Abstract
Kleiber’s law, or the ¾-power law scaling of the metabolic rate with body mass, is considered one of the few quantitative laws in biology, yet its physiological basis remains unknown. Here, we report Kleiber’s law scaling in the planarian Schmidtea mediterranea. Its reversible and life history-independent changes in adult body size over 2 orders of magnitude reveal that Kleiber’s law does not emerge from the size-dependent decrease in cellular metabolic rate, but from a size-dependent increase in mass per cell. Through a combination of experiment and theoretical analysis of the organismal energy balance, we further show that the mass allometry is caused by body size dependent energy storage. Our results reveal the physiological origins of Kleiber’s law in planarians and thus have general implications for understanding a fundamental scaling law in biology.
Introduction
Body size varies strikingly across animal phylogeny. From small crustaceans weighing a few ng to Blue Whales weighing in excess of 150 000 kg, body mass variations span more than 16 orders of magnitude (Makarieva et al., 2008; Sears & Calambokidis, 2002). In spite of such tremendous variation in scale and physiology, the organismal metabolic rate (P; defined as the heat produced by the organism per unit time measured in Watts, which is related to the rate of oxygen consumption (McDonald, 2002)) nevertheless follows a general scaling relationship with body mass (M). As originally described by Kleiber in 1932 (Max Kleiber, 1932), P can be expressed by a power-law of the form P = aMb, with b being the scaling exponent and a proportionality constant a. Although reported values of b vary somewhat between studies or specific animal species, a value of b ≈ ¾ is typically observed (Banavar, Cooke, Rinaldo, & Maritan, 2014; Blaxter, 1989; Brody, 1945; Calder, 1984; Hemmingsen, 1960; M Kleiber, 1961; Peters, 1983; Schmidt-Nielsen, 1984; G B West & Brown, 2005; Whitfield, 2006) and this allometric relation between mass and metabolic rate is consequently referred to as the “three-quarter” or “Kleiber’s law”. This implies that the specific metabolic rate (P/M) decreases as body mass increases, which is commonly interpreted as reflecting a size-dependent decrease of cellular metabolic rates. Surprisingly, despite being known since more than 80 years and termed one of the few quantitative laws in biology (Geoffrey B West, 1999), the physiological basis of Kleiber’s law remains under intense debate. The fact that all animals, irrespective of physiology, habitat or life style, obey Kleiber’s law suggests a fundamental constraint in animal metabolism (G B West & Brown, 2005). Many hypotheses have been proposed that suggest a variety of origins of Kleiber’s law. A major class of hypotheses are based on internal physical constraints (Glazier, 2005), for example space-filling fractal transportation networks (Goeffrey B West, Brown, & Enquist, 1997) or size-dependent limitation of resource transport across external and internal body surfaces (Davison, 1955; Mcmahon, 1973). Another class of hypotheses concerns external ecological constraints, for example the optimization of body size for maximising reproductive fitness (Kozlowski & Weiner, 1997). However, experimental validations have proven difficult, due to inter-species differences in anatomy or ageing-associated physiological changes within a species. As a result, all hypotheses regarding the origins of Kleiber’s law remain controversial also because a suitable model system has not been established.
Flatworm laboratory models offer interesting opportunities in this respect. Although usually studied for their regenerative abilities and pluripotent adult stem cells (Reddien & Alvarado, 2004; Rink, 2012; Saló & Agata, 2012), the model species S. mediterranea and other planarians display tremendous changes in body size. They grow when fed and literally shrink when starving (Baguñà et al., 1990), which in S. mediterranea amounts to reversible body length fluctuations between ~0.5 mm and ~20 mm. Such >40-fold changes in body length in a laboratory model facilitate quantifications of P and M as pre-condition for applying and testing of theoretical approaches. Moreover, the commonly studied asexual strain of S. mediterranea and other asexual planarians do not seem to age, thus rendering their reversible size changes independent of organismal aging (Glazier, 2005). Previous studies of metabolic rate scaling in planarians suggest a size-dependence of O2-consumption (Daly & Matthews, 1982; Hyman, 1919), but the size dependence of P has so far not been systematically quantified. We here report that metabolic rate scaling in S. mediterranea indeed follows Kleiber’s law and we apply a combination of experiments and theory to understand its physiological basis. Our analysis of the organismal energy balance reveals that the size-dependent decrease in the specific metabolic rate does not reflect a decrease in the metabolic rate per cell, but instead an increase in the mass per cell. Further, we demonstrate that the cell mass allometry reflects a size-dependent increase in lipid and glycogen stores. Our results therefore demonstrate that size-dependent energy storage causes Kleiber’s law scaling in planarians.
Results
Planarians display Kleiber’s law scaling of the metabolic rate
Kleiber’s law describes the scaling of metabolic rate with the mass of animals. In order to test whether the tremendous body size fluctuations of S. mediterranea (Figure 1A) follow Kleiber’s law, we needed to devise methods to accurately quantify the mass and metabolic rate of planarians.
To measure mass, we quantified both the dry and wet mass of individual planarians. Though dry mass measurements avoid the challenging removal of residual water from the mucus-coated animals, they are lethal and can therefore only be carried out once. As shown in Figure 1B, the wet and dry mass of S. mediterranea vary over > 2 orders of magnitude. Moreover, the near-constant ratio between wet and dry mass (~ 5; implying 80% water content) indicates minimal variations of the water content and thus facile interconversion of the two mass measurements.
In order to quantify metabolic rate, we measured the heat generated by live planarians of different sizes via microcalorimetry. Microcalorimetry measures the integrated heat generated by metabolic processes inside the animal and therefore provides a pathway-independent measure of total metabolic activity (Kemp & Guan, 1997). Cohorts of equally-sized 2 week-starved animals were enclosed in vials and their heat emission measured over a period of > 24 h (Figure 1 – figure supplement 1). Since animals were not immobilized, our measurements effectively reflect the routine metabolic rate that is generally used for aquatic animals (Dall, 1986). As shown in Figure 1C, the metabolic rate measurements increase with mass over nearly 3 orders of magnitude (from ~ 0.02 to 10 µW). The data points can be fit with a single power law that accurately describes the size-dependence of the metabolic rate across the entire size range. Intriguingly, the value of the scale exponent is 0.75 ± 0.01 and thus identical with the ~ 0.75 exponent associated with Kleiber’s law in inter-species comparisons. Consequently, the slope of the planarian data points (red) exactly parallels the characteristic slope of extensive published data sets of specific metabolic rate measurements (Makarieva et al., 2008) (Figure 1D). While the offsets between endo-and ectotherm traces might reflect different temperature regimes as previously noted (Hemmingsen, 1960; Makarieva et al., 2008), the common slopes stresses the universal nature of the ¾ law exponent across animal phylogeny. The fact that the same power law exponent is associated with the entire growth/degrowth-dependent body size interval of a planarian suggests that the same underlying principles are at work and that S. mediterranea is therefore a suitable model system for probing the physiological basis of Kleiber’s law.
Size-dependence of planarian growth/degrowth dynamics
The physiological causes of planarian body size fluctuations are growth and degrowth. Therefore, understanding their underlying regulation might provide insights into the size-dependence of the metabolic rate. Planarian body size measurements are challenging due to their soft and highly deformable bodies. We therefore adapted our semi-automated live-imaging pipeline that extracts size measurements from multiple movie frames displaying the animals in an extended body posture (Werner, Rink, Riedel-Kruse, & Friedrich, 2014). We found that plan area provides the most robust size measure (Figure 2 – figure supplement 1 and (Werner et al., 2014)), which we therefore use in the following. One first important question is to what extent size changes reflect a change in cell number. Since previous cell number estimates produced conflicting results (Romero & Baguñà, 1991; Takeda, Nishimura, & Agata, 2009) we developed two independent assays. First, we combined cell dissociation (Romero & Baguñà, 1991) with automated counting of fluorescently stained nuclei (Figure 2A, top and Figure 2 – figure supplement 2). Second, we used quantitative Western blotting to quantify the amount of the core Histone H3 in whole worm lysates, which we found to increase linearly with the number of cells (Figure 2A, bottom). Applying both assays to individually sized S. mediterranea revealed a close agreement between the two methods and scaling of cell numbers with plan area by a power law with the exponent 1.19 (Figure 2B), consistent with the previous conclusion that planarian body size changes largely reflect changes in cell numbers (Baguñà et al., 1990). Further, knowledge of the cell number/area scaling law allows the accurate interconversion of plan area into cell numbers in the experiments below.
To measure growth and degrowth rates, we quantified the change in plan area of individual S. mediterranea subjected to feeding at regular time intervals (Figure 2C) or continuous starvation (Figure 2D). Although individual measurements were noisy due to the aforementioned size quantification challenges, the data on >100 animals cumulatively reveal stereotypic time trajectories for both growth and degrowth (Figure 2C-D, insets). Therefore, planarian growth and degrowth dynamics are highly coordinated at the organismal level and our data are suitable for extracting the underlying rate constants. As shown in Figure 2E, we found that the growth rate of S. mediterranea decreases with body size, consistent with previous data (Baguñà et al., 1990). Unexpectedly, our analysis additionally revealed a similar size dependence of the degrowth rate. Interestingly, both growth and degrowth rates appeared to be largely independent of feeding history and thus solely a function of size (Figure 2 – figure supplement 3A). Taken together, our findings demonstrate that not only the specific metabolic rate (Figure 1C-D), but also the growth/degrowth rates decrease with body size in S. mediterranea.
Systems-level control of planarian growth dynamics
Since growth reflects the metabolic assimilation of environmental resources and degrowth their subsequent catabolism, both are related to the overall metabolic rate of the animal. Therefore, the size dependence of growth/degrowth (Figure 2E) and metabolic rate (Figure 1C-D) might reflect a common physiological origin of the underlying scaling laws. We therefore devised a theoretical framework of planarian growth/degrowth as a function of the metabolic energy budget (Figure 3A). The central element of our model and previous approaches (Hou et al., 2008; Kooijman, 2009) is the organismal energy content E, which represents the sum of all physiologically accessible energy stores (e.g., carbohydrates, lipids and proteins). The energy content E fuels all metabolic processes within the animal, which collectively convert E into heat as measured by our microcalorimetry approach (Figure 1C-D). Hence, starvation results in a decrease of E, overall net catabolism and degrowth. However, E increases if the influx of energy obtained from the food (J) exceeds the energy lost through heat (P), which leads to net assimilation of resources and thus growth. The fact that planarians grow/degrow largely by a change in total cell numbers (Figure 2B) (Baguñà et al., 1990; Romero & Baguñà, 1991), fundamentally interconnects the organismal energy balance to organismal cell numbers. While excess energy from food intake stimulates increased cell proliferation (Baguñà, 1974) and growth, a starvation-induced net loss of energy decreases total cell numbers and thus, body size. Therefore, our framework relates changes in cell number during growth/degrowth to the energy content of the animal (Figure 3A). Importantly, our model does not make any assumptions regarding the underlying cellular or metabolic mechanisms, but simply states the physical energy balance of planarians.
With our quantitative data as experimental constraint (Figure 2C-E), the model allows us to explore hypothetical systems-level control paradigms of growth/degrowth dynamics (see also Figure 3 – figure supplement 1). In the first paradigm (Figure 3B, left column), dynamic changes in the organismal energy content depend on feeding conditions. Changes in cell number (e.g., rates of cell division and/or cell death) depend on the energy content per cell (Figure 3 – figure supplement 2). Consequently, two planarians with the same cell number might have different energy levels depending on the respective feeding history. In paradigm 2 (Figure 3B, centre column), the energy content is proportional to total cell number, i.e. it scales isometrically. Thus, growth occurs when “surplus” energy obtained from food is converted into new cells, whereas degrowth is the consequence of catabolism of existing cells in order to replenish metabolic energy. In paradigm 3, the energy content is also tightly coupled to cell number, but scales in a size-dependent manner with a characteristic exponent c, i.e. it scales allometrically. Theoretical analysis reveals that all three paradigms can approximate the measured growth/degrowth dynamics (Figure 3C). However, they differ in their specific predictions of the scaling behaviours of E, P and J with organismal cell number N (Figure 3B).
In order to experimentally distinguish between the paradigms, we consequently quantified E, P and J as a function of cell number (N). In order to obtain values for P/N (metabolic rate/cell), we converted our measurements of P as a function of dry mass (Figure 1 – figure supplement 1B) using the scaling laws for N and dry mass with plan area (Figure 2B and Figure 3 – figure supplement 3A). As shown in Figure 3D, the P/N estimates are of the order of 1 pW, similar to the average metabolic rate of a human cell (Bianconi et al., 2013; Purves & Sadava, 2004). Further, P/N is essentially independent of organismal cell number and animal size (scale exponent 0.05 +/-0.02), which rules out paradigm 2 (Figure 3B) as possible control principle. The size independence of P/N is further intriguing, as it implies that the size dependence of P/M as foundational basis of Kleiber’s law originates from size dependencies of M/N (mass per cell; see below).
To measure the food intake J, we developed an assay based on the homogenous dispersion of a known amount of small fluorescent beads in a known volume of planarian sustenance food (liver paste). Lysis of pre-sized animals immediately after feeding and quantification of bead numbers in the lysate thus provided a measure of the ingested food volume as a function of size (Figure 3 – figure supplement 3B-D). Although individual measurements varied significantly (likely reflecting inter-animal differences under our ad libitum feeding conditions), J/N did not display a clear size dependence (exponent 0.00 ± 0.03) (Figure 3E). Therefore, the volume of ingested food and thus energy uptake remains proportional to organismal cell number across the entire size range, which argues against both paradigms 1 and 2 (Figure 3B).
To approximate the energy content E of entire worms, we turned to bomb calorimetry. This method quantifies the heat release upon complete combustion of dried tissue in pure oxygen, thus providing a measure of gross energy content (McDonald, 2002). Our assay conditions allowed reproducible quantification of E of as little as 3 mg of dried tissue (Figure 3 – figure supplement 3E), corresponding to 200 planarians of a length of 2 mm (Figure 3 – figure supplement 3A and Figure 2 – figure supplement 1D). Intriguingly, E/N significantly increased with organismal cell numbers (scaling exponent 0.38 ± 0.03, Figure 3F), as assumed by paradigm 3 (Figure 3B). Moreover, the experimentally measured scaling exponent of the energy content agrees quantitatively with the prediction of paradigm 3 on basis of the experimentally measured growth/degrowth rates (Figure 3F; black solid line). The experimentally measured gross energy content and the physiologically accessible energy content E (green and black solid lines in Figure 3F) differ by a constant factor (2). The fact that the scaling exponent follows the prediction of paradigm 3 demonstrates the quantitative agreement between model and experiment and identifies size-dependent energy storage as systems-level control paradigm of planarian growth/degrowth dynamics.
Size dependence of physiological energy stores
Since animals store energy in the form of biochemical compounds, size-dependent energy storage should consequently result in biochemically measurable effects. Little is currently known about planarian energy metabolism, but animals generally store metabolic energy in the form of triglycerides (TGs) inside lipid droplets (Birsoy, Festuccia, & Laplante, 2013). We therefore stained cross-sections of large and small animals with the lipid droplet marker LD540 (Spandl, White, Peychl, & Thiele, 2009). Both revealed prominent lipid droplets primarily within the intestinal epithelium, thus suggesting that the planarian intestine serves as a fat storage organ, as in C. elegans (Mak, 2012). However, the amount and size of the droplets per cell notably increased in large animals (Figure 4A). To obtain a quantitative measure of the lipid content size-dependence, we optimized total lipid extraction for planarians (Figure 4 – figure supplement 1A) and used mass spectrometry to measure the absolute amounts of various lipid classes (Figure 4 – figure supplement 1B). The 88-fold increase in TGs per unit cell in large planarians as compared to small animals (Figure 4B) demonstrates a striking size dependence of lipid stores in S. mediterranea.
To further assess a possible size dependence of carbohydrate stores, we applied Best’s Carmine stain to cross-sections of large and small animals in order to probe for glycogen granules (Figure 4C, left). Comparison between adjacent sections with and without amyloglucosidase pre-treatment as specificity control (Figure 4C, right) together with the expression patterns of glycogen synthesis genes (Figure 4 – figure supplement 1C) both indicate a storage role of the planarian intestine for glycogen granules, thus again emphasizing the organ’s likely central role in energy homeostasis. Interestingly, also the intensity of glycogen staining appeared stronger in large animals (Figure 4C, right) and the quantification of glycogen content in animal extracts by an enzyme-based assay (Figure 4 – figure supplement 1D-F) demonstrated a > 8-fold increase in the amount of glycogen/cell in large over small animals (Figure 4). Therefore, both the lipid and carbohydrates stores are strongly size-dependent in S. mediterranea, which conclusively confirms our model’s prediction of size-dependent energy storage as a systems-level control paradigm of planarian growth and degrowth.
Energy reserves and cell number govern Kleiber’s law in planarians
The size-dependent increase in the mass of lipid and glycogen stores is intriguing also in light of the previous indications that Kleiber’s law in planarians might originate from a size-dependent increase in mass per cell, rather than a decrease in metabolic rate (Figure 3D). To explore this potential link between the regulation of growth dynamics and Kleiber’s law, we first investigated the relative contributions of mass allometries to the emergence of the ¾ exponent. As a direct test, we derived the size dependence of cell numbers versus mass, using the various scaling laws established during the course of this study. As shown in Figure 5A, cell numbers scale with wet and dry mass with scale exponents of 0.74 ± 0.01 and 0.72 ± 0.01, respectively. This demonstrates that the mass per cell indeed increases disproportionately with size and with a very similar scaling exponent as for Kleiber’s law (Figure 1C). In conjunction with the practically size-independent scaling of cell number and metabolic rate (Figure 5B, scaling exponent 0.96 ± 0.02), these data demonstrate conclusively that the ¾ exponent of the metabolic rate/mass scaling law derives from the underlying scaling law of mass/cell.
To quantitatively assess the contributions of energy stores to the mass/cell scaling exponent and thus to Kleiber’s law, we analysed the composition of the dry mass in small, medium and large animals. In addition to storage lipids and glycogen, we quantified total protein (Figure 5 – figure supplement 1A), non-glycogen carbohydrates (Figure 5 – figure supplement 1B-C) and other polar and non-polar lipids (Figure 4 – figure supplement 1B). In comparison with the 8 and 88-fold increase of glycogen and TG contributions to dry mass/cell, the relative contribution of protein, other polar/non-polar lipids and non-glycogen carbohydrates varied less between small and large animals (Figure 5C). Our quantitative assays further allowed us to assess the absolute mass contribution of each compound class to the size-dependent dry mass increase and thus to the origins of the ¾ exponent. Intriguingly, the latter was largely explained by the mass of triglycerides and glycogen, with additional minor contributions from other carbohydrates, polar/non-polar lipids and protein (Figure 5C). Overall, our results therefore demonstrate that size-dependent energy storage causes Kleiber’s law scaling in S. mediterranea.
Discussion
Here, we make use of the dramatic and reversible body size changes in the planarian S. mediterranea to probe the physiological basis of Kleiber’s law. Contrary to comparative approaches that generally start from a priori assumptions and subsequently examine large multi-species data sets for supporting evidence, our finding that planarians obey Kleiber’s law scaling allows us to bring an experimental approach in a model system to bear on the problem. Growth/degrowth in asexual planarians (e.g., the strain examined here) reversibly scales the size of a fully developed adult body plan. This likely exposes size-dependent physiological constraints more clearly than in other animals, where ontogenic growth is often accompanied by developmental changes. Our combination of quantitative and theoretical analysis of growth and degrowth dynamics demonstrate that Kleiber’s law scaling in planarians originates not from a size-dependent decrease in specific metabolic rate, but from a size-dependent increase in average cellular mass. Further, our demonstration that the ¾ exponent is largely caused by size-dependent lipid and glycogen stores firmly ties the physiological origins of planarian Kleiber’s law scaling to energy metabolism. To our knowledge, our results provide a first experimentally founded demonstration of the physiological origins of Kleiber’s law scaling in an animal species.
The fact that we find the cellular metabolic rate to be size-independent contrasts with multiple proposals that envisage the origins of Kleiber’s law in a size-dependent decrease of cellular metabolic activity, e.g., by decreasing mitochondrial density (Smith, 1956). However, our use of microcalorimetry as a pathway-independent read-out of the post-absorptive metabolic rate leaves open the possibility of size-dependencies in the use of specific metabolic pathways. In this context, it is interesting to note that the ratio between our experimentally measured gross energy content (by bomb calorimetry) and net energy usage (modelling of growth dynamics data on basis of paradigm 3; Figure 3B) remains constant across the entire size range (Figure 3F). This entails that the metabolic processes that assimilate ingested food or catabolise energy stores are largely size-independent (constant food conversion rate of 2.6, in line with other aquatic organisms (Tacon & Metian, 2008); Figure 3 – figure supplement 3F). Instead, what changes in a size-dependent manner is the relative proportion of organismal energy resources that is channelled into the formation of metabolically active cells versus metabolically inert energy stores. While small planarians “invest” largely in new cells and little into stores, large animals predominantly store ingested food energy and produce few new cells. Allometric scaling of fat content with mass in mammals (Scale exponent 1.19 (Calder, 1984; Pitts & Bullard, 1968)) raises the possibility that similar physiological trade-offs may contribute to P/M allometries in other animals.
Our demonstration of size-dependent energy storage as physiological cause of Kleiber’s law in planarians also narrows the quest for a quantitative understanding of the ¾ scale exponent. Interestingly, the trade-off between energy storage and addition of new cells converges on a central premise of the Dynamic Energy Budget (DEB) theory, which can derive the ¾ exponent out of the assumption of surface-limited energy store mobilization (Maino, Kearney, Nisbet, & Kooijman, 2014). However, planarians assimilate and distribute metabolic energy via the branched tubular network of their intestine (Forsthoefel, Park, & Newmark, 2011) (termed “gastrovasculature”). This also makes the intrinsic transport capacity limitations of space-filling fractal networks a possible origin of the ¾ exponent, as per the WEB theory (Goeffrey B West et al., 1997). Further, it is also conceivable that neither process is rate-limiting and that size-dependent energy storage emerges as a consequence of a size-dependence of stem cell division probabilities, for example. Importantly, our results establish an experimental system for the systematic experimental evaluation of these and other theories and thus also the mechanistic basis of Kleiber’s law.
Author Contributions
Conceptualization: A.T., S.W., O.F., J.C.R., B.M.F., F.J.; methodology: A.T., O.F., S.W., Y.Q, O.K.; formal analysis: S.W., A.T., O.F., O.K.; investigation: A.T., O.F., S. W., J.P., O.K., Y.Q.; software: S.W.; resources: J.C.R., K.F., A.S., F.S.; data curation: S.W., A.T., O.F., O.K.; writing – original draft: A.T., S. W., O.F., J.C.R.; writing – review & editing: J.C.R., F.J., B.M.F., A.T., S.W., O.F., J.P., K.F., O.K., A.S.; visualization: A.T., S.W., O.F.; funding acquisition: J.C.R., F.J., B.M.F.; K.F. All authors read and approved of the manuscript.
Competing interests
The authors declare no competing financial interests.
Data and materials availability
All data on which the conclusions of this paper are based are presented in the figures, figure supplements or source data that was submitted with this manuscript.
Materials and Methods
Fitting of power laws
Power law exponents were obtained from linear fits (robust regression using a bisquare weighing function, “robustfit” function in MATLAB) in the log-log plot. We only directly fitted the measured data. If a data set is derived from several measurements (e.g. metabolic rate vs. wet mass is derived from measurements of metabolic rate vs. dry mass and dry mass vs. wet mass), the power law estimate is computed from the original fits of the individual measurements. The respective standard error is obtained via error propagation.
Animal husbandry
The asexual (CIW4) strain of S. mediterranea was kept in plastic containers in 1X Montjuïc salt water (1.6 mM NaCl, 1.0 mM CaCl2, 1.0 mM MgSO4, 0.1 mM MgCl2,0.1 mM KCl, 1.2 mM NaHCO3) with 25 mg/L gentamycin sulfate. The animals were fed homogenized organic calf liver paste and were fed at least one week prior to all experiments if not otherwise indicated. Animals were kept at 20 °C before and during experiments.
Measurement of planarian body size
Movies of gliding planarians were taken with a Nikon Multizoom AZ 100M (0.5x objective) using dark field illumination (facilitates planarian body segmentation). The following camera (DS-Fi1) settings were used: frame rate 3 Hz, exposure time 6 ms, 15 s movie length, 1280 × 960-pixel resolution, conversion factor 44 pixel/mm. Animals were placed one at a time inside a Petri dish and typically 1 - 4 movies taken, depending on the animal’s behaviour. Movies were converted from AVI to MP4 format using Handbreak to reduce the file size. Movies were subsequently analysed using custom-made MATLAB software (MathWorks, Natick, Massachusetts, USA). Typically, those frames were analysed in which the animals were gliding in a straight line (typically 10 frames). See also (Werner et al., 2014).
Microcalorimetry
Size-matched planarians were placed inside 4 ml glass ampoules (TA Instruments, Cat. No.: 24.20.0401) partially filled with 2 ml of planarian water and supplemented with 10 mM HEPES for improved buffering. No HEPES was used in 22 out of 82 samples, however, no difference in animal health and/or heat generation was observed (data not shown). The ampoules were sealed with aluminium Caps (TA Instruments, Cat. No.: 86.33.0400) using a dedicated crimping tool (TA Instruments, cat. #: 3339). The measurements were performed in a multichannel microcalorimeter (TAMIII, TA Instruments), whereby 12 samples were measured simultaneously including 1-2 controls without animals. The ampoules were first inserted half way and kept in this position for 15 min in order to equilibrate with the temperature inside the device. Then, ampoules were placed completely inside the respective channels whereby they were sitting on top of a thermoelectric detector that measured the heat production in relation to an oil bath, which was kept at a constant temperature of 20 °C. Before the actual measurements, the system was left to equilibrate for another 45 min. The measurements lasted between 2-3 days. Animal behaviour was not controlled and the animals were able to freely move inside the ampoule. Immediately after the metabolic rate measurements, animal dry mass was determined by drying over night at 60 °C either on weighing paper or inside 0.5 ml tubes and subsequent weighing on a microbalance (RADWAG MYA 5.2Y). The mass per animal was obtained by dividing the collective mass by the number of animals.
Cell counting based on Histone H3 protein quantification
Generating standard curves for converting Histone H3 content into cell number: cells from 15 animals (length 5-8 mm) were dissociated and counted out by FACS essentially as previously described (Tejada-Romero, Evans, & Aboobaker, 2012). Following enzymatic digestion of the tissue, the resulting cell suspension was filtered through a CellTrics 50 µm mesh (Partec, Cat. No.: 04-0042-2317) and incubated in Hoechst (33342) for 1.5 h on a rotator. Subsequently, cells were pelleted once (700 rpm, 10 min) and the supernatant replaced with fresh CMFH. The volume was adjusted to obtain a cell concentration suitable for FACS (typically 1-5·106 cells/ml). Following cell sorting, cells were kept on ice until further processing. Cells were counted with a FACS ARIA III cell sorter (Beckton Dickinson) with standard filter settings and sorted into 2 ml tubes. Typically, 105 cells were sorted per tube. Following FACS, cells were frozen at - 80 ° C until further use.
Determination of total cell number in different-sized planarians using quantitative Western blotting: plan area was measured using above-mentioned method (see also Figure 2 – figure supplement 1A-C). Subsequently, individual animals were lysed in 6 M Urea, 2% SDS, 130 mM DTT, 1 µg/ul BSA, 1 µg/ul BSA-AlexaFluor680 conjugate (ThermoFisher Scientific, Ca. No.: A34787), protease inhibitor cocktail and ≥ 2.5 U/ml Benzonase Nuclease (SIGMA, Cat. No.: E1014). Lysis was allowed to proceed for 1 - 1.5 h at room temperature, remaining tissue pieces were completely lysed by tapping the tubes and vortexing. Meanwhile, the cells for the standard curve (see above) were lysed by directly applying the lysis solution onto the frozen cells. Protein concentrations were measured in 1:5 or 1:10 dilutions using a NanoDrop spectrophotometer (Thermo Fisher Scientific) (absorbance at 280 nm). Finally, the samples were mixed with 4x Laemmli buffer (4x stock: 400 mM DTT, 200 mM Tris-HCl, 8% SDS, 40% glycerol, 0.5 mg/ml Bromophenol Blue) and incubated for 10 min at 60 °C before spinning down at 13000 rpm for 5 min. The samples were run on NuPAGE Novex 4-12% Bis-Tris protein gels (Invitrogen, Cat. No.: NP0322BOX) in 1x MOPS running buffer (ThermoFisher Scientific, Cat. No.: NP0001). The loaded volumes for the standard curve corresponded to 15000, 22500, 30000, 37500 and 45000 cells (linear signal range) and the volume of the whole-animal lysates was corresponding to 50 µg of protein, ensuring that the samples were lying within the range of the standard curve. 4 technical replicates were carried out per experiment (analysis of 5 individual animals) by running 2 chambers with 2 gels each at 140 mA for 1 h. Proteins were transferred onto Whatman Protran nitrocellulose membrane (SIGMA, Cat. No.: Z613630) for 2 h in transfer buffer (20% MeOH/1x MOPS). Membranes were blocked for 1 h at room temperature and continuous agitation in 1x TBS-T (10 mM Tris base, 150 mM NaCl, 0.1% (w/v) Tween-20, pH 7.4) and 5% (w/v) nonfat dry milk. Afterwards, membranes were incubated over night at 4 °C with anti-Histone H3 antibody (Abcam, Cat. No.: ab1791) followed by at least 3 washes in TBS-T for 10 min. Membranes were then incubated with a fluorophore-conjugated secondary antibody (anti-rabbit IRDye 680LT, LICOR, Cat. No.: 926-68023) diluted 1:20000 in blocking solution followed by extensive washing in TBS-T (1x 5 min, 3x 10 min) and one final wash step in TBS (10 min). Afterwards, membranes were dried at room temperature for at least 1 h and imaged on an Odyssey SA Li-Cor Infrared Imaging System (LICOR). The relative fluorescent band intensity was quantified using the gel-analysing tool in Fiji (Schindelin et al., 2012). The fraction of cells from whole-animal lysates loaded onto the gel was calculated from the standard curve on each blot separately. The total number of cells in the animals was calculated as follows: number of cells loaded/volume loaded × total volume of original lysate. The obtained values were finally averaged over all 4 technical replicates.
Image-based cell counting
First, plan area of individual animals was measured using above-mentioned method (see also Figure 2 – figure supplement 1A-C). For cell dissociation, individual animals were placed inside maceration solution (Romero & Baguñà, 1991) (acetic acid, glycerol, dH2O at a ratio of 1:1:13 including 1 µg/ml BSA + 10 µg/ml Hoechst 33342, no methanol) and the total volume adjusted according to animal size. The solution also contained typically about 1.3 × 106 fluorescent beads/ml (FluoSpheres Sulfate Microspheres, 4 µm, red fluorescent 580/605 nm, ThermoFisher Scientific, Cat. No.: F8858) the concentration of which was determined with a Neubauer chamber for each experiment (including 10-18 animals). Dissociation was allowed to proceed at room temperature for about 15 min after which cells of remaining tissue clumps were further dissociated by taping and vortexing. Per animal, 2 µl drops of the cell suspension were pipetted into 6-10 wells of a glass bottom 96-well plate (Greiner, Cat. No.: 655090) and the drops dried over night at room temperature. Subsequently, the entire drops were imaged on an Operetta high-content imaging system (PerkinElmer). The number of cells and beads were automatically counted using an imaging pipeline built in CellProfiler (Carpenter et al., 2006) (Figure 2 – figure supplement 2). The total number of cells was calculated from each separate well/drop by the following formula: sum of cells in analysed images/sum of beads in analysed images x known total number of beads in original cell suspension. For each animal, the calculated total cell number was averaged across 9-10 wells.
Measurement of energy content using a bomb calorimeter
Size-matched planarians were placed inside a combustion crucible and lyophilized overnight in a lyophiliser (Heto LyoLab 3000). Then, the samples were weighed on an analytical balance (Sartorius Entris, readability: 0.1 mg) and the mass per animal was obtained by dividing the collective mass by the number of animals – thus, allowing further conversion into organismal cell numbers. Afterwards, the combustion enthalpy was measured by combustion in the presence of high pressure O2 inside a bomb calorimeter (IKA C 6000 global standards) running in adiabatic mode. Benzoic acid pellets (IKA C723, Cat. No.: 0003243000) were used as a standard for calibration as well as a burning aid for the samples. In between lyophilizing and combustion, the samples were kept inside a drying chamber to prevent humidification.
Dry and wet mass measurements
To obtain the dry mass versus area and dry mass versus length scaling laws, the plan area of individuals animals was measured using aforementioned method. Afterwards, animals were individually placed on round pre-weighed glass cover slips and dried over night at approximately 60 °C. Subsequently, each animal was weighed 3 times on an analytical microbalance (Sartorius Research 210 P) to obtain an average mass value. Wet mass was measured by removing as much of residual water as possible while individual animals were placed inside a 0.5 ml tube. After further exposing the animals to air for 30-40 min to evaporate remaining water outside of the animal, animals were weighed on a microbalance (RADWAG MYA 5.2Y).
Food intake assay
Plan area of individual animals (two and three weeks starved) was measured using the above-mentioned method (see also Figure 2 – figure supplement 1A-C). Planarians were fed with organic homogenized calf liver paste, which was mixed with about 6.5*105 per 1 µl liver red fluorescence beads (FluoSpheres Sulfate Microspheres, 4 µm, fluorescent 580/605 nm, ThermoFisher Scientific, Cat. No.: F8858) coated in 1mg/ml BSA. Single animals (or for calibration 2 µl of liver/beads mix) were dissociated into single cells in maceration solution (see above) containing 0.1% Tween-20 and about 300/µl yellow-green fluorescence beads (FluoSpheres Sulfate Microspheres, 4 µm, fluorescent 505/515 nm, ThermoFisher Scientific, Cat. No.: F8859) for volume normalization (see further below). 1 µl drops of the animal and liver macerates as well as from maceration solution only were distributed into 10 wells of a glass bottom 96-well plate (Greiner, Cat. No.: 655090) and dried over night at room temperature in the dark. Whole drops were imaged on an Operetta high content imaging system (PerkinElmer) and the number of red and yellow-green beads were automatically counted using CellProfiler (Carpenter et al., 2006). The volume of liver eaten per animal was calculated as follow:
Total number of red beads per 1 animal = Number of red beads in 1 µl drop of worm suspension x Total volume of original maceration solution
Total number of red beads per 1 µl liver = (Number of red beads in 1 µl drop of liver suspension / 2) x Volume of maceration solution
Volume of liver eaten per animal = Total number of red beads per 1 animal / Total number of red beads per 1 µl liver
To account for possible pipetting errors leading to variation in drop volumes, the volume of liver eaten per animal was normalized to the ratio between yellow-green beads in the drops of the animal macerate and in the drops of maceration solution only.
Lipid droplet stain
Two weeks starved small worms were killed in 5 % N-Acetyl-Cystein (NAC) and large worms in 7.5 % NAC (5 min at room temperature) and fixed in 4 % PFA for 2 days at 4°C. Fixed worms were embedded in 4 % low-melting-point agarose and sectioned using a vibratome (100 µm, Leica, Germany). Sections were treated with 0.5 % Triton X-100 in PBS for 2h and incubated in PBS with lipid droplet dye LD540 (kind gift from Christoph Thiele, Bonn) (0.5 µg/ml) and DAPI (1 µg/ml) overnight at room temperature. After thoroughly washing with 0.3% Triton X-100 in PBS and a short rinse in PBS, the sections were optically cleared with the slightly modified SeeDB protocol (Ke, Fujimoto, & Imai, 2013) as follows: Sections were incubated sequentially with increasing concentrations of aqueous fructose solution (25 % for 4 h, 50 % for 4 h, 75 % and 100 % fructose for overnight) and finally with the saturated fructose solution overnight. All steps were carried out at room temperature. The sections were mounted on glass slides with the SeeDB solution and confocal images were taken on a Zeiss LSM 700 inverted microscope (20x objective, Zeiss Plan-Apochromat, 0.8 numerical aperture) using 80 % 2,2’-Thiodiethanol (Staudt, Lang, Medda, Engelhardt, & Hell, 2007) as immersion media.
Lipid extraction and quantification by shotgun mass spectrometry
Synthetic lipid standards were purchased from Avanti Polar Lipids, Inc. (Alabaster, AL, USA). Stocks of internal standards were stored in glass ampoules at −20°C until used for lipid extraction. Planarians of different size (40 small, length ~ 4 mm; 20 medium, ~ 8 mm; and 6 large, ~ 16 mm) were pooled and homogenized in ice-cold isopropanol mixed with acetonitrile (1:1). Analysis of lipid extracts obtained under different homogenization conditions to prevent TG degradation (Figure 4 – figure supplement 1) was performed on HPTLC silica gel plates (Merck, Cat.No.: 105633) with the solvent system n-hexane/diethylether/acetic acid (70:30:1, vol/vol/vol). Lipids were visualized by spraying plates with 3 g cupric acetate in 100 ml of aqueous 10 % phosphoric acid solution and heating at 180 °C for 10 min. Protein amount in the homogenates was determined by BCA. 50 µg of total protein was extracted with MTBE/MeOH as described in (Sales et al., 2016; Sales, Knittelfelder, & Shevchenko, 2017; Schuhmann et al., 2012). Briefly, 700 µl of 10:3 MTBE/MeOH containing one internal standard for each lipid class was added to the dried homogenates. Samples were vortexed for 1h at 4 °C. Phase separation was induced by adding 140 µl of water and vortexing for 15 min at 4 °C, followed by centrifugation at 13400 rpm for 15 min. The upper phase was collected, evaporated and reconstituted in 600 µl of 2:1 MeOH/CHCl3. 15 µl of total lipid extract was diluted with 85 µl 4:2:1 IPA/MeOH/CHCl3 containing 7.5 mM ammonium formate for mass spectrometric analysis. For the measurement of phosphatidylserines (PS), 15 µl of lipid extract were diluted with 85 ul 4:1 EtOH/CHCl3 containing 0.1% triethylamine.
Mass spectrometric analysis was performed on a Q Exactive instrument (Thermo Fischer Scientific, Bremen, Germany) equipped with a robotic nanoflow ion source TriVersa NanoMate (Advion BioSciences, Ithaca, NY, USA) using nanoelectrospray chips with a diameter of 4.1 µm. The ion source was controlled by the Chipso?t 8.3.1 so?tware (Advion BioSciences). Ionization voltage was + 0.96 kV in positive and - 0.96 kV in negative mode; backpressure was set at 1.25 psi in both modes by polarity switching (Schuhmann et al., 2012). The temperature of the ion transfer capillary was 200 °C; S-lens RF level was set to 50 %. Each sample was analysed for 5.7 min. FTMS spectra were acquired within the range of m/z 400–1000 from 0 min to 1.5 min in positive and within the range of m/z 350–1000 from 4.2 min to 5.7 min in negative mode at a mass resolution of R m/z 200 = 140000, automated gain control (AGC) of 3 × 106 and with a maximal injection time of 3000 ms. Free cholesterol was quantified by parallel reaction monitoring FT MS/MS within runtime 1.51 to 4.0 min. For FT MS/MS micro scans were set to 1, isolation window to 0.8 Da, normalized collision energy to 12.5%, AGC to 5 × 104 and maximum injection time to 3000 ms. PS was measured for 1.5 min in an additional acquisition in negative FTMS mode with optimized nanoMate parameters (backpressure 1.00 psi and voltage – 2.00 kV). All acquired data was filtered by PeakStrainer (https://git.mpi-cbg.de/labShevchenko/PeakStrainer/wikis/home) (Schuhmann et al., 2017). Lipids were identified by LipidXplorer so?tware (Herzog et al., 2012). Molecular Fragmentation Query Language (MFQL) queries were compiled for PC, PC O-, LPC, LPC O-, PE, PE O-, LPE, PI, LPI, PA, LPA, PS, SM, TG, DG, Cer, Chol, CE lipid classes (see Table 1 for meaning of all abbreviations). The identification relied on accurately determined intact lipid masses (mass accuracy better than 5 ppm). Lipids were quantified by comparing the isotopically corrected abundances of their molecular ions with the abundances of internal standards of the same lipid class. The amount of lipids per animal was calculated based on the known volume of homogenization buffer and the known number of animals. Lipid amounts were normalized to cell number using the previously established scaling relationship between cell number and area (Figure 2B) and between length and area (Figure 2 – figure supplement 1D).
Histological staining for glycogen on planarian cross sections
Fixation: two weeks-starved small (~ 4mm) and large (13mm −16mm) animals were anesthetized and relaxed for 5 min on ice by supplementing chilled planarian water with 0.0485% w/v Linalool (Sigma, L2602). Planarians were fixed in cold alcoholic Bouins fixative (15ml Picric acid (saturated alcoholic solution, TCS Biosciences, Cat. No.: HS660), 12 ml 32 % PFA, 2 ml glacial Acetic acid and 15 ml Ethanol) for overnight at 4°C and washed with 70 % Ethanol for following two days.
Paraffin embedding and sectioning: Fixed animals were dehydrated by alcohol-xylene series (1x 10 min in 70 % ethanol and 2x for 30 min in 96 %, 100 % ethanol and xylene, respectively). Xylene was replaced by melted paraffin at 60 °C, which was exchanged three times, after 30 min, after several hours overnight and again after 30 min, which was followed by embedding. Cross-sections of 10 µm thickness were obtained using a microtome (Thermofisher Scientific, Microm HM355S). The sections were dewaxed and hydrated by xylene-ethanol series (2x 10 min Xylene, 2x 1min 100 %, 96 % and 1×1 min 70 %, 40 %, ethanol and water). Prior to staining, one of two adjacent sections was treated (for 2 h, at 37 °C) with 0.2 N acetate buffer (pH 4.8) containing amyloglucosidase (0.03 U/µl) (Sigma A1602), while the other section with buffer only. By rinsing the sections with water, the digested glycogen was washed out on the section treated with amyloglucosidase but not on the section without enzyme treatment.
For glycogen visualization, we used Best’s Carmine staining method. The Carmine stock and - working solutions (Carmine (C.I. 75470) Carl Roth, 6859.1) as well the differentiating solution were prepared as described in Romeis - Mikroskopische Technik (Mulisch & Welsch, 2010). The sections were treated for 10 min with Carmine working solutions following by differentiating solution 2x for 1 min. Sections were briefly rinsed with 80 % ethanol and treated 2x for 1 min with 100 % Ethanol and 2x for 2 min with Xylene and mounted in Cytoseal(tm)XYL (Richard-Allan Scientific; 8312-4). Stained sections were imaged with an Olympus BX61 Upright Microscope with 5x and 20x objectives.
Glycogen assay
Two weeks-starved animals were homogenized in water (40 worms of 4 mm length in 0.5 ml, 20 worms of 8 mm in 1ml and 10 worms of 16 mm in 1ml) using zirconia/silica beads (1.0 mm diameter, Carl Roth GmbH+Co.KG, Cat.No:11079110z) at 4°C for 10 min. After brief centrifugation, the samples were flash frozen in liquid nitrogen and sonicated (Covaris S2 Sonicator) for 1 min. The homogenate was used for glycogen and total carbohydrate quantifications. The glycogen quantification method was adapted to planarians based on a protocol for Drosophila larvae from the C. Thummel lab (University of Utah). Heat-treated homogenate (70°C, 10 min) was centrifuged at 13400 rpm for 2 min and the supernatant was taken for the measurements. The extracted glycogen was digested to glucose by amyloglucosidase treatment (Sigma, Cat. No.: A1602) (0.015 U/µl of 0.2 M acetate buffer, pH 4.8) for 2 h at 37 °C. The glucose content was measured using the glucose assay kit (Sigma, Cat. No.: GAGO-20). The assay was performed in black 96-well glass bottom plates (Greiner Bio-One, Cat. No.: 655090) and the absorption spectra was measured using Envision Microplate Reader (Perkin Elmer). Additionally, to assess background levels of free glucose, the supernatant without amyloglucosidase treatment was measured. Planarians do not contain free Glucose at detectable levels (data not shown). Glucose and Glycogen amounts were determined using a standard curve built on a glucose and glycogen dilution series, respectively. Glycogen extraction using hot 30 % KOH (Figure 4 – figure supplement 1D) was performed as previously published (Rasouli, Shokri-Afra, & Ostovar-Ravari, 2015).
Total carbohydrate measurement
Determination of total carbohydrate was carried out on whole homogenates (same as used in glycogen assay) using the phenol-sulfuric acid method. In brief, the homogenate was heated with the 96% H2SO4 at 90°C for 15 min, mixed with phenol (saturated with 0.1M citrate buffer, pH 4.3, Sigma, Cat. No.: P4682) (Homogenate: H2SO4: phenol at a ratio of 1:5:5) and distributed into a 96-well plate (Thermo Scientific Nunc, Cat. No: 167008). The absorbance was measured at 492 nm Envision Microplate Reader (Perkin Elmer). Carbohydrate amounts were determined using the glycogen standard curve (see previous section). The amount of glycogen and total carbohydrates per animal was calculated based on the known volume of homogenisation buffer and the known number of animals. Glycogen and carbohydrate amounts were normalised to organismal cell number using the previously established scaling relationship between cell number and area (Figure 2B) and between length and area (Figure 2 – figure supplements 1D). The non-glycogen carbohydrate amount was calculated by subtracting the determined glycogen from the carbohydrate amount.
Protein measurements
Planarians of approximately 4, 8 and 16 mm length were chosen and protein amounts were determined using the Pierce 660nm Protein Assay Reagent (ThermoFisher Scientific, Cat. No.: 22660) according to the manufacturer’s instructions. To ensure compatibility with the used lysis solution (see below), the Pierce 660nm Protein Assay Reagent was complemented with Ionic Detergent Compatibility Reagent (ThermoFisher Scientific, Cat. No.: 22663). Planarian lysates were prepared as follows: 44 small (length 4 mm), 10 medium (8 mm) and large (16 mm) animals were placed inside 1.5 ml tubes and rinsed once with dH2O. A lysis solution containing 10 M Urea, 2 % s odium dodecyl sulfate (SDS), 130 mM dithiothreitol (DTT), 2.5 µg/ml Benzonase (home-made) and a protease inhibitor cocktail was added and the animals incubated for 10 min followed by homogenisation using a motorized plastic pestle. Volumes of lysis buffer used were 235 µl for small, 335 µl for medium and 2 ml for large animals. Subsequently, lysates were cleared by centrifugation at 13000 rpm for 1 minute. The assay was performed in black 96-well glass bottom plates (Greiner Bio-One, Cat. No.: 655090) and the resulting absorption spectra measured using a FLUOstar Omega Microplate Reader (BMG LABTECH).
Whole mount in situ hybridization
Whole mount in situ hybridization (WISH) was essentially performed as previously described (King & Newmark, 2013; Pearson et al., 2009).
Statistics
All statistical analyses were carried out using GraphPad Prism version 7.0c for Mac OSX (GraphPad Software, La Jolla, California, USA).
Software
Excel for Mac (Microsoft, Redmond, Washington, USA) and KNIME(Berthold et al., 2007) (KNIME AG, Zurich, Switzerland) were used for data handling and calculations; GraphPad Prism v7.0c (GraphPad Software, La Jolla, USA) was used for statistical analyses and data visualization; MATLAB (MathWorks, Natick, Massachusetts, USA) was used for planarian body size measurements, theoretical analysis of models, data handling and visualisation; CellProfiler (Carpenter et al., 2006) was used for image analysis; Fiji (Schindelin et al., 2012) was used for Western blot quantification and image processing; Adobe Photoshop CS5 and Illustrator CS5 (Adobe Systems, San Jose, California, USA) were used for image processing and generating figures; the manuscript was prepared for submission using Word for Mac (Microsoft, Redmond, Washington, USA).
Figure supplements
Figure 3 – figure supplement 1 (text only). Implementation of the theoretical model
The model describes the dynamic changes of total physiological energy E, defined as the fraction of energy in the body that can be metabolized and released as heat, see Figure 3A. The physiological energy E thus decreases due to metabolic heat production P and increases due to feeding, where J captures the net influx of physiological energy (taking into account a potentially elevated metabolism during feeding): . The dot denotes the time derivative. The average energy per cell is computed by dividing the total physiological energy by the total number of cells N: e = E/N. Thus, the energy per cell changes according to: , where we define j = J/N, p = P/N and the growth rate K = Ṅ/N. An increasing cell number decreases the energy per cell.
Paradigm 1 assumes that cell division and cell death directly depend on the energy available per cell e. For simplicity, we consider a linear relationship between the growth rate and the energy per cell: K = K0(e/es − 1), with K+ being a characteristic rate of growth and degrowth and es being the critical energy per cell at which planarians switch between growth and degrowth (Figure 3 – figure supplement 2A, dashed line). Thus, we can describe the energy dynamics by ė = j – p – K0(e/es − 1)e. During starvation, j = 0 and the growth rate is decreasing, which requires (red curve). The maximum of ė is at e = es/2 and from follows that p > esK0/4. During feeding, where j > p the curve is shifted upwards and e ends up in a growth regime (blue curve). For a constant energy influx j, the equation for has a stable fixed point with e* > es for j > 0. Thus, the animal would grow at a constant rate K* = K0(e*/es − 1). In order for the growth rate to decrease with animal size (Figure 2E), the energy influx per cell j(N) must not be constant but has to be a decreasing function of N, hence, we choose j(N) = j0/(1 + N).
Figure 3 – figure supplement 2B shows a time course of the organismal cell number N when going through several rounds of feeding (blue) and starvation (red), always switching at a certain size, specifically at N = 0.5 · 106 cells and N = 4.5 · 106 cells (lower and upper dashed lines, respectively). In the beginning of the starvation interval, we see an overshoot where the animal still grows although feeding has stopped. As a result, we observe rather generic growth and degrowth kinetics, independent of initial values for energy and cell number or the feeding scheme, see Figure 3 – figure supplement 2C. Any perturbation decays quickly and there is no strong dependence on feeding history.
Paradigm 2 and 3 assume a constant relationship between cell number and physiological energy content of the worm: E~N and E~Nc, respectively. In consequence and Ṅ/N = Ė/(Ec), respectively, which can be related to metabolic rate and feeding influx via during degrowth and via during growth. In paradigm 2, E/N is constant, therefore both P/N and J/N have to depend on N to explain the growth and degrowth rates. In paradigm 3, both P/N and J/N can be chosen to be constant.
To fit the growth dynamics in Figure 2C by paradigm 1, we use the following parameters:
j0/es = 14%/d, p/es = 1.3%/d, K0 = 4.3%/d, initial conditions N(0) = 3 · 106 and e(0)/es = 1 as well as a switch between feeding and starvation regimes at N = 0.05 · 106 and N = 6.5 · 106. Yet, several combinations of parameter values can fit the measurement equally well. From a fit of paradigm 2 in Figure 2C, we obtain P/E = 243 N−1.35%/d and J/E = 214 N−0.28%/d. Finally, from a fit of paradigm 3 to the data, we obtain E/P = 0.34 N0.38d and J/P = 3.0, see Figure 2C.
List of figure supplements
Figure 1 – figure supplement 1.
Measurement of body size and metabolic rate.
Figure 2 – figure supplement 1.
Validation of image-based quantification of organismal cell number.
Figure 2 – figure supplement 2.
Degrowth rates are independent of feeding history.
Figure 3 – figure supplement 1 (text only).
Implementation of the theoretical model.
Figure 3 – figure supplement 2.
Further explanation of model paradigm 1.
Figure 3 – figure supplement 3.
Paradigm validation.
Figure 4 – figure supplement 1.
Alternative assays confirm lipid and glycogen storage in planarians.
Figure 5 – figure supplement 1.
Standard curve protein and validation of total carbohydrate measurement
List of source data
Figure – source data 1.
Numerical data wet mass vs. dry mass measurements.
Figure 2 – source data 1.
Numerical data cell number measurements.
Figure 2 – source data 2.
Raw numerical data Histone H3 method (quantitative Western blotting)
Figure 2 – source data 3.
CellProfiler results tables image-based approach.
Figure 2 – source data 4.
MATLAB code for extraction of planarian body size.
Figure 2 – source data 5.
Numerical data growth/degrowth.
Figure 3 – source data 1.
Numerical data for Figure 3.
Figure 4 – source data 1
Raw images lipid droplet and glycogen.
Figure 4 – source data 2
Raw data lipid mass spectrometry, glycogen assay and statistics tables.
Figure 5 – source data 1
Raw data and statistics tables for measurement of other lipids, carbohydrates and protein.
Figure 1 – figure supplement 1 – source data 1
Raw data metabolic rate measurements.
Figure 2 – figure supplement 1 – source data 1
CellProfiler pipeline, numerical data, raw images and segmentation for validation of image-based cell counting.
Figure 3 – figure supplement 3 – source data 1
Numerical data for Figure 2 – figure supplement 3.
List of supplementary files
List of scaling relationships.
Acknowledgements
We thank N. Alt, J. Richter, J. Ferria, A. Mishra, M. Toth and I. Smith for size quantifications, K.-O. Linde and IKA Werke GmbH & Co. for microcalorimetry support, Passant Atallah (IPF Dresden) and Michal Surma (Lipotype GmbH) for support with the animal mass measurements and H. Andreas and S. von Kannen for technical support. We thank the CMCB technology platform TU Dresden (EM and Histology) and the following MPI-CBG core facilities for their support: Cell technologies, Technology development studio, and scientific computing.