, Volume 592, Issue 1, pp 315–328 | Cite as

Stochastic parallel processing can shape photosynthesis–irradiance curves in phytoplankton—the Q model

  • Mark Honti
Primary Research Paper


A mechanistic model was formulated that describes the rate of photosynthesis based on an analogy with queuing systems of operational research. The parallel electron processing capacity of the plastoquinone pool was hypothesized to be the key element in the photosynthetic electron transport chain, determining the process of light saturation for phytoplankton. The state of the plastoquinone pool was described mathematically by a continuous-time Markov chain. The model assumes that traditional photosynthesis measurements using incubation under constant irradiance can be regarded as stochastic equilibria. The model was tested on a set of photosynthesis–irradiance measurements taken in Lake Balaton (Hungary). It clearly outperformed the two most common empirical photosynthesis–irradiance models used in limnology by delivering the best-fit in most cases. Thus, the traditional limnological practice of choosing the right empirical, two-parameter photosynthesis–irradiance model that produces the best-fit can be replaced by simple calibration of three parameters, including a new one describing the degree of parallelism in the photosynthetic units. This parameter was found to specify the curvature of the photosynthesis–irradiance function.


Photosynthetic unit Plastoquinone Queueing theory 



Irradiance (quanta m−2 s−1)


saturation light intensity (quanta m−2 s−1)


Electron transport chain


Exciton generation rate on a PSU (e s−1)


Number of possible states of a PSU (–)


Number of reduced PQ molecules at state i (–)


Probability (–)


PSU specific rate of photosynthesis (mol O2 s−1)


Maximal rate of biomass specific photosynthesis (mol O2 (mol Chl)−1 s−1)




Photosynthetic unit


Number of PQ molecules in a PSU (–)


Reaction centre


Initial slope of the P B versus E curve (mol O2 m2 quanta−1 (mol Chl)−1)


Biomass specific number of photosynthetic units (mol PSU (mol Chl)−1)


Relative probability (–)


Functional adsorption cross-section of PSU (m2)


Turnover time of PQ (s−1)


Biochemical yield of photosynthesis (mol O2 quanta−1)


Quantum yield of photosynthesis (e quanta−1)



This study was supported financially by the ‘Phytoplankton-on-line’ (EVK1-CT-1999-00037) project. Additional financial support was provided by the National Office for Research and Development (“BALÖKO” project). I thank Dr. Vera Istvánovics for discussions and data and Dr. László Koncsos for mathematical guidance.

Supplementary material

10750_2007_0764_ESM.pdf (222 kb)
ESM (PDF 179 kb)


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Water Research Group of the Hungarian Academy of Sciences at the Department of Sanitary and Environmental EngineeringBudapest University of Technology and EconomicsBudapestHungary

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