Photosynthesis *in silico*
pp 17-29 |
Cite as

# Scaling and Integration of Kinetic Models of Photosynthesis: Towards Comprehensive E-Photosynthesis

Mathematical models are essential to understand dynamic behavior of complex biological systems. Photosynthesis as it occurs in a natural environment reflects not only the primary biophysical and biochemical reactions but also a network of regulatory interactions that act across timescales and spatial boundaries. Modeling such a tightly regulated biosystem is feasible when the model is reduced to describe only a rather particular experimental situation such as fluorescence response to a single turnover light flash or the dynamics around the steady-state of Calvin—Benson cycle. Then, the external egulatory interactions can be considered negligible or not changing so that the investigated dynamics can be predicted by modeling the system with only few key components that are relevant for the given time and complexity scale. Such an empiric dimensionality reduction has been successfully applied in photosynthesis research, leading to a mosaic of partial models that map along the Z-scheme of light reactions as well as covering parts of carbon metabolism. The validity ranges of the partial models are frequently not overlapping, leaving gaps in the photosynthesis modeling space. Filling the gaps and, even more important, modeling of regulatory interactions between modeled entities are hampered by incompatibility of the partial models that focus on different time scales or that are restricted to particular experimental situations. This led us to propose the Comprehensive Modeling Space, CMS where the partial photosynthesis models would be shared by means of the Systems Biology Mark-Up Language, SBML, which is the de-facto standard for the formal representation of biochemical models. The model validity is defined by a customized extension of the biology-wide standard of Minimum Information Requested in the Annotation of Biochemical Models, MIRIAM. The hierarchy and connectivity of the partial models within the Comprehensive Modeling Space is determined by rigorous dimensionality reduction techniques. Here, we exemplify the principles of the comprehensive modeling approach based on partial models of the Photosystem II.

## Keywords

Partial Model Light Reaction System Biology Markup Language Biochemical Model Primary Charge Separation## Preview

Unable to display preview. Download preview PDF.

## References

- Condon M and Ivanov R (2004) Empirical balanced truncation of nonlinear systems. J Nonlinear Sci 14: 405–414CrossRefGoogle Scholar
- Duysens LNM and Sweers HE (1963) Mechanism of the two photochemical reactions in algae as studied by means of fluorescence. In: Studies on Microalgae and Photosynthetic Bacteria, pp. 353–372. University of Tokyo Press, TokyoGoogle Scholar
- Emerson R and Arnold W (1932) A separation of the reactions in photosynthesis by means of intermittent light. J Gen Physiol 15: 391–420CrossRefGoogle Scholar
- Gaffron H and Wohl K (1936) Zur Theorie der Assimilation. Naturwissenschaften 24: 103–107CrossRefGoogle Scholar
- Hill R and Bendall F (1960) Function of the two cytochrome components in chloroplasts: a working hypothesis. Nature 186: 136–137CrossRefGoogle Scholar
- Holzwarth AR, Müller MG, Reus M, Nowaczyk M, Sander J and Rögner M (2006) Kinetics and mechanism of electron transfer in intact photosystem II and in the isolated reaction center: pheophytin is the primary electron acceptor. Proc Natl Acad Sci USA 103: 6895–6900PubMedCrossRefGoogle Scholar
- Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P and Kummer U (2006) COPASI — a COmplex PAthway SImulator. Bioinformatics 22: 3067– 3074PubMedCrossRefGoogle Scholar
- Hucka M, Finney A, Sauro H, Bolouri H, Doyle J, Kitano H, Arkin A, Bornstein B, Bray D, Cornish-Bowden A, Cuellar A, Dronov S, Gilles E, Ginkel M, Gor V, Goryanin I, Hedley W, Hodgman T, Hofmeyr J-H, Hunter P, Juty N, Kasberger J, Kremling A, Kummer U, Le Novére N, Loew L, Lucio D, Mendes P, Minch E, Mjolsness E, Nakayama Y, Nelson M, Nielsen P, Sakurada T, Schaff J, Shapiro B, Shimizu T, Spence H, Stelling J, Takahashi K, Tomita M, Wagner J and Wang J (2003) The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19: 524–531PubMedCrossRefGoogle Scholar
- Laisk A and Edwards G (2000) A mathematical model of C
_{4}photosynthesis: the mechanism of concentrating CO_{2}in NADP-malic enzyme type species. Photosynth Res 66: 199–224PubMedCrossRefGoogle Scholar - Lazár D (2006) The polyphasic chlorophyll a fluorescence rise measured under high intensity of exciting light. Funct Plant Biol 33: 9–30CrossRefGoogle Scholar
- Le Novère N, Finney A, Hucka M, Bhalla US, Campagne F, Collado-Vides J, Crampin EJ, Halstead M, Klipp E, Mendes P, Nielsen P, Sauro H, Shapiro B, Snoep JL, Spence HD, and Wanner BL (2005) Minimum information requested in the annotation of biochemical models (MIRIAM). Nature Biotech 23: 1509–1515CrossRefGoogle Scholar
- Liebermeister W, Baur U and Klipp E (2005) Biochemical network models simplified by balanced truncation. The FEBS J 272: 4034–4043CrossRefGoogle Scholar
- Maertens J, Donckels BMR, Lequeux G and Vanrolleghem PA (2005) Metabolic model reduction by metabolite pooling on the basis of dynamic phase planes and metabolite correlation analysis. In: Proceedings of the Conference on Modeling and Simulation in Biology, pp. 147–151. Linköping, SwedenGoogle Scholar
- Nedbal L, Březina V, Adamec F, Štys D, Oja V, Laisk A and Govindjee (2003) Negative feedback regulation is responsible for the non-linear modulation of photosynthetic activity in plants and cyanobacteria exposed to a dynamic light environment. Biochim Biophys Acta 1607: 5–17PubMedCrossRefGoogle Scholar
- Nedbal L, Březina V, Červený J and Trtílek M (2005) Photosynthesis in dynamic light: Systems biology of unconventional chlorophyll fluorescence transients in
*Synechocystis*sp. PCC6803. Photosynth Res 84: 99–106PubMedCrossRefGoogle Scholar - Nedbal L, Červený J, Rascher U and Schmidt H (2007) Ephotosynthesis: a comprehensive modeling approach to understand chlorophyll fluorescence transients and other complex dynamic features of photosynthesis in fluctuating light. Photosynth Res 93: 223–234PubMedCrossRefGoogle Scholar
- Okino MS and Mavrovouniotis ML (1998) Simplification of mathematical models of chemical reaction systems. Chem Rev 98: 391–408PubMedCrossRefGoogle Scholar
- Poolman M, Assmus H and Fell D (2004) Applications of metabolic modelling to plant metabolism. J Exp Bot 55: 1177–1186PubMedCrossRefGoogle Scholar
- Rios-Estepa R and Lange BM (2007) Experimental and mathematical approaches to modeling plant metabolic networks. Phytochemistry 68: 2351–2374PubMedCrossRefGoogle Scholar
- Rodriguez N, Donizelli M and Le Novere N (2007) SBM-Leditor: effective creation of models in the Systems Biology Markup Language (SBML). BMC Bioinformatics 8: 79PubMedCrossRefGoogle Scholar
- Rugh WJ (1996) Linear System Theory. PrenticeHall, NJ, USAGoogle Scholar
- Shapiro BE, Hucka M, Finney A and Doyle J (2004) MathS-BML: a package for manipulating SBML-based biological models. Bioinformatics 20: 2829–2831PubMedCrossRefGoogle Scholar
- Schmidt H and Jirstrand M (2006) Systems biology toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22: 514–515PubMedCrossRefGoogle Scholar
- Skogestad S and Postlethwaite I (1996) Mutlivariable Feedback Control. Wiley, Hoboken, NJ, USAGoogle Scholar
- Zhu X-G, de Sturler E and Long SP (2007) Optimizing the distribution of resources between enzymes of carbon metabolism can dramatically increase photosynthetic rate: a numerical simulation using an evolutionary algorithm. Plant Physiol 145: 513–526PubMedCrossRefGoogle Scholar