Skip to main content
SpringerLink
Log in

Comparison of Monte Carlo Simulations of Cytochrome b6f with Experiment Using Latin Hypercube Sampling

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

We have programmed a Monte Carlo simulation of the Q-cycle model of electron transport in cytochrome b6f complex, an enzyme in the photosynthetic pathway that converts sunlight into biologically useful forms of chemical energy. Results were compared with published experiments of Kramer and Crofts (Biochim. Biophys. Acta 1183:72–84, 1993). Rates for the simulation were optimized by constructing large numbers of parameter sets using Latin hypercube sampling and selecting those that gave the minimum mean square deviation from experiment. Multiple copies of the simulation program were run in parallel on a Beowulf cluster. We found that Latin hypercube sampling works well as a method for approximately optimizing very noisy objective functions of 15 or 22 variables. Further, the simplified Q-cycle model can reproduce experimental results in the presence or absence of a quinone reductase (Qi) site inhibitor without invoking ad hoc side-reactions.

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

Similar content being viewed by others

References

  • Alric, J., Pierre, Y., Picot, D., Lavergne, J., & Rappaport, F., (2005). Spectral and redox characterization of the heme ci of the cytochrome b6f complex. Proc. Natl. Acad. Sci. USA, 102(44), 15860–15865.

    Article  Google Scholar 

  • Blythe, R. A., & Evans, M. R. (2007). Nonequilibrium steady states of matrix-product form: a solver’s guide. J. Phys. A, Math. Theor., 40, R333–R441.

    Article  MathSciNet  MATH  Google Scholar 

  • Cape, J. L., Bowman, M. K., & Kramer, D. M. (2006). Understanding the cytochrome bc complexes by what they don’t do. The Q-cycle at 30. Trends Plant Sci., 11, 46–55.

    Article  Google Scholar 

  • Cape, J. L., Bowman, M. K., & Kramer, D. M. (2007). A semiquinone intermediate generated at the Qo site of the cytochrome bc1 complex. Importance for the Q-cycle and superoxide production. Proc. Natl. Acad. Sci. USA, 104, 7887–7892.

    Article  Google Scholar 

  • Cooley, J. W., Nitschke, W., & Kramer, D. M. (2008). The cytochrome bc1 and related bc complexes, the Rieske/cytochrome b complex as the functional core of a central electron/proton transfer complex. In C. N. Hunter, F. Daldal, M. C. Thurnauer, & J. T. Beatty (Eds.), The purple photosynthetic bacteria (pp. 451–473). Dordrecht: Springer.

    Google Scholar 

  • Cramer, W. A., Zhang, H., Yan, J., Kurisu, G., & Smith, J. L. (2006). Transmembrane traffic in the cytochrome b6f complex. Annu. Rev. Biochem., 75, 769–790.

    Article  Google Scholar 

  • Davey, K. R. (2008). Latin hypercube sampling and pattern search in magnetic field optimization problems. IEEE Trans. Magn., 44(6), 974–977.

    Article  Google Scholar 

  • Dekker, J. P., & Boekema, E. J. (2005). Supramolecular organization of thylakoid membranes in green plants. Biochim. Biophys. Acta, 1706, 12–39.

    Article  Google Scholar 

  • de Lacrois de Lavalette, A., Barucq, L., Alric, J., Rappaport, F., & Zito, F. (2009). Is the redox state of the ci heme of the cytochrome b6f complex dependent on the occupation and structure of the qi site and vice versa? J. Biol. Chem., 284(31), 20822–20829.

    Article  Google Scholar 

  • Derrida, B. (2007). Non-equilibrium steady states: fluctuations and large deviations of the density and current. J. Stat. Mech., P07023.

  • Frenklach, M., Packard, A., Seiler, P., & Feeley, R. (2004). Collaborative data processing in developing predictive models of complex reaction systems. Int. J. Chem. Kinet., 36(1), 57–66.

    Article  Google Scholar 

  • Fu, M. C. (2002). Optimization for simulation: theory vs. practice. INFORMS J. Comput., 14, 192–215.

    Article  MathSciNet  Google Scholar 

  • Gillespie, D. T. (1976). A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys., 22, 403–434.

    Article  MathSciNet  Google Scholar 

  • Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81, 2340–2361.

    Article  Google Scholar 

  • Helton, J. C., & Davis, F. J. (2003). Latin hypercube sampling and the propagation of uncertainty in analysis of complex systems. Reliab. Eng. Syst. Saf., 81, 23–69.

    Article  Google Scholar 

  • Helton, J. C., Johnson, J. D., Sallaberry, C. J., & Storlie, C. B. (2006). Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab. Eng. Syst. Saf., 91, 1175–1209.

    Article  Google Scholar 

  • Hill, T. L. (1977). Free energy transduction in biology (p. 6). New York: Academic Press.

    Google Scholar 

  • Kallas, T. (1994). The cytochrome b6f complex. In D. A. Bryant (Ed.), The molecular biology of cyanobacteria (pp. 259–317). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Kirchhoff, H. (2008). Molecular crowding and order in photosynthetic membranes. Trends Plant Sci., 13, 201–207.

    Article  Google Scholar 

  • Kirchhoff, H., Horstmann, S., & Weiss, E. (2000). Control of the photosynthetic electron transport by PQ diffusion microdomains in thylakoids of higher plants. Biochim. Biophys. Acta, 1459, 148–168.

    Article  Google Scholar 

  • Kleijnen, J. P. C., Sanchez, S. M., Lucas, T. W., & Cioppa, T. M. (2005). A user’s guide to the brave new world of designing simulation experiments. INFORMS J. Comput., 17, 263–289.

    Article  Google Scholar 

  • Kramer, D. M., & Crofts, A. J. (1993). The concerted reduction of high and low potential chains of the bf complex by plastoquinol. Biochim. Biophys. Acta, 1183, 72–84.

    Article  Google Scholar 

  • Kurisu, G., Zhang, H., Smith, J. L., & Cramer, W. A. (2003). Structure of the cytochrome b6f complex of oxygenic photosynthesis: tuning the cavity. Science, 302, 1009–1014.

    Article  Google Scholar 

  • McKay, M. D., Beckman, R. J., & Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239–245.

    Article  MathSciNet  MATH  Google Scholar 

  • Minasny, B. (2004). Latin hypercube sampling. Matlab Central, www.mathworks.com/matlabcentral/fileexchange/authors/11803.

  • Muller, F., Crofts, A. R., & Kramer, D. M. (2002). Multiple Q-cycle bypass reactions at the Qo site of the cytochrome bc1 complex. Biochemistry, 41, 7866–7874.

    Article  Google Scholar 

  • Ort, D. R., & Kramer, D. (2009). Photosynthesis: the light reactions. Encycl. Life Sci.. doi:10.1002/9780470015902.a0001309.pub2.

    Google Scholar 

  • Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical recipes in Fortran (2nd ed., pp. 402–406). Cambridge: Cambridge Univ. Press.

    MATH  Google Scholar 

  • Rich, P., Heathcote, P., & Moss, D. A. (1987). Kinetic Studies of Electron Transfer in a hybrid system constructed from the cytochrome bf complex and photosystem I. Biochim. Biophys. Acta, 892(1), 138–151.

    Article  Google Scholar 

  • Saltelli, A., Ratto, M., Tarantola, S., & Campolongo, F. (2006). Sensitivity analysis practices: strategies for model-based inference. Reliab. Eng. Syst. Saf., 91, 1109–1125.

    Article  Google Scholar 

  • Shinkarev, V. P., & Wraight, C. A. (2007). Intermonomer electron transfer in the bc(1) complex dimer is controlled by the energized state and by impaired electron transfer between low and high potential hemes. FEBS Lett, 581, 1535–1541.

    Article  Google Scholar 

  • Smith, J. L., Zhang, H., Yan, J., Kurisu, G., & Cramer, W. A. (2004). Cytochrome bc complexes: a common core of structure and function surrounded by diversity in the outlying provinces. Curr. Opin. Struct. Biol., 14, 432–439.

    Article  Google Scholar 

  • Soriano, G. M., Ponamarev, M. V., Carrell, C. J., Xia, D., Smith, J. L., & Cramer, W. A. (1999). Comparison of the cytochrome bc1 complex with the anticipated structure of the cytochrome b6f complex: De plus ca change de plus c’est la meme chose. J. Bioenerg. Biomembr., 31, 201–213.

    Article  Google Scholar 

  • Spear, R. C. (1997). Large simulation models: calibration, uniqueness and goodness of fit. Environ. Model. Softw., 12, 219–228.

    Article  Google Scholar 

  • Tremmel, I. G., Kirchhoff, H., Weis, E., & Farquhar, G. D. (2003). Dependence of plastoquinol diffusion on the shape, size, and density of integral thylakoid proteins. Biochim. Biophys. Acta, 1607, 97–109.

    Article  Google Scholar 

  • Tremmel, I. G., Weis, E., & Farquhar, G. D. (2007). Macromolecular crowding and its influence on possible reaction mechanisms in photosynthetic electron flow. Biochim. Biophys. Acta, 1767, 353–361.

    Article  Google Scholar 

Download references

Author information

Author notes

  1. David M. Kramer

    Present address: Biochemistry & Molecular Biology, DOE-Plant Research Laboratory, Michigan State University, East Lansing, MI, 48824, USA

Authors and Affiliations

  1. Department of Mathematics, Washington State University, Pullman, WA, 99164, USA

    Mark F. Schumaker

  2. Institute for Biological Chemistry, Washington State University, Pullman, WA, 99164, USA

    David M. Kramer

Authors
  1. Mark F. Schumaker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David M. Kramer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark F. Schumaker.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schumaker, M.F., Kramer, D.M. Comparison of Monte Carlo Simulations of Cytochrome b6f with Experiment Using Latin Hypercube Sampling. Bull Math Biol 73, 2152–2174 (2011). https://doi.org/10.1007/s11538-010-9616-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-010-9616-2

Keywords

Search

Navigation