Cancer as a Model System for Testing Metabolic Scaling Theory

Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, mostly absent from past efforts are studies that directly, and independently, measure metabolic rate from respiration and vascular architecture for the same organ, organism, or tissue. Lack of these measures may lead to inconsistent results and conclusions about metabolism, growth, and allometric scaling. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical images of lung cancer, serving as a first-of-its-kind test of metabolic scaling theory, and identifying potential quantitative imaging biomarkers indicative of tumor growth. We analyze data for 535 clinical PET-CT scans of patients with non-small cell lung carcinoma to establish the presence of metabolic scaling between tumor metabolism and tumor volume. Furthermore, we use computer vision and mathematical modeling to examine predictions of metabolic scaling based on the branching geometry of the tumor-supplying blood vessel networks in a subset of 56 patients diagnosed with stage II-IV lung cancer. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yield metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results: (1) inform energetic models of growth and development for tumor forecasting; (2) identify imaging biomarkers in vascular geometry related to blood volume and flow; and (3) highlight unique opportunities to develop and test the metabolic scaling theory of ecology in tumors transitioning from avascular to vascular geometries.

Long-term experimental evolution decouples size and production costs in Escherichia coli

Body size covaries with population dynamics across lifes domains. Theory holds that metabolism imposes fundamental constraints on the coevolution of size and demography. However, studies of interspecific patterns are confounded by other factors that covary with size and demography, and experimental tests of the causal links remain elusive. Here we leverage a 60,000-generation experiment in which Escherichia coli populations evolved larger cells to examine intraspecific metabolic scaling and correlations with demographic parameters. Metabolic theory successfully predicted the relations among size, metabolism, and maximum population density, with strong support for Damuths law of energy equivalence in this experiment. In contrast, populations of larger cells grew faster than those of smaller cells, contradicting the fundamental assumption that costs of production should increase proportionately with size. The finding that the costs of production are substantially decoupled from size requires re-examining the evolutionary drivers and ecological consequences of biological size more generally.

Idea Paper: Effects of gonad type and body mass on the time required for sex change in fishes

Sex change is a well-known phenomenon in teleost fishes, and it takes several days to a few months depending on the species and direction of sex change. However, the underlying factors influencing the time required for sex change (TS) remain unclear. Given that the time for producing a new gonad largely determines TS, the gonad type (i.e., whether fish retain the gonad of opposite sex or not [delimited or non-delimited]) and metabolic rate are the ultimate determinants of TS. This study sought to test two hypotheses: (1) the delimited gonad shortens TS; and (2) TS scales with mass0.1–0.2, because the metabolic scaling exponent (β) in fishes is 0.8–0.9 and biological times scale with mass1−β in general. We compiled data on TS for 12 female-to-male and 14 male-to-female sex-changing species from the literature. Results of individual examinations of the effects of gonad type and mass were consistent with our hypotheses. However, upon simultaneous examination of the effects of gonad type and mass, these effects became unclear because of their strong multicollinearity. The compiled data for delimited and non-delimited gonads were biased toward the smaller and larger species, respectively, precluding us from being able to statistically distinguish between these effects. Small species with non-delimited gonads and large species with delimited gonads exist; however, their TS has not been measured with high temporal resolution thus far. Therefore, additional experiments on these species are required to statistically distinguish between, as well as to better understand, the effects of gonad type and mass on TS.

Biological scaling in green algae: the role of cell size and geometry

The Metabolic Scaling Theory (MST), hypothesizes limitations of resource-transport networks in organisms and predicts their optimization into fractal-like structures. As a result, the relationship between population growth rate and body size should follow a cross-species universal quarter-power scaling. However, the universality of metabolic scaling has been challenged, particularly across transitions from bacteria to protists to multicellulars. The population growth rate of unicellulars should be constrained by external diffusion, ruling nutrient uptake, and internal diffusion, operating nutrient distribution. Both constraints intensify with increasing size possibly leading to shifting in the scaling exponent. We focused on unicellular algae Micrasterias. Large size and fractal-like morphology make this species a transitional group between unicellular and multicellular organisms in the evolution of allometry. We tested MST predictions using measurements of growth rate, size, and morphology-related traits. We showed that growth scaling of Micrasterias follows MST predictions, reflecting constraints by internal diffusion transport. Cell fractality and density decrease led to a proportional increase in surface area with body mass relaxing external constraints. Complex allometric optimization enables to maintain quarter-power scaling of population growth rate even with a large unicellular plan. Overall, our findings support fractality as a key factor in the evolution of biological scaling.

Consistent scaling of whole-shoot respiration between Moso bamboo (Phyllostachys pubescens) and trees

Both Moso bamboo (Phyllostachys pubescens) and tree forests have a large biomass; they are considered to play an important role in ecosystem carbon budgets. The scaling relationship between individual whole-shoot (i.e., aboveground parts) respiration and whole-shoot mass provides a clue for comparing the carbon budgets of Moso bamboo and tree forests. However, nobody has empirically demonstrated whether there is a difference between these forest types in the whole-shoot scaling relationship. We developed whole-shoot chambers and measured the shoot respiration of 58 individual mature bamboo shoots from the smallest to the largest in a Moso bamboo forest, and then compared them with that of 254 tree shoots previously measured. For 30 bamboo shoots, we measured the respiration rate of leaves, branches, and culms. We found that the scaling exponent of whole-shoot respiration of bamboo fitted by a simple power function on a log–log scale was 0.843 (95 % CI 0.797–0.885), which was consistent with that of trees, 0.826 (95 % CI 0.799–0.851), but higher than 3/4, the value typifying the Kleiber’s rule. The respiration rates of leaves, branches, and culms at the whole-shoot level were proportional to their mass, revealing a constant mean mass-specific respiration of 1.19, 0.224, and 0.0978 µmol CO2 kg− 1 s− 1, respectively. These constant values suggest common traits of organs among physiologically integrated ramets within a genet. Additionally, the larger the shoots, the smaller the allocation of organ mass to the metabolically active leaves, and the larger the allocation to the metabolically inactive culms. Therefore, these shifts in shoot-mass partitioning to leaves and culms caused a negative metabolic scaling of Moso bamboo shoots. The observed convergent metabolic scaling of Moso bamboo and trees may facilitate comparisons of the ecosystem carbon budgets of Moso bamboo and tree forests.