Excitonic coupling effect on the circular dichroism spectrum of sodium-pumping rhodopsin KR2

FIG. 6. CD spectra of the KR2 pentamer calculated with the exciton model using

the excitonic coupling of 10 cm−1 , 20 cm−1 , 30 cm−1 , 40 cm−1 , 50 cm−1 , and

100 cm−1 . The values are given per monomer.

V. CONCLUSIONS

In this paper, we investigated the excitonic coupling effect on

the CD spectrum of the KR2 pentamer using the exciton model

combined with the TDFI method. The TDFI method allows for

an accurate description and detailed analysis of excitonic coupling, in terms of Coulomb, exchange, and CT interactions. Taking advantage of this benefit, we investigated the major contributions to excitonic coupling. The results of this study clearly showed

a dominant contribution of the Coulomb interaction to the excitonic coupling value. In contrast, the exchange and CT interactions

resulted in negligible contributions. The results also indicated that

EET between retinal chromophores is less likely to occur in KR2

because of the small magnitude of excitonic coupling (25.1 cm−1 ).

The excitonic coupling values were employed for the spectral calculations with the exciton model. As a result, the main features of

the experimental absorption and CD spectra of KR2 were successfully reproduced. Based on these results, we explored the mechanism of the CD spectral shape observed in the KR2 pentamer.

As a result of the analysis, the excitonic coupling between retinal

chromophores was found to be indispensable for the quantitative

description of the red-shifted CD band compared to the monomer

spectrum. Further analysis revealed that the weak excitonic coupling

of about 20 cm−1 plays a crucial role in the single positive CD band

of KR2.

This is the first computational study on the CD spectrum of

KR2. The findings of this study provide the basis for understanding

the origin of the KR2 CD spectrum. The exciton model combined

with TDFI used in this study is a promising approach for calculating

CD spectra. Although the QM/MM calculation based on the SAC-CI

method for the KR2 pentamer is not realistic due to the huge computational cost, the exciton model combined with TDFI enables the CD

J. Chem. Phys. 153, 045101 (2020); doi: 10.1063/5.0013642

Published under license by AIP Publishing

N. Berova, K. Nakanishi, and R. W. Woody, Circular Dichroism: Principles and

Applications, 2nd ed. (Wiley VCH, New York, 2000).

C. A. Hasselbacher, J. L. Spudich, and T. G. Dewey, “Circular dichroism of

halorhodopsin: Comparison with bacteriorhodopsin and sensory rhodopsin I,”

Biochemistry 27, 2540–2546 (1988).

J. Y. Cassim, “Unique biphasic band shape of the visible circular dichroism of

bacteriorhodopsin in purple membrane,” Biophys. J. 63, 1432–1442 (1992).

C. M. Davis, P. L. Bustamante, and P. A. Loach, “Reconstitution of bacterial core light-harvesting complexes of Rhodobacter sphaeroides and Rhodospirillum rubrum with isolated α- and β-polypeptides, bacteriochlorophyll a, and

carotenoid,” J. Biol. Chem. 270, 5793–5804 (1995).

S. Georgakopoulou, R. van Grondelle, and G. van der Zwan, “Circular dichroism of carotenoids in bacterial light-harvesting complexes: Experiments and

modeling,” Biophys. J. 87, 3010–3022 (2004).

J. Adolphs, F. Müh, M. E.-A. Madjet, M. S. am Busch, and T. Renger, “Structurebased calculations of optical spectra of photosystem I suggest an asymmetric lightharvesting,” J. Am. Chem. Soc. 132, 3331–3343 (2010).

G. Pescitelli and R. W. Woody, “The exciton origin of the visible circular

dichroism spectrum of bacteriorhodopsin,” J. Phys. Chem. B 116, 6751–6763

(2012).

N. Harada and K. Nakanishi, Circular Dichroic Spectroscopy: Exciton Coupling in

Organic Stereochemistry (University Science Books, Mill Valley, CA, 1983).

I. Tinoco, Jr., “Theoretical aspects of optical activity,” Adv. Chem. Phys. 4, 113–

160 (1962).

10

R. W. Woody, “Improved calculation of the nπ∗ rotational strength in polypeptides,” J. Chem. Phys. 49, 4797–4806 (1968).

11

N. Harada and K. Nakanishi, “Determining the chiralities of optically active

glycols,” J. Am. Chem. Soc. 91, 3989–3991 (1969).

12

P. M. Bayley, E. B. Nielsen, and J. A. Schellman, “Rotatory properties of

molecules containing two peptide groups: Theory,” J. Phys. Chem. 73, 228–243

(1969).

13

W. J. Goux and T. M. Hooker, Jr., “Chiroptical properties of proteins. I. Nearultraviolet circular dichroism of ribonuclease S,” J. Am. Chem. Soc. 102, 7080–

7087 (1980).

14

J. D. Hirst, “Improving protein circular dichroism calculations in the farultraviolet through reparametrizing the amide chromophore,” J. Chem. Phys. 109,

782–788 (1998).

15

N. A. Besley and J. D. Hirst, “Theoretical studies toward quantitative protein

circular dichroism calculations,” J. Am. Chem. Soc. 121, 9636–9644 (1999).

16

N. Sreerama and R. W. Woody, “Computation and analysis of protein circular

dichroism spectra,” Methods Enzymol. 383, 318–351 (2004).

17

W. Kuhn, “The physical significance of optical rotatory power,” Trans. Faraday

Soc. 26, 293–308 (1930).

153, 045101-7

The Journal

of Chemical Physics

18

J. G. Kirkwood, “On the theory of optical rotatory power,” J. Chem. Phys. 5,

479–491 (1937).

19

J. Frenkel, “On the transformation of light into heat in solids. II,” Phys. Rev. 37,

1276–1294 (1931).

20

J. C. Chang, “Monopole effects on electronic excitation interactions between

large molecules. I. Application to energy transfer in chlorophylls,” J. Chem. Phys.

67, 3901–3909 (1977).

21

B. P. Krueger, G. D. Scholes, and G. R. Fleming, “Calculation of couplings and

energy-transfer pathways between the pigments of LH2 by the ab initio transition

density cube method,” J. Phys. Chem. B 102, 5378–5386 (1998).

22

S. Tretiak, C. Middleton, V. Chernyak, and S. Mukamel, “Exciton Hamiltonian for the bacteriochlorophyll system in the LH2 antenna complex of purple

bacteria,” J. Phys. Chem. B 104, 4519–4528 (2000).

23

C.-P. Hsu, G. R. Fleming, M. Head-Gordon, and T. Head-Gordon, “Excitation energy transfer in condensed media,” J. Chem. Phys. 114, 3065–3072

(2001).

24

M. F. Iozzi, B. Mennucci, J. Tomasi, and R. Cammi, “Excitation energy

transfer (EET) between molecules in condensed matter: A novel application

of the polarizable continuum model (PCM),” J. Chem. Phys. 120, 7029–7040

(2004).

25

K. F. Wong, B. Bagchi, and P. J. Rossky, “Distance and orientation dependence

of excitation transfer rates in conjugated systems: Beyond the Förster theory,”

J. Phys. Chem. A 108, 5752–5763 (2004).

26

M. E. Madjet, A. Abdurahman, and T. Renger, “Intermolecular Coulomb couplings from ab initio electrostatic potentials: Application to optical transitions

of strongly coupled pigments in photosynthetic antennae and reaction centers,”

J. Phys. Chem. B 110, 17268–17281 (2006).

27

J. Neugebauer, “Couplings between electronic transitions in a subsystem formulation of time-dependent density functional theory,” J. Chem. Phys. 126, 134116

(2007).

28

B. Fückel, A. Köhn, M. E. Harding, G. Diezemann, G. Hinze, T. Basché, and

J. Gauss, “Theoretical investigation of electronic excitation energy transfer in

bichromophoric assemblies,” J. Chem. Phys. 128, 074505 (2008).

29

R. F. Fink, J. Pfister, H. M. Zhao, and B. Engels, “Assessment of quantum

chemical methods and basis sets for excitation energy transfer,” Chem. Phys. 346,

275–285 (2008).

30

J. Vura-Weis, M. D. Newton, M. R. Wasielewski, and J. E. Subotnik, “Characterizing the locality of diabatic states for electronic excitation transfer by

decomposing the diabatic coupling,” J. Phys. Chem. C 114, 20449–20460

(2010).

31

T. Kawatsu, K. Matsuda, and J. Hasegawa, “Bridge-mediated excitation energy

transfer pathways through protein media: A slater determinant-based electronic

coupling calculation combined with localized molecular orbitals,” J. Phys. Chem.

A 115, 10814–10822 (2011).

32

A. A. Voityuk, “Estimation of electronic coupling for photoinduced charge separation and charge recombination using the fragment charge difference method,”

J. Phys. Chem. C 117, 2670–2675 (2013).

33

K. J. Fujimoto, “Electronic coupling calculations with transition charges,

dipoles, and quadrupoles derived from electrostatic potential fitting,” J. Chem.

Phys. 141, 214105 (2014).

34

B. Błasiak, M. Maj, M. Cho, and R. W. Góra, “Distributed multipolar expansion

approach to calculation of excitation energy transfer couplings,” J. Chem. Theory

Comput. 11, 3259–3266 (2015).

35

K. J. Fujimoto and S. Hayashi, “Electronic Coulombic coupling of excitationenergy transfer in xanthorhodopsin,” J. Am. Chem. Soc. 131, 14152–14153

(2009).

36

K. J. Fujimoto, “Transition-density-fragment interaction combined with transfer integral approach for excitation-energy transfer via charge-transfer states,”

J. Chem. Phys. 137, 034101 (2012).

37

K. J. Fujimoto, in Chemical Science of π-Electron Systems, edited by T. Akasaka,

A. Osuka, S. Fukuzumi, H. Kandori, and Y. Aso (Springer, Tokyo, Japan, 2015),

pp. 761–777.

38

K. J. Fujimoto, “Transition-density-fragment interaction approach for

exciton-coupled circular dichroism spectra,” J. Chem. Phys. 133, 124101

(2010).

J. Chem. Phys. 153, 045101 (2020); doi: 10.1063/5.0013642

Published under license by AIP Publishing

ARTICLE

scitation.org/journal/jcp

39

K. J. Fujimoto and S. P. Balashov, “Vibronic coupling effect on circular dichroism spectrum: Carotenoid–retinal interaction in xanthorhodopsin,” J. Chem.

Phys. 146, 095101 (2017).

40

K. J. Fujimoto and C. Kitamura, “A theoretical study of crystallochromy:

Spectral tuning of solid-state tetracenes,” J. Chem. Phys. 139, 084511

(2013).

41

K. Inoue, H. Ono, R. Abe-Yoshizumi, S. Yoshizawa, H. Ito, K. Kogure, and

H. Kandori, “A light-driven sodium ion pump in marine bacteria,” Nat. Commun.

4, 1678 (2013).

42

H. E. Kato, K. Inoue, R. Abe-Yoshizumi et al., “Structural basis for Na+ transport

mechanism by a light-driven Na+ pump,” Nature 521, 48–53 (2015).

43

I. Gushchin, V. Shevchenko, V. Polovinkin et al., “Crystal structure of a lightdriven sodium pump,” Nat. Struct. Mol. Biol. 22, 390–395 (2015).

44

K. Inoue, M. Konno, R. Abe-Yoshizumi, and H. Kandori, “The role of the NDQ

motif in sodium-pumping rhodopsins,” Angew. Chem., Int. Ed. 54, 11536–11539

(2015).

45

H. Kandori, K. Inoue, and S. P. Tsunoda, “Light-driven sodium-pumping

rhodopsin: A new concept of active transport,” Chem. Rev. 118, 10646–10658

(2018).

46

K. Deisseroth, G. Feng, A. K. Majewska, G. Miesenbock, A. Ting, and M. J.

Schnitzer, “Next-generation optical technologies for illuminating genetically targeted brain circuits,” J. Neurosci. 26, 10380–10386 (2006).

47

Y. I. Wu, D. Frey, O. I. Lungu, A. Jaehrig, I. Schlichting, B. Kuhlman, and K. M.

Hahn, “A genetically encoded photoactivatable Rac controls the motility of living

cells,” Nature 461, 104–108 (2009).

48

E. S. Koganov, V. Brumfeld, N. Friedman, and M. Sheves, “Origin of circular

dichroism of xanthorhodopsin. A study with artificial pigments,” J. Phys. Chem. B

119, 456–464 (2015).

49

M. Shibata, K. Inoue, K. Ikeda, M. Konno, M. Singh, C. Kataoka,

R. Abe-Yoshizumi, H. Kandori, and T. Uchihashi, “Oligomeric states of microbial rhodopsins determined by high-speed atomic force microscopy and circular

dichroic spectroscopy,” Sci. Rep. 8, 8262 (2018).

50

P. -O. Löwdin, “On the non-orthogonality problem connected with the use of

atomic wave functions in the theory of molecules and crystals,” J. Chem. Phys. 18,

365–375 (1950).

51

A. Warshel and M. Levitt, “Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of

lysozyme,” J. Mol. Biol. 103, 227–249 (1976).

52

W. Kohn and L. J. Sham, “Self-consistent equations including exchange and

correlation effects,” Phys. Rev. 140, A1133 (1965).

53

C. Lee, W. Yang, and R. G. Parr, “Development of the Colle–Salvetti correlationenergy formula into a functional of the electron density,” Phys. Rev. B 37, 785–789

(1988).

54

J. Wang, P. Cieplak, and P. A. Kollman, “How well does a restrained electrostatic

potential (RESP) model perform in calculating conformational energies of organic

and biological molecules?,” J. Comput. Chem. 21, 1049–1074 (2000).

55

K. Fujimoto and W. Yang, “Density-fragment interaction approach for

quantum-mechanical/molecular-mechanical calculations with application to

the excited states of a Mg2+ -sensitive dye,” J. Chem. Phys. 129, 054102

(2008).

56

H. Nakatsuji, “Cluster expansion of the wavefunction. Excited states,” Chem.

Phys. Lett. 59, 362–364 (1978).

57

E. Runge and E. K. U. Gross, “Density-functional theory for time-dependent

systems,” Phys. Rev. Lett. 52, 997–1000 (1984).

58

T. Yanai, D. P. Tew, and N. C. Handy, “A new hybrid exchange–correlation

functional using the Coulomb-attenuating method (CAM-B3LYP),” Chem. Phys.

Lett. 393, 51–57 (2004).

59

H. M. Senn and W. Thiel, “QM/MM methods for biomolecular systems,”

Angew. Chem., Int. Ed. 48, 1198–1229 (2009).

60

J. W. Ponder, Tinker4.2 (Washington University, St. Louis, MO, 2004).

61

M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., Gaussian09, Revision A.02,

Gaussian, Inc., Wallingford, CT, 2009.

62

S. P. Balashov, E. S. Imasheva, V. A. Boichenko, J. Antón, J. M. Wang, and

J. K. Lanyi, “Xanthorhodopsin: A proton pump with a light-harvesting carotenoid

antenna,” Science 309, 2061–2064 (2005).

153, 045101-8

The Journal

of Chemical Physics

63

S. P. Balashov, E. S. Imasheva, and J. K. Lanyi, “Induced chirality of the

light-harvesting carotenoid salinixanthin and its interaction with the retinal of

xanthorhodopsin,” Biochemistry 45, 10998–11004 (2006).

64

T. Polívka, S. P. Balashov, P. Chábera, E. S. Imasheva, A. Yartsev,

V. Sundström, and J. K. Lanyi, “Femtosecond carotenoid to retinal energy transfer

in xanthorhodopsin,” Biophys. J. 96, 2268–2277 (2009).

J. Chem. Phys. 153, 045101 (2020); doi: 10.1063/5.0013642

Published under license by AIP Publishing

ARTICLE

scitation.org/journal/jcp

65

G. D. Scholes, R. D. Harcourt, and K. P. Ghiggino, “Rate expressions for excitation transfer. III. An ab initio study of electronic factors in excitation transfer and

exciton resonance interactions,” J. Chem. Phys. 102, 9574–9581 (1995).

66

T. Tsukamoto, T. Kikukawa, T. Kurata, K.-H. Jung, N. Kamo, and M. Demura,

“Salt bridge in the conserved His-Asp cluster in Gloeobacter rhodopsin contributes

to trimer formation,” FEBS Lett. 587, 322–327 (2013).

153, 045101-9

...