## Abstract

We investigate the effects of trophic lifestyle and two types of major evolutionary transitions in individuality—the endosymbiotic acquisition of organelles and development of multicellularity—on organellar and cellular metabolism and allometry. We develop a quantitative framework linking the size and metabolic scaling of eukaryotic cells to the abundance, size and metabolic scaling of mitochondria and chloroplasts and analyse a newly compiled, unprecedented database representing unicellular and multicellular cells covering diverse phyla and tissues. Irrespective of cellularity, numbers and total volumes of mitochondria scale linearly with cell volume, whereas chloroplasts scale sublinearly and sizes of both organelles remain largely invariant with cell size. Our framework allows us to estimate the metabolic scaling exponents of organelles and cells. Photoautotrophic cells and organelles exhibit photosynthetic scaling exponents always less than one, whereas chemoheterotrophic cells and organelles have steeper respiratory scaling exponents close to one. Multicellularity has no discernible effect on the metabolic scaling of organelles and cells. In contrast, trophic lifestyle has a profound and uniform effect, and our results suggest that endosymbiosis fundamentally altered the metabolic scaling of free-living bacterial ancestors of mitochondria and chloroplasts, from steep ancestral scaling to a shallower scaling in their endosymbiotic descendants.

## 1. Introduction

Because cells are a fundamental unit of living organisms, the development of general theories governing their metabolism, anatomy and evolution is vital to biology. Cells exhibit tremendous diversity in architecture, function and size [1], varying by over 16 orders of magnitude in cell volume [2]. The evolution of cellular diversity involved major evolutionary transitions in individuality: the emergence of new individuals possessing heritable variation in fitness at increasingly higher levels of organization, from unicellular prokaryotes to eukaryotic unicells to multicellular eukaryotic organisms [3–6]. This hierarchical evolution entailed fundamental reorganization in the metabolic design of organisms. The proto-eukaryote's acquisition of mitochondria through the endosymbiosis of an Alphaproteobacterium resulted in the internalization of ATP-producing surfaces, thereby facilitating an increase in maximum cell size from approximately 10^{8} µm^{3} in prokaryotes to approximately 10^{13} µm^{3} in eukaryotes [2,7,8]. The subsequent endosymbiosis of cyanobacteria allowed eukaryotes to adopt phototrophic lifestyles. As both endosymbionts coevolved with their eukaryotic hosts, they evolved into host-dependent organelles—mitochondria and chloroplasts—with reduced genomes and more specialized physiologies [9]. Subsequent evolutionary innovations in cellular organization created complex new environments—multicellular organisms—which permitted differentiation into even greater varieties of cell types [10] and led to the evolution of complex intercellular transportation and signalling networks regulating cellular metabolism.

Metabolic rate—the rate of energy metabolism of a living system—is one of the most fundamental biological traits and influences a variety of traits and dynamics of living systems from organelles and cells to organisms, communities and ecosystems [11,12]. Allometric scaling functions of the form *Y* = *y*_{0}*V ^{α}* characterize relationships between a system's traits (

*Y*), such as metabolic rate, and its mass or volume (

*V*), where

*y*

_{0}is the normalization parameter and

*α*is the scaling exponent. Although the field of allometry has largely focused on the scaling of whole organisms, allometric scaling functions can also apply to individual cells within multicellular organisms and to organelles [8,13]. Historically, the scaling of metabolic rate and associated biological rates with organism size was thought to approximately follow a power law with an exponent of approximately 3/4, a scaling relationship known as ‘Kleiber's law’ considered to apply to prokaryotes, unicellular eukaryotes and multicellular organisms [14,15]. However, the mechanisms underlying observed scaling relations and generality of the relationships are controversial [16], and researchers have presented theory and data questioning the relevance of this scaling law to unicellular eukaryotes and prokaryotes [17–21]. Also, little is known about the metabolic scaling of mitochondria, chloroplasts and cells within multicellular organisms because of challenges associated with estimating the metabolic rates of the lower-level units of organisms.

In bacteria, growing evidence suggests that rates of respiration and photosynthesis largely exhibit superlinear scaling (*α* > 1), with photosynthesis apparently scaling less steeply than respiration [19,21,22]—should mitochondria and chloroplasts, which evolved from bacteria, also exhibit superlinear scaling or has endosymbiotic evolution and multicellularity fundamentally altered their scaling? In unicellular eukaryotes, respiration rate exhibits linear scaling for a variety of heterotrophic and phototrophic protists [17,19,23]. In contrast, photosynthetic rate may scale sublinearly [24–26], although others have also suggested linearity when examining scaling across size classes within a community [27–29], indicating that more research is warranted. Should these scaling relations be the same for cells of multicellular organisms, with phototrophy exhibiting shallower scaling than heterotrophy, or is cellular scaling altered in multicellular organisms by the metabolic specialization of cell types and regulation of metabolism through complex intercellular signalling and resource exchange networks? New approaches and syntheses of data are needed to elucidate the degree to which metabolic scaling relations can be altered by evolutionary and ecological factors and clarify the physiological underpinnings of observed metabolic scaling relations [30].

Researchers have proposed that the linear respiratory scaling in unicellular eukaryotes may be the result of the endosymbiotic internalization of respiratory membranes [2,8,19]. Theory shows that internalizing respiratory membranes can enable cells to achieve linear scaling of respiratory surface area, by allowing cells to increase the number of mitochondria linearly with increasing cell size while keeping mitochondrion size invariant [8,20]. The resulting linear scaling in respiratory membrane area allows aerobes to obtain linear metabolic scaling, as long as resource procurement and transport do not constrain metabolic scaling. In contrast with respiration rate, the photosynthetic rate of eukaryotic cells may typically exhibit sublinear scaling, as theory suggests that there are diminishing returns in an organism's ability to capture light energy with increasing cell size [31–33] and growth rate and biomass production rate, presumed to be proportional to photosynthetic rate, have been reported to scale sublinearly [26].

Because eukaryotic cells rely on their mitochondria and chloroplasts for energy transduction, and the volumes and per cell numbers of these organelles vary across eukaryotes by several orders of magnitude [1,34–37], integral understanding of metabolic evolution and design principles requires elucidating the rules governing the abundance, size and metabolic scaling of organelles. Unfortunately, understanding of the variation in the size, number and total volume of mitochondria and chloroplasts is limited [13,38]. Researchers have reported positive intraspecific relationships within a cell type between the total volume of mitochondria or chloroplasts and cell size [38–42]. However, few studies have examined interspecific scaling relationships. Interspecific linear scaling of total mitochondrial volume with cell size was recently reported in heterotrophic protists [20], but limited work has been done on the interspecific scaling of the number and size of mitochondria and chloroplasts, which can mediate the relationship between the scaling of cell metabolic rate and total organelle volume (as shown in the Quantitative Framework section).

These topics are also of practical concern. Changes in environmental conditions, such as carbon dioxide and water availability, can affect the size, structure and number of organelles and cells [37,43]. Developing mechanistic, predictive models of global change and ecosystem ecology—models that scale up from the metabolism of organelles and cells to populations and ecosystems—may thus require understanding the scaling rules dictating how organelle and cell size and structure influence metabolic rate [27,44].

Here, we develop a quantitative framework linking the metabolic scaling and size of eukaryotic cells to the metabolic scaling, abundance and individual size of mitochondria and chloroplasts. This framework can be used to estimate metabolic scaling exponents of organelles and cells from data on intracellular numbers of organelles, organelle size and cell size, and to clarify the functional implications of different organellar scaling strategies of cells. We thus use this framework to analyse and interpret data assembled from the published literature, which comprises 181 photoautotrophic and heterotrophic species of unicellular and multicellular eukaryotes representing 55 different cell types from diverse tissues, morphologies and ploidies. The approach allows us to investigate the scaling strategies governing the intracellular abundance and size of chloroplasts and mitochondria, the metabolic scaling of organelles and cells, and how trophic lifestyle and the major evolutionary transitions in individuality involving endosymbiosis and multicellularity affected these scaling relations.

## 2. Quantitative framework

The metabolic rate of a cell (*B*_{c}, in units of power per cell, such as J s^{−1} cell^{−1}) increases with cell volume *V*_{c} as and, analogous to whole cells, the scaling of organelle metabolic rate *B*_{org} with individual organelle volume *V*_{org} can be characterized by where *b*_{c} and *b*_{org} are normalization coefficients. In aerobic eukaryotes, the value of *B*_{c} is related to the number of organelles involved in the metabolic activity, *N*_{org} (organelles per cell), and by the unit organelle's metabolic rate, *B*_{org}, giving More specifically, *B*_{c} = *N*_{mt}*B*_{mt}/(1 − *c _{s}*) for respiration and

*B*

_{c}=

*N*

_{cp}

*B*

_{cp}for photosynthesis, defined to be the cell's net photosynthetic rate (gross photosynthesis minus photorespiration). Subscripts ‘mt’ and ‘cp’ denote mitochondria and chloroplasts, respectively.

*c*

_{s}is the proportion of total metabolic rate resulting from substrate-level phosphorylation in the cytosol. It is a small fraction of total metabolic rate, because mitochondria dominate the aerobic cell's respiration ([45]; see also electronic supplementary material).

*c*

_{s}cannot vary very much owing to the biochemistry of aerobic respiration (electronic supplementary material), so for simplicity, we make the first-order assumption that it is invariant of cell size.

Substituting into we obtain which when applied to respiration and photosynthetic rates gives
2.1*a*and
2.1*b*

Thus, larger cells can match increasing energetic demands by increasing the number and size of their organelles, as well as by increasing *b*_{org}.

In this paper, we focus on examining variation in *N*_{org} and *V*_{org}, rather than in *b*_{org}. We do this for both theoretical and practical reasons. First, there are functional trade-offs and biophysical limits to the density of enzymes on membranes [46] and the alteration of organelle geometry [8] that constrain the degree to which organisms can alter *b*_{org} (electronic supplementary material), whereas organisms can vary the number and size of organelles such as mitochondria and chloroplasts by several orders of magnitude. Thus, across many orders of magnitude variation in cell size, the primary strategies for matching increasing metabolic demand are likely to be increasing the number and/or size of organelles. Second, obtaining sufficient data to examine variation in *b*_{org} would represent a new set of challenges beyond the scope of this paper. Third, variation in *b*_{org} with cell size would not affect most of our results, affecting only our estimates of *α*_{c} and likely only by a negligible amount (electronic supplementary material). Nevertheless, an interesting future avenue of research will be to quantify variation in *b*_{org} and associated variations in organelle form and function, and so in the electronic supplementary material we present scaling theory quantifying the linkages between variation in *b*_{org}, cellular metabolic scaling, and the number, size and metabolic scaling of organelles.

Three basic scaling strategies are thus available to ensure the matching of energy supply and demand across orders of magnitude variation in cell size: (i) strategy **N**, modify only the *number* of organelles per cell; (ii) strategy **V**, modify only organelle unit *volume*; or (iii) strategy **M**, a *mixture* of changes in both organelle number and unit volume. A consequence of these strategies is that the cell's total volume of mitochondria, *V*_{MT}, and total volume of chloroplasts, *V*_{CP}, must vary positively with *V*_{c}: and , where *δ*_{mt} and *δ*_{cp} are exponents.

To empirically investigate cell and organelle metabolic scaling, we capitalize on linkages between the metabolic scaling of cells and the number, size and metabolic scaling of organelles. Substituting into equations (2.1) and re-arranging gives which log-transformed becomes
2.2where for respiration and for photosynthesis. The exponent *α*_{c} quantifies the scaling of the whole-cell respiration rate (which is dark respiration in photoautotrophic cells) when *N*_{mt} and *V*_{mt} are analysed and the scaling of whole-cell photosynthetic rate when *N*_{cp} and *V*_{cp} are analysed. With equation (2.2), multiple linear regression can be used to estimate metabolic scaling exponents, as long as there is limited collinearity between *V*_{org} and *V*_{c}. Equation (2.2) predicts that if then there should be an inverse relationship between the number of organelles per cell and organelle size, analogous to scaling relations between population abundance and body size in ecology, such as Damuth's rule [47,48].

By building on the above equations, we can make more explicit how organelle metabolic scaling exponents and the allometric scaling of the number, size and total volume of organelles underpin cellular metabolic scaling exponents. Through substitutions of , , , and into where *δ*, *r* and *q* are the scaling exponents for either mitochondria or chloroplasts and *V*_{ORG} is the total volume of mitochondria or chloroplasts, we obtain
2.3*a*and
2.3*b*

Equation (2.3*a*) show that if then cell metabolic scaling should parallel the scaling of the number of organelles, because changes in cellular metabolic scaling are underpinned by changes in the number of organelles rather than in the size of organelles. Similarly, equation 2.3*b* shows that if or *α*_{org} = 1, then cellular metabolic scaling should parallel total organelle volume scaling.

In summary, the scaling theory quantifies the linkages between the number, size and metabolic scaling of organelles and the metabolic scaling of cells. The framework can be used to interpret the functional significance of changes in the number, volume and total volume of mitochondria and chloroplasts with cell size, and it can be used to provide estimates of metabolic scaling exponents for organelles and cells.

## 3. Methods

We searched the literature using Google Scholar and Web of Science. When cell or organelle volumes were not reported, we calculated volume using reported cell major and minor axis length measurements or, when necessary, by estimating cell lengths and widths using the associated published micrographs, Matlab's image processing toolbox, and formulae for basic cell geometries [49]. Likewise, when number of organelles or total organelle volume were not reported, but a paper reported other kinds of useful data, such as organellar volume fractions, we used standard methods of quantitative microscopy, stereology and tomography to estimate these quantities [50]. The data comprise fungi, protists, multicellular algae, vascular plants, bryophytes, invertebrates, fish, mammals and the fungal and protist constituents of lichen (see electronic supplementary material, table S14 for species list). The types of cells composing multicellular organisms in our database are listed in the electronic supplementary material. We included only aerobically growing cells, because anaerobic cells make less use of their mitochondria and so different scaling rules might be expected for anaerobic cells. We classified each cell according to whether it is a unicellular organism or is a cellular unit of a multicellular organism, and whether the cell exhibited photoautotrophic or chemoheterotrophic metabolism (see electronic supplementary material, for details of operational definitions).

For multicellular organisms, averages of log_{10}-transformed data for each cell type within a species were used. For unicellular organisms, species-level averages of log_{10}-transformed data were used, with the exception of species having pronouncedly different morphologies in their different life stages, such as stages of different ploidy or amoeboid versus flagellated stages. In these cases, averages for each cell type from a given unicellular species were used. We used geometric means instead of arithmetic means because it is the conventional method in allometry and because geometric means provide a more representative measure of variation in the central tendencies of lognormal-like distributions (typical of the size distributions of living systems) while also accurately representing normal distributions. Significance levels were set at the 5% level. We used general linear models (GLMs) to determine *p*-values and effects on organelle response variables of the fixed factors cellularity and trophic lifestyle of cells and organelles (when appropriate), the covariate log cell volume, and interactions between fixed factors and the covariate.

All fitted regression lines and estimated bivariate scaling exponents in the main text were determined using reduced major axis (RMA) regression (a.k.a., geometric regression; see electronic supplementary material for details on our reasoning) on the log-transformed data. For similar reasons, there are stronger theoretical and statistical bases for employing type 2 regression when using equation (2.2) to estimate organelle and cell metabolic scaling exponents. However, multiple regression is required to estimate the metabolic scaling exponents, but no standard multiple regression techniques exist that use a type 2 regression model. We thus developed an approach that addresses this issue. Essentially, the approach consists of providing ‘GLM-adjusted’ RMA slopes, which can be calculated by taking the geometric mean of the GLM OLS slope and GLM inverse-estimated ordinary least-squares (OLS) slope for a given scaling relationship (see electronic supplementary material for details). This approach resembles RMA regression slopes, which likewise can be calculated by taking the geometric mean of the OLS and inverse-estimated OLS slopes [51]. Note that when interpreting scaling results from the literature in the Discussion and Introduction we have also chosen to use RMA exponents. When not reported, these are straightforwardly calculated by dividing a reported OLS exponent by its associated correlation coefficient [31].

## 4. Results

We found that the number of mitochondria *N*_{mt} increases linearly as in chemoheterotrophs, and slightly but significantly less steeply (*p* = 0.034) in photoautotrophs as with no significant effect of multicellularity (figure 1, *p* = 0.874, 95% CIs used herein, electronic supplementary material, table S3). Effects of cell size on mitochondrion unit volume, *V*_{mt}, are insignificant in a GLM with log*V*_{c}, trophic lifestyle, and multicellularity as predictors (*p* = 0.092, electronic supplementary material, table S4). Although in chemoheterotrophs *V*_{mt} is clearly invariant of *V*_{c} (*r*^{2} = 0.003), *V*_{mt} may increase slightly in photoautotrophs, at least in unicells (overall: *r*^{2} = 0.094, *p* = 0.18; unicells: *r*^{2} = 0.42, *p* = 0.025, exponent *q* = 0.38; multicells: *r*^{2} = 0.096, *p* = 0.102, electronic supplementary material, figure S1 and table S4); however, even in these unicells, there is much greater variance in the number of mitochondria than mitochondrion volume. Thus, mitochondria in chemoheterotrophic organisms appear to adhere strictly to strategy **N**, and although photoautotrophs emphasize strategy **N**, there is some indication that they may also rely slightly on a mixed strategy, at least in unicells.

In comparison, both the number and unit volume of chloroplasts increase significantly with *V*_{c} in unicellular and multicellular organisms, with no significant effect of multicellularity on the exponents (all *p* > 0.05): and (figure 1 and electronic supplementary material, figure S1 and table S5). However, allometric scaling of individual chloroplast volume is largely driven by cells containing a single chloroplast, all of which are unicellular (in these cells, *r*^{2} = 0.96, electronic supplementary material, figure S2), whereas little of the variation in chloroplast volume is explained by cell size in cells with more than one chloroplast (*r*^{2} = 0.25). Also, across all cells, cell volume explains much less of the variation in chloroplast volume compared with the number of chloroplasts (38% compared with 19%). Thus, multicellular chloroplasts predominantly adhere to strategy **N**; however, there is strong evidence of a mixed strategy **M** for chloroplasts in unicells.

The total mitochondrial and chloroplast volumes increase with cell volume across an immense range of sizes, taxonomic affiliations and cell types (figure 2). GLM analyses suggest that neither the slope (exponent) nor the intercept were significantly affected by multicellularity (all *p* > 0.40, electronic supplementary material, table S1–S2 and text). However, scaling differs between trophic groups: chemoheterotrophs exhibit clear linear scaling for mitochondria (*δ*_{mt} = 1.06 ± 0.09), whereas photoautotrophs exhibit shallower, but near-linear scaling for mitochondria (*δ*_{mt} = 0.89 ± 0.11) and clear sublinear scaling for chloroplasts (*δ*_{cp} = 0.83 ± 0.09). Because mitochondrion size is invariant of cell size in heterotrophs, cell metabolic scaling in heterotrophs should also be linear, paralleling the observed linear scaling of the number and total volume of mitochondria (see equations (2.3)).

We can use GLMs and equation (2.2) to estimate organellar and cellular metabolic scaling exponents, because we found limited collinearity between organelle size and cell size (electronic supplementary material, tables S4 and S6, figure S1; see electronic supplementary material text for methodological details). We found that metabolic scaling exponents for mitochondria, chloroplasts and cells appear to be largely independent of multicellularity, with organellar metabolic scaling apparently different from their prokaryotic ancestors. GLMs did not identify a significant effect of multicellularity on the respiratory rate scaling of mitochondria and cells (all *p* > 0.17), and mitochondria and entire cells both exhibit linear respiratory rate scaling (CIs overlap with one: table 1). Photosynthetic rate scaling of chloroplasts is indistinguishable between unicellular and multicellular organisms (*p* = 0.53), and both chloroplasts and cells exhibit similar sublinear photosynthetic scaling with exponents of 0.844 and 0.837, respectively (CIs do not overlap with one). A notable exception is that, unlike vascular plants, a large number of unicellular algae host only a single chloroplast. Unfortunately, our database contains an insufficient number of species of unicells hosting more than one chloroplast (and for which we also have chloroplast unit volume data) to explore differences in photosynthetic scaling between cells of unicellular and multicellular organisms. However, given that the scaling of total chloroplast volume, number of chloroplasts and chloroplast unit volume with cell size (as well as the scaling of chloroplast photosynthetic rate with chloroplast size) do not differ between unicellular and multicellular organisms, our analyses suggest that whole-cell photosynthetic scaling is similarly invariant of cellular organization (see electronic supplementary material, text).

In contrast, we found fundamental differences between respiratory and photosynthetic scaling and significant effects of trophic group on respiratory scaling of cells. Respiratory scaling relations in organelles and cells are approximately linear (95% CIs overlap with one), whereas photosynthetic scaling relations of organelles and cells are all clearly sublinear (95% CIs do not overlap with one). GLM analysis further indicates that whole-cell respiratory scaling is significantly higher than whole-cell photosynthetic scaling (*p* = 0.04, electronic supplementary material, table S13). Host cell trophic group also influences whole-cell respiratory scaling: although whole-cell respiratory scaling is near-linear in both chemoheterotrophs and photoautotrophs, it is significantly lower in photoautotrophs than chemoheterotrophs, as instead of (*p* = 0.02, electronic supplementary material, table S7).

## 5. Discussion

By documenting, comparing and contrasting scaling relations in the number, size and total volume of mitochondria and chloroplasts across diverse species and niches, our results help clarify the organelle scaling strategies of cells, as well as raise questions warranting further investigation. When it comes to their mitochondria, cells predominantly follow strategy **N**, increasing the number of mitochondria while keeping mitochondrion size invariant with increasing cell size. Having multiple smaller mitochondria provides cells with multiple locations for oxidative phosphorylation and other metabolic functions of mitochondria, allowing cells to more readily supply ATP and other metabolites to various parts of the cell, to more readily access resources (e.g. oxygen) from throughout the cell, and to facilitate crucial communication and transport between the nucleus and mitochondria by decreasing the average distance between these organelles [7,52]. For example, in plant cells, the numerous mitochondria are often co-located next to chloroplasts (producers of oxygen), following the chloroplasts as they move in response to changing light conditions [53]. Also, significantly increasing the size of mitochondria may require more substantial evolutionary changes than increasing the number of mitochondria. In contrast with heterotrophs and multicellular phototrophs, the data indicate that unicellular phototrophs may increase the size of their mitochondria slightly in addition to their number of mitochondria, but more research is required to establish the significance of this scaling.

Chloroplasts from multicellular organisms also adhere to strategy **N**; however, there is evidence of a mixed strategy **M** for chloroplasts in unicellular cells—a variety of unicellular algae of varying sizes have only one chloroplast. The observed sublinear scaling in the number and total volume of chloroplasts approximately parallels reported sublinear scaling of pigment content per cell in algae [26]. The parallel scaling implies that the amount of chlorophyll per chloroplast is roughly invariant of cell size in unicells having more than one chloroplast. Because chloroplasts apparently exhibit sublinear metabolic scaling, increasing the number of chloroplasts rather than the size of a single chloroplasts is the strategy that, all else being equal, maximizes photosynthetic capacity (see electronic supplementary material). The adoption of strategy **N** in plant cells is thus consistent with the presumed role of photosynthetic leaf cells—to maximize carbon fixation.

Another benefit of having multiple chloroplasts is that it allows cells to move their chloroplasts into different spatial configurations in response to changing conditions, For example, some cells configure their chloroplasts to reduce their exposure to light under damaging high-light conditions, such as by stacking the organelles as vertical columns. This benefit has been proposed to be the reason why land plants evolved to have multiple chloroplasts in their photosynthetic cells [54]. In many aquatic unicells, altering the spatial arrangement of chloroplasts may no longer effectively alter exposure to photoradiation, as some cells cannot readily maintain a constant orientation (aspect) in the water and also turbidity leads to light scattering [55]. It is also possible that a single larger chloroplast requires fewer resources to build and maintain than multiple chloroplasts having the equivalent photosynthetic capacity. For example, with multiple chloroplasts, more chloroplast DNA must be regularly repaired and more resources may have to be devoted to elaborate cytoskeletal structures necessary to position and move chloroplasts through the cell. So, it may be that the reduced benefits of having multiple chloroplasts in aquatic unicellular algae are outweighed by the costs of maintaining multiple chloroplasts.

Although our results point to general scaling strategies employed by cells, there is also considerable unexplained variation in the number and size of organelles. An important line of future investigation will be to determine the degree to which this variation reflects the niches of species and cell types, positioning of cells within tissues of plants and animals, varying environmental conditions [37,56] and evolutionary contingencies. For example, many phytoplankton acquired chloroplasts through secondary or tertiary endosymbiosis—by hosting a eukaryotic endosymbiont already containing a chloroplast [57,58]. The evolution of these species thus involved a greater number of evolutionary transitions in individuality that may have consequences for their form and function. Owing to often having multiple layers of membranes and relic structures, which the host species has not yet had sufficient evolutionary time to streamline, these species may not be able to accommodate as many chloroplasts.

By providing one of the first tests of theory proposed to explain linear metabolic scaling of respiration rate in protists [8,19,20], our findings shed light on the mechanisms underpinning metabolic scaling relations and regulating cellular metabolism. The theory suggests that eukaryotic cells attain linear metabolic scaling by linearly increasing the number of mitochondria, and thus respiratory membrane area, with cell size, allowing aerobes to obtain linear metabolic scaling so long as resource procurement and transport do not constrain metabolic scaling. Our results are consistent with these predictions, suggesting that resource acquisition and transport do not constrain scaling in these cells. Furthermore, our findings provide further evidence that unicellular eukaryotes do not commonly follow Kleiber's three-quarter power law or even sublinear respiratory scaling more generally, and they suggest that cells of multicellular eukaryotes also exhibit linear respiratory scaling rather than three-quarter scaling (95% CIs of exponent do not overlap with 0.75).

Our finding of sublinear scaling of photosynthetic rate adds to a growing body of research pointing to a tendency for photosynthetic rates to exhibit sublinear interspecific allometric scaling in eukaryotic algae [24–26]. The observed sublinear scaling of chloroplast and host cell photosynthetic rate is consistent with theory and physiological models, which predict that photoautotrophic cells should exhibit sublinear scaling of photosynthetic rate because of diminishing returns in their ability to capture light energy with increasing cell size (e.g. from the ‘package effect’; [31–33]). Because the whole-cell respiration rate in photoautotrophic cells scales linearly even though photosynthetic rate scales sublinearly, our results suggest that photosynthetic rates in smaller cells do not impose a strong constraint on respiratory scaling; otherwise, respiration would have to scale similarly to photosynthesis in order to avoid outpacing photosynthetic scaling with increasing size and the concomitant mismatching of energy supply and demand. However, the observed slightly but significantly shallower scaling of respiration in photoautotrophs compared with heterotrophs points to a constraint on respiratory scaling that is unique to photoautotrophs, which is likely a consequence of the shallower scaling of photosynthesis. The difference in scaling between respiration and photosynthetic rate in photoautotrophs implies a decrease in energetic efficiency with increasing cell size—that a greater proportion of the carbon fixed in larger cells is allocated to mitochondrial respiration (dark respiration) and so unavailable for use in carbon storage and biomass growth. Thus, larger photoautotrophic cells may increasingly face constraints related to obtaining and allocating carbon to growth and reproduction.

Interpreting metabolic scaling relations within the context of major evolutionary transitions in individuality elucidates these transitions' effects on metabolic design. Our analyses suggest that the transitions in individuality accompanying the endosymbiosis of mitochondria and chloroplasts fundamentally altered the metabolic scaling of both the newly incorporated lower-level units—mitochondria and chloroplasts—as well as of the eukaryotic host cells. Endosymbiosis of the proto-mitochondrion apparently led to linear respiratory scaling in eukaryotic cells, as well as altering the proto-mitochondrion's metabolic scaling from steep superlinearity in chemoheterotrophic bacteria [19,21] to the near-linearity observed here in mitochondria. Endosymbiosis of proto-chloroplasts altered their photosynthetic scaling from apparently superlinearity in cyanobacteria [22] to sublinearity in chloroplasts. These shifts are consistent with arguments proposing the observed superlinearity results from increased genome and metabolic network size associated with increasing cell size [19]. The increased metabolic network size enhances catabolic capabilities of the network [59], and the larger genome size also accommodates higher numbers of copies of highly expressed genes, such as rRNA genes, allowing higher rates of transcription, translation and biosynthesis necessary for maintaining the catabolic networks fuelling high metabolic rates [60]. Because mitochondria and chloroplasts have reduced genomes and specialized metabolic networks, they are unlikely to benefit from these effects and so succumb to surface, light and transportation constraints imposing shallower scaling. Endosymbiosis of proto-chloroplast cyanobacteria also fundamentally altered their host cell's metabolic scaling—the resulting phototrophic lifestyles led to shallower metabolic scaling. In contrast, multicellular evolution apparently had little effect on cell and organelle metabolic scaling, suggesting a conservation of general design principles governing the metabolism of eukaryotic cells.

## Data accessibility

We are in the process of curating our database to publish it as a data paper. In the interim, the data used to conduct our analyses are available upon request.

## Authors' contributions

J.O. and V.S. designed the research; J.O., V.S., and M.M. collected data; J.O. and V.S. performed graphical and statistical analyses; J.O. contributed new reagents/analytic tools; J.O. and V.S. wrote the paper; M.M. provided feedback during manuscript preparation.

## Competing interests

We have no competing interests.

## Funding

Support to J.O. was provided by a NASA Astrobiology Institute Postdoctoral Fellowship and an Exploration Postdoctoral Fellowship from the Arizona State University's School of Earth and Space Exploration.

## Acknowledgements

We dedicate this paper to Dr. Val Smith, who was an integral part of the research and writing of this paper. Dr. Smith passed away just a week before this manuscript was accepted for publication. He was a professor at University of Kansas for more than 20 years, devoting his outstanding research to a variety of disciplines, from phytoplankton ecology to biofuels and disease ecology. Dr. Smith had a deeply caring and energetic personality, and his inspiring enthusiasm for science will always remain with us. He will be greatly missed as our friend and mentor. We also thank J.H. Brown for his feedback and support in the early stages of the project and anonymous reviewers for their thoughtful feedback.

- Received March 16, 2016.
- Accepted April 22, 2016.

- © 2016 The Author(s)

Published by the Royal Society. All rights reserved.