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arXiv · 2403.00001

Metabolic scaling in small life forms

Mark E. Ritchie·Christopher P. Kempes
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Abstract

Metabolic scaling is one of the most important patterns in biology. Theory explaining the 3/4-power size-scaling of biological metabolic rate does not predict the non-linear scaling observed for smaller life forms. Here we present a new model for cells $<10^{-8}$ m$^{3}$ that maximizes power from the reaction-displacement dynamics of enzyme-catalyzed reactions. Maximum metabolic rate is achieved through an allocation of cell volume to optimize a ratio of reaction velocity to molecular movement. Small cells $< 10^{-17}$ m$^{3}$ generate power under diffusion by diluting enzyme concentration as cell volume increases. Larger cells require bulk flow of cytoplasm generated by molecular motors. These outcomes predict curves with literature-reported parameters that match the observed scaling of metabolic rates for unicells, and predicts the volume at which Prokaryotes transition to Eukaryotes. We thus reveal multiple size-dependent physical constraints for microbes in a model that extends prior work to provide a parsimonious hypothesis for how metabolism scales across small life.

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Mark E. Ritchie, Christopher P. Kempes. 2023-12-16. Metabolic scaling in small life forms. https://arxiv.org/abs/2403.00001

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