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.

Tree growth as affected by stem and crown structure

Key message Prediction of tree growth based on size or mass as proposed by the Metabolic Scaling Theory is an over-simplification and can be significantly improved by consideration of stem and crown morphology. Tree growth and metabolic scaling theory, as well as corresponding growth equations, use tree volume or mass as predictors for growth. However, this may be an over-simplification, as the future growth of a tree may, in addition to volume or mass, also depend on its past development and aspects of the current inner structure and outer morphology. The objective of this evaluation was to analyse the effect of selected structural and morphological tree characteristics on the growth of common tree species in Europe. Here, we used eight long-term experiments with a total of 24 plots and extensive individual measurements of 1596 trees in monospecific stands of European beech (Fagus sylvatica L.), Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and sessile oak (Quercus petraea (Matt.) Liebl.). Some of the experiments have been systematically surveyed since 1870. The selected plots represent a broad range of stand density, from fully to thinly stocked stands. We applied linear mixed models with random effects for analysing and modelling how tree growth and productivity are affected by stem and crown structure. We used the species-overarching relationship $$\mathrm{iv}={{a}_{0}\times v}$$ iv = a 0 × v between stem volume growth, $$\mathrm{iv}$$ iv and stem volume, $$v,$$ v , as the baseline model. In this model $${a}_{0}$$ a 0 represents the allometric factor and α the allometric exponent. Then we included tree age, mean stem volume of the stand and structural and morphological tree variables in the model. This significantly reduced the AIC; RMSE was reduced by up to 43%. Interestingly, the full model estimating $$\mathrm{iv}$$ iv as a function of $$v$$ v and mean tree volume, crown projection area, crown ratio and mean tree ring width, revealed a $$\alpha \cong 3/4$$ α ≅ 3 / 4 scaling for the relationship between $$\mathrm{iv}\propto {v}^{\alpha }$$ iv ∝ v α . This scaling corresponded with Kleiber’s rule and the West-Brown-Enquist model of the metabolic scaling theory. Simplified approaches based on stem diameter or tree mass as predictors may be useful for a rough estimation of stem growth in uniform stands and in cases where more detailed predictors are not available. However, they neglect other stem and crown characteristics that can have a strong additional effect on the growth behaviour. This becomes of considerable importance in the heterogeneous mixed-species stands that in many countries of the world are designed for forest restoration. Heterogeneous stand structures increase the structural variability of the individual trees and thereby cause a stronger variation of growth compared with monocultures. Stem and crown characteristics, which may improve the analysis and projection of tree and stand dynamics in the future forest, are becoming more easily accessible by Terrestrial laser scanning.

Testing allometric scaling relationships in plant roots

Background Metabolic scaling theory predicts that plant productivity and biomass are both size-dependent. However, this theory has not yet been tested in plant roots. Methods In this study, we tested how metabolic scaling occurs in plants using a comprehensive plant root dataset made up of 1016 observations from natural habitats. We generated metabolic scaling exponents by log-transformation of root productivity versus biomass. Results Results showed that the metabolic scaling exponents of fine root (< 2 mm in diameter) productivity versus biomass were close to 1.0 for all ecosystem types and functional groups. Scaling exponents decreased in coarse roots (> 2 mm in diameter). Conclusions We found isometric metabolic scaling in fine roots, a metabolically active organ similar to seedlings or saplings. Our findings also indicate a shift in metabolic scaling during plant development. Overall, our study supports the absence of any unified single constant scaling exponent for metabolism-biomass relationships in terrestrial plants, especially for forests with woody species.

A regional-scale assessment of using metabolic scaling theory to predict ecosystem properties

Metabolic scaling theory (MST) is one of ecology's most high-profile general models and can be used to link size distributions and productivity in forest systems. Much of MST's foundation is based on size distributions following a power law function with a scaling exponent of −2, a property assumed to be consistent in steady-state ecosystems. We tested the theory's generality by comparing actual size distributions with those predicted using MST parameters assumed to be general. We then used environmental variables and functional traits to explain deviation from theoretical expectations. Finally, we compared values of relative productivity predicted using MST with a remote-sensed measure of productivity. We found that fire-prone heath communities deviated from MST-predicted size distributions, whereas fire-sensitive rainforests largely agreed with the theory. Scaling exponents ranged from −1.4 to −5.3. Deviation from the power law assumption was best explained by specific leaf area, which varies along fire frequency and moisture gradients. While MST may hold in low-disturbance systems, we show that it cannot be applied under many environmental contexts. The theory should remain general, but understanding the factors driving deviation from MST and subsequent refinements is required if it is to be applied robustly across larger scales.

On the importance of the megabiota to the functioning of the biosphere

A prominent signal of the Anthropocene is the extinction and population reduction of the megabiota – the largest animals and plants on the planet. However, we lack a predictive framework for the sensitivity of megabiota during times of rapid global change and how they impact the functioning of ecosystems and the biosphere. Here, we extend metabolic scaling theory and use global simulation models to demonstrate that the megabiota (i) are more prone to extinction due to human land use, hunting, and climate change; (ii) their loss has a negative impact on ecosystem metabolism and functioning; and (iii) their continued reduction will significantly decrease biosphere functioning. Analyses of several forest and animal datasets and large-scale simulation models largely support these predictions. Global simulations show that continued loss of large animals could lead to a 44%, 18% and 92% reduction in terrestrial heterotrophic biomass, metabolism, and fertility respectively. Landscapes with megabiota buffer ecosystem functioning, diversity, and likely human health. As a result, policies that emphasize the promotion of large trees and animals will have disproportionate impact on biodiversity, ecosystem processes, and climate mitigation.

Adaptive diversification of growth allometry in the plant Arabidopsis thaliana

Seed plants vary tremendously in size and morphology. However, variation and covariation between plant traits may at least in part be governed by universal biophysical laws and biological constants. Metabolic Scaling Theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of resource uptake. This constrains variation in physiological traits and in the rate of biomass accumulation, so that they can be expressed as mathematical functions of plant size with near constant allometric scaling exponents across species. However, observed variation in scaling exponents questions the evolutionary drivers and the universality of allometric equations. We have measured growth scaling and fitness traits of 451 Arabidopsis thaliana accessions with sequenced genomes. Variation among accessions around the scaling exponent predicted by MST correlated with relative growth rate, seed production and stress resistance. Genomic analyses indicate that growth allometry is affected by many genes associated with local climate and abiotic stress response. The gene with the strongest effect, PUB4, has molecular signatures of balancing selection, suggesting that intraspecific variation in growth scaling is maintained by opposing selection on the trade-off between seed production and abiotic stress resistance. Our findings support a core MST prediction and suggest that variation in allometry contributes to local adaptation to contrasting environments. Our results help reconcile past debates on the origin of allometric scaling in biology, and begin to link adaptive variation in allometric scaling to specific genes.Significance statementAre there biological constants unifying phenotypic diversity across scales? Metabolic Scaling Theory (MST) predicts mathematical regularity and constancy in the allometric scaling of growth rate with body size across species. Here, we show that adaptation to climate in Arabidopsis thaliana is associated with local strains that substantially deviate from the values predicted by MST. This deviation can be linked to increased stress tolerance at the expense of seed production, and it occurs through selection on genes that are involved in abiotic stress response and that are geographically correlated with climatic conditions. This highlights the evolutionary role of allometric diversification and helps establish the physiological bases of plant adaptation to contrasting environments.