Physical Approaches to Metabolic Scaling in Living Systems

Abstract

Living systems continuously transform matter and energy through the chemical processes that constitute their metabolism. The overall metabolic rate of an organism correlates positively with its body mass, however both the exact scaling behavior and possible explanations for this behavior have been under intense debate for two centuries. This review synthesizes empirical findings and theoretical frameworks on the energetics of living systems from an interdisciplinary perspective, with a focus on physical concepts. A general thermodynamic framework to study metabolism is laid out, together with a coarse-grained description of metabolic biochemistry. The rich history of experimental work in this field is surveyed, revealing a variety of metabolic scaling patterns at different levels of biological organization, from individual cells to whole populations. Several biophysical models proposed to explain the sublinear scaling of metabolic rate with body mass are summarized. Though the traditional focus has been on adult organisms, the review also highlights recent advances that probe metabolism during development. Improvements in experimental techniques, extensive datasets, and a host of open questions, suggest the field will continue gaining momentum in the near term. The review concludes with an outlook for this future progress: an interdisciplinary approach to elucidate metabolic scaling across different developmental stages and organism sizes.

Figures (11)

• Figure 1: Coarse-grained cellular energy metabolism. Left panel: energy metabolism composed of glycolysis, fermentation, mitochondrial respiration and biosynthesis. Glycolysis and respiration are the two major pathways that produce ATP, the energy currency of the cell. The tricarboxylic acid (TCA) cycle, the electron transport chain (ETC), the proton leak and oxidative phosphorylation (OXPHOS) are indicated. Each arrow represents a net chemical reaction, as defined in Eq. \ref{['eq:netreactions']}, or transport across cellular compartments. Right panel: energy balance of ATP production and hydrolysis. ATP demand represents all the ATP consuming processes in the cell.
• Figure 2: Net fluxes into and out of living systems. Coarse-grained metabolism at the whole system level for cells, tissues, and the entire animal can be described via net input (nutrients, oxygen) and output (waste, heat, and internal compositional change) fluxes. These fluxes can be linked by macrochemical reactions, Eq. \ref{['eq:netreactions']}. The metabolic rate is defined as the rate of heat release of the organism to the environment. Eq. \ref{['qdotmacrochemical2']} relates the heat release rate ($\dot{Q}$) to macrochemical reaction rates $\mathcal{R}_{\beta}$ and associated enthalpy changes $\Delta H_{\beta}$.
• Figure 3: Schematic of Lavoisier and Laplace's 1783 guinea pig experimental setup, the first direct measurement of the metabolic rate $\dot{Q}$ of a living organism. Left: the calorimeter where the animal was placed in a wire basket surrounded by ice. The water from the melted ice, collected in the vessel below, was used to estimate $\dot{Q}$. Bottom right: detail of the wire basket. Top right: the bell jar apparatus used for the follow-up respirometry measurements. After spending up to ten hours in the calorimeter, the guinea pig was placed for the same duration inside the bell jar in a basin containing a shallow pool of mercury. Gas volume changes due to oxygen consumption and carbon dioxide production could be measured by tracking the height of the mercury within the jar. Image credit: Oeuvres de Lavoisier, vol. II, plate II (public domain).
• Figure 4: (a) Basal metabolic rate $B$ versus wet mass $M$ for organisms across various domains of life, adapted from the data sets collected in hoehler2023metabolic. For each class of organisms we show the best-fit exponent $\alpha$ for the scaling $B \sim M^{\alpha}$ within the class. The dashed line represents a global fit to linear scaling, $B \sim M$. (b) Same as panel (a), except showing $b = B/M$, the mass-specific basal metabolic rate. The dashed line corresponds to the mean mass-specific value, $\bar{b} = 3.94\times 10^{-3}$ W/g. The dotted line represents Kleiber law scaling, $B \sim M^{3/4}$, or equivalently $b \sim M^{-1/4}$. $R^2$ values are shown from linear regression on the log-log plotted $b$ data (solid lines), color coded by class. In both panels the star represents the largest organism for which $B$ was directly measured (an orca), while the triangle represents the smallest organism (the bacterium F. tularensis).
• Figure 5: Examples of mass-specific basal metabolic rates $b=B/M$ versus $M$ within a single species. Top: five instars (developmental stages) L1 to L5 of the tobacco hornworm, the larva of the moth Manduca sextasears2012ontogenetic. For each instar, the best fit exponent $\gamma$ for the scaling $b \sim M^\gamma$ is shown, along with the $R^2$ value for linear regression on the log-log plot. Kleiber scaling corresponds to $\gamma = -1/4$. The dashed line indicates the mean $\bar{b}$ for all species, taken from Fig. \ref{['interspecies']}(b). Bottom: the planarian Schmidtea mediterranea for a range of body sizes induced by feeding or starvation thommen2019body. In both species, the data was converted from dry mass to wet mass as described in the references, and for the hornworm case the $B$ was converted from units of $\mu$L CO$_2$ hr$^{-1}$ to W using the measured M. sexta respiratory ratio $\Phi_{\text{CO}_2}/\Phi_{\text{O}_2} = -0.88$alleyne1997effects and the Thornton's rule value $\Delta h_{\rm ox} = -450$ kJ/mol.