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Collection : Elife (E-Journal - Via Crossref)

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Figure 3. Size-dependent scaling of energy content explains growth/degrowth dynamics. ; (A) Planarian energy balance model. At the organismal level, changes in the physiological energy content E result from a change in the net energy influx J (feeding) and/or heat loss P (metabolic rate). Dividing E, J and P by the total cell number N approximates the energy balance on a per-cell basis. (B) Three hypothetical control paradigms of E during growth and degrowth (columns), which make specific predictions regarding the size-dependence of J/N, E/N and P/N (rows). Prediction traces and scale exponents were generated by modelling the measured growth/degrowth rates (Figure 2E) with the indicated control paradigm assumptions (see also Appendix 1 and Figure 3—figure supplement 1). (C) Fit of the three control paradigms to the measured growth/degrowth rates (Figure 2E). (D) Metabolic rate per cell (P/N) versus organismal cell number (N). Data points were derived by conversion of the measurements from the metabolic rate/dry mass scaling law (Figure 1—figure supplement 1B) via the measured cell number/plan area (Figure 2B) and plan area/dry mass conversion laws (Figure 3—figure supplement 2A). The scaling exponent ± standard error was derived from the respective linear fit (green line) and represents the exponent b of the power law y = axb. (E) Energy influx per cell versus organismal cell number (N). Data points reflect single-animal quantifications of ingested liver volume per plan area as shown in Figure 3—figure supplement 2B–D, converted into energy influx/cell using the plan area/cell number scaling law (Figure 2B) and the assumption that 1 µl of liver paste corresponds to 6.15 J (USDA Agricultural Research Service, 2016; Overmoyer et al., 1987). Circles, 2 weeks starved and triangles, 3 weeks starved animals. The scaling exponent ± standard error was derived from linear fits (green line) and represents the exponent b of the power law y = axb. (F) Energy content per cell (E/N) versus organismal cell number (N). Data points reflect bomb calorimetry quantifications of heat release upon complete combustion of size matched cohorts of known dry mass as shown in Figure 3—figure supplement 2E, converted via the measured cell number/plan area (Figure 2B) and plan area/dry mass conversion laws (Figure 3—figure supplement 2A). Circles, 1 week starved and triangles, 3 weeks starved animals. The scaling exponent ± standard error was derived from a linear fit (green line) to the data and represents the exponent b of the power law y = axb. Solid black line, prediction from model three for the physiological energy content per cell assuming a constant metabolic rate P/N = 1 pW. Dashed line corresponds to respective prediction under the assumption that the physiological energy (solid black line) amounts to 50% of combustible gross energy in the animal. See Figure 3—source data 1 for numerical data of (C)-(F).

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Figure 2. Growth and degrowth dynamics in S.mediterranea. ; (A) Assays to measure organismal cell numbers. (Top) image-based quantification of nuclei (grey) versus tracer beads (magenta) following whole animal dissociation in presence of the volume tracer beads. (Bottom) Histone H3 protein quantification by quantitative Western blotting, which scales linearly with the number of FACS-sorted cells (bottom right). The line represents a fitted linear regression (data of 4 technical replicates) and serves as standard for converting the H3 band in planarian lysates (bottom left) run on the same gel into cell numbers. Values are shown as mean ± standard deviation. (B) Organismal cell number versus plan area scaling, by nuclei counts (circles) or Histone H3 protein amounts (triangles) (see also Figure 2—figure supplements 1 and 2). The scaling exponent ± standard error was derived from a linear fit and represents the exponent b of the power law y = axb. Each data point represents one individual animal and the mean of several technical replicates, Histone H3 method: nine independent experiments including five animals each; image-based approach: four independent experiments including 18, 10, 10 and 12 animals each. See Figure 2—source datas 1–3 for numerical data. (C) Plan area changes of individual animals during growth. * indicate feeding time points (1x per week). (D) Plan area change of individual animals during degrowth. (E) Size-dependence of growth (blue) and degrowth rates (red) (see also Figure 2—figure supplement 3A). Individual data points were calculated by exponential fits to traces in (C) and (D) (growth: two overlapping time windows, degrowth: three overlapping time windows) and using the cell number/area scaling law from (B) to express rates as % change in cell number/day. The positive growth rates and negative degrowth rates are plotted on the same axis to facilitate comparison of size dependence. See Figure 2—source data 5 for data of (C) and (D).

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Figure 2—figure supplement 1. Measurement of planarian body size. ; (A) Body outline variations of one individual extracted from multiple frames of a single movie. The red outline marks the outline in the first frame. (B) Illustration of the pipeline for extracting plan area and length measurements of individual planarians from movie sequences, see also (Werner et al., 2014). (i) raw movie frame, ii) use of a Canny filter on background-corrected frames to identify edges, iii) dilation-erosion cycle to fill segmentation gaps in a subsequent step, iv) refinement of animal perimeter by finding the steepest intensity change across the body edge (blue lines intersecting on the left, example plot of the intensity change across one blue line on the right), (v) resulting boundary outline (blue; yielding plan area measurement) and midline (red; yielding length measurement), overlaid on the original image to illustrate accuracy of the procedure. Stated plan area and length measurements in this manuscript always represent the median of up to 180 individually quantified movie frames displaying the same animal in an extended body posture. Scale bars, 1 mm. See Figure 2—source data 4 for MATLAB script. (C) Accuracy comparison between area (top, red) and length measurement traces (bottom, blue). The traces represent a concatenation of 2 independent movie sequences of the same animal, before (left half) and after 1 week of starvation (right half). The plan area trace illustrates better resolution of the degrowth during the starvation period, which is harder to discern in the noisier length measurements. (D) Histogram analysis of the coefficients of variation (ratio standard deviation/mean) across a data set of 2470 individual length versus plan area measurements determined as described in (A–C). The slight right shift of the length measurement histogram (blue) as compared to the area measurement histogram (red) quantitatively confirms the lower variability of the plan area measurements, which is why plan area was generally used as a size measure in this study. (E) Plot of the length versus plan area measurements as described in (A–C) of 1390 individual measurements selected to collectively represent the entire range of body sizes in S. mediterranea. Individual data points are represented by black dots, the green line represents a linear fit to the data in the log-log plot (inset). The tight fit over the entire size range demonstrates a tight regulation of body shape during growth/degrowth. The scaling exponent ± error was derived from the linear fit and represents the exponent b of the power law y = axb. See Figure 2—figure supplement 1—source data 1for data of (D) and (E).

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Figure 2—figure supplement 3. Degrowth rates are independent of feeding history. ; (A) Growth (blue) and degrowth rates (red) plotted as the % change in area/day. Individual data points were calculated by exponential fits to individual animal growth/degrowth trajectories shown in Figure 2C and D (growth: two overlapping time windows, degrowth three overlapping time windows). The positive growth rates and negative degrowth rates are plotted on the same axis to facilitate comparison of size dependencies. These data were also used to generate Figure 2E by conversion into % change in cell number/day using the cell number/area scaling relationship from Figure 2B. (B) Degrowth rates from (A) colour-coded according to time since start of food deprivation; early (blue), 1–4 weeks; middle (red), 4–7 weeks; late (green), 7–10 weeks. Solid line represents a power law (y = axb) fit to the early (blue) time points. Blue band represents the 95% confidence interval for the early (blue) degrowth rates; note that middle (red) and late (green) degrowth rates lie mostly within this interval, indicating the lack of a feeding history dependence within the covered time interval.

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Figure 1. Kleiber’s law scaling during S.mediterranea body size changes. ; (A) Feeding (growth) and starvation (degrowth) dependent body size changes of Schmidtea mediterranea. Scale bar, 1 mm. (B) Wet versus dry mass scaling with body size. The scaling exponent ± standard error was derived from a linear fit for wet mass > 0.5 mg and represents the exponent b of the power law y = axb. See Figure 1—source data 1 for numerical data. (C) Metabolic rate versus wet mass scaling by microcalorimetry. The metabolic rate was determined by a horizontal line fitted to the stabilised post-equilibration heat flow trace (Figure 1—figure supplement 1) and the post-experimental dry mass determination of all animals in the vial was re-converted into wet mass by the scaling relation from (B). Each data point represents a vial average of a size-matched cohort. The scaling exponent ± standard error was derived from a linear fit and represents the exponent b of the power law y = axb. (D) Metabolic rate versus wet mass scaling in planarians from (C) (red) in comparison with published interspecies comparisons (Makarieva et al., 2008) amongst ectotherms (grey) or endotherms (black). Dots correspond to individual measurements; black and blue solid lines trace the 3/4 scaling exponent; red line, linear fit to the planarian data. By convention (Makarieva et al., 2008), measurements from homeotherms obtained at different temperatures were converted to 37 °C, measurements from poikilotherms and our planarian measurements to 25 °C, using the following factor: 2(25∘C−20∘C)/10∘C=20.5 (20 °C: planarian data acquisition temperature).

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Figure 2—source data 5. Numerical data growth/degrowth.

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Figure 3—figure supplement 1. Further explanation of model paradigm 1. ; (A) Dynamic behaviour of the energy content per cell during feeding and starvation in paradigm 1. Graph shows the change of the energy content per cell ė as a function of the energy content per cell e during starvation and feeding. See Appendix 1 for a detailed description of paradigm 1. (B) 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. (C) A generic growth/degrowth dynamic is observed irrespective of the initial cell number, initial energy content or the feeding scheme. Any perturbation decays quickly and there is no strong dependence on feeding history. See Appendix 1 for details.

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