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Open Access Research article

Modeling the dependence of respiration and photosynthesis upon light, acetate, carbon dioxide, nitrate and ammonium in Chlamydomonas reinhardtii using design of experiments and multiple regression

Stéphanie Gérin1, Grégory Mathy2 and Fabrice Franck1*

Author Affiliations

1 Laboratory of Bioenergetics, Department of Life Sciences, Faculty of Sciences, University of Liege, Boulevard du Rectorat 27, Liege, 4000, Belgium

2 Cell Culture Process Sciences, UCB Pharma, Avenue de l¿Industrie, Braine l¿Alleud, 1420, Belgium

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BMC Systems Biology 2014, 8:96  doi:10.1186/s12918-014-0096-0

Published: 16 August 2014



In photosynthetic organisms, the influence of light, carbon and inorganic nitrogen sources on the cellular bioenergetics has extensively been studied independently, but little information is available on the cumulative effects of these factors. Here, sequential statistical analyses based on design of experiments (DOE) coupled to standard least squares multiple regression have been undertaken to model the dependence of respiratory and photosynthetic responses (assessed by oxymetric and chlorophyll fluorescence measurements) upon the concomitant modulation of light intensity as well as acetate, CO2, nitrate and ammonium concentrations in the culture medium of Chlamydomonas reinhardtii. The main goals of these analyses were to explain response variability (i.e. bioenergetic plasticity) and to characterize quantitatively the influence of the major explanatory factor(s).


For each response, 2 successive rounds of multiple regression coupled to one-way ANOVA F-tests have been undertaken to select the major explanatory factor(s) (1st-round) and mathematically simulate their influence (2nd-round). These analyses reveal that a maximal number of 3 environmental factors over 5 is sufficient to explain most of the response variability, and interestingly highlight quadratic effects and second-order interactions in some cases. In parallel, the predictive ability of the 2nd-round models has also been investigated by k-fold cross-validation and experimental validation tests on new random combinations of factors. These validation procedures tend to indicate that the 2nd-round models can also be used to predict the responses with an inherent deviation quantified by the analytical error of the models.


Altogether, the results of the 2 rounds of modeling provide an overview of the bioenergetic adaptations of C. reinhardtii to changing environmental conditions and point out promising tracks for future in-depth investigations of the molecular mechanisms underlying the present observations.

Statistics; Bioenergetics; Metabolism; Network; Plasticity; Environment