BACKGROUND
in plants and algae, energy transduction processes involve the respiratory and photosynthetic electron transport chains, which take place at the level of the mitochondrial inner membrane and the thylakoid, respectively, through chemi-osmotic mechanisms coupling electron transport and adp phosphorylation  <cit> .
an ubiquinol-o <dig> terminal oxidase  which competes with complex iii for electrons is also found in the mitochondrial inner membrane and is responsible for a cyanide-insensitive “alternative” respiratory pathway, opposed to the “cytochromial” pathway due to complexes iii and iv.
aox activity does not contribute to the building of the electrochemical proton gradient and is therefore qualified as “energy-dissipating”.
this enzyme has long been known to be responsible for heat production in the thermogenic tissues of higher plants  but is also thought to play important roles in non-thermogenic cells in some circumstances by limiting the production of superoxide anion by complexes i and iii and accelerating the turnover of reduced cofactors to ensure a continuous operation of the primary metabolism  <cit> .
over the last century, efficient techniques have been developed to study respiration and photosynthesis in vivo <cit> .
in green microalgae, they can easily be characterized in terms of o <dig> consumption/production rate of cell suspensions using an aqueous phase clark-type polarographic electrode.
determination of the apparent maximal activities  of the cytochromial and alternative pathways is enabled by the use of specific inhibitors, i.e.
cyanide and substituted hydroxamic acids, respectively  <cit> , <cit> .
monitoring chlorophyll fluorescence is also a particularly suitable method for studying the functional properties of the photosynthetic apparatus  <cit> .
in this field, pulse-amplitude modulated  fluorimetry is the tool of choice, since it enables to monitor chlorophyll fluorescence without any interference of the actinic light applied to induce the biological response  <cit> .
this technology gives access to several important parameters characterizing photosynthesis, notably the quantum yield of photosystem ii  and the non-photochemical quenching of chlorophyll fluorescence , which is actually made of  <dig> components: qe , qt  and qi   <cit> – <cit> .
in contrast to higher plants, state transitions have been demonstrated to be very dynamic in green microalgae, so that qt can importantly contribute to the overall npq together with qe  <cit> .
the unicellular green alga chlamydomonas reinhardtii is considered as a model to study the metabolism and bioenergetics of photosynthetic organisms  <cit> .
as shown in figure  <dig>  c. reinhardtii is not only able to grow photoautotrophically by using light energy to fix co <dig> into organic molecules, but can also assimilate acetate as an exogenous organic carbon source under the form of acetyl-coa through atp-dependent enzymatic reactions  <cit> .
these features enable cells to grow mixotrophically in the light by harnessing inorganic  and organic  carbon sources, and even heterotrophically in the dark by oxidizing acetyl-coa through the glyoxylate and tricarboxylic acid  cycles to promote the production of reduced cofactors and atp.
the glyoxylate cycle, which bypasses the  <dig> decarboxylation steps of the tca cycle, also accounts for the net biomass accumulation because its c <dig> intermediates can be used in biosynthetic pathways  <cit> .
an important feature of co <dig> fixation in c. reinhardtii relies on the carbon concentrating mechanism , a whole-cell enzymatic machinery enabling to increase co <dig> availability in the local environment of rubisco through the dehydration of accumulated bicarbonate to counterbalance the weak catalytic activity of the enzyme and limit its oxygenase activity under low co <dig> conditions  <cit> , <cit> .
the ccm consists of several isoforms of carbonic anhydrases  catalyzing the interconversion of co <dig> and bicarbonate in different sub-cellular compartments but also of diverse inorganic carbon membrane transporters  <cit> , <cit> .
c. reinhardtii can assimilate nitrate and ammonium as inorganic nitrogen sources, but ammonium is preferred to nitrate when they are present together in the medium, consistently with the lower energy cost of ammonium assimilation  <cit> , <cit> .
nitrate assimilation first requires its reduction into ammonium, which can then be incorporated within organic molecules under the form of glutamate through the gs/gogat cycle in the chloroplast   <cit> , <cit> .
reduced cofactors and atp being necessary for inorganic nitrogen assimilation mainly originate from photophosphorylation under photoautotrophic culture conditions, but also from the glyoxylate and tca cycles coupled to oxidative phosphorylation in mixotrophically-grown cells  <cit> , <cit> .
as illustrated in figure  <dig> and demonstrated by recent bioinformatics- and literature-based models of the c. reinhardtii metabolic network, the assimilatory pathways of light, carbon and inorganic nitrogen are tightly interconnected through complex exchanges of metabolites, energy and reducing power which are strictly regulated in response to environmental changes to maintain cellular homeostasis  <cit> – <cit> .
these features strongly suggest that bioenergetics is likely to be influenced by the cumulative effect of different factors and even by interactions between some of them.
however, to our knowledge, most reported studies have only focused on the qualitative or semi-quantitative influence of one or a few environmental factor on respiration and/or photosynthesis while other factors were kept constant.
design of experiments  coupled to multiple regression are powerful statistical tools to model the dependence of a physical, chemical or biological process to different intrinsic or extrinsic factors with a limited number of experiments  <cit> .
they are commonly used in diverse applied research fields, in particular for the screening of culture conditions aiming to heighten the production of biomass and/or molecules of interest  by diverse organisms  <cit> – <cit> .
the methodology has successfully been applied to different microalgae to optimize culture medium for heterotrophic growth, starch and lipid production, co <dig> fixation as well as metabolite extraction for bio-industrial purposes  <cit> – <cit> .
in the present work, doe coupled to standard least squares multiple regression have been used to model the dependence of several respiratory and photosynthetic responses upon the concomitant modulation of light intensity and acetate, co <dig>  nitrate and ammonium concentrations in the culture medium of c. reinhardtii.
bioenergetic responses of interest have been defined as the dark cellular respiration  and the apparent maximal activities of the cytochromial  and alternative  respiratory pathways, as well as the quantum yield of photosystem ii in saturating light , the gross o <dig> evolution  and the non-photochemical quenching of chlorophyll fluorescence  measured under a light intensity of  <dig> μmolphotons.m− <dig> s− <dig>  which is sufficient to saturate photosynthesis but not to induce photoinhibition  <cit> .
the main goals of this study were to determine which environmental factor induce most of the response variability  mostly account for bioenergetic plasticity) and to characterize quantitatively the influence of these major explanatory factors.
such goals have been achieved through a  <dig> step approach consisting of a 1st-round of multiple regression aiming to detect the factor of interest, which were then selected for a 2nd-round to generate predictive models enabling to simulate the mathematical profile of their influence.
we discuss the results with regards to data reported in literature and we propose biological hypotheses attempting to rationalize the present observations and to provide new promising tracks for future in-depth investigations of the molecular mechanisms underlying bioenergetic plasticity in photosynthetic organisms.
RESULTS
design of experiments
a doe assuming first- and second-order effects was constructed on the basis of the features summarized in table  <dig> to define a limited number of combinations of values for the different environmental factors which altogether were sufficient to cover the whole design space.
jmp calculated that the doe had to contain at least  <dig> combinations for an unbiased subsequent modeling, and we decided to raise this number up to  <dig>  to ensure more confidence toward the analyses.
the resulting doe is a  <dig> level fractional factorial design with additional center points  with some extra-points typically characterizing the central composite and box-behnken types of designs   <cit> .
a  <dig> dimensional representative example of factor dispatching within the design space is illustrated in figure  <dig> for acetate, ammonium and nitrate concentrations.
x
min
/
m
1
x
max
/
m
2
m, modality; xmin and xmax, minimal and maximal values of the working range ; m <dig> and m <dig>   <dig> modalities of co <dig> concentration.
pearson's correlation coefficients  were calculated to verify that altogether the different doe items were uniformly covering all directions of the design space.
these analyses demonstrated that the factors did not relevantly correlate to each other .
however, while also considering second-order effects, a much more important correlation was detected in a small number of cases .
remarkably, an absolute correlation of approximately  <dig>  was systematically observed between each single factor and its combination with co <dig> concentration.
this feature does not reflect a sub-optimal experimental design , but is rather an artificial bias attributable to the definition of co <dig> concentration as an ordinal factor.
due to this particularity, contrarily to the other second-order interactions , the combination between co <dig> concentration and another factor cannot be expressed as a continuous product term, but rather as a  <dig> component term with a specific modality for co <dig> concentration and a specific numeric value for the other interacting factor.
in such a situation, calculating the correlation between a single factor and its interaction with co <dig> concentration implies to correlate this factor with itself.
the observation of an absolute correlation coefficient inferior to  <dig> is only attributable to the definition in doe of a different number of points for the  <dig> co <dig> modalities for each value of the other interacting factor.
as shown in table  <dig>  an important correlation  could also be noticed between squared acetate and nitrate concentrations, which indicates a lack of test points in a particular region of the design space.
such a collinearity can generate a bias in modeling  only if these squared concentrations are implied together in the statistical analyses .
|r|
the symbol "*" is used to represent second-order effects  of individual factors.
measurements of the responses
bioenergetic responses were measured for the  <dig> combinations of factors defined in doe and are summarized in additional file  <dig>  measurements were not replicated because a global compensation of the individual experimental errors was expected in subsequent regression processes.
figure  <dig> presents typical oxymetric and chlorophyll fluorescence traces obtained for one of the center points  and explains the calculations of respiratory  and photosynthetic  responses.
it has to be noticed that cr and macyt could not be measured in a few cases  but that the amount of experimental data  remains nevertheless largely sufficient for an unbiased subsequent modeling.
as emphasized by the high relative standard deviations of the data , every response is distributed within a wide range of values, which provides a highly favorable experimental background for regression processes.
selection of the major explanatory factor
the 1st-round of modeling was performed using the available set of experimental data to detect the factor accounting for most of the response variability.
first- and second-order effects were assumed, i.e.
it was hypothesized that the responses could depend on each factor linearly or quadratically  but also on the interaction between  <dig> factors.
this feature rose up to  <dig> the number of effects which had actually to be involved in the modeling processes, making necessary to get a previous selection to avoid any possible underestimation of important contributions.
for this purpose, stepwise regressions were undertaken to define the subset of effects which would provide altogether the smallest aicc  in subsequent modeling.
the selected effects are listed in table  <dig> with the corresponding aicc, clearly showing that the latter is always dramatically lower than the aicc including all  <dig> initial effects.
cyt
alt
factor
β
p-value
factor
β
p-value
factor
β
p-value
4
+
4
+
4
+
4
+
4
+
Φpsii
800
800
800
factor
β
p-value
factor
β
p-value
factor
β
p-value
3
−
]*[no
3
−
3
−
]*[no
3
−
3
−
aiccall and aiccmod correspond to hypothetical models which would comprise every  <dig> initial effects and the 1st-round models which only contain the stepwise-selected effects, respectively.
rmsef standardized in terms of percentage of the average scale  is displayed to facilitate error comparison among models.
numbers ranging from  <dig> to  <dig> classify the different effects by increasing order of individual p-value, and β-weights are also provided.
statistically significant p-values  are surrounded by *.
effects which are highlighted in bold were considered as major explanatory ones and selected for the 2nd-round of modeling.
modeling was performed through standard least squares multiple regression with the stepwise-selected effects to establish a predictive mathematical equation  associating a theoretical response with each of the  <dig> experimental values .
in equations, co <dig> concentration  is present under the form of an additional extension term due to its definition as an ordinal factor: this extension is equal to zero for  <dig> % co <dig> and different from zero for  <dig> % co <dig> .
as summarized in table  <dig>  r <dig>  r <dig> adjusted  and fitting root-mean-square error  were calculated to evaluate the goodness of fit, and whole-model and lack-of-fit anova tests were performed to assess the statistical significance of the models.
rmsef was also standardized in terms of percentage of the average scale of the response  in order to facilitate comparisons of regression error among models.
remarkably, the statistical insignificance of lack-of-fit tests  suggests that no important effect remained unselected through the stepwise regression processes.
the values of r <dig>  r <dig> adjusted  and rmsef  as well as the p-values of the whole-model anova tests  tend to indicate that altogether the effects selected through stepwise regression account for an important part of the response variability.
the relative contribution of the different effects to the models was further investigated by calculating anova tests and β-weights  for individual effects .
the absolute value of the latter parameter participates  to characterize the extent to which the effect contributes to the model, and its sign assesses whether the effect exerts a positive or negative influence on the response.
as shown in table  <dig> , high absolute β-weights are always associated with small p-values.
in most cases, β-weights and individual anova tests lead to establish the same order of importance for the different effects, with the exception of p <dig> for which light intensity exhibits a smaller p-value than squared nitrate concentration  but not a higher absolute β-weight ; however, the  <dig> parameters similarly point out that these effects are major explanatory ones.
in case of p <dig>  2 second-order effects which had been shown to correlate to each other with |r| =  <dig> , i.e.
squared acetate and nitrate concentrations , were selected through the stepwise regression process.
these effects exhibit high absolute β-weights and small p-values  comparatively to most of the other effects of the model , suggesting that the regression could have been affected by a lack of experimental data in some regions of the design space.
however, the observation of an insignificant lack-of-fit anova test  and of similar r <dig> adjusted and standardized rmsef values  than those of the other models  tend to indicate that no bias was introduced due to this correlation.
as shown in table  <dig>  one or several effect which do not exert any statistically significant influence  can be found within the models, and considerable differences can even be observed among the relative contribution of the statistically significant effects as indicated by the important heterogeneity of their p-values  and absolute β-weights .
these features suggest that some effect within the models do not substantially influence the responses despite their selection through the stepwise regression processes.
consequently, to avoid overfitting and select the effects which altogether are sufficient to explain most of the response variability, a trial-and-error method consisting of several steps of multiple regression was used: 1st-round effects were removed successively by descending order of p-value  and modeling was tested with the remaining effects at each step of the process.
the remaining effects were considered as major explanatory ones when the removal of the less important of them  led to the observation of a significant lack-of-fit anova test  and/or a r <dig> coefficient lower than  <dig>   .
as expected, the selected effects  had been shown to exhibit small p-values  and high absolute β-weights  in the 1st-round models comparatively to the unselected effects, which confirms their particularly important contribution.
as emphasized in table  <dig> , maximum  <dig> different environmental factors over  <dig>  appear to be sufficient to explain an important part of the response variability.
acetate concentration and light intensity are major explanatory factors for every response except for Φpsii <dig>  for which light intensity is the only one.
in addition, ammonium and nitrate concentrations seem to influence to a large extent respiratory  and other photosynthetic  responses, respectively, unlike co <dig> concentration which does not appear to be an important effector of bioenergetic plasticity.
mathematical simulation of the influence of the major explanatory factor
the 2nd-round of multiple regression was performed with the effects selected through the 1st-round  in order to build a simplified model for each response.
a few unselected first-order effects were also included in the modeling processes for npq <dig>  and p <dig>  because of the selection of second-order effects containing these factors .
this process led to establish a simplified mathematical expression  associating a new predicted response with each of the  <dig> experimental values:  cr= <dig> + <dig> acetate+ <dig> light− <dig> nh4+− <dig> acetate− <dig> nh4+− <dig>    macyt= <dig> + <dig> acetate+ <dig> light− <dig> nh4+   maalt= <dig> + <dig> acetate+ <dig> light− <dig> nh4+− <dig> acetate− <dig> − <dig> acetate− <dig> nh4+− <dig>    Φpsii800= <dig> + <dig> light   npq800= <dig> − <dig> acetate− <dig> light− <dig> no3−− <dig> no3−− <dig> − <dig> acetate− <dig> light− <dig>   p800= <dig> − <dig> acetate+ <dig> light+ <dig> no3−+183acetate− <dig> − <dig> no3−− <dig>
an exhaustive list of the 2nd-round predicted responses is provided in additional file  <dig>  which also summarizes the 1st-round predicted responses obtained prior to the restriction of the models to the major explanatory factor.
aicc, r <dig>  r <dig> adjusted, rmsef, β-weights and anova tests for whole-model, individual effects and lack-of-fit were calculated and are summarized in figure  <dig> and additional file  <dig>  comparatively to the 1st-round models, the observations that r <dig> and r <dig> adjusted decreased by maximum  <dig>  and  <dig>  units, respectively, and that aicc and rmsef did not increase by more than  <dig>  units and 8% of the response average scale, respectively, tend to confirm that the eliminated effects did not substantially account for the response variability.
as expected, β-weights and p-values of the individual anova tests are similar to those of the 1st-round , so that the relative contribution of the essential effects described in table  <dig> seems to be globally conserved.
in figure  <dig>  experimental values  are plotted as a function of predicted responses  calculated from equations  <dig> to  <dig>  the y = ŷ straight line  and the 95%-confidence intervals of the whole-model anova tests are also represented for visual evaluation of goodness of fit and statistical significance, respectively .
r <dig>  r <dig> adjusted and rmsef of the different responses  are shown to be ≥ <dig> , ≥ <dig>  and ≤47% of the response average scale, respectively, except in case of npq <dig> for which r2 =  <dig>  and r <dig> adjusted =  <dig> .
anova test p-values  appear to be inferior or equal to  <dig>  .
in figure  <dig>  contour plots representing the evolution of the experimental  and predicted  responses as a function of the  <dig> factors exhibiting the smallest individual effect p-values  are compared and reveal closely related global profiles.
for Φpsii <dig>  contour plots were replaced by line plots since this response was modeled with only  <dig> factor  in the 2nd-round.
these different observations tend to confirm that altogether the effects included in the 2nd-round of modeling are sufficient to explain an important part of the response variability.
figure  <dig> presents a graphical simulation of the influence of each factor as predicted by the 2nd-round models with the corresponding β-weight and individual effect anova test p-value .
the mathematical profile of each factor was established by applying a specific value  to the other factors of the model within equations  <dig> to  <dig> to generate a new single-unknown predictive equation.
in case of quadratic profile, the factor value for which the response is maximal or minimal  is displayed and the β-weights and p-values are provided for the first- and second-order parameter estimates.
the profile of light intensity is not presented for npq <dig> since this factor does not relevantly account for response variability per se ; its presence in the model is exclusively due to a second-order interaction with acetate concentration as detailed below.
as expected, in case of linear dependence, increasing and decreasing profiles are associated with positive and negative β-weights, respectively; for quadratic relationships, the type of dependence  is pointed out by the sign of the β-weight of the second-order effect , which is positive for convex profiles and negative for concave ones.
as illustrated in figure  <dig>  cr linearly depends on acetate concentration , light intensity  and ammonium concentration  with p <  <dig>  .
macyt exhibits a similar dependence upon these factors with the following parameters: β =  <dig> /p <  <dig>  for acetate concentration, β =  <dig> /p =  <dig>  for light intensity and β = − <dig> /p =  <dig>  for ammonium concentration .
maalt is linearly modulated by light intensity  and ammonium concentration , and is also quadratically influenced by acetate concentration  .
Φpsii <dig> and p <dig> linearly increase with light intensity  with p <  <dig> .
in addition p <dig> also quadratically depends on nitrate  and acetate  .
npq <dig> is quadratically modulated by nitrate concentration , and also linearly decreases with acetate concentration  .
in most cases, mathematical profiles  are not influenced by the other factors of the model since modifying their value only induces a translation of the graphs along the ordinate axis without alteration of their general shape.
however, as revealed by the occurrence of product terms within equations  <dig> to  <dig> , a mutual influence between the individual effects of acetate and ammonium concentrations can be observed in case of cr  and maalt , as well as a strong influence of light intensity on the individual effect of acetate concentration in case of npq <dig> .
the negative sign of β-weights indicates that heightening the value of one of the interacting factors leads to a decrease of the slope  characterizing the profile of the other factor.
in figure  <dig>  the influence of each interacting factor is independently simulated for  <dig> different values of the other one  by the same procedure as described for figure  <dig> .
no graph is presented for light intensity in case of npq <dig> since this factor poorly contributes to the model  whatever the acetate concentration is.
remarkably, for cr and maalt, the effects of acetate and ammonium concentrations appear to be weakened and strengthened, respectively, by increasing the value of the other factor .
concerning maalt, rising ammonium concentration also generates a displacement of the optimal acetate concentration towards smaller values .
for npq <dig>  a relevant effect of acetate concentration is only observed upon high irradiance .
validation of the 2nd-round models: cross-validation and experimental validation on new random combinations
in parallel to the main goals of the present study , we wondered whether the 2nd-round models could also be used as tools to predict the responses associated with any combination of factors within the range of doe .
in order to investigate the predictive ability of the 2nd-round models, experimental data were divided into k =  <dig> subsets  and k-fold cross-validation was undertaken.
each of the  <dig> test sets was compared to the corresponding training model  in terms of cross-validation mean absolute error  and root-mean-square error .
table  <dig> presents for each response the average maecv and rmsecv summarizing the deviation of the  <dig> test data sets to their respective training model, as well as the average r <dig>  r <dig> adjusted, maef  and rmsef summarizing the analytical error of the  <dig> training models .
the average scales of the different responses are also provided as a reference to assess the extent of the deviations.
as shown in table  <dig>  the r <dig>  r <dig> adjusted, maef and rmsef of the training models are identical or very similar to those of the 2nd-round models .
remarkably, the maecv and rmsecv characterizing the deviation of the test data sets to their respective training model do not exceed the analytical error of more than 37% for maecv and 21% for rmsecv, and these proportions are reduced to 29% and 12%, respectively, if p <dig> is not taken into account.
r
2
2
f
f
2
2
f
f
cv
cv
ev
ev
ma
cyt
ma
alt
Φpsii
800
npq
800
p
800
cross-validation was performed by the k-fold method with k = 5; the r <dig>  r <dig> adjusted, mae and rmse presented for the training models  and the test data sets  are the average values compiling the  <dig> iterations.
for each response, the average scale  is also provided as a reference to assess the importance of the deviations.
r <dig> adj., r <dig> adjusted.
in addition to cross-validation, the predictive ability of the 2nd-round models was also evaluated by measuring the bioenergetic responses for  <dig> new randomly-generated combinations of factors  with  <dig> experimental replicates each  .
every algal culture was undertaken with  <dig> % co <dig> for technical convenience since co <dig> concentration was not included in the 2nd-round models.
because of the quite large standard deviations related to npq <dig> measurements ,  <dig> more combinations were tested for photosynthetic responses  in order to increase confidence toward the general tendency of data.
the predicted responses associated with the random combinations were calculated from equations  <dig> to  <dig>  as summarized in additional file  <dig>  the deviation of the experimental validation data sets  to the 2nd-round models was assessed in terms of experimental validation mean absolute error  and root-mean-square error  ; this deviation is also illustrated in figure  <dig>  in which the experimental values are plotted as a function of the predicted ones.
as shown in table  <dig>  the maeev and rmseev of the experimental validation data are inferior to the analytical error of the 2nd-round models for cr, macyt, maalt and npq800; for Φpsii <dig> and p <dig>  they exceed the analytical error of only  <dig> and 27% for maeev and  <dig> and 19% for rmseev, respectively.
as clearly evidenced while comparing figure  <dig> and figure 8a, it has to be noticed that the responses measured for the new random combinations do not cover the full range observed in the doe study .
this feature could be attributable to the random choice of the factor values for the  <dig> or  <dig> validation points without consideration of the responses predicted by the 2nd-round models.
4
+
3
−
2
cyt
alt
800
800
800
data result from  <dig> independent sets of cultures and measurements.
, acetate concentration.
altogether, these different validation results indicate that the 2nd-round models can be used as tools to predict the responses associated with any combination of factors, with an inherent average deviation being quantified by the maef and rmsef characterizing the analytical error of the models.
as deduced from table  <dig>  this deviation is comprised between  <dig> and 36% of the response average scale for maef and  <dig> and 47% for rmsef.
discussion
in the present work, doe coupled to standard least squares multiple regression have been used to model the dependence of different respiratory  and photosynthetic  responses upon the concomitant modulation of light, carbon and inorganic nitrogen sources in the culture medium of c. reinhardtii.
this methodology was applied to characterize the extent to which the different environmental factors contribute to bioenergetic plasticity  as well as the mathematical profile of their influence for those accounting for most of the response variability .
altogether, these analyses provide an overview of the bioenergetic adaptations resulting from global changes in culture conditions.
this type of sequential statistical approach, which is commonly undertaken for the optimization of industrial production yields and the design and analysis of “-omics” experiments, had never been used to characterize the bioenergetic plasticity of photosynthetic cells.
the individual influence exerted by one or a few environmental factor  on the cellular bioenergetics and metabolism had extensively been studied independently, but little information was available concerning their cumulative effect and their relative contribution to bioenergetic plasticity in a context in which they vary concomitantly in the medium.
the present analyses demonstrate that maximum  <dig> environmental factors over  <dig> are sufficient to explain most of the response variability  and remarkably evidence squared effects and second-order interactions in some cases .
as shown in figure  <dig>  comparatively to the other responses, lower r <dig> and r <dig> adjusted characterize the 2nd-round models obtained for npq <dig> .
such discrepancies could  be attributable to the higher experimental error inherent to npq <dig> measurements .
in order to check whether the 2nd-round models could also be used to predict the responses associated with any combination of factors within the range of doe , k-fold cross-validation and experimental validation tests on new random combinations have been undertaken.
the similarity between the deviation of the validation points  and the analytical error of the training or 2nd-round models  tend to confirm the predictive ability of the 2nd-round models .
it must nevertheless be emphasized that deviations of  <dig> to 36% of the response average scale  or  <dig> to 47%  corresponding to the analytical error of the 2nd-round models are inherent to the predictions.
in literature, o <dig> evolution commonly appears to be normalized in terms of chlorophyll concentration.
however, in the present analyses, it was rather chosen to use protein concentration because of the high dependence of c. reinhardtii pigment content upon culture conditions, particularly light and acetate  <cit> – <cit> .
our unconventional normalization strategy could therefore generate apparent discrepancies between previously reported studies and the present results in some cases.
in the following sections, the authors will attempt to propose literature-based hypotheses addressing the possible biological implications of their observations.
they insist on emphasizing that these hypotheses must not be considered as firm assertions, but rather aim to provide tracks for future in-depth molecular investigations.
light stimulates co <dig> fixation through the calvin cycle and provides mitochondrial respiration with oxidizable substrates
the gross photosynthetic o <dig> evolution and the quantum yield of photosystem ii of c. reinhardtii cells adapted to moderate light intensities  have been measured under  <dig> μmolphotons.m− <dig> s− <dig>  under such a so-called “saturating” intensity, the electron transport rate  is not limited by light availability but rather by the capacity of downstream metabolic pathways that consume photo-generated reductant and atp .
in these conditions, the gross o <dig> evolution  can primarily be considered as representative of the capacity of these pathways, even if numerous studies indicate that complex photosynthesis-associated o2-consuming processes  can also importantly contribute in some circumstances to modulate this response in c. reinhardtii <cit> .
the present analyses indicate that light intensity exerts a positive linear influence on Φpsii <dig> and p <dig> .
accordingly, the maximal gross o <dig> evolution was previously reported to be doubled in c. reinhardtii cells grown under illumination of  <dig> μmolphotons.m− <dig> s− <dig> comparatively to a lower illumination of  <dig> μmolphotons.m− <dig> s− <dig> <cit> .
these observations could  be attributable to the well-known stimulation of the expression and activity of calvin cycle enzymes by light  <cit> , in good agreement with the higher co <dig> fixation rates observed upon increasing illumination in c. reinhardtii <cit> .
this improvement of co <dig> fixation by light was reported to be correlated to higher cellular metabolite content, respiratory o <dig> consumption and tca cycle-mediated co <dig> production, in line with the linear stimulation of cr, macyt and maalt by light which could also be detected here .
for macyt and maalt, the term “apparent” is used because measurements were carried out on entire cells but not on isolated mitochondria.
the availability of respiratory substrates could therefore not be directly controlled, so that the measured maximal activities could have been underestimated comparatively to the actual capacities if the intracellular reductant concentration was insufficient to saturate the mitochondrial electron transport chain in the presence of kcn or salicylhydroxamic acid .
in apparent contradiction with these considerations, the present analyses did not retain co <dig> concentration as a major explanatory factor of bioenergetic plasticity .
such an absence of influence had already been highlighted for the maximal gross o <dig> evolution in a previous study, in which the sum between the net o <dig> evolution monitored under  <dig> μmolphotons.m− <dig> s− <dig> and the dark respiration measured before illumination was shown to be similar in low and high co2-grown c. reinhardtii cells  <cit> .
these observations could be explained by the existence of a low co2-inducible ccm in c. reinhardtii, by which a high co <dig> availability for rubisco is maintained in low co <dig> condition.
several transcriptomic analyses demonstrated that adaptation to different co <dig> concentrations mainly occurs through the regulation of the genetic expression of ccm components but not calvin cycle enzymes in c. reinhardtii <cit> – <cit> .
moreover, transferring c. reinhardtii cells from high to low co <dig> external concentration was shown to result in a transient decrease of the amount of the small and large rubisco subunits before returning  to the levels characterizing high co2-grown cells  <cit> .
altogether, these different observations and the present ones tend to indicate that adaptation to low co <dig> environment in c. reinhardtii principally occurs through ccm induction but not calvin cycle regulation.
acetate down-regulates the capacity of the calvin cycle and promotes its own uptake and storage to counteract the osmotic stress associated with high extracellular acetate concentrations
the present analyses indicate that p <dig> depends on acetate concentration following a quadratic convex profile with a minimal value for  <dig>  g.l− <dig> .
in a previous study, the net o <dig> evolution measured under  <dig> μmolphotons.m− <dig> s− <dig> was shown to decrease with acetate concentrations ranging from  <dig> to  <dig>  g.l− <dig>  but rates had been normalized in terms of chlorophyll concentration and cultures conducted under the same saturating light intensity than that of measurements   <cit> .
in c. reinhardtii and chlorogonium elongatum , acetate is known to repress the expression of the genes encoding the small and large rubisco subunits , thereby lowering the capacity for co <dig> fixation through the calvin cycle  <cit> – <cit> .
in this context, carbon originating from acetate can substitute for up to half the photoautotrophically-generated biomass content  <cit> , <cit> , and light-driven photosynthetic reactions importantly contribute to provide reductant and atp for biosynthetic acetate assimilation   <cit> .
in heterotrophically-grown c. reinhardtii cells, acetate storage as starch is also known to be promoted through the improvement of the expression and activity of enzymes of the glyoxylate cycle  and gluconeogenesis  <cit> , <cit> .
in parallel to its influence on carbon metabolism, acetate inhibits c. reinhardtii heterotrophic growth beyond  <dig>  g.l− <dig> in the medium   <cit> .
from this concentration, the osmotic potential reaches a critical value beyond which active transport processes are impaired and energy requirements for cellular maintenance are considerably heightened.
interestingly, for p <dig>  the present analyses point out a “concentration of inflexion”  which is very close to the critical substrate inhibition concentration of  <dig>  g.l− <dig> .
this observation tends to indicate that p <dig> could be influenced by  <dig> independent acetate-responsive metabolic processes consuming photo-generated reductant and atp: the calvin cycle  and the biosynthetic assimilation of acetate .
acetate stimulates mitochondrial respiration by heightening the intracellular reductant content and the capacity of the cytochrome pathway
the present analyses indicate that acetate concentration exerts a positive linear influence on cr and macyt .
accordingly, when grown in an acetate-containing medium, c. reinhardtii cells were previously shown to exhibit a twice-enhanced respiratory rate   <cit>  as well as increased transcript levels for diverse components of oxidative phosphorylation, suggesting a higher capacity of the cytochrome pathway  <cit> .
in parallel, maalt depends on acetate concentration following a quadratic concave profile with an optimum for  <dig>  g.l− <dig>  as illustrated in figure 6c, this response can nevertheless be considered as linearly stimulated up to  <dig>  g.l− <dig> acetate without further increase beyond this concentration.
this observation tends to indicate that substrate-saturation of the alternative pathway in the presence of kcn could be reached beyond  <dig>  g.l− <dig> acetate, which would imply that aox capacity is not responsive to acetate concentration.
accordingly, enhancement of the capacity of the cytochrome pathway was already suggested to contribute to the acetate-induced improvement of dark respiration without concomitant modification of aox capacity  <cit> .
acetate inhibits npq through repression of the lhcsr3-dependent qe component
the present analyses demonstrate that acetate concentration exerts a negative linear influence on npq <dig> , but only in case of high light intensity .
interestingly, the extent of qe has recently emerged as being dramatically lowered by the presence of acetate in the growth medium, as notably evidenced by finazzi and co-workers who demonstrated that qt is the major contributor to the global npq in mixotrophically-grown c. reinhardtii cells  <cit> .
even if the molecular mechanisms underlying the functional relationship between npq and acetate are not yet understood, the present results tend to confirm these findings and indicate that the magnitude of the inhibitory effect of acetate on qe could depend on its external concentration.
recently, qe has been proposed to be mediated by lhcsr <dig>  a light-harvesting complex orthologue which is only expressed upon high irradiance  <cit> , <cit> .
npq plasticity induced in response to changing environmental conditions  could therefore be disabled in the dark and low light intensities due to the down-regulation of lhcsr <dig>  these interpretations must be considered with caution due to the impossibility to distinguish the contributions of qe and qt to the global npq here.
mitochondrial respiration contributes to provide nitrate assimilation with reductant through the acetate-dependent activity of aox
ammonium concentration is shown here to exert a negative linear influence on cr, macyt and maalt .
in selenastrum minutum , mitochondrial respiration was proposed to play a role in nitrate assimilation by acting as a trigger factor for the tca cycle.
this would in turn promote the production and export of reductant in the cytoplasm and the chloroplast to support nitrate reduction  <cit> .
in c. reinhardtii, the enzymatic activity and genetic expression of proteins involved in nitrate assimilation are known to be repressed by ammonium  <cit> , <cit> .
these regulatory events are responsible for a strict control of inorganic nitrogen uptake and assimilation by ammonium availability and enable to preferentially exploit this reduced n form if nitrate is also present in the medium  <cit> .
such a primary control of nitrate assimilation by ammonium could rationalize the present observations with regards to the postulated role of mitochondrial respiration in this metabolic process.
for maalt, ammonium concentration is the factor which explains the highest proportion of response variability .
interestingly, the gene encoding aox  is known to be located within a gene cluster which also encodes components of the nitrate assimilatory pathway and is tightly regulated by the nitrogen source  <cit> ; consequently, aox expression and capacity were shown to be induced by nitrate and repressed by ammonium in a concentration-dependent manner  <cit> .
with regards to the peculiar genetic localization and regulation of aox <dig>  the postulated role of mitochondrial respiration in nitrate assimilation was proposed to be essentially mediated by aox, as also indicated by a recent comparative proteomic study published by our group  <cit> .
the present results are in good agreement with these findings.
interestingly, a mutual influence could be detected between the individual effects of acetate and ammonium concentrations for cr and maalt .
as illustrated in figure 7a and b , the effect of acetate concentration is attenuated by ammonium.
for maalt, there is also a displacement of the optimal acetate concentration toward smaller values with increasing ammonium concentration .
these results are consistent with a negative influence of ammonium concentration on aox capacity.
they also tend to confirm that the involvement of mitochondrial respiration in nitrate assimilation is essentially mediated by aox since no relevant second-order interaction was retained for macyt.
reciprocally, as illustrated in figure 7a and b , ammonium concentration exerts a relevant influence on cr and maalt only upon high acetate concentration .
this observation tends to indicate that acetate assimilation could provide the tca cycle with oxidizable substrates to support the involvement of aox in nitrate assimilation.
nitrate assimilation is retro-inhibited to prevent the deleterious effects of nitrite and ammonium intracellular accumulation
the present analyses demonstrate that nitrate concentration exerts a quadratic concave influence on p <dig> with an optimum for  <dig>  mm .
in c. reinhardtii, photosynthesis is known to contribute to provide nitrate reduction with electrons   <cit> , <cit> , <cit> , so that the rate of nitrate assimilation can influence p <dig> in the same way as for the calvin cycle.
the effect of nitrate on p <dig> can therefore be thought to result  from  <dig> distinct metabolic processes of which the relative importance varies with nitrate concentration: substrate stimulation of reductase activity  and retro-inhibition of nitrate reduction by nitrate-derived intracellular ammonium .
such a retro-inhibition could attenuate the production of nitrite and ammonium  and prevent the deleterious effects which would result from their intracellular accumulation   <cit> , <cit> , <cit> .
similarly to p <dig>  npq <dig> also depends on nitrate concentration following a quadratic concave profile with an optimum for  <dig>  mm .
assuming that the nadph-to-atp stoechiometric ratio of nitrate assimilation is superior to the yield of photosynthesis, the reoxidation of photo-generated reductant may not be paralleled with atp turnover.
this feature could result in heightening Δph across the thylakoid membrane, which would in turn stimulate high energy state chlorophyll de-excitation  in an extent depending on the rate of nitrate assimilation.
CONCLUSIONS
in the present work, doe coupled to standard least squares multiple regression have been applied to model the dependence of respiration and photosynthesis upon light, carbon and inorganic nitrogen sources in c. reinhardtii through a  <dig> step approach consisting of  <dig> successive rounds of modeling.
this methodology enabled to demonstrate that maximum  <dig> environmental factors over  <dig> account for most of the variability of the different responses  and also permitted to obtain a mathematical simulation of the influence of the major explanatory factors.
altogether, these results provide an overview of the adaptations of c. reinhardtii bioenergetic pathways to changing culture conditions and point out new promising tracks for future more specific investigations.
in order to further characterize the molecular adaptations underlying the present functional observations, we have undertaken a doe-based comparative proteomic analysis  coupled to the determination of pigment and lipid composition by chromatography, of which the results are currently being modeled.

 in plants and algae, energy transduction processes involve the respiratory and photosynthetic electron transport chains, which take place at the level of the mitochondrial inner membrane and the thylakoid, respectively, through chemi-osmotic mechanisms coupling electron transport and adp phosphorylation. an ubiquinol-o terminal oxidase which competes with complex iii for electrons is also found in the mitochondrial inner membrane and is responsible for a cyanide-insensitive “alternative” respiratory pathway, opposed to the “cytochromial” pathway due to complexes iii and iv. aox activity does not contribute to the building of the electrochemical proton gradient and is therefore qualified as “energy-dissipating”. this enzyme has long been known to be responsible for heat production in the thermogenic tissues of higher plants but is also thought to play important roles in non-thermogenic cells in some circumstances by limiting the production of superoxide anion by complexes i and iii and accelerating the turnover of reduced cofactors to ensure a continuous operation of the primary metabolism. over the last century, efficient techniques have been developed to study respiration and photosynthesis in vivo. in green microalgae, they can easily be characterized in terms of o consumption/production rate of cell suspensions using an aqueous phase clark-type polarographic electrode. determination of the apparent maximal activities of the cytochromial and alternative pathways is enabled by the use of specific inhibitors, i.e. cyanide and substituted hydroxamic acids, respectively,. monitoring chlorophyll fluorescence is also a particularly suitable method for studying the functional properties of the photosynthetic apparatus. in this field, pulse-amplitude modulated fluorimetry is the tool of choice, since it enables to monitor chlorophyll fluorescence without any interference of the actinic light applied to induce the biological response. this technology gives access to several important parameters characterizing photosynthesis, notably the quantum yield of photosystem ii and the non-photochemical quenching of chlorophyll fluorescence, which is actually made of components: qe, qt and qi –. in contrast to higher plants, state transitions have been demonstrated to be very dynamic in green microalgae, so that qt can importantly contribute to the overall npq together with qe. the unicellular green alga chlamydomonas reinhardtii is considered as a model to study the metabolism and bioenergetics of photosynthetic organisms. as shown in figure  c. reinhardtii is not only able to grow photoautotrophically by using light energy to fix co into organic molecules, but can also assimilate acetate as an exogenous organic carbon source under the form of acetyl-coa through atp-dependent enzymatic reactions. these features enable cells to grow mixotrophically in the light by harnessing inorganic and organic carbon sources, and even heterotrophically in the dark by oxidizing acetyl-coa through the glyoxylate and tricarboxylic acid cycles to promote the production of reduced cofactors and atp. the glyoxylate cycle, which bypasses the decarboxylation steps of the tca cycle, also accounts for the net biomass accumulation because its c intermediates can be used in biosynthetic pathways. an important feature of co fixation in c. reinhardtii relies on the carbon concentrating mechanism, a whole-cell enzymatic machinery enabling to increase co availability in the local environment of rubisco through the dehydration of accumulated bicarbonate to counterbalance the weak catalytic activity of the enzyme and limit its oxygenase activity under low co conditions,. the ccm consists of several isoforms of carbonic anhydrases catalyzing the interconversion of co and bicarbonate in different sub-cellular compartments but also of diverse inorganic carbon membrane transporters,. c. reinhardtii can assimilate nitrate and ammonium as inorganic nitrogen sources, but ammonium is preferred to nitrate when they are present together in the medium, consistently with the lower energy cost of ammonium assimilation,. nitrate assimilation first requires its reduction into ammonium, which can then be incorporated within organic molecules under the form of glutamate through the gs/gogat cycle in the chloroplast,. reduced cofactors and atp being necessary for inorganic nitrogen assimilation mainly originate from photophosphorylation under photoautotrophic culture conditions, but also from the glyoxylate and tca cycles coupled to oxidative phosphorylation in mixotrophically-grown cells,. as illustrated in figure  and demonstrated by recent bioinformatics- and literature-based models of the c. reinhardtii metabolic network, the assimilatory pathways of light, carbon and inorganic nitrogen are tightly interconnected through complex exchanges of metabolites, energy and reducing power which are strictly regulated in response to environmental changes to maintain cellular homeostasis –. these features strongly suggest that bioenergetics is likely to be influenced by the cumulative effect of different factors and even by interactions between some of them. however, to our knowledge, most reported studies have only focused on the qualitative or semi-quantitative influence of one or a few environmental factor on respiration and/or photosynthesis while other factors were kept constant. design of experiments coupled to multiple regression are powerful statistical tools to model the dependence of a physical, chemical or biological process to different intrinsic or extrinsic factors with a limited number of experiments. they are commonly used in diverse applied research fields, in particular for the screening of culture conditions aiming to heighten the production of biomass and/or molecules of interest by diverse organisms –. the methodology has successfully been applied to different microalgae to optimize culture medium for heterotrophic growth, starch and lipid production, co fixation as well as metabolite extraction for bio-industrial purposes –. in the present work, doe coupled to standard least squares multiple regression have been used to model the dependence of several respiratory and photosynthetic responses upon the concomitant modulation of light intensity and acetate, co nitrate and ammonium concentrations in the culture medium of c. reinhardtii. bioenergetic responses of interest have been defined as the dark cellular respiration and the apparent maximal activities of the cytochromial and alternative respiratory pathways, as well as the quantum yield of photosystem ii in saturating light, the gross o evolution and the non-photochemical quenching of chlorophyll fluorescence measured under a light intensity of μmolphotons.m− s− which is sufficient to saturate photosynthesis but not to induce photoinhibition. the main goals of this study were to determine which environmental factor induce most of the response variability mostly account for bioenergetic plasticity) and to characterize quantitatively the influence of these major explanatory factors. such goals have been achieved through a step approach consisting of a 1st-round of multiple regression aiming to detect the factor of interest, which were then selected for a 2nd-round to generate predictive models enabling to simulate the mathematical profile of their influence. we discuss the results with regards to data reported in literature and we propose biological hypotheses attempting to rationalize the present observations and to provide new promising tracks for future in-depth investigations of the molecular mechanisms underlying bioenergetic plasticity in photosynthetic organisms.  design of experiments a doe assuming first- and second-order effects was constructed on the basis of the features summarized in table  to define a limited number of combinations of values for the different environmental factors which altogether were sufficient to cover the whole design space. jmp calculated that the doe had to contain at least combinations for an unbiased subsequent modeling, and we decided to raise this number up to to ensure more confidence toward the analyses. the resulting doe is a level fractional factorial design with additional center points with some extra-points typically characterizing the central composite and box-behnken types of designs. a dimensional representative example of factor dispatching within the design space is illustrated in figure  for acetate, ammonium and nitrate concentrations. x min / m 1 x max / m 2 m, modality; xmin and xmax, minimal and maximal values of the working range; m and m modalities of co concentration. pearson's correlation coefficients were calculated to verify that altogether the different doe items were uniformly covering all directions of the design space. these analyses demonstrated that the factors did not relevantly correlate to each other. however, while also considering second-order effects, a much more important correlation was detected in a small number of cases. remarkably, an absolute correlation of approximately was systematically observed between each single factor and its combination with co concentration. this feature does not reflect a sub-optimal experimental design, but is rather an artificial bias attributable to the definition of co concentration as an ordinal factor. due to this particularity, contrarily to the other second-order interactions, the combination between co concentration and another factor cannot be expressed as a continuous product term, but rather as a component term with a specific modality for co concentration and a specific numeric value for the other interacting factor. in such a situation, calculating the correlation between a single factor and its interaction with co concentration implies to correlate this factor with itself. the observation of an absolute correlation coefficient inferior to is only attributable to the definition in doe of a different number of points for the co modalities for each value of the other interacting factor. as shown in table  an important correlation could also be noticed between squared acetate and nitrate concentrations, which indicates a lack of test points in a particular region of the design space. such a collinearity can generate a bias in modeling only if these squared concentrations are implied together in the statistical analyses. |r| the symbol "*" is used to represent second-order effects of individual factors. measurements of the responses bioenergetic responses were measured for the combinations of factors defined in doe and are summarized in additional file measurements were not replicated because a global compensation of the individual experimental errors was expected in subsequent regression processes. figure  presents typical oxymetric and chlorophyll fluorescence traces obtained for one of the center points and explains the calculations of respiratory and photosynthetic responses. it has to be noticed that cr and macyt could not be measured in a few cases but that the amount of experimental data remains nevertheless largely sufficient for an unbiased subsequent modeling. as emphasized by the high relative standard deviations of the data, every response is distributed within a wide range of values, which provides a highly favorable experimental background for regression processes. selection of the major explanatory factor the 1st-round of modeling was performed using the available set of experimental data to detect the factor accounting for most of the response variability. first- and second-order effects were assumed, i.e. it was hypothesized that the responses could depend on each factor linearly or quadratically but also on the interaction between factors. this feature rose up to the number of effects which had actually to be involved in the modeling processes, making necessary to get a previous selection to avoid any possible underestimation of important contributions. for this purpose, stepwise regressions were undertaken to define the subset of effects which would provide altogether the smallest aicc in subsequent modeling. the selected effects are listed in table  with the corresponding aicc, clearly showing that the latter is always dramatically lower than the aicc including all initial effects. cyt alt factor β p-value factor β p-value factor β p-value 4 + 4 + 4 + 4 + 4 + Φpsii 800 800 800 factor β p-value factor β p-value factor β p-value 3 − ]*[no 3 − 3 − ]*[no 3 − 3 − aiccall and aiccmod correspond to hypothetical models which would comprise every initial effects and the 1st-round models which only contain the stepwise-selected effects, respectively. rmsef standardized in terms of percentage of the average scale is displayed to facilitate error comparison among models. numbers ranging from to classify the different effects by increasing order of individual p-value, and β-weights are also provided. statistically significant p-values are surrounded by *. effects which are highlighted in bold were considered as major explanatory ones and selected for the 2nd-round of modeling. modeling was performed through standard least squares multiple regression with the stepwise-selected effects to establish a predictive mathematical equation associating a theoretical response with each of the experimental values. in equations, co concentration is present under the form of an additional extension term due to its definition as an ordinal factor: this extension is equal to zero for % co and different from zero for % co. as summarized in table  r r adjusted and fitting root-mean-square error were calculated to evaluate the goodness of fit, and whole-model and lack-of-fit anova tests were performed to assess the statistical significance of the models. rmsef was also standardized in terms of percentage of the average scale of the response in order to facilitate comparisons of regression error among models. remarkably, the statistical insignificance of lack-of-fit tests suggests that no important effect remained unselected through the stepwise regression processes. the values of r r adjusted and rmsef as well as the p-values of the whole-model anova tests tend to indicate that altogether the effects selected through stepwise regression account for an important part of the response variability. the relative contribution of the different effects to the models was further investigated by calculating anova tests and β-weights for individual effects. the absolute value of the latter parameter participates to characterize the extent to which the effect contributes to the model, and its sign assesses whether the effect exerts a positive or negative influence on the response. as shown in table , high absolute β-weights are always associated with small p-values. in most cases, β-weights and individual anova tests lead to establish the same order of importance for the different effects, with the exception of p for which light intensity exhibits a smaller p-value than squared nitrate concentration but not a higher absolute β-weight; however, the parameters similarly point out that these effects are major explanatory ones. in case of p 2 second-order effects which had been shown to correlate to each other with |r| = , i.e. squared acetate and nitrate concentrations, were selected through the stepwise regression process. these effects exhibit high absolute β-weights and small p-values comparatively to most of the other effects of the model, suggesting that the regression could have been affected by a lack of experimental data in some regions of the design space. however, the observation of an insignificant lack-of-fit anova test and of similar r adjusted and standardized rmsef values than those of the other models tend to indicate that no bias was introduced due to this correlation. as shown in table  one or several effect which do not exert any statistically significant influence can be found within the models, and considerable differences can even be observed among the relative contribution of the statistically significant effects as indicated by the important heterogeneity of their p-values and absolute β-weights. these features suggest that some effect within the models do not substantially influence the responses despite their selection through the stepwise regression processes. consequently, to avoid overfitting and select the effects which altogether are sufficient to explain most of the response variability, a trial-and-error method consisting of several steps of multiple regression was used: 1st-round effects were removed successively by descending order of p-value and modeling was tested with the remaining effects at each step of the process. the remaining effects were considered as major explanatory ones when the removal of the less important of them led to the observation of a significant lack-of-fit anova test and/or a r coefficient lower than. as expected, the selected effects had been shown to exhibit small p-values and high absolute β-weights in the 1st-round models comparatively to the unselected effects, which confirms their particularly important contribution. as emphasized in table , maximum different environmental factors over appear to be sufficient to explain an important part of the response variability. acetate concentration and light intensity are major explanatory factors for every response except for Φpsii for which light intensity is the only one. in addition, ammonium and nitrate concentrations seem to influence to a large extent respiratory and other photosynthetic responses, respectively, unlike co concentration which does not appear to be an important effector of bioenergetic plasticity. mathematical simulation of the influence of the major explanatory factor the 2nd-round of multiple regression was performed with the effects selected through the 1st-round in order to build a simplified model for each response. a few unselected first-order effects were also included in the modeling processes for npq and p because of the selection of second-order effects containing these factors. this process led to establish a simplified mathematical expression associating a new predicted response with each of the experimental values: cr= + acetate+ light− nh4+− acetate− nh4+− macyt= + acetate+ light− nh4+ maalt= + acetate+ light− nh4+− acetate− − acetate− nh4+− Φpsii800= + light npq800= − acetate− light− no3−− no3−− − acetate− light− p800= − acetate+ light+ no3−+183acetate− − no3−− an exhaustive list of the 2nd-round predicted responses is provided in additional file which also summarizes the 1st-round predicted responses obtained prior to the restriction of the models to the major explanatory factor. aicc, r r adjusted, rmsef, β-weights and anova tests for whole-model, individual effects and lack-of-fit were calculated and are summarized in figure  and additional file comparatively to the 1st-round models, the observations that r and r adjusted decreased by maximum and units, respectively, and that aicc and rmsef did not increase by more than units and 8% of the response average scale, respectively, tend to confirm that the eliminated effects did not substantially account for the response variability. as expected, β-weights and p-values of the individual anova tests are similar to those of the 1st-round, so that the relative contribution of the essential effects described in table  seems to be globally conserved. in figure  experimental values are plotted as a function of predicted responses calculated from equations  to the y = ŷ straight line and the 95%-confidence intervals of the whole-model anova tests are also represented for visual evaluation of goodness of fit and statistical significance, respectively. r r adjusted and rmsef of the different responses are shown to be ≥, ≥ and ≤47% of the response average scale, respectively, except in case of npq for which r2 =  and r adjusted = . anova test p-values appear to be inferior or equal to. in figure  contour plots representing the evolution of the experimental and predicted responses as a function of the factors exhibiting the smallest individual effect p-values are compared and reveal closely related global profiles. for Φpsii contour plots were replaced by line plots since this response was modeled with only factor in the 2nd-round. these different observations tend to confirm that altogether the effects included in the 2nd-round of modeling are sufficient to explain an important part of the response variability. figure  presents a graphical simulation of the influence of each factor as predicted by the 2nd-round models with the corresponding β-weight and individual effect anova test p-value. the mathematical profile of each factor was established by applying a specific value to the other factors of the model within equations  to to generate a new single-unknown predictive equation. in case of quadratic profile, the factor value for which the response is maximal or minimal is displayed and the β-weights and p-values are provided for the first- and second-order parameter estimates. the profile of light intensity is not presented for npq since this factor does not relevantly account for response variability per se; its presence in the model is exclusively due to a second-order interaction with acetate concentration as detailed below. as expected, in case of linear dependence, increasing and decreasing profiles are associated with positive and negative β-weights, respectively; for quadratic relationships, the type of dependence is pointed out by the sign of the β-weight of the second-order effect, which is positive for convex profiles and negative for concave ones. as illustrated in figure  cr linearly depends on acetate concentration, light intensity and ammonium concentration with p < . macyt exhibits a similar dependence upon these factors with the following parameters: β =  /p <  for acetate concentration, β =  /p =  for light intensity and β = − /p =  for ammonium concentration. maalt is linearly modulated by light intensity and ammonium concentration, and is also quadratically influenced by acetate concentration. Φpsii and p linearly increase with light intensity with p < . in addition p also quadratically depends on nitrate and acetate. npq is quadratically modulated by nitrate concentration, and also linearly decreases with acetate concentration. in most cases, mathematical profiles are not influenced by the other factors of the model since modifying their value only induces a translation of the graphs along the ordinate axis without alteration of their general shape. however, as revealed by the occurrence of product terms within equations  to, a mutual influence between the individual effects of acetate and ammonium concentrations can be observed in case of cr and maalt, as well as a strong influence of light intensity on the individual effect of acetate concentration in case of npq. the negative sign of β-weights indicates that heightening the value of one of the interacting factors leads to a decrease of the slope characterizing the profile of the other factor. in figure  the influence of each interacting factor is independently simulated for different values of the other one by the same procedure as described for figure . no graph is presented for light intensity in case of npq since this factor poorly contributes to the model whatever the acetate concentration is. remarkably, for cr and maalt, the effects of acetate and ammonium concentrations appear to be weakened and strengthened, respectively, by increasing the value of the other factor. concerning maalt, rising ammonium concentration also generates a displacement of the optimal acetate concentration towards smaller values. for npq a relevant effect of acetate concentration is only observed upon high irradiance. validation of the 2nd-round models: cross-validation and experimental validation on new random combinations in parallel to the main goals of the present study, we wondered whether the 2nd-round models could also be used as tools to predict the responses associated with any combination of factors within the range of doe. in order to investigate the predictive ability of the 2nd-round models, experimental data were divided into k =  subsets and k-fold cross-validation was undertaken. each of the test sets was compared to the corresponding training model in terms of cross-validation mean absolute error and root-mean-square error. table  presents for each response the average maecv and rmsecv summarizing the deviation of the test data sets to their respective training model, as well as the average r r adjusted, maef and rmsef summarizing the analytical error of the training models. the average scales of the different responses are also provided as a reference to assess the extent of the deviations. as shown in table  the r r adjusted, maef and rmsef of the training models are identical or very similar to those of the 2nd-round models. remarkably, the maecv and rmsecv characterizing the deviation of the test data sets to their respective training model do not exceed the analytical error of more than 37% for maecv and 21% for rmsecv, and these proportions are reduced to 29% and 12%, respectively, if p is not taken into account. r 2 2 f f 2 2 f f cv cv ev ev ma cyt ma alt Φpsii 800 npq 800 p 800 cross-validation was performed by the k-fold method with k = 5; the r r adjusted, mae and rmse presented for the training models and the test data sets are the average values compiling the iterations. for each response, the average scale is also provided as a reference to assess the importance of the deviations. r adj., r adjusted. in addition to cross-validation, the predictive ability of the 2nd-round models was also evaluated by measuring the bioenergetic responses for new randomly-generated combinations of factors with experimental replicates each. every algal culture was undertaken with % co for technical convenience since co concentration was not included in the 2nd-round models. because of the quite large standard deviations related to npq measurements, more combinations were tested for photosynthetic responses in order to increase confidence toward the general tendency of data. the predicted responses associated with the random combinations were calculated from equations  to as summarized in additional file the deviation of the experimental validation data sets to the 2nd-round models was assessed in terms of experimental validation mean absolute error and root-mean-square error; this deviation is also illustrated in figure  in which the experimental values are plotted as a function of the predicted ones. as shown in table  the maeev and rmseev of the experimental validation data are inferior to the analytical error of the 2nd-round models for cr, macyt, maalt and npq800; for Φpsii and p they exceed the analytical error of only and 27% for maeev and and 19% for rmseev, respectively. as clearly evidenced while comparing figure  and figure 8a, it has to be noticed that the responses measured for the new random combinations do not cover the full range observed in the doe study. this feature could be attributable to the random choice of the factor values for the or validation points without consideration of the responses predicted by the 2nd-round models. 4 + 3 − 2 cyt alt 800 800 800 data result from independent sets of cultures and measurements., acetate concentration. altogether, these different validation results indicate that the 2nd-round models can be used as tools to predict the responses associated with any combination of factors, with an inherent average deviation being quantified by the maef and rmsef characterizing the analytical error of the models. as deduced from table  this deviation is comprised between and 36% of the response average scale for maef and and 47% for rmsef. discussion in the present work, doe coupled to standard least squares multiple regression have been used to model the dependence of different respiratory and photosynthetic responses upon the concomitant modulation of light, carbon and inorganic nitrogen sources in the culture medium of c. reinhardtii. this methodology was applied to characterize the extent to which the different environmental factors contribute to bioenergetic plasticity as well as the mathematical profile of their influence for those accounting for most of the response variability. altogether, these analyses provide an overview of the bioenergetic adaptations resulting from global changes in culture conditions. this type of sequential statistical approach, which is commonly undertaken for the optimization of industrial production yields and the design and analysis of “-omics” experiments, had never been used to characterize the bioenergetic plasticity of photosynthetic cells. the individual influence exerted by one or a few environmental factor on the cellular bioenergetics and metabolism had extensively been studied independently, but little information was available concerning their cumulative effect and their relative contribution to bioenergetic plasticity in a context in which they vary concomitantly in the medium. the present analyses demonstrate that maximum environmental factors over are sufficient to explain most of the response variability and remarkably evidence squared effects and second-order interactions in some cases. as shown in figure  comparatively to the other responses, lower r and r adjusted characterize the 2nd-round models obtained for npq. such discrepancies could be attributable to the higher experimental error inherent to npq measurements. in order to check whether the 2nd-round models could also be used to predict the responses associated with any combination of factors within the range of doe, k-fold cross-validation and experimental validation tests on new random combinations have been undertaken. the similarity between the deviation of the validation points and the analytical error of the training or 2nd-round models tend to confirm the predictive ability of the 2nd-round models. it must nevertheless be emphasized that deviations of to 36% of the response average scale or to 47% corresponding to the analytical error of the 2nd-round models are inherent to the predictions. in literature, o evolution commonly appears to be normalized in terms of chlorophyll concentration. however, in the present analyses, it was rather chosen to use protein concentration because of the high dependence of c. reinhardtii pigment content upon culture conditions, particularly light and acetate –. our unconventional normalization strategy could therefore generate apparent discrepancies between previously reported studies and the present results in some cases. in the following sections, the authors will attempt to propose literature-based hypotheses addressing the possible biological implications of their observations. they insist on emphasizing that these hypotheses must not be considered as firm assertions, but rather aim to provide tracks for future in-depth molecular investigations. light stimulates co fixation through the calvin cycle and provides mitochondrial respiration with oxidizable substrates the gross photosynthetic o evolution and the quantum yield of photosystem ii of c. reinhardtii cells adapted to moderate light intensities have been measured under μmolphotons.m− s− under such a so-called “saturating” intensity, the electron transport rate is not limited by light availability but rather by the capacity of downstream metabolic pathways that consume photo-generated reductant and atp. in these conditions, the gross o evolution can primarily be considered as representative of the capacity of these pathways, even if numerous studies indicate that complex photosynthesis-associated o2-consuming processes can also importantly contribute in some circumstances to modulate this response in c. reinhardtii. the present analyses indicate that light intensity exerts a positive linear influence on Φpsii and p. accordingly, the maximal gross o evolution was previously reported to be doubled in c. reinhardtii cells grown under illumination of μmolphotons.m− s− comparatively to a lower illumination of μmolphotons.m− s−. these observations could be attributable to the well-known stimulation of the expression and activity of calvin cycle enzymes by light, in good agreement with the higher co fixation rates observed upon increasing illumination in c. reinhardtii. this improvement of co fixation by light was reported to be correlated to higher cellular metabolite content, respiratory o consumption and tca cycle-mediated co production, in line with the linear stimulation of cr, macyt and maalt by light which could also be detected here. for macyt and maalt, the term “apparent” is used because measurements were carried out on entire cells but not on isolated mitochondria. the availability of respiratory substrates could therefore not be directly controlled, so that the measured maximal activities could have been underestimated comparatively to the actual capacities if the intracellular reductant concentration was insufficient to saturate the mitochondrial electron transport chain in the presence of kcn or salicylhydroxamic acid. in apparent contradiction with these considerations, the present analyses did not retain co concentration as a major explanatory factor of bioenergetic plasticity. such an absence of influence had already been highlighted for the maximal gross o evolution in a previous study, in which the sum between the net o evolution monitored under μmolphotons.m− s− and the dark respiration measured before illumination was shown to be similar in low and high co2-grown c. reinhardtii cells. these observations could be explained by the existence of a low co2-inducible ccm in c. reinhardtii, by which a high co availability for rubisco is maintained in low co condition. several transcriptomic analyses demonstrated that adaptation to different co concentrations mainly occurs through the regulation of the genetic expression of ccm components but not calvin cycle enzymes in c. reinhardtii –. moreover, transferring c. reinhardtii cells from high to low co external concentration was shown to result in a transient decrease of the amount of the small and large rubisco subunits before returning to the levels characterizing high co2-grown cells. altogether, these different observations and the present ones tend to indicate that adaptation to low co environment in c. reinhardtii principally occurs through ccm induction but not calvin cycle regulation. acetate down-regulates the capacity of the calvin cycle and promotes its own uptake and storage to counteract the osmotic stress associated with high extracellular acetate concentrations the present analyses indicate that p depends on acetate concentration following a quadratic convex profile with a minimal value for  g.l−. in a previous study, the net o evolution measured under μmolphotons.m− s− was shown to decrease with acetate concentrations ranging from to  g.l− but rates had been normalized in terms of chlorophyll concentration and cultures conducted under the same saturating light intensity than that of measurements. in c. reinhardtii and chlorogonium elongatum, acetate is known to repress the expression of the genes encoding the small and large rubisco subunits, thereby lowering the capacity for co fixation through the calvin cycle –. in this context, carbon originating from acetate can substitute for up to half the photoautotrophically-generated biomass content,, and light-driven photosynthetic reactions importantly contribute to provide reductant and atp for biosynthetic acetate assimilation. in heterotrophically-grown c. reinhardtii cells, acetate storage as starch is also known to be promoted through the improvement of the expression and activity of enzymes of the glyoxylate cycle and gluconeogenesis,. in parallel to its influence on carbon metabolism, acetate inhibits c. reinhardtii heterotrophic growth beyond  g.l− in the medium. from this concentration, the osmotic potential reaches a critical value beyond which active transport processes are impaired and energy requirements for cellular maintenance are considerably heightened. interestingly, for p the present analyses point out a “concentration of inflexion” which is very close to the critical substrate inhibition concentration of  g.l−. this observation tends to indicate that p could be influenced by independent acetate-responsive metabolic processes consuming photo-generated reductant and atp: the calvin cycle and the biosynthetic assimilation of acetate. acetate stimulates mitochondrial respiration by heightening the intracellular reductant content and the capacity of the cytochrome pathway the present analyses indicate that acetate concentration exerts a positive linear influence on cr and macyt. accordingly, when grown in an acetate-containing medium, c. reinhardtii cells were previously shown to exhibit a twice-enhanced respiratory rate as well as increased transcript levels for diverse components of oxidative phosphorylation, suggesting a higher capacity of the cytochrome pathway. in parallel, maalt depends on acetate concentration following a quadratic concave profile with an optimum for  g.l− as illustrated in figure 6c, this response can nevertheless be considered as linearly stimulated up to  g.l− acetate without further increase beyond this concentration. this observation tends to indicate that substrate-saturation of the alternative pathway in the presence of kcn could be reached beyond  g.l− acetate, which would imply that aox capacity is not responsive to acetate concentration. accordingly, enhancement of the capacity of the cytochrome pathway was already suggested to contribute to the acetate-induced improvement of dark respiration without concomitant modification of aox capacity. acetate inhibits npq through repression of the lhcsr3-dependent qe component the present analyses demonstrate that acetate concentration exerts a negative linear influence on npq, but only in case of high light intensity. interestingly, the extent of qe has recently emerged as being dramatically lowered by the presence of acetate in the growth medium, as notably evidenced by finazzi and co-workers who demonstrated that qt is the major contributor to the global npq in mixotrophically-grown c. reinhardtii cells. even if the molecular mechanisms underlying the functional relationship between npq and acetate are not yet understood, the present results tend to confirm these findings and indicate that the magnitude of the inhibitory effect of acetate on qe could depend on its external concentration. recently, qe has been proposed to be mediated by lhcsr a light-harvesting complex orthologue which is only expressed upon high irradiance,. npq plasticity induced in response to changing environmental conditions could therefore be disabled in the dark and low light intensities due to the down-regulation of lhcsr these interpretations must be considered with caution due to the impossibility to distinguish the contributions of qe and qt to the global npq here. mitochondrial respiration contributes to provide nitrate assimilation with reductant through the acetate-dependent activity of aox ammonium concentration is shown here to exert a negative linear influence on cr, macyt and maalt. in selenastrum minutum, mitochondrial respiration was proposed to play a role in nitrate assimilation by acting as a trigger factor for the tca cycle. this would in turn promote the production and export of reductant in the cytoplasm and the chloroplast to support nitrate reduction. in c. reinhardtii, the enzymatic activity and genetic expression of proteins involved in nitrate assimilation are known to be repressed by ammonium,. these regulatory events are responsible for a strict control of inorganic nitrogen uptake and assimilation by ammonium availability and enable to preferentially exploit this reduced n form if nitrate is also present in the medium. such a primary control of nitrate assimilation by ammonium could rationalize the present observations with regards to the postulated role of mitochondrial respiration in this metabolic process. for maalt, ammonium concentration is the factor which explains the highest proportion of response variability. interestingly, the gene encoding aox is known to be located within a gene cluster which also encodes components of the nitrate assimilatory pathway and is tightly regulated by the nitrogen source; consequently, aox expression and capacity were shown to be induced by nitrate and repressed by ammonium in a concentration-dependent manner. with regards to the peculiar genetic localization and regulation of aox the postulated role of mitochondrial respiration in nitrate assimilation was proposed to be essentially mediated by aox, as also indicated by a recent comparative proteomic study published by our group. the present results are in good agreement with these findings. interestingly, a mutual influence could be detected between the individual effects of acetate and ammonium concentrations for cr and maalt. as illustrated in figure 7a and b, the effect of acetate concentration is attenuated by ammonium. for maalt, there is also a displacement of the optimal acetate concentration toward smaller values with increasing ammonium concentration. these results are consistent with a negative influence of ammonium concentration on aox capacity. they also tend to confirm that the involvement of mitochondrial respiration in nitrate assimilation is essentially mediated by aox since no relevant second-order interaction was retained for macyt. reciprocally, as illustrated in figure 7a and b, ammonium concentration exerts a relevant influence on cr and maalt only upon high acetate concentration. this observation tends to indicate that acetate assimilation could provide the tca cycle with oxidizable substrates to support the involvement of aox in nitrate assimilation. nitrate assimilation is retro-inhibited to prevent the deleterious effects of nitrite and ammonium intracellular accumulation the present analyses demonstrate that nitrate concentration exerts a quadratic concave influence on p with an optimum for  mm. in c. reinhardtii, photosynthesis is known to contribute to provide nitrate reduction with electrons,,, so that the rate of nitrate assimilation can influence p in the same way as for the calvin cycle. the effect of nitrate on p can therefore be thought to result from distinct metabolic processes of which the relative importance varies with nitrate concentration: substrate stimulation of reductase activity and retro-inhibition of nitrate reduction by nitrate-derived intracellular ammonium. such a retro-inhibition could attenuate the production of nitrite and ammonium and prevent the deleterious effects which would result from their intracellular accumulation,,. similarly to p npq also depends on nitrate concentration following a quadratic concave profile with an optimum for  mm. assuming that the nadph-to-atp stoechiometric ratio of nitrate assimilation is superior to the yield of photosynthesis, the reoxidation of photo-generated reductant may not be paralleled with atp turnover. this feature could result in heightening Δph across the thylakoid membrane, which would in turn stimulate high energy state chlorophyll de-excitation in an extent depending on the rate of nitrate assimilation.  in the present work, doe coupled to standard least squares multiple regression have been applied to model the dependence of respiration and photosynthesis upon light, carbon and inorganic nitrogen sources in c. reinhardtii through a step approach consisting of successive rounds of modeling. this methodology enabled to demonstrate that maximum environmental factors over account for most of the variability of the different responses and also permitted to obtain a mathematical simulation of the influence of the major explanatory factors. altogether, these results provide an overview of the adaptations of c. reinhardtii bioenergetic pathways to changing culture conditions and point out new promising tracks for future more specific investigations. in order to further characterize the molecular adaptations underlying the present functional observations, we have undertaken a doe-based comparative proteomic analysis coupled to the determination of pigment and lipid composition by chromatography, of which the results are currently being modeled. 
here, sequential statistical analyses based on design of experiments coupled to standard least squares multiple regression have been undertaken to model the dependence of respiratory and photosynthetic responses upon the concomitant modulation of light intensity as well as acetate, co nitrate and ammonium concentrations in the culture medium of chlamydomonas reinhardtii. 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. 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. altogether, the results of the 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. the main goals of these analyses were to explain response variability and to characterize quantitatively the influence of the major explanatory factor. these analyses reveal that a maximal number of environmental factors over is sufficient to explain most of the response variability, and interestingly highlight quadratic effects and second-order interactions in some cases. for each response, successive rounds of multiple regression coupled to one-way anova f-tests have been undertaken to select the major explanatory factor and mathematically simulate their influence. 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.
 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 coupled to standard least squares multiple regression have been undertaken to model the dependence of respiratory and photosynthetic responses upon the concomitant modulation of light intensity as well as acetate, co nitrate and ammonium concentrations in the culture medium of chlamydomonas reinhardtii. the main goals of these analyses were to explain response variability and to characterize quantitatively the influence of the major explanatory factor.  for each response, successive rounds of multiple regression coupled to one-way anova f-tests have been undertaken to select the major explanatory factor and mathematically simulate their influence. these analyses reveal that a maximal number of environmental factors over 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 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. statisticsbioenergeticsmetabolismnetworkplasticityenvironment 