Photosynthesis Research

, Volume 125, Issue 1–2, pp 123–140 | Cite as

Modeling of the redox state dynamics in photosystem II of Chlorella pyrenoidosa Chick cells and leaves of spinach and Arabidopsis thaliana from single flash-induced fluorescence quantum yield changes on the 100 ns–10 s time scale

  • N. E. Belyaeva
  • F.-J. Schmitt
  • V. Z. Paschenko
  • G. Yu. Riznichenko
  • A. B. Rubin
Regular Paper


The time courses of the photosystem II (PSII) redox states were analyzed with a model scheme supposing a fraction of 11–25 % semiquinone (with reduced \({\text{Q}}_{\text{B}}^{ - }\)) RCs in the dark. Patterns of single flash-induced transient fluorescence yield (SFITFY) measured for leaves (spinach and Arabidopsis (A.) thaliana) and the thermophilic alga Chlorella (C.) pyrenoidosa Chick (Steffen et al. Biochemistry 44:3123−3132, 2005; Belyaeva et al. Photosynth Res 98:105–119, 2008, Plant Physiol Biochem 77:49–59, 2014) were fitted with the PSII model. The simulations show that at high-light conditions the flash generated triplet carotenoid 3Car(t) population is the main NPQ regulator decaying in the time interval of 6–8 μs. So the SFITFY increase up to the maximum level \(F_{\text{m}}^{\text{STF}}\)/F 0 (at ~50 μs) depends mainly on the flash energy. Transient electron redistributions on the RC redox cofactors were displayed to explain the SFITFY measured by weak light pulses during the PSII relaxation by electron transfer (ET) steps and coupled proton transfer on both the donor and the acceptor side of the PSII. The contribution of non-radiative charge recombination was taken into account. Analytical expressions for the laser flash, the 3Car(t) decay and the work of the water-oxidizing complex (WOC) were used to improve the modeled P680+ reduction by YZ in the state S 1 of the WOC. All parameter values were compared between spinach, A. thaliana leaves and C. pyrenoidosa alga cells and at different laser flash energies. ET from \({\text{Q}}_{\text{A}}^{ - } \;{\text{to}}\;{\text{Q}}_{\text{B}}^{( - )}\) slower in alga as compared to leaf samples was elucidated by the dynamics of \({\text{Q}}_{\text{A}}^{ - } ,{\text{ Q}}_{\text{B}}^{ - }\) fractions to fit SFITFY data. Low membrane energization after the 10 ns single turnover flash was modeled: the ∆Ψ(t) amplitude (20 mV) is found to be about 5-fold smaller than under the continuous light induction; the time-independent lumen pHL, stroma pHS are fitted close to dark estimates. Depending on the flash energy used at 1.4, 4, 100 % the pHS in stroma is fitted to 7.3, 7.4, and 7.7, respectively. The biggest ∆pH difference between stroma and lumen was found to be 1.2, thus pH- dependent NPQ was not considered.


Fluorescence yield Single turnover flash Photosystem II Model simulation Electron transfer Dissipative energy losses Proton transfer Water oxidizing complex 





Photosystem II


Reaction center (PSII)

P680, P680

Chlorophyll a acting as the electron donor in PSII

Phe, Ph

Primary electron acceptor, pheophytin

QA and QB

Primary and secondary plastoquinone electron acceptors of PSII


Triplet carotenoid state


Tyrosine 161 of the PSII D1 polypeptide


Water oxidizing complex





\({\text{H}} _{\text{L}}^{ + } ,{\text{ H}}_{\text{S}}^{ + }\)

Protons in lumen, in stroma

pHL, pHS

pH in lumen, in stroma


Electrical potential across the thylakoid membrane


Excitation energy transfer


Electron transfer


Proton transfer




Electron transport chain

Cyt b6f

Cytochrome b 6 f complex


Light excitation rate (time dependent)


Rate constant of quenching by triplet carotenoids


Rate constant of fluorescence emission


Rate constant of the electron donation to the oxidized P680+•


Light emitting diode


Photon flux density


Minimal FL yield


Maximal FL yield induced by multiturnover light


Maximal FL yield excited by single turnover flash


Single flash-induced transient fluorescence yield


Single turnover flash

FWHM, fwhm

Full width at half-maximum



This work was supported by the RFBR 11-04-01268-a, 14-04-01536, by BMBF RUS 10/026, 11/014, BMBF project “Quantum” (FKZ 13N10076) and by COST action MP1205. We are grateful to Prof. A.A. Bulychev for fruitful discussions.


  1. Baake E, Schlöder JP (1992) Modelling the fast fluorescence rise of photosynthesis. Bull Math Biol 54:999–1021CrossRefGoogle Scholar
  2. Baker NR, Harbinson J, Kramer DM (2007) Determining the limitations and regulation of photosynthetic energy transduction in leaves. Plant Cell Environ 30:1107–1125PubMedCrossRefGoogle Scholar
  3. Bao H, Dilbeck PL, Burnap RL (2013) Proton transport facilitating water-oxidation: the role of second sphere ligands surrounding the catalytic metal cluster. Photosynth Res 116:215–229PubMedCrossRefGoogle Scholar
  4. Belyaeva NE (2004) Generalized model of primary photosynthetic processes in chloroplasts. Ph D thesis, MoscowGoogle Scholar
  5. Belyaeva NE, Paschenko VZ, Renger G, Riznichenko GYu, Rubin AB (2006) Application of photosystem II model for analysis of fluorescence induction curves in the 100 ns–10 s time domain after excitation with a saturating light pulse. Biophysics 51(6):860–872CrossRefGoogle Scholar
  6. Belyaeva NE, Schmitt F-J, Steffen R, Paschenko VZ, Riznichenko GYu, Chemeris YuK, Renger G, Rubin AB (2008) PS II model-based simulations of single turnover flash-induced transients of fluorescence yield monitored within the time domain of 100 ns–10 s on dark-adapted Chlorella pyrenoidosa cells. Photosynth Res 98:105–119PubMedCrossRefGoogle Scholar
  7. Belyaeva NE, Schmitt F-J, Paschenko VZ, Riznichenko GYu, Rubin AB, Renger G (2011a) PS II model based analysis of transient fluorescence yield measured on whole leaves of Arabidopsis thaliana after excitation with light flashes of different energies. BioSystems 103(2):188–195PubMedCrossRefGoogle Scholar
  8. Belyaeva NE, Bulychev AA, Riznichenko GYu, Rubin AB (2011b) A model of photosystem II for the analysis of fast fluorescence rise in plant leaves. Biophysics 56(3):464–477CrossRefGoogle Scholar
  9. Belyaeva NE, Schmitt F-J, Paschenko VZ, Riznichenko GYu, Rubin AB, Renger G (2014) Model based analysis of transient fluorescence yield induced by actinic laser flashes in spinach leaves and cells of green alga Chlorella pyrenoidosa Chick. Plant Physiol Biochem 77:49–59PubMedCrossRefGoogle Scholar
  10. Björn LO, Papageorgiou GC, Blankenship RE, Govindjee (2009) A viewpoint: why chlorophyll a? Photosynth Res 99:85–98PubMedCrossRefGoogle Scholar
  11. Blankenship RE (2002) Molecular mechanisms of photosynthesis. Blackwell, OxfordCrossRefGoogle Scholar
  12. Bowes JM, Crofts AR (1980) Binary oscillations in the rate of reoxidation of the primary acceptor of photosystem II. Biochim Biophys Acta 590:373–384PubMedCrossRefGoogle Scholar
  13. Bulychev AA (1984) Different kinetics of membrane potential formation in dark-adapted and preilluminated chloroplasts. Biochim Biophys Acta 766(3):647–652CrossRefGoogle Scholar
  14. Bulychev AA, Vredenberg WJ (1999) Light-triggered electrical events in the thylakoid membrane of plant chloroplast. Physiol Plant 105:577–584CrossRefGoogle Scholar
  15. Bulychev AA, Vredenberg WJ (2001) Modulation of photosystem II chlorophyll fluorescence by electrogenic events generated by photosystem I. Bioelectrochemistry 54:157–168PubMedCrossRefGoogle Scholar
  16. Bulychev AA, Niyazova MM, Turovetsky VB (1986) Electro-induced changes of chlorophyll fluorescence in individual intact chloroplasts. Biochim Biophys Acta 850:218–225CrossRefGoogle Scholar
  17. Bulychev AA, Niyazova MM, Rubin AB (1987) Fluorescence changes of chloroplasts caused by the shifts of membrane-potential and their dependence on the redox state of the acceptor of photosystem II. Biol Membr 4:262–269Google Scholar
  18. Cardona T, Sedoud A, Cox N, Rutherford AW (2012) Charge separation in photosystem II: a comparative and evolutionary overview. Biochim Biophys Acta 1817:26–43PubMedCrossRefGoogle Scholar
  19. Christen G, Seeliger A, Renger G (1999) P680+ reduction kinetics and redox transition probability of the water oxidising complex as a function of pH and H/D isotope exchange in spinach thylakoids. Biochemistry 38:6082–6092PubMedCrossRefGoogle Scholar
  20. Crofts AR, Wraight CA (1983) The electrochemical domain of photosynthesis. Biochim Biophys Acta 726:149–185CrossRefGoogle Scholar
  21. Cruz JA, Sacksteder CA, Kanazawa A, Kramer DM (2001) Contribution of electric field (Δψ) to steady-state transthylakoid proton motive force (pmf) in vivo and in vitro. Control of pmf parsing into Δψ and ΔpH by ionic strength. Biochemistry 40:1226–1237PubMedCrossRefGoogle Scholar
  22. Cruz JA, Kanazawa A, Treff N, Kramer DM (2005) Storage of light-driven transthylakoid proton motive force as an electric field (Δψ) under steady-state conditions in intact cells of Chlamydomonas reinhardtii. Photosynth Res 85:221–233PubMedCrossRefGoogle Scholar
  23. Dau H (1994) Molecular mechanism and quantitative models of variable photosystem II fluorescence. Photochem Photobiol 60:1–23CrossRefGoogle Scholar
  24. Dau H, Sauer K (1991) Electric field effect on chlorophyll fluorescence and its relation to photosystem II charge separation reactions studied by a salt jump technique. Biochim Biophys Acta 1089:49–60CrossRefGoogle Scholar
  25. Dau H, Sauer K (1992) Electric field effect on the picosecond fluorescence of photosystem II and its relation to the energetics and kinetics of primary charge separation. Biochim Biophys Acta 1102:91–106CrossRefGoogle Scholar
  26. de Wijn R, van Gorkom HJ (2001) Kinetics of electron transfer from Q(a) to Q(b) in photosystem II. Biochemistry 40:11912–11922PubMedCrossRefGoogle Scholar
  27. Ebenhöh O, Houwaart T, Lokstein H, Schlede S, Tirok K (2011) A minimal mathematical model of nonphotochemical quenching of chlorophyll fluorescence. Biosystems 103(2):196–204.
  28. Eckert H-J, Renger G (1988) Temperature dependence of P680+ reduction in O2-evolving PS II membrane fragments at different redox states Si of the water oxidizing system. FEBS Lett 236:425–431CrossRefGoogle Scholar
  29. Gibasiewicz K, Dobek A, Breton J, Leibl W (2001) Modulation of primary radical pair kinetics and energetics in photosystem II by the redox state of the quinone electron acceptor QA. Biophys J 80:1617–1630Google Scholar
  30. Govindjee (1982) Photosynthesis, vol 2. Academic Press, New YorkGoogle Scholar
  31. Govindjee N (1995) Sixty-three years since Kautsky: chlorophyll a fluorescence. Aust J Plant Physiol 22:131–160CrossRefGoogle Scholar
  32. Hope AB (1993) The chloroplast cytochrome bf complex: a critical focus on function. Biochim Biophys Acta 1143:1–22PubMedCrossRefGoogle Scholar
  33. Kern J, Renger G (2007) Photosystem II: structure and mechanism of the water:plastoquinone-oxido:reductase. Photosynth Res 94:183–202PubMedCrossRefGoogle Scholar
  34. Kramer DM, Sacksteder CA, Cruz JA (1999) How acidic is the lumen? Photosynth Res 60:151–163CrossRefGoogle Scholar
  35. Kramer DM, Cruz JA, Kanazawa A (2003) Balancing the central roles of the thylakoid proton gradient. Trends Plant Sci 8:27–32PubMedCrossRefGoogle Scholar
  36. Kroon BMA, Thoms S (2006) From electron to biomass: a mechanistic model to describe phytoplankton photosynthesis and steady-state growth rates. J Phycol 42:593–609Google Scholar
  37. Kühn P, Eckert H-J, Eichler H-J, Renger G (2004) Analysis of the P680+• reduction pattern and its temperature dependence in oxygen evolving PS II core complexes from thermophilic cyanobacteria and higher plants. Phys Chem Chem Phys 6:4838–4843CrossRefGoogle Scholar
  38. Kuvykin IV, Ptushenko VV, Vershubskii AV, Tikhonov AN (1807) Regulation of electron transport in C(3) plant chloroplasts in situ and in silico: short-term effects of atmospheric CO(2) and O(2). Biochim Biophys Acta 1807(3):336–347CrossRefGoogle Scholar
  39. Laible PD, Zipfel W, Owens TG (1994) Excited state dynamics in chlorophyll-based antennae: the role of transfer equilibrium. Biophys J 66:844–860PubMedCentralPubMedCrossRefGoogle Scholar
  40. Laisk A, Walker DA (1989) A mathematical model of electrone transport. Thermodynamic necessity for photosystem II regulation. Proc R Soc Lond B237:417–444CrossRefGoogle Scholar
  41. Laisk A, Eichelmann H, Oja V (2006) C3 photosynthesis in silico. Photosynth Res 90:45–66PubMedCrossRefGoogle Scholar
  42. Lazár D (2003) Chlorophyll a fluorescence rise induced by high light illumination of dark-adapted plant tissue studied by means of a model of photosystem II and considering photosystem II heterogeneity. J Theor Biol 220:469–503PubMedCrossRefGoogle Scholar
  43. Lazár D (2013) Simulations show that a small part of variable chlorophyll a fluorescence originates in photosystem I and contributes to overall fluorescence rise. J Theor Biol 335:249–264PubMedCrossRefGoogle Scholar
  44. Lebedeva GV, Belyaeva NE, Riznichenko GYu, Rubin AB, Demin OV (2000) Kinetic model of photosystem II of higher green plants. Russ J Phys Chem 74:1702–1710Google Scholar
  45. Lebedeva GV, Belyaeva NE, Demin OV, Riznichenko GYu, Rubin AB (2002) Kinetic model of primary photosynthetic processes in chloroplasts. Description of the fast phase of chlorophyll fluorescence induction under different light intensities. Biophysics 47:968–980Google Scholar
  46. Leibl W, Breton J, Deprez J, Trissl HW (1989) Photoelectric study on the kinetics of trapping and charge stabilization in oriented PS II membranes. Photosynth Res 22:257–275PubMedCrossRefGoogle Scholar
  47. Meyer TJ, Hang M, Huynh V, Thorp HH (2007) The role of proton coupled electron transfer (PCET) in water oxidation by photosystem II. Wiring for protons. Angew Chem Int Ed 46(28):5284–5304CrossRefGoogle Scholar
  48. Müh F, Glöckner C, Hellmich J, Zouni A (2012) Light-induced quinone reduction in photosystem II. Biochim Biophys Acta 1817:44–65PubMedCrossRefGoogle Scholar
  49. Noguchi T (2015) Fourier transform infrared difference and time-resolved infrared detection of the electron and proton transfer dynamics in photosynthetic water oxidation. Biochim Biophys Acta 1847:35–45PubMedCrossRefGoogle Scholar
  50. Papageorgiou GC, Govindjee (eds) (2004) Chlorophyll a fluorescence: a signature of photosynthesis. Advances in photosynthesis and respiration, vol 19. Springer, DordrechtGoogle Scholar
  51. Papageorgiou GC, Tsimilli-Michael M, Stamatakis K (2007) The fast and slow kinetics of chlorophyll fluorescence induction in plants, algae and cyanobacteria: a viewpoint. Photosynth Res 94:275–290PubMedCrossRefGoogle Scholar
  52. Renger G (2001) Photosynthetic water oxidation to molecular oxygen: apparatus and mechanism. Biochim Biophys Acta 1503:210–228PubMedCrossRefGoogle Scholar
  53. Renger G (2004) Coupling of electron and proton transfer in oxidative water cleavage in photosynthesis. Biochim Biophys Acta 1655:195–204PubMedCrossRefGoogle Scholar
  54. Renger G (2007) Oxidative photosynthetic water splitting: energetics, kinetics and mechanism. Photosynth Res 92:407–425PubMedCrossRefGoogle Scholar
  55. Renger G (2012) Mechanism of light induced water splitting. In Photosystem II of oxygen evolving photosynthetic organisms. Biochim Biophys Acta 1817:1164–1176PubMedCrossRefGoogle Scholar
  56. Renger G, Holzwarth AR (2005) Primary electron transfer. In: Wydrzynski TJ, Satoh K (eds) Photosystem II: the light-driven water: plastoquinone oxidoreductase. Springer, Berlin, pp 139–175Google Scholar
  57. Renger G, Renger T (2008) Photosystem II, the machinery of photosynthetic water splitting. Photosynth Res 98:53–81PubMedCrossRefGoogle Scholar
  58. Renger G, Schulze A (1985) Quantitative analysis of fluorescence induction curves in isolated spinach chloroplasts. Photobiochem Photobiophys 9:79–87Google Scholar
  59. Renger G, Eckert HJ, Bergmann A, Bernarding J, Liu B, Napiwotzki A, Reifarth F, Eichler HJ (1995) Fluorescence and spectroscopic studies on exciton trapping and electron transfer in photosystem II of higher plants. Aust J Plant Physiol 22:167–181CrossRefGoogle Scholar
  60. Reynolds IA, Johnson EA, Tanford C (1985) Incorporation of membrane potential into theoretical analysis of electrogenic ion pumps. Proc Natl Acad Sci USA 82:6869–6873PubMedCentralPubMedCrossRefGoogle Scholar
  61. Riznichenko GYu, Lebedeva GV, Demin OV, Rubin AB (1999) Kinetic mechanisms of biological regulation in photosynthetic organisms. J Biol Phys 25:177–192PubMedCentralPubMedCrossRefGoogle Scholar
  62. Roelofs TA, Lee CH, Holzwarth AR (1992) Global target analysis of picosecond chlorophyll fluorescence kinetic from pea chloroplasts. Biophys J 61:1147–1163PubMedCentralPubMedCrossRefGoogle Scholar
  63. Rubin A, Riznichenko G (2009) Modeling of the primary processes in a photosynthetic membrane. In: Laisk A, Nedbal L, Govindjee (eds) Photosynthesis in silico: understanding complexity from molecules to ecosystems, advances in photosynthesis and respiration, vol 29. Springer, Dordrecht, pp 151–176CrossRefGoogle Scholar
  64. Rutherford AW, Crofts AR, Inoue Y (1982) Thermoluminescence as a probe of photosystem II photochemistry—the origin of the flash-induced glow peaks. Biochim Biophys Acta 682:457–465CrossRefGoogle Scholar
  65. Samson G, Bruce D (1996) Origins of the low yield of chlorophyll fluorescence induced by single turnover flash in spinach thylakoids. Biochim Biophys Acta 1276:147–153CrossRefGoogle Scholar
  66. Schatz GH, Brock H, Holzwarth AR (1988) Kinetic and energetic model for the primary processes in photosystem II. Biophys J 54:397–405PubMedCentralPubMedCrossRefGoogle Scholar
  67. Schödel R, Hillmann F, Schrötter T, Irrgang K-D, Voigt J, Renger G (1996) Kinetics of excited states of pigment clusters in solubilized light-harvesting complex II: photon density-dependent fluorescence yield and transmittance. Biophys J 71:3370–3380PubMedCentralPubMedCrossRefGoogle Scholar
  68. Schödel R, Irrgang K-D, Voigt J, Renger G (1998) Rate of carotenoid triplet formation in solubilized light harvesting complex II (LHCII) from spinach. Biophys J 75:3143–3153PubMedCentralPubMedCrossRefGoogle Scholar
  69. Schreiber U, Schliwa U, Bilger W (1986) Continuous recording of photochemical and non-photochemical chlorophyll fluorescence quenching with a new type of modulation fluorometer. Photosynth Res 10:51–62PubMedCrossRefGoogle Scholar
  70. Semenov AYu, Cherepanov DA, Mamedov MD (2008) Electrogenic reactions and dielectric properties of photosystem II. Photosynth Res 98:121–130PubMedCrossRefGoogle Scholar
  71. Shevela D, Eaton-Rye JJ, Shen J-R, Govindjee (2012) Photosystem II and the unique role of bicarbonate: a historical perspective. Biochim Biophys Acta 1817:1134–1151PubMedCrossRefGoogle Scholar
  72. Steffen R (2003) Time-resolved spectroscopic investigations of photosystem II. PhD thesis. BerlinGoogle Scholar
  73. Steffen R, Christen G, Renger G (2001) Time-resolved monitoring of flash-induced changes of fluorescence quantum yield and decay of delayed light emission in oxygen-evolving photosynthetic organisms. Biochemistry 40:173–180PubMedCrossRefGoogle Scholar
  74. Steffen R, Eckert H-J, Kelly AA, Dörmann PG, Renger G (2005) Investigations on the reaction pattern of photosystem II in leaves from Arabidopsis thaliana by time-resolved fluorometric analysis. Biochemistry 44:3123–3132PubMedCrossRefGoogle Scholar
  75. Stirbet A, Govindjee N (2012) Chlorophyll a fluorescence induction: a personal perspective of the thermal phase, the J-I–P rise. Photosynth Res 113:15–61PubMedCrossRefGoogle Scholar
  76. Stirbet A, Govindjee Strasser BJ, Strasser RJ (1998) Chlorophyll a fluorescence induction in higher plants: modeling and numerical simulation. J Theor Biol 193:131–151CrossRefGoogle Scholar
  77. Stirbet AD, Rosenau Ph, Ströder AC, Strasser RJ (2001) Parameter optimisation of fast chlorophyll fluorescence induction model. Math Comput Simul 56:443–450CrossRefGoogle Scholar
  78. Strasser RJ, Tsimilli-Michael M, Srivastava A (2004) Analysis of the chlorophyll fluorescence transient. In: Papageorgiou GC, Govindjee (eds) Chlorophyll fluorescence: a signature of photosynthesis. Advances in photosynthesis and respiration, vol 19. Springer, Dordrecht, pp 321–362CrossRefGoogle Scholar
  79. Strasser RJ, Tsimilli-Michael M, Qiang S, Goltsev V (2010) Simultaneous in vivo recording of prompt and delayed fluorescence and 820-nm reflection changes during drying and after rehydration of the resurrection plant Haberlea rhodopensis. Biochim Biophys Acta 1797:1313–1326PubMedCrossRefGoogle Scholar
  80. Tikhonov AN (2012) Energetic and regulatory role of proton potential in chloroplasts. Biochemistry (Moscow) 77:956–974CrossRefGoogle Scholar
  81. Tikhonov AN (2013) pH-dependent regulation of electron transport and ATP synthesis in chloroplasts. Photosynth Res 116:511–534PubMedCrossRefGoogle Scholar
  82. Umena Y, Kawakami K, Shen J-R, Kamiya N (2011) Crystal structure of oxygen-evolving photosystem II at a resolution of 1.9 Å. Nature 473(7345):55–60PubMedCrossRefGoogle Scholar
  83. van Kooten O, Snel JFH, Vredenberg WJ (1986) Photosynthetic free energy transduction to the electric potential changes across the thylakoid membrane. Photosynth Res 9:211–227PubMedCrossRefGoogle Scholar
  84. Vredenberg WJ (2000) A 3-state model for energy trapping and fluorescence in PS II incorporating radical pair recombination. Biophys J 79:26–38PubMedCentralPubMedCrossRefGoogle Scholar
  85. Vredenberg WJ (2011) Kinetic analysis and mathematical modeling of primary photochemical and photoelectrochemical processes in plant photosystems. BioSystems 103:139–151CrossRefGoogle Scholar
  86. Wydrzynski T, Satoh K (eds) (2005) Photosystem II: light-induced water: Plastoquinone oxidoreductase, advances in photosynthesis and respiration, vol 22. Springer, DordrechtGoogle Scholar
  87. Zhu XG, Govindjee Baker NR, deSturler E, Ort DR, Long SP (2005) Chlorophyll a fluorescence induction kinetics in leaves predicted from a model describing each discrete step of excitation energy and electron transfer associated with photosystem II. Planta 223:114–133PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • N. E. Belyaeva
    • 1
  • F.-J. Schmitt
    • 2
  • V. Z. Paschenko
    • 1
  • G. Yu. Riznichenko
    • 1
  • A. B. Rubin
    • 1
  1. 1.Department of Biophysics, Biology FacultyM.V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Max-Volmer-Laboratory of Biophysical Chemistry, Institute of ChemistryTechnical University BerlinBerlinGermany

Personalised recommendations