Skip to main content
SpringerLink
Log in

Mathematical Modeling in Biology: Part 2. Models of Protein Interaction Processes in a Photosynthetic Membrane

  • Published:
Biology Bulletin Reviews Aims and scope Submit manuscript

Abstract

The second part of the article concerns agent-based, multiparticle, Brownian and molecular dynamic models. In these models, the motion and interaction of individual proteins—electron carriers (Brownian multiparticle models) and individual atoms in molecules—electron carriers and their complexes (molecular dynamics) are described based on the apparatus of Brownian and molecular modeling. Direct multiparticle models explicitly simulate the Brownian diffusion of mobile protein carriers and their electrostatic interactions with multienzyme complexes, both in solution and in the interior of a biomembrane. Analysis of these models reveals the role of diffusion and electrostatic factors in the regulation of electron transport, the effect of the of reaction volume geometry, and ionic strength and pH of the cell medium on the rate of electron transport reactions between protein carriers. Through joint application methods of kinetic and Brownian multiparticle modeling make it possible to study the regulation mechanisms of electron transport processes at the subcellular and molecular levels and also mechanisms of electron-flow switching in plant and algae cells and to evaluate the optimal conditions for the obtainment of target products in microalgae cells, e.g., hydrogen as an alternative fuel. The prospects for various methods of mathematical modeling used to study subcellular systems are discussed in the conclusion. The paper is based on the results obtained at the Department of Biophysics, Biological Faculty, Moscow State University.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

REFERENCES

  1. Albertsson, P.-A., The domain structure and function of the thylakoid membrane, Res. Rec. Dev. Bioenerg., 2000, vol. 1, pp. 143–171.

    CAS  Google Scholar 

  2. Albertsson, P.-A., A quantitative model of the domain structure of the photosynthetic membrane, Trends Plant Sci., 2001, vol. 6, pp. 349–354.

    Article  CAS  PubMed  Google Scholar 

  3. Antal, T.K., Krendeleva, T.E., and Rubin, A.B., Study of photosystem 2 heterogeneity in the sulfur-deficient green alga Chlamydomonas reinhardtii, Photosynth. Res., 2007, vol. 94, pp. 13–22.

    Article  CAS  PubMed  Google Scholar 

  4. Cruz-Gallardo, I., Díaz-Moreno, I., Díaz-Quintana, A., and De la Rosa, M.Á., The cytochrome f–plastocyanin complex as a model to study transient interactions between redox proteins, FEBS Lett., 2012, vol. 586, no. 5, pp. 646–652.

    Article  CAS  PubMed  Google Scholar 

  5. Dekker, J.P. and Boekema, E.J., Supramolecular organization of thylakoid membrane proteins in green plants, Biochim. Biophys. Acta, Bioenerg., 2005, vol. 1706, nos. 1–2, pp. 12–39.

    Article  CAS  Google Scholar 

  6. Diakonova, A.N., Khruschev, S.S., Kovalenko, I.B., et al., The role of electrostatic interactions in the formation of ferredoxin–ferredoxin NADP+ reductase and ferredoxin–hydrogenase complexes, Biophysics (Moscow), 2016a, vol. 61, no. 4, pp. 572–579.

    Article  CAS  Google Scholar 

  7. Diakonova, A.N., Khrushchev, S.S., Kovalenko, I.B., et al., Influence of pH and ionic strength on electrostatic properties of ferredoxin, FNR, and hydrogenase and the rate constants of their interaction, Phys. Biol., 2016b, vol. 13, no. 5, p. e056004.

    Article  CAS  Google Scholar 

  8. Fedorov, V.A., Kovalenko, I.B., Khruschev, S.S., et al., Comparative analysis of plastocyanin–cytochrome f complex formation in higher plants, green algae and cyanobacteria, Physiol. Plant., 2019, vol. 166, no. 1, pp. 320–335.

    Article  CAS  PubMed  Google Scholar 

  9. Finkel’shtein, A.V. and Ptitsyn, O.B., Vvedenie v fiziku belka. Kurs lektsii (Introduction into Protein Physics: Lecturers), Moscow: KDU, 2002.

  10. Finkelstein, A. and Ptitsyn, O., Protein Physics, New York: Academic, 2016.

    Google Scholar 

  11. Gross, E.L. and Pearson, D.C., Brownian dynamics simulations of the interaction of Chlamydomonas cytochrome f with plastocyanin and cytochrome c 6, Biophys. J., 2003, vol. 85, pp. 2055–2068.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Gross, E.L. and Rosenberg, I., A Brownian dynamics study of the interaction of Phormidium cytochrome f with various cyanobacterial plastocyanins, Biophys. J., 2006, vol. 90, pp. 366–380.

    Article  CAS  PubMed  Google Scholar 

  13. Haehnel, W., Ratajczak, R., and Robenek, H., Lateral distribution and diffusion of plastocyanin in chloroplast thylakoids, J. Cell Biol., 1989, vol. 108, pp. 1397–1405.

    Article  CAS  PubMed  Google Scholar 

  14. Khrushchev, S.S., Abaturova, A.M., D’yakonova, A.N., et al., Multi-particle Brownian dynamics software ProKSim for protein-protein interactions modeling, Komp’yut. Issled. Model., 2013, vol. 5, no. 1, pp. 47–64.

    Google Scholar 

  15. Khruschev, S.S., Abaturova, A.M., Diakonova, A.N., et al., Brownian-dynamics simulations of protein–protein interactions in the photosynthetic electron transport chain, Biophysics (Moscow), 2015a, vol. 60, no. 2, pp. 212–231.

    Article  CAS  Google Scholar 

  16. Khruschev, S.S., Abaturova, A.M., Fedorov, V.A., et al., The identification of intermediate states of the electron-transfer proteins plastocyanin and cytochrome f diffusional encounters, Biophysics (Moscow), 2015b, vol. 60, no. 4, pp. 513–521.

    Article  CAS  Google Scholar 

  17. Kirchhoff, H., Mukherjee, U., and Galla, H.-J., Molecular architecture of the thylakoid membrane: lipid diffusion space for plastoquinone, Biochemistry, 2002, vol. 41, pp. 4872–4882.

    Article  CAS  PubMed  Google Scholar 

  18. Knyazeva, O.S., Kovalenko, I.B., Abaturova, A.M., et al., Multiparticle computer simulation of plastocyanin diffusion and interaction with cytochrome f in the electrostatic field of the thylakoid membrane, Biophysics (Moscow), 2010, vol. 55, no. 2, pp. 221–227.

    Article  Google Scholar 

  19. Kovalenko, I.B., Abaturova, A.M., Gromov, P.A., et al., Direct simulation of plastocyanin and cytochrome f interactions in solution, Phys. Biol., 2006, vol. 3, pp. 121–129.

    Article  CAS  PubMed  Google Scholar 

  20. Kovalenko, I.B., Abaturova, A.M., Gromov, P.A., et al., Computer simulation of plastocyanin-cytochrome f complex formation in the thylakoid lumen, Biophysics (Moscow), 2008a, vol. 53, no. 2, pp. 140–146.

    Article  Google Scholar 

  21. Kovalenko, I., Diakonova, A., Abaturova, A., and Riznichenko, G., Direct computer simulation of ferredoxin and FNR complex formation in solution, Proc. 16th Int. Symp. on Flavins and Flavoproteins, Zaragoza Jaca: Prensas Universitarias, 2008b, pp. 437–442.

  22. Kovalenko, I.B., Abaturova, A.M., Riznichenko, G.Yu., and Rubin, A.B., A novel approach to computer simulation of protein-protein complex formation, Dokl. Biochem. Biophys., 2009, vol. 427, no. 1, pp. 215–217.

    Article  CAS  PubMed  Google Scholar 

  23. Kovalenko, I.B., Diakonova, A.N., Abaturova, A.M., et al., Direct computer simulation of ferredoxin and FNR complex formation in solution, Phys. Biol., 2010, vol. 7, no. 2, p. e026001.

    Article  CAS  Google Scholar 

  24. Kovalenko, I.B., Abaturova, A.M., Diakonova, A.N., et al., Computer simulation of protein–protein association in photosynthesis, Math. Model. Nat. Phenom., 2011a, vol. 6, pp. 39–54.

    Article  Google Scholar 

  25. Kovalenko, I.B., Diakonova, A.N., Riznichenko, G.Yu., and Rubin, A.B., Computer simulation of interaction of photosystem I with plastocyanin and ferredoxin, BioSystems, 2011b, vol. 103, pp. 180–187.

    Article  CAS  PubMed  Google Scholar 

  26. Kovalenko, I.B., Knyazeva, O.S., Riznichenko, G.Yu., and Rubin, A.B., Computer simulation of plastocyanin interaction with cytochrome f and photosystem I in cyanobacterium Phormidium laminosum, Biophysics (Moscow), 2014, vol. 59, no. 1, pp. 1–5.

    Article  CAS  Google Scholar 

  27. Kovalenko, I.B., Khrushchev, S.S., Fedorov, V.A., et al., The role of electrostatic interactions in the process of diffusional encounter and docking of electron transport proteins, Dokl. Biochem. Biophys., 2016, vol. 468, no. 1, pp. 183–186.

    Article  CAS  PubMed  Google Scholar 

  28. Kovalenko, I.B., Knyaseva, O.S., Antal, T.K., et al., Multiparticle brownian dynamics simulation of experimental kinetics of cytochrome bf oxidation and photosystem I reduction by plastocyanin, Physiol. Plant., 2017, vol. 161, pp. 88–96.

    Article  CAS  PubMed  Google Scholar 

  29. Martin, E., Samoilova, R.I., Narasimhulu, K.V., et al., Hydrogen bonding and spin density distribution in the QB semiquinone of bacterial reaction centers and comparison with the QA site, J. Am. Chem. Soc., 2011, vol. 133, pp. 5525–5537.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Melis, A. and Happe, T., Hydrogen production. Green algae as a source of energy, Plant Physiol., 2001, vol. 12, pp. 3740–3748.

    Google Scholar 

  31. Meyer, T.E., Zhao, Z.G., Cusanovich, M.A., and Tollin, G., Transient kinetics of electron transfer from a variety of c-type cytochromes to plastocyanin, Biochemistry, 1993, vol. 32, pp. 4552–4559.

    Article  CAS  PubMed  Google Scholar 

  32. Pearson, D.C. and Gross, E.L., Brownian dynamics study of the interaction between plastocyanin and cytochrome f, Biophys. J., 1998, vol. 75, pp. 2698–2711.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Plyusnina, T.Yu., Riznichenko, G.Yu., and Rubin, A.B., Regulation of electron-transport pathways in cells of Chlamydomonas reinhardtii under stress conditions, Russ. J. Plant Physiol., 2013, vol. 60, no. 4, pp. 518–528.

    Article  CAS  Google Scholar 

  34. Riznichenko, G.Yu. and Kovalenko, I.B., Multiparticle models of Brownian dynamics for the description of photosynthetic electron transfer involving protein mobile carriers, Int. J. Appl. Res. Bioinf., 2019, vol. 9, no. 1, pp. 1–19.

    Google Scholar 

  35. Riznichenko, G.Yu., Kovalenko, I.B., Abaturova, A.M., et al., New direct dynamic models of protein interactions coupled to photosynthetic electron transport reactions, Biophys. Rev., 2010, vol. 2, no. 3, pp. 101–110.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Riznichenko, G.Yu., Kovalenko, I.B., Abaturova, A.M., et al., Multiparticle computer simulation of protein interactions in the photosynthetic membrane, Biophysics (Moscow), 2011, vol. 56, no. 5, pp. 757–767.

    Article  Google Scholar 

  37. Riznichenko, G.Yu., Belyaeva, N.E., Kovalenko, I.B., et al., Kinetic and multiparticle models of photosynthetic electron transport, in Sovremennye problemy fotosinteza (Modern Problems of Photosynthesis), Allakhverdiev, S.I., Rubin, A.B., and Shuvalov, V.A., Eds., Izhevsk: Inst. Komp’yut. Issled., 2014, vol. 2, pp. 41–100.

  38. Riznichenko, G.Yu., Plyusnina, T.Yu., Diakonova, A.N., et al., pH regulation of hydrogen-generating microalgae photosynthetic chain. Kinetic and multiparticle Brownian models, in Nonlinearity: Problems, Solutions and Applications, Uvarova, L.A., Nadykto, A.B., and Latyshev, A.V., Eds., New York: Nova Science, 2017, pp. 181–202.

  39. Ruban, A., The Photosynthetic Membrane: Molecular Mechanisms and Biophysics of Light Harvesting, Chichester: Wiley, 2012.

    Book  Google Scholar 

  40. Rubin, A.B., Compendium of Biophysics, New York: Wiley, 2017.

    Book  Google Scholar 

  41. Rubin, A.B. and Riznichenko, G.Yu., Mathematical Biophysics, New York: Springer-Verlag, 2014.

    Book  Google Scholar 

  42. Vernadskii, V.I., Biosfera i noosfera (Biosphere and Noosphere), Moscow: Airis-Press, 2018.

  43. Ubbink, M., Ejdebeck, M., Karlsson, B.G., and Bendall, D.S., The structure of the complex of plastocyanin and cytochrome f, determined by paramagnetic NMR and restrained rigid-body molecular dynamics, Structure, 1998, vol. 6, pp. 323–335.

    Article  CAS  PubMed  Google Scholar 

  44. Ullmann, G.M., Knapp, E.-W., and Kostic, N.M., Computational simulation and analysis of dynamic association between plastocyanin and cytochrome f. Consequences for the electrontransfer reaction, J. Am. Chem. Soc., 1997, vol. 119, pp. 42–52.

    Article  CAS  Google Scholar 

  45. Ustinin, D.M., Kovalenko, I.B., Grachev, E.A., et al., Direct multiparticle computer modeling of photosynthetic electron transport chain, in Dinamicheskie modeli protsessov v kletkakh i subkletochnykh nanostrukturakh (Dynamic Models of the Processes in Cells and Subcellular Nanostructures), Riznichenko, G.Yu. and Rubin, A.B., Eds., Moscow: Regul. Khaoticheskaya Din., 2010, pp. 241–262.

  46. Ustinin, D.M., Kovalenko, I.B., Riznichenko, G.Yu., and Rubin, A.B., Combination of different simulation techniques in the complex model of photosynthetic membrane, Komp’yut. Issled. Model., 2013, vol. 5, no. 1, pp. 65–81.

    Google Scholar 

  47. Yacoby, I., Pochekailov, S., Toporik, H., et al., Photosynthetic electron partitioning between [FeFe]-hydrogenase and ferredoxin:NADP+-oxidoreductase (FNR) enzymes in vitro, Proc. Natl. Acad. Sci. U.S.A., 2011, vol. 108, pp. 9395–9401.

    Article  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors are grateful to the staff of the Biophysics Department whose research results are presented in this work: I.B. Kovalenko, A.M. Abaturova, A.N. Dyakonova, V.A. Fedorov, T.K. Antal, T.Yu. Plyusnina, S.S. Khrushchev. They also thank all other employees and graduate students of the Biophysics Department, whose long-term joint work made it possible to obtain the results presented in this article.

We are also grateful to V.A. Sochivko for help with the preparation of the drawings. We are grateful to the Russian Foundation for Basic Research for many years of support in the study of photosynthesis. We are grateful to the Center for Shared Use of Ultra-High Performance Computing Resources of the Moscow State University for the opportunity to perform calculations with our models.

Funding

The work presented in the article was carried out at the Biophysics Department of the Faculty of Biology of the Moscow State University in the framework of state assignments. The work was partially financed by the Russian Foundation for Basic Research, project nos. 17-04-00676, 17-04-20003, 18-04-20001, and 20-04-00465 and the Russian National Foundation, grant 20-64-46018.

Author information

Authors and Affiliations

  1. Department of Biophysics, Faculty of Biology, Moscow State University, Moscow, Russia

    G. Yu. Riznichenko & A. B. Rubin

Authors
  1. G. Yu. Riznichenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. B. Rubin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Yu. Riznichenko.

Ethics declarations

Conflict of interests. The authors declare that they have no conflicts of interest.

Statement on the welfare of humans or animals. This article does not contain any studies involving animals performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Riznichenko, G.Y., Rubin, A.B. Mathematical Modeling in Biology: Part 2. Models of Protein Interaction Processes in a Photosynthetic Membrane. Biol Bull Rev 11, 110–121 (2021). https://doi.org/10.1134/S2079086421020080

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2079086421020080

Keywords:

Search

Navigation