the quinone in these two types of reaction centers must be different. EPR measurements revealed that there are striking difference in the binding and function of phylloquinone (A1) in PS I and ubiquione (QA) in the bacterial center of R. sphaeroides (Kamlowski et al., 1998). As a type I center, PS I

(Reproduced with permission from Nature publishing Group).

**2. Quinones in photosystem I** 

**Figure 1.** Four protein complexes, including photosystem II, cytochrome b6f, photosystem I, and ATP synthase, are responsible for the electron transfer reactions in photosynthesis. (from http://www.answersingenesis.org/articles/tj/v17/n3/photosynthesis).

Photosystem I is a pigment-protein complex consisting of more than 11 polypeptides embedded in the photosynthetic membrane and catalyzes light-induced electron transfer from reduced plastocyanin (or cytochrome c6) to oxidized ferredoxin (or flavodoxin). The electron transfer pathway and the electron transfer cofactors in photosystem I is shown as a black arrows in Figure 1. The primary electron donor is P700, a pair of chlorophyll a molecules. After absorbing light photon energy, P700 becomes excited species P700\* and delivers one electron to the primary electron acceptor A0, a chlorophyll a molecule. The reduced A0 anion donates its electron to the secondary acceptor A1, a phylloquione or vitamin K1 molecule. The reduced A1 anion transfer the electron to FX, FA, FB, and finally to ferrodoxin for producing NADPH+.

The three-dimensional structure of cyanobacterial PS I at 2.5 A resolution has been obtained and revealed much of the detailed orientation and binding site of electron transfer cofactors. These structural details offer a solid basis for structure and function studies at an atomic level (Figure 2). The almost complete symmetric arrangement of cofactors in PS I suggested the electron transfer might involve two electron transfer branches (A side and B side). This is different from the electron transfer mechanism in type II centers. For example, in bacterial and PS II, only one electron transfer branch (L side or D1 side) is active. The M-side (or D2 side) electron transfer is inactive and may provide protective role in the reaction center in regulating excess light energy.

**Figure 2.** X-ray crystallographic structure (upper panel) and the arrangment of the cofactors (lower pahnel) in photosystem I from cyanobacterium *Synechococcus* elongatus (Jordan et al., 2001) (Reproduced with permission from Nature publishing Group).

#### **2. Quinones in photosystem I**

484 Thermodynamics – Fundamentals and Its Application in Science

a two-electron reduction with concomitant protonation.

acceptor, A1, and three tertiary iron-sulfur cluster electron acceptors, FA, FB, and FX. Type II centers use two quinone acceptors: QA undergoes one-electron reduction, and QB undergoes

**Figure 1.** Four protein complexes, including photosystem II, cytochrome b6f, photosystem I, and ATP

Photosystem I is a pigment-protein complex consisting of more than 11 polypeptides embedded in the photosynthetic membrane and catalyzes light-induced electron transfer from reduced plastocyanin (or cytochrome c6) to oxidized ferredoxin (or flavodoxin). The electron transfer pathway and the electron transfer cofactors in photosystem I is shown as a black arrows in Figure 1. The primary electron donor is P700, a pair of chlorophyll a molecules. After absorbing light photon energy, P700 becomes excited species P700\* and delivers one electron to the primary electron acceptor A0, a chlorophyll a molecule. The reduced A0 anion donates its electron to the secondary acceptor A1, a phylloquione or vitamin K1 molecule. The reduced A1 anion transfer the electron to FX, FA, FB, and finally to

The three-dimensional structure of cyanobacterial PS I at 2.5 A resolution has been obtained and revealed much of the detailed orientation and binding site of electron transfer cofactors. These structural details offer a solid basis for structure and function studies at an atomic level (Figure 2). The almost complete symmetric arrangement of cofactors in PS I suggested the electron transfer might involve two electron transfer branches (A side and B side). This is different from the electron transfer mechanism in type II centers. For example, in bacterial and PS II, only one electron transfer branch (L side or D1 side) is active. The M-side (or D2 side) electron transfer is inactive and may provide protective role in the reaction center in

synthase, are responsible for the electron transfer reactions in photosynthesis. (from

http://www.answersingenesis.org/articles/tj/v17/n3/photosynthesis).

ferrodoxin for producing NADPH+.

regulating excess light energy.

A quinone molecule is a perfect electron transfer cofactor due to its reversible electrochemical redox properties and plays a key role in photosynthetic electron transfer process. For example, both type I and type II reaction centers contain a quinone that operates as an intermediate electron acceptor and as a one-electron carrier. However, the local protein environment and chemical properties of the quinone in these two types of reaction centers must be different. EPR measurements revealed that there are striking difference in the binding and function of phylloquinone (A1) in PS I and ubiquione (QA) in the bacterial center of R. sphaeroides (Kamlowski et al., 1998). As a type I center, PS I contain a bound menaquinone, usually phylloquinone (A1, vitamin K1, 2-methyl-3-phytyl-1,4-naphthoquinone). In contrast, PS II uses the plasoquinone (Ap). The chemical structures of A1 and AP are shown in Figure 3.

Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods 487

of the *menA* gene was yielded. The transformation of the wild type strain of *Synechocystis* 6803 and isolation of segregated mutants was performed to obtain the *menA* null strain. The recombinant DNA construct of inactivation of the *menB* gene was generated in the similar way. Two 1.0 kb fragments from upstream and downstream of the *menB* gene were amplified by PCR. The amplified fragments were cloned into pBluescript and a 2.0-kb EcoRI

fragment containing the streptomycine/spectinomycine resistance cassettes.

**Figure 4.** Biosynthetic pathway of phylloquinone in cyanobacterium *Synechocystis* sp. PCC 6803 (Johnson et al., 2000) (Reproduced with permission from the American Society for Biochemistry and

Molecular Biology).

To investigate the function of ubiquinone in bacterial photosynthesis, the native quinone can be removed by organic solvent extraction and replaced with 22 other quinones. The rate of electron transfer in these reconstituted reaction center, Gibbs free energy, enthalpy changes, and apparent entropy changes were determined by EPR, transient time-resolved absorption spectroscopy, theoretical calculation and modeling, and photoacoustic spectroscopy (Gunner and Dutton, 1989; Edens et al., 2000). The molecular volume changes of charge separation due to electrostriction correlates with the size of quinones as expected (Edens et al., 2000). However, the methodology of replacement of quinone is not successful in PS I.

**Figure 3.** Chemical structures of quinones in photosynthesis. A1 is native quinone in photosystem I, and AP is a plastoquinone in photosystem II.

A biological method to replace phylloquinone was devised by Chitnis and Golbeck (Johnson et al., 2000; Semenov et al., 2000). The strategy to disallow A1 function is to inactivate genes that code for enzymes involved in the biosynthetic pathway of phylloquinone. The synthesis of the phylloquione in *Synechocystis* sp. PCC 6803 was shown in Figure 4, which is similar to the biosynthesis of menoquinone in E. coli (Sharma et al., 1996). It is proposed that menF/entC, menD, menE, and menB are responsible for 1,4-dihydroxy-2-naphthoate synthesis. The menA catalyzes the addition of phytyl chain. The gerC2 gene codes for the 2 thytyl-1,4-naphthoquinone methyl transferase enzyme, which catalyzed the methylation step to produce phylloquinone.

To generate a recombinant DNA construction for inactivation of the *menA* gene, two DNA fragment were amplified from *Synechocystis* sp. PCC 6803 genomic DNA by polymerase chain reaction (PCR) (Figure 5). The PstI and ApaI restriction sites were incorporated in both fragments. The first amplification product was digested with EegI and PstI, and the second fragment was digested with PstI and ApaI restriction enzymes. The fragments was ligated with the pBluescript vector, and the kanamycin resistance gene was cloned. The 442-bp part of the *menA* gene was yielded. The transformation of the wild type strain of *Synechocystis* 6803 and isolation of segregated mutants was performed to obtain the *menA* null strain. The recombinant DNA construct of inactivation of the *menB* gene was generated in the similar way. Two 1.0 kb fragments from upstream and downstream of the *menB* gene were amplified by PCR. The amplified fragments were cloned into pBluescript and a 2.0-kb EcoRI fragment containing the streptomycine/spectinomycine resistance cassettes.

486 Thermodynamics – Fundamentals and Its Application in Science

of A1 and AP are shown in Figure 3.

AP is a plastoquinone in photosystem II.

step to produce phylloquinone.

contain a bound menaquinone, usually phylloquinone (A1, vitamin K1, 2-methyl-3-phytyl-1,4-naphthoquinone). In contrast, PS II uses the plasoquinone (Ap). The chemical structures

To investigate the function of ubiquinone in bacterial photosynthesis, the native quinone can be removed by organic solvent extraction and replaced with 22 other quinones. The rate of electron transfer in these reconstituted reaction center, Gibbs free energy, enthalpy changes, and apparent entropy changes were determined by EPR, transient time-resolved absorption spectroscopy, theoretical calculation and modeling, and photoacoustic spectroscopy (Gunner and Dutton, 1989; Edens et al., 2000). The molecular volume changes of charge separation due to electrostriction correlates with the size of quinones as expected (Edens et al., 2000). However, the methodology of replacement of quinone is not successful in PS I.

**Figure 3.** Chemical structures of quinones in photosynthesis. A1 is native quinone in photosystem I, and

A biological method to replace phylloquinone was devised by Chitnis and Golbeck (Johnson et al., 2000; Semenov et al., 2000). The strategy to disallow A1 function is to inactivate genes that code for enzymes involved in the biosynthetic pathway of phylloquinone. The synthesis of the phylloquione in *Synechocystis* sp. PCC 6803 was shown in Figure 4, which is similar to the biosynthesis of menoquinone in E. coli (Sharma et al., 1996). It is proposed that menF/entC, menD, menE, and menB are responsible for 1,4-dihydroxy-2-naphthoate synthesis. The menA catalyzes the addition of phytyl chain. The gerC2 gene codes for the 2 thytyl-1,4-naphthoquinone methyl transferase enzyme, which catalyzed the methylation

To generate a recombinant DNA construction for inactivation of the *menA* gene, two DNA fragment were amplified from *Synechocystis* sp. PCC 6803 genomic DNA by polymerase chain reaction (PCR) (Figure 5). The PstI and ApaI restriction sites were incorporated in both fragments. The first amplification product was digested with EegI and PstI, and the second fragment was digested with PstI and ApaI restriction enzymes. The fragments was ligated with the pBluescript vector, and the kanamycin resistance gene was cloned. The 442-bp part

**Figure 4.** Biosynthetic pathway of phylloquinone in cyanobacterium *Synechocystis* sp. PCC 6803 (Johnson et al., 2000) (Reproduced with permission from the American Society for Biochemistry and Molecular Biology).

In the left of the panel A in Figure 5 shows the restriction maps of the genomic regions surrounding *menA* gene in the wild type and mutant strains. A 440-bp fragment in the *menA* gene was deleted and replaced by a 1.3 kb kanamycine resistance cartridge. PCR amplification of the *menA* locus of the wild type produced the expected 1.9 kb fragment (panel A right, Figure 5). Southern blot hybridization analyses confirmed the interruption of the *menA* gene as expected. Insertional inactivation of the menB gene was also confirmed by both Southern blot hybridization and PCR amplification of menB locus from the mutant strain. The part of the menB gene was deleted and replaced with a 2-kb spectinomycin resistance cartridge (left, panel B in Figure 5). The PCR amplification of the menB locus of the wild type produced the expected fragment of 920 bp (right, panel B in Figure 5), confirming the inactivation of the menB gene.

Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods 489

almost identical to those of the phylloquinone A1 in the wild type PS I. In addition, EPR measurements show that plastoquinone has been recruited into the A1 site and functions as

As shown in Figure 6, the rates of electron transfer from P700 to A0 and A1 in the mutants are similar to the wild type PS I. However, the kinetic parameter from A1 anion to FX is quite different in the *menA* and *menB* null mutants. The time-resolved optical studies revealed that the forward electron transfer from A1 anion to FX is slowed 1000-fold, to 15 and 300 �s, compared to 20 and 200 ns in the wild type PS I (Semenov et al., 2000; Johnson et al., 2001). Based the kinetic data of electron transfer in *menA* and *menB* mutant, the redox potential of AP in *menA* and *menB* PS I is estimated to be more oxidizing than phylloquinone so that electron transfer from AP anion to FX is thermodynamically unfavorable in the mutants

**Figure 6.** Kinetic data of electron transfer steps in native and *menA*/*menB* null mutants of *Synechocystis*

Pulsed photoacoustic spectroscopy can provide a direct measurement of thermodynamic parameters such as volume change and enthalpy changes that accompany electron transfer reactions (Braslavsky, 1985; Carpentier et al., 1990; Arnaut et al., 1992; Small et al., 1992; Losi et al., 1995; Edens et al., 2000; Malkin, 2000; Herbert et al., 2001; Feitelson and Mauzerall, 2002; Delosme, 2003; Hou and Mauzerall, 2006; Hou and Sakmar, 2010; Hou, 2011; Hou and Mauzerall, 2011). With prior knowledge of the change in Gibbs free energy of the corresponding reactions, the apparent entropy change (TS) of the reaction can be calculated. This is an important parameter, knowledge of which is required to fully understand the mechanism of electron transfer, and it has been largely underreported in the literature. The H, V, and TS of electron transfer in the photosynthetic reaction center

**4. Thermodynamics of** *menA* **and** *menB* **Null Mutants** 

an efficient one electron carrier (Zybailov et al., 2000).

(right panel of Figure 6).

sp. PCC 6803

**Figure 5.** Construct and confirmation of *menA* and *menB* null mutants by inactivation of *menA* and *menB* genes in *Synechocystis* sp. PCC 6803 (Johnson et al., 2000) (Reproduced with permission from the American Society for Biochemistry and Molecular Biology).

### **3. Physiological, structural, and kinetics of** *menA* **and** *menB* **null mutants**

The *menA* and *menB* null mutants are able to grow photoheterotrophically and photoautotrophically under low light conditions. The expression level of active PS I in the *menA* and *menB* mutant are 50-60% of the wild type stain. HPLC analysis indicates that the absence of phylloquinone in PS I and that the presence of high level of plastoquinone in PS I (Johnson et al., 2000). EPR, electron nuclear double resonance, and electron spin echo modulation data suggested that the orientation and distance of the foreign quinone AP are almost identical to those of the phylloquinone A1 in the wild type PS I. In addition, EPR measurements show that plastoquinone has been recruited into the A1 site and functions as an efficient one electron carrier (Zybailov et al., 2000).

488 Thermodynamics – Fundamentals and Its Application in Science

confirming the inactivation of the menB gene.

American Society for Biochemistry and Molecular Biology).

In the left of the panel A in Figure 5 shows the restriction maps of the genomic regions surrounding *menA* gene in the wild type and mutant strains. A 440-bp fragment in the *menA* gene was deleted and replaced by a 1.3 kb kanamycine resistance cartridge. PCR amplification of the *menA* locus of the wild type produced the expected 1.9 kb fragment (panel A right, Figure 5). Southern blot hybridization analyses confirmed the interruption of the *menA* gene as expected. Insertional inactivation of the menB gene was also confirmed by both Southern blot hybridization and PCR amplification of menB locus from the mutant strain. The part of the menB gene was deleted and replaced with a 2-kb spectinomycin resistance cartridge (left, panel B in Figure 5). The PCR amplification of the menB locus of the wild type produced the expected fragment of 920 bp (right, panel B in Figure 5),

**Figure 5.** Construct and confirmation of *menA* and *menB* null mutants by inactivation of *menA* and *menB* genes in *Synechocystis* sp. PCC 6803 (Johnson et al., 2000) (Reproduced with permission from the

**3. Physiological, structural, and kinetics of** *menA* **and** *menB* **null mutants** 

The *menA* and *menB* null mutants are able to grow photoheterotrophically and photoautotrophically under low light conditions. The expression level of active PS I in the *menA* and *menB* mutant are 50-60% of the wild type stain. HPLC analysis indicates that the absence of phylloquinone in PS I and that the presence of high level of plastoquinone in PS I (Johnson et al., 2000). EPR, electron nuclear double resonance, and electron spin echo modulation data suggested that the orientation and distance of the foreign quinone AP are As shown in Figure 6, the rates of electron transfer from P700 to A0 and A1 in the mutants are similar to the wild type PS I. However, the kinetic parameter from A1 anion to FX is quite different in the *menA* and *menB* null mutants. The time-resolved optical studies revealed that the forward electron transfer from A1 anion to FX is slowed 1000-fold, to 15 and 300 �s, compared to 20 and 200 ns in the wild type PS I (Semenov et al., 2000; Johnson et al., 2001). Based the kinetic data of electron transfer in *menA* and *menB* mutant, the redox potential of AP in *menA* and *menB* PS I is estimated to be more oxidizing than phylloquinone so that electron transfer from AP anion to FX is thermodynamically unfavorable in the mutants (right panel of Figure 6).

**Figure 6.** Kinetic data of electron transfer steps in native and *menA*/*menB* null mutants of *Synechocystis* sp. PCC 6803

### **4. Thermodynamics of** *menA* **and** *menB* **Null Mutants**

Pulsed photoacoustic spectroscopy can provide a direct measurement of thermodynamic parameters such as volume change and enthalpy changes that accompany electron transfer reactions (Braslavsky, 1985; Carpentier et al., 1990; Arnaut et al., 1992; Small et al., 1992; Losi et al., 1995; Edens et al., 2000; Malkin, 2000; Herbert et al., 2001; Feitelson and Mauzerall, 2002; Delosme, 2003; Hou and Mauzerall, 2006; Hou and Sakmar, 2010; Hou, 2011; Hou and Mauzerall, 2011). With prior knowledge of the change in Gibbs free energy of the corresponding reactions, the apparent entropy change (TS) of the reaction can be calculated. This is an important parameter, knowledge of which is required to fully understand the mechanism of electron transfer, and it has been largely underreported in the literature. The H, V, and TS of electron transfer in the photosynthetic reaction center from *Rb. sphaeroides* have been measured using pulsed photoacoustics (Edens et al., 2000; Nagy et al., 2001). In oxygenic photosynthetic systems, the same parameters of electron transfer in PS I trimers and in Mn depleted PS II reaction center cores from *Synechocystis* sp. PCC 6803 and higher plants have been investigated using similar techniques (Delosme et al., 1994; Hou et al., 2001). These data were confirmed by photoacoustic measurements on whole cells of *Synechocystis* sp. PCC 6803 (Boichenko et al., 2001). The thermodynamic parameters of bacterial reaction centers were found to be similar to those of PS I and dramatically different from those of PS II.

Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods 491

**Figure 7.** Photoacoustic waves of photosystem I complexes from the photoacoustic reference sample (curve 1), *menA* (curve 3), *menB* (curve 4), and wild-type (curve 2) strains of *Synechocystis* sp. PCC 6803 on the 1-microsecond time scale (Hou et al., 2009) (Reproduced with permission from the American

The quantum yield of photochemistry can be estimated from measurements of the effective cross section (Φσ). In Figure 8 (lower panel), the quantum yield of charge separation in *menA*/*B* PS I was estimated to be 85%, a value slightly lower than the 96% quantum yield in wild-type PS I. Taken together, they suggest that the volume contractions in *menA*/*B* PS I on the microsecond time scale are -172 Å3, and the quantum yields of photochemistry are ca. 8510%. The observed reaction on the microsecond time scale is attributed to the formation

enthalpy changes in *menA* and *menB* null mutants were determined to be 0.640.1 eV and 0.740.1 eV from the difference in slopes in Figure 9, respectively, according to the method

Figure 10 is the typical photoacoustic wave on the fast nanosecond time scale reaction. Curve 1 is the positive signal from a photoacoustic reference at 25 °C, and curves 2, 3, and 4 show large negative signals from wild-type PS I, *menA* PS I, and *menB* PS I, respectively, at 3.8 °C. They indicate that the volume contractions of the mutants are roughly two thirds of the wild type and are similar to those on the microsecond time scale. Figure 11 shows the analysis of photoacoustic data of the mutants and the wild type on the nanosecond time scale. The volume changes during charge separation in *menA*/*B* PS I were smaller, -17 Å3, than that of wild type PS I, -21 Å3. These values are identical to those of the mutants on the microsecond time scale, which indicate that there are no kinetic volume components between the 20 ns and 1 μs time scales in the mutants. It also demonstrates that the photoacoustic methodology on both time scales is reliable. The data in Figure 11 indicate that the enthalpy changes in both mutants are similar, -0.7 eV, which is very close to that on

for *menA*/*B* PS I. The

from excited P700\*for the wild-type PS I and of P700+AP-

described previously (Hou et al., 2001; Hou et al., 2009).

Chemical Society).

of P700+FA/B-

the microsecond time scale.

Using the fit by convolution of photoacoustic waves on the nanosecond and microsecond time scales, the thermodynamic parameters of different kinetic steps in *Synechocystis* PS I were resolved (Hou and Mauzerall, 2006). A large negative enthalpy (-0.8 eV) and large volume change (-23 Å3) for the P700\* to A1- FX step and a positive enthalpy (+0.4 eV) and a small volume change (-3 Å3) for the A1- FX to FA/B-step were observed. For the fast reaction the free energy change for the P700\* A1- FX step is -0.63 eV, and the entropy change (TΔS, T=25 °C) is -0.2 eV. For the slow reaction, A1- FX to FA/B- , the free energy is -0.14 eV (43), and the entropy change (TΔS) is positive, +0.54 eV. The positive entropy contribution is even larger than the positive enthalpy, indicating that the A1- FX to FA/B - step in *Synechocystis* PS I is entropy driven.

The photoacoustic waves produced by forming a charge-separated radical pair upon light excitation of PS I trimers consist of at least two major components: (1) the heat output (QRC), which includes the enthalpy change of the reaction and other rapidly released heat, and (2) the volume change of the reaction (ΔVRC). The thermal signal disappears at the temperature of maximum density of the suspending medium, Tm, near or below 4 °C, thus leaving only the volume term (Hou, 2011). Wild-type PS I trimers produced large negative PA signals at 3.8 °C (Figure 7, curve 2) which originate directly from the volume contraction via electrostriction. The volume change in wild-type PS I is -25 Å3. In contrast, *menA/B* PS I shows a smaller signal (Figure 7, curves 3 and 4). There is no major difference in the volume contraction between *menA* PS I and *menB* PS I. This may be expected since plastoquinone-9 is present in the A1 sites in PS I in both mutants.

To confirm the values of the volume change and to estimate the quantum yield of charge separation in *menA*/*B* PS I, two different approaches are utilized: (1) volume yield measurements and (2) saturation measurements. The detailed description of these two procedures has been given previously (Hou et al., 2001; Hou, 2011). The fits of the volume yield curves for the mutants and wild-type PS I are shown in Figure 8. The apparent volume contractions of *menA* PS I and *menB* PS I are -14 and -16 Å3, respectively, compared to -25 Å3 for wild-type PS I. In the second saturation method, every PS I complex is excited to obtain the maximum PA signal. In this method, one must calculate the number of PS I centers in the illuminated volume of the cell (∼0.34 mL), N, to obtain the real volume change ΔVs. In this analytical method, the volume change does not contain the quantum yield. As shown in Figure 8, the saturation value of volume change (ΔVs) in *menA*/*B* PS I was ∼-17 Å3, which is slightly higher than that using the volume yield method. These findings confirm the previous results and argue that the quantum yield of photochemistry in the mutants is not low.

dramatically different from those of PS II.

volume change (-23 Å3) for the P700\* to A1-

than the positive enthalpy, indicating that the A1-

is present in the A1 sites in PS I in both mutants.

small volume change (-3 Å3) for the A1-

is -0.2 eV. For the slow reaction, A1-

free energy change for the P700\* A1-

entropy driven.

from *Rb. sphaeroides* have been measured using pulsed photoacoustics (Edens et al., 2000; Nagy et al., 2001). In oxygenic photosynthetic systems, the same parameters of electron transfer in PS I trimers and in Mn depleted PS II reaction center cores from *Synechocystis* sp. PCC 6803 and higher plants have been investigated using similar techniques (Delosme et al., 1994; Hou et al., 2001). These data were confirmed by photoacoustic measurements on whole cells of *Synechocystis* sp. PCC 6803 (Boichenko et al., 2001). The thermodynamic parameters of bacterial reaction centers were found to be similar to those of PS I and

Using the fit by convolution of photoacoustic waves on the nanosecond and microsecond time scales, the thermodynamic parameters of different kinetic steps in *Synechocystis* PS I were resolved (Hou and Mauzerall, 2006). A large negative enthalpy (-0.8 eV) and large

FX to FA/B-

entropy change (TΔS) is positive, +0.54 eV. The positive entropy contribution is even larger

The photoacoustic waves produced by forming a charge-separated radical pair upon light excitation of PS I trimers consist of at least two major components: (1) the heat output (QRC), which includes the enthalpy change of the reaction and other rapidly released heat, and (2) the volume change of the reaction (ΔVRC). The thermal signal disappears at the temperature of maximum density of the suspending medium, Tm, near or below 4 °C, thus leaving only the volume term (Hou, 2011). Wild-type PS I trimers produced large negative PA signals at 3.8 °C (Figure 7, curve 2) which originate directly from the volume contraction via electrostriction. The volume change in wild-type PS I is -25 Å3. In contrast, *menA/B* PS I shows a smaller signal (Figure 7, curves 3 and 4). There is no major difference in the volume contraction between *menA* PS I and *menB* PS I. This may be expected since plastoquinone-9

To confirm the values of the volume change and to estimate the quantum yield of charge separation in *menA*/*B* PS I, two different approaches are utilized: (1) volume yield measurements and (2) saturation measurements. The detailed description of these two procedures has been given previously (Hou et al., 2001; Hou, 2011). The fits of the volume yield curves for the mutants and wild-type PS I are shown in Figure 8. The apparent volume contractions of *menA* PS I and *menB* PS I are -14 and -16 Å3, respectively, compared to -25 Å3 for wild-type PS I. In the second saturation method, every PS I complex is excited to obtain the maximum PA signal. In this method, one must calculate the number of PS I centers in the illuminated volume of the cell (∼0.34 mL), N, to obtain the real volume change ΔVs. In this analytical method, the volume change does not contain the quantum yield. As shown in Figure 8, the saturation value of volume change (ΔVs) in *menA*/*B* PS I was ∼-17 Å3, which is slightly higher than that using the volume yield method. These findings confirm the previous

results and argue that the quantum yield of photochemistry in the mutants is not low.

FX step and a positive enthalpy (+0.4 eV) and a

, the free energy is -0.14 eV (43), and the

FX to FA/B - step in *Synechocystis* PS I is

FX to FA/B-step were observed. For the fast reaction the

FX step is -0.63 eV, and the entropy change (TΔS, T=25 °C)

**Figure 7.** Photoacoustic waves of photosystem I complexes from the photoacoustic reference sample (curve 1), *menA* (curve 3), *menB* (curve 4), and wild-type (curve 2) strains of *Synechocystis* sp. PCC 6803 on the 1-microsecond time scale (Hou et al., 2009) (Reproduced with permission from the American Chemical Society).

The quantum yield of photochemistry can be estimated from measurements of the effective cross section (Φσ). In Figure 8 (lower panel), the quantum yield of charge separation in *menA*/*B* PS I was estimated to be 85%, a value slightly lower than the 96% quantum yield in wild-type PS I. Taken together, they suggest that the volume contractions in *menA*/*B* PS I on the microsecond time scale are -172 Å3, and the quantum yields of photochemistry are ca. 8510%. The observed reaction on the microsecond time scale is attributed to the formation of P700+FA/B from excited P700\*for the wild-type PS I and of P700+AP for *menA*/*B* PS I. The enthalpy changes in *menA* and *menB* null mutants were determined to be 0.640.1 eV and 0.740.1 eV from the difference in slopes in Figure 9, respectively, according to the method described previously (Hou et al., 2001; Hou et al., 2009).

Figure 10 is the typical photoacoustic wave on the fast nanosecond time scale reaction. Curve 1 is the positive signal from a photoacoustic reference at 25 °C, and curves 2, 3, and 4 show large negative signals from wild-type PS I, *menA* PS I, and *menB* PS I, respectively, at 3.8 °C. They indicate that the volume contractions of the mutants are roughly two thirds of the wild type and are similar to those on the microsecond time scale. Figure 11 shows the analysis of photoacoustic data of the mutants and the wild type on the nanosecond time scale. The volume changes during charge separation in *menA*/*B* PS I were smaller, -17 Å3, than that of wild type PS I, -21 Å3. These values are identical to those of the mutants on the microsecond time scale, which indicate that there are no kinetic volume components between the 20 ns and 1 μs time scales in the mutants. It also demonstrates that the photoacoustic methodology on both time scales is reliable. The data in Figure 11 indicate that the enthalpy changes in both mutants are similar, -0.7 eV, which is very close to that on the microsecond time scale.

Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods 493

**Figure 10.** Photoacoustic waves of the photoacoustic reference sample (curve 1), wild-type (curve 2), *menA* (curve 3), and *menB* (curve 4) mutants of *Synechocystis* sp. PCC 6803 on the nanosecond time scale

**Figure 11.** Enthalpy changes determined by plotting the linear fit of the photoacoustic intensity vs. temperature (water expansitivity) on the nanosecond time scale (Hou et al., 2009) (Reproduced with

permission from the American Chemical Society).

(Hou et al., 2009) (Reproduced with permission from the American Chemical Society).

**Figure 8.** Molecular volume changes determined by volume yield method (left panel) and saturation curve method (right panel) on the 1-microsecond time scale (Hou et al., 2009) (Reproduced with permission from the American Chemical Society).

**Figure 9.** Enthalpy changes determined by analyzing the linear fit of the photoacoustic intensity vs. temperature (water expansitivity) on the 1-microsecond time scale (Hou et al., 2009) (Reproduced with permission from the American Chemical Society).

permission from the American Chemical Society).

permission from the American Chemical Society).

**Figure 8.** Molecular volume changes determined by volume yield method (left panel) and saturation curve method (right panel) on the 1-microsecond time scale (Hou et al., 2009) (Reproduced with

**Figure 9.** Enthalpy changes determined by analyzing the linear fit of the photoacoustic intensity vs. temperature (water expansitivity) on the 1-microsecond time scale (Hou et al., 2009) (Reproduced with

**Figure 10.** Photoacoustic waves of the photoacoustic reference sample (curve 1), wild-type (curve 2), *menA* (curve 3), and *menB* (curve 4) mutants of *Synechocystis* sp. PCC 6803 on the nanosecond time scale (Hou et al., 2009) (Reproduced with permission from the American Chemical Society).

**Figure 11.** Enthalpy changes determined by plotting the linear fit of the photoacoustic intensity vs. temperature (water expansitivity) on the nanosecond time scale (Hou et al., 2009) (Reproduced with permission from the American Chemical Society).

To summarize the thermodynamic data, the volume changes, free energies, and enthalpy and entropy changes on *menA*/*B* PS I in comparison with those on the wild-type PS I are listed in Figure 12. Opened arrows are the early step forming P700+A1 from P700\* for the wildtype PS I or P700+AP from P700\* for the mutants, and solid arrows are the number of the following reaction: P700+AP- to P700+FA/B- . As shown in panel A, the volume contraction of the early step of the photoreaction in the mutants (-17 Å3) is smaller than that in the wild type (- 21 Å3). Similarly, the enthalpy change (-0.7 eV) of the early step in the mutants is smaller than that (-0.8 eV) in wild-type PS I (Figure 12B). Assuming a redox potential of -0.6 V for plastoquinone-9 in the A1 site (21), the free energy (-0.7 eV) of this early reaction in the mutants is larger than the value (-0.6 eV) in the wild type as indicated in Figure 12C. Taking the difference of free energy and enthalpy change in the mutants, the apparent entropy change of the early step in mutants is zero. In contrast, the apparent entropy change in the wild type is calculated to be +0.2 eV. Since the apparent entropy change for the overall reaction of the generation of P700+FA/B from P700\* is +0.35 eV (32), it implies that the latter reaction in the mutants, i.e., the P700+AP-FA/B to P700+APFA/B- reaction, is almost completely entropy driven (TΔS ) +0.4 eV and ΔG ) -0.1 eV) (Figure 12D).

Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods 495

in wild-type PS I. The volume contraction of electron transfer from P700

(25.3 Å) in *menA*/*B* PS I is the same as the distance

from P700\* is then -0.71 eV. Similarly, the free energy for

from P700\* in *menA*/*B* PS I is -0.7 0.07 eV. This is close

from P700\* in the wild-type PS I, the electron transfer

reaction is -0.060.10 eV in the mutants. Knowing the free energy

to FA/B would be associated with a positive enthalpy change of +0.3 eV and

naphthoquinone ring in phylloquinone. Electron spin-echo modulation experiments showed

to AP is estimated to be larger (-30 Å3) than the observed one (-17 Å3). Thus a positive volume due to a protein conformational change may be possible. We offer a molecular explanation of the difference in the volume change predicted via electrostriction and that of the observed value (-17 Å3). A simple explanation would be that the quantum yield of photochemistry is lower (for example, ∼0.7) in *menA*/*B* PS I. This, however, is unlikely because our pulse saturation data revealed a quantum yield of ∼85% in PS I from both mutants, which is only sufficiently lower than the quantum yield of 96% in wild type PS I to explain less than half of the effect. Further support for a high quantum yield is that the light saturation dependence of the flavodoxin reduction rate in *menA*/*B* PS I is similar to that of wild-type PS I. These two arguments are consistent in showing that the smaller volume

The smaller volume contraction may be caused by the following two factors: compressibility of protein and polarity of quinone pocket. The first factor is the effect of the foreign plastoquinone on the compressibility of the local environment of the protein. The orientation and distance of plastoquinone- 9 in the mutants are known to be similar to phylloquinone in the wild-type PS I. However, since the pocket of A1 is adapted to phylloquinone, the smaller plastoquinone with the longer tail may not fit well into the protein. If the effect of the larger tail is to crowd the hydrophobic site, this could decrease the compressibility of the local domain and so decrease ΔVel. Alternatively, the A1 binding region in *menA*/*B* PS I may be more polar; i.e., it has a larger effective ε, compared to the wild-type PS I. This could be due to the small size of plastoquinone-9, allowing a water molecule to be present. This possibility also could explain the change in potential of the

By use of the electron transfer theory and kinetic data, the redox potential of plastoquinone at the A1 site was estimated to be -0.61 V (Hou et al., 2009). However, the error to be at least

producing P700+FA/B- from P700\*FA/B is -0.77 eV (35). Thus we infer that the free energy of

of the electron transfer step in wild-type PS I and *menA*/*B* PS I, the entropic contribution (T ΔS) can be determined by the Gibbs relation ΔG = ΔH - TΔS. The enthalpy change

to the estimated free energy of this reaction (-0.70 eV), and thus the apparent entropy change is close to zero (Figure 12). Considering the enthalpy change (-0.4 eV) of the overall

The entropy of electron transfer reactions is often assumed to be zero. However, the free energy calculated from kinetic measurements of reverse electron transfer in bacterial

thus is completely entropy driven as the free energy is zero in the mutants.

that the distance between P700+ and AP-

change in the *menA*/B PS I is not caused by a low quantum yield.

quinone because of hydrogen bonding to the water.

0.1 V. The ΔG for producing P700+AP-

occurring on the formation of P700+AP-

reaction for the formation of P700+FA/B-

FA/B to P700+APFA/B-

P700+AP-

reaction from AP-

between P700+ and A1-

**Figure 12.** Thermodynamics of electron transfer reactions in photosystem I from the *menA*/*menB* null mutants and wild-type strains of *Synechocystis* sp. PCC 6803 (Hou et al., 2009) (Reproduced with permission from the American Chemical Society).

In the case of *menA*/*B* PS I, photoacoustic measurements on the microsecond time scale reveal the volume contraction to be -17 Å3. Considering our time window of 0.1-10 μs, this value is assigned to the formation of P700+AP from P700\*AP. The intermediate step of electron transfer from P700+AP-FA/B to P700+APFA/B would be accompanied by a volume change of -9 Å3, assuming the replacement of A1 with AP causes no change in the FA/B clusters. For *menA*/*B* PS I, the size of the benzoquinone ring in plastoquinone-9 (AP) is smaller than the

naphthoquinone ring in phylloquinone. Electron spin-echo modulation experiments showed that the distance between P700+ and AP- (25.3 Å) in *menA*/*B* PS I is the same as the distance between P700+ and A1 in wild-type PS I. The volume contraction of electron transfer from P700 to AP is estimated to be larger (-30 Å3) than the observed one (-17 Å3). Thus a positive volume due to a protein conformational change may be possible. We offer a molecular explanation of the difference in the volume change predicted via electrostriction and that of the observed value (-17 Å3). A simple explanation would be that the quantum yield of photochemistry is lower (for example, ∼0.7) in *menA*/*B* PS I. This, however, is unlikely because our pulse saturation data revealed a quantum yield of ∼85% in PS I from both mutants, which is only sufficiently lower than the quantum yield of 96% in wild type PS I to explain less than half of the effect. Further support for a high quantum yield is that the light saturation dependence of the flavodoxin reduction rate in *menA*/*B* PS I is similar to that of wild-type PS I. These two arguments are consistent in showing that the smaller volume change in the *menA*/B PS I is not caused by a low quantum yield.

494 Thermodynamics – Fundamentals and Its Application in Science

following reaction: P700+AP- to P700+FA/B-

reaction of the generation of P700+FA/B-

reaction in the mutants, i.e., the P700+AP-

permission from the American Chemical Society).

value is assigned to the formation of P700+AP-

FA/B to P700+APFA/B-

transfer from P700+AP-

type PS I or P700+AP-

listed in Figure 12. Opened arrows are the early step forming P700+A1-

entropy driven (TΔS ) +0.4 eV and ΔG ) -0.1 eV) (Figure 12D).

To summarize the thermodynamic data, the volume changes, free energies, and enthalpy and entropy changes on *menA*/*B* PS I in comparison with those on the wild-type PS I are

early step of the photoreaction in the mutants (-17 Å3) is smaller than that in the wild type (- 21 Å3). Similarly, the enthalpy change (-0.7 eV) of the early step in the mutants is smaller than that (-0.8 eV) in wild-type PS I (Figure 12B). Assuming a redox potential of -0.6 V for plastoquinone-9 in the A1 site (21), the free energy (-0.7 eV) of this early reaction in the mutants is larger than the value (-0.6 eV) in the wild type as indicated in Figure 12C. Taking the difference of free energy and enthalpy change in the mutants, the apparent entropy change of the early step in mutants is zero. In contrast, the apparent entropy change in the wild type is calculated to be +0.2 eV. Since the apparent entropy change for the overall

**Figure 12.** Thermodynamics of electron transfer reactions in photosystem I from the *menA*/*menB* null mutants and wild-type strains of *Synechocystis* sp. PCC 6803 (Hou et al., 2009) (Reproduced with

In the case of *menA*/*B* PS I, photoacoustic measurements on the microsecond time scale reveal the volume contraction to be -17 Å3. Considering our time window of 0.1-10 μs, this

assuming the replacement of A1 with AP causes no change in the FA/B clusters. For *menA*/*B* PS I, the size of the benzoquinone ring in plastoquinone-9 (AP) is smaller than the

from P700\* for the mutants, and solid arrows are the number of the

. As shown in panel A, the volume contraction of the

from P700\* is +0.35 eV (32), it implies that the latter

FA/B to P700+APFA/B- reaction, is almost completely

from P700\*AP. The intermediate step of electron

would be accompanied by a volume change of -9 Å3,

from P700\* for the wild-

The smaller volume contraction may be caused by the following two factors: compressibility of protein and polarity of quinone pocket. The first factor is the effect of the foreign plastoquinone on the compressibility of the local environment of the protein. The orientation and distance of plastoquinone- 9 in the mutants are known to be similar to phylloquinone in the wild-type PS I. However, since the pocket of A1 is adapted to phylloquinone, the smaller plastoquinone with the longer tail may not fit well into the protein. If the effect of the larger tail is to crowd the hydrophobic site, this could decrease the compressibility of the local domain and so decrease ΔVel. Alternatively, the A1 binding region in *menA*/*B* PS I may be more polar; i.e., it has a larger effective ε, compared to the wild-type PS I. This could be due to the small size of plastoquinone-9, allowing a water molecule to be present. This possibility also could explain the change in potential of the quinone because of hydrogen bonding to the water.

By use of the electron transfer theory and kinetic data, the redox potential of plastoquinone at the A1 site was estimated to be -0.61 V (Hou et al., 2009). However, the error to be at least 0.1 V. The ΔG for producing P700+AP from P700\* is then -0.71 eV. Similarly, the free energy for producing P700+FA/B- from P700\*FA/B is -0.77 eV (35). Thus we infer that the free energy of P700+AP-FA/B to P700+APFA/B reaction is -0.060.10 eV in the mutants. Knowing the free energy of the electron transfer step in wild-type PS I and *menA*/*B* PS I, the entropic contribution (T ΔS) can be determined by the Gibbs relation ΔG = ΔH - TΔS. The enthalpy change occurring on the formation of P700+AP from P700\* in *menA*/*B* PS I is -0.7 0.07 eV. This is close to the estimated free energy of this reaction (-0.70 eV), and thus the apparent entropy change is close to zero (Figure 12). Considering the enthalpy change (-0.4 eV) of the overall reaction for the formation of P700+FA/B from P700\* in the wild-type PS I, the electron transfer reaction from AP to FA/B would be associated with a positive enthalpy change of +0.3 eV and thus is completely entropy driven as the free energy is zero in the mutants.

The entropy of electron transfer reactions is often assumed to be zero. However, the free energy calculated from kinetic measurements of reverse electron transfer in bacterial reaction centers shows that the free energy is time- and temperature dependent, particularly on the less than nanosecond time scale. The kinetics of these decays can only be described as "distributed", and simple analysis in terms of a single component is not trustworthy. Protein dynamics may play a key role in this electron transfer step. However, the question of whether these "relaxations" are enthalpy and/or entropy driven remains to be answered. The slow (microsecond) component observed in wild-type PS I could be such a relaxation, but only the ΔV was determined. The difference between observed enthalpies and estimated free energies as entropies highlights the problem. In addition to reaction centers of Rb. sphaeroides, similar positive entropic contribution in PS I preparations of *Synechocystis* sp. PCC 6803 were observed, but not in PS II preparations. Charge movement, but not charge separation due to proton transfer, may be the difference in PS II on the 1 μs time scale. Clear-cut and large negative entropic contribution is seen in the model system of triplet porphyrin-to-ferricyanide electron transfer in aqueous solution, where "relaxations" are too fast to be relevant.

Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods 497

fold, to 15 to 300 μs, compared to 20 and 200 ns in the wild type. Using the electron transfer theory and kinetic data, the redox potential of plastoquinone at the A1 site was estimated to be -0.61 V, more oxidizing that phylloquinone. The electron transfer from AP anion to FX is

Photoacoustic measurements reveal that the quantum yield of charge separation in *menA* and *menB* is slightly lower (85%) than that of the wild type. The thermodynamic parameters of the two electron transfer steps, including molecular volume changes, reaction enthalpy and apparent entropy, were obtained in *menA* and *menB* null mutants and are considerable different from the wild type. The experimental data demonstrates that the not only the kinetics but also the thermodynamics of electron transfer reaction in photosystem I are affected by the recruitment of the foreign quinone into the A1 site. One of the most intriguing conclusions is that although free energy for the electron transfer from AP anion to FX in *menA* and *menB* mutant is close to zero, the apparent entropy (TΔS) for this reaction is positive, +0.4 eV. This indicates that the entropy plays a key role in the electron transfer from AP anion to FX. As shown in Figure 13, the electron transfer from P700 to A1 is enthalpy driven; the electron transfer from A1 to FA/FB is entropy driven. The driving force of electron transfer in photosynthetic systems is not only dependent on the bonding energy of the cofactor and interaction energy with the protein (enthalpy) but also dependent on the

thermodynamically unfavorable in the *menA* and *menB* null mutants.

available states of interaction with the protein (entropy).

**Author details** 

Harvey J.M. Hou\*

Corresponding Author

*University of Massachusetts Dartmouth, USA* 

*University of Massachusetts Dartmouth, USA* 

*Alabama State University, USA* 

Xuejing Hou

 \*

**Figure 13.** The enthalpy and entropy driven steps in *Synechocystis* 6803 photosystem I

## **5. Conclusion**

In this chapter, thermodynamics of electron transfers in biological system can be assessed by using a combination of molecular genetics and sophisticated biophysical techniques, in particular, pulsed photoacoustic spectroscopy. Photosynthesis involves light-induced charge separation and subsequently a series of electron transfer reactions and is an ideal system for the detailed study on electron transfer mechanisms in chemistry and biology. In contrast to the susceptible and vulnerable of photosystem II complex to environment, photosystem I complex is much more stable and a perfect choice for such a study. As quinones play a central role in electron transfer reactions in both anoxygenic and oxygenic photosynthesis, the phylloquinone (A1) of photosystem I is chosen as a probe to explore the effect and regulation of electron cofactors on kinetics and thermodynamics in vivo. The usual approach of chemical modification or replacement of phylloquinone may alter the bonding pocket of the cofactor and the interaction with its proteins.

Molecular genetic technique is utilized to block the biosynthesis of the cofactor, phylloquinone, in the cynobacterium *Synechocystis* sp. PCC 6803 and replace the phylloquinone in the A1 site with different foreign quinones. The effect of the foreign quinones on the electron transfer is systematically studied by biophysical methodologies. Specifically, the *menA* and *menB* genes, which code for phytyl transferase and 1.4 dihydroxy-2-naphthoae synthase, respectively, are inactivated to prevent the synthesis of phylloquinone. In spite of the demonstrated absence of phylloquinone, the *menA* and *menB* null mutants grow photoheterotrophically. HPLC and EPR measurement show that plastoquinone-9 (AP) has been recruited into the A1 site and functions as an efficient oneelectron transfer carrier. The orientation and distance between the plastoquinone and other cofactors are the same as that of the wild type. Time-resolved optical studies indicate that the forward electron transfer from A1 anion to the iron-sulfur cluster (FX) is slowed 1000fold, to 15 to 300 μs, compared to 20 and 200 ns in the wild type. Using the electron transfer theory and kinetic data, the redox potential of plastoquinone at the A1 site was estimated to be -0.61 V, more oxidizing that phylloquinone. The electron transfer from AP anion to FX is thermodynamically unfavorable in the *menA* and *menB* null mutants.

Photoacoustic measurements reveal that the quantum yield of charge separation in *menA* and *menB* is slightly lower (85%) than that of the wild type. The thermodynamic parameters of the two electron transfer steps, including molecular volume changes, reaction enthalpy and apparent entropy, were obtained in *menA* and *menB* null mutants and are considerable different from the wild type. The experimental data demonstrates that the not only the kinetics but also the thermodynamics of electron transfer reaction in photosystem I are affected by the recruitment of the foreign quinone into the A1 site. One of the most intriguing conclusions is that although free energy for the electron transfer from AP anion to FX in *menA* and *menB* mutant is close to zero, the apparent entropy (TΔS) for this reaction is positive, +0.4 eV. This indicates that the entropy plays a key role in the electron transfer from AP anion to FX. As shown in Figure 13, the electron transfer from P700 to A1 is enthalpy driven; the electron transfer from A1 to FA/FB is entropy driven. The driving force of electron transfer in photosynthetic systems is not only dependent on the bonding energy of the cofactor and interaction energy with the protein (enthalpy) but also dependent on the available states of interaction with the protein (entropy).

**Figure 13.** The enthalpy and entropy driven steps in *Synechocystis* 6803 photosystem I

## **Author details**

496 Thermodynamics – Fundamentals and Its Application in Science

are too fast to be relevant.

**5. Conclusion** 

reaction centers shows that the free energy is time- and temperature dependent, particularly on the less than nanosecond time scale. The kinetics of these decays can only be described as "distributed", and simple analysis in terms of a single component is not trustworthy. Protein dynamics may play a key role in this electron transfer step. However, the question of whether these "relaxations" are enthalpy and/or entropy driven remains to be answered. The slow (microsecond) component observed in wild-type PS I could be such a relaxation, but only the ΔV was determined. The difference between observed enthalpies and estimated free energies as entropies highlights the problem. In addition to reaction centers of Rb. sphaeroides, similar positive entropic contribution in PS I preparations of *Synechocystis* sp. PCC 6803 were observed, but not in PS II preparations. Charge movement, but not charge separation due to proton transfer, may be the difference in PS II on the 1 μs time scale. Clear-cut and large negative entropic contribution is seen in the model system of triplet porphyrin-to-ferricyanide electron transfer in aqueous solution, where "relaxations"

In this chapter, thermodynamics of electron transfers in biological system can be assessed by using a combination of molecular genetics and sophisticated biophysical techniques, in particular, pulsed photoacoustic spectroscopy. Photosynthesis involves light-induced charge separation and subsequently a series of electron transfer reactions and is an ideal system for the detailed study on electron transfer mechanisms in chemistry and biology. In contrast to the susceptible and vulnerable of photosystem II complex to environment, photosystem I complex is much more stable and a perfect choice for such a study. As quinones play a central role in electron transfer reactions in both anoxygenic and oxygenic photosynthesis, the phylloquinone (A1) of photosystem I is chosen as a probe to explore the effect and regulation of electron cofactors on kinetics and thermodynamics in vivo. The usual approach of chemical modification or replacement of phylloquinone may alter the

Molecular genetic technique is utilized to block the biosynthesis of the cofactor, phylloquinone, in the cynobacterium *Synechocystis* sp. PCC 6803 and replace the phylloquinone in the A1 site with different foreign quinones. The effect of the foreign quinones on the electron transfer is systematically studied by biophysical methodologies. Specifically, the *menA* and *menB* genes, which code for phytyl transferase and 1.4 dihydroxy-2-naphthoae synthase, respectively, are inactivated to prevent the synthesis of phylloquinone. In spite of the demonstrated absence of phylloquinone, the *menA* and *menB* null mutants grow photoheterotrophically. HPLC and EPR measurement show that plastoquinone-9 (AP) has been recruited into the A1 site and functions as an efficient oneelectron transfer carrier. The orientation and distance between the plastoquinone and other cofactors are the same as that of the wild type. Time-resolved optical studies indicate that the forward electron transfer from A1 anion to the iron-sulfur cluster (FX) is slowed 1000-

bonding pocket of the cofactor and the interaction with its proteins.

Xuejing Hou *University of Massachusetts Dartmouth, USA* 

Harvey J.M. Hou\* *University of Massachusetts Dartmouth, USA Alabama State University, USA* 

<sup>\*</sup> Corresponding Author

## **Acknowledgement**

This work was supported by the Alabama State University and University of Massachusetts Dartmouth. The photoacoustic measurements were conducted in the laboratory of Professor David Mauzerall at Rockefeller University. The author thanks Professor John Golbeck and Dr. Gaozhong Shen for their collaboration and stimulating discussions on *menA*/*menB* project. He is also grateful to his students, Fan Zhang and Lien-Yang Chou, for data analysis and assistance.

Probing the Thermodynamics of Photosystem I by Spectroscopic and Mutagenic Methods 499

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**1. Introduction**

http://dx.doi.org/10.5772/51630

C.A.S. Silva

**Thermodynamics** 

Additional information is available at the end of the chapter

mechanics.

the event horizon) is a lightlike surface.

A black hole is, by definition, a region in spacetime in which the gravitational field is so strong that it precludes even light from escaping to infinity. A black hole is formed when a body of mass M contracts to a size less than the so called gravitational radius *rg* = 2*GM*/*c*2. (G is the Newton's gravitational constant, and c is the speed of light). The velocity required to leave the boundary of the black hole and move away to infinity (the escape velocity) equals the speed of light. In this way, one easily concludes that neither signals nor particles can escape from the region inside the black hole since the speed of light is the limiting propagation velocity for physical signals. From the fact that no signals can escape from a black hole, while physical objects and radiation can fall into it, the surface bounding the black hole in spacetime (called

**Chapter 20**

**Fuzzy Spheres Decays and Black Hole** 

The term "black hole" was introduced by Wheeler in 1967 although the theoretical study of these objects has quite a long history. The very possibility of the existence of such objects was first discussed by Michell and Laplace within the framework of the Newtonian theory at the end of the 18th century [1–3]. In general relativity context, the problem arose within a year after the theory had been developed, i.e., after Schwarzschild (1916) obtained the first exact

In particular, black hole developments in the last forty years have shown that black holes have thermodynamics properties like entropy and temperature, and as a consequence of the instability of the vacuum in strong gravitational fields, they are sources of quantum radiation [4–6]. String theory and loop quantum gravity, lately, showed that the origin of the black hole thermodynamics must be related with the quantum structure of the spacetime, bringing together the developments in black hole physics and the improvement of our understanding on the nature of the spacetime in quantum gravity regime [7, 8]. In this way, it is believed that black holes may play a major role in our attempts to shed some light on the quantum nature of the spacetime such as the role played by atoms in the early development of quantum

and reproduction in any medium, provided the original work is properly cited.

©2012 Silva, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

(spherically symmetric) solution of Einstein's equations in vacuum.

