Enzymatic origin and various curvatures of metabolic scaling in microbes

The famous and controversial power law is a basal metabolic scaling model mainly derived from the "surface rule" or a fractal transport network. However, this law neglects biological mechanisms in the important active state. Here, we hypothesized that the relative metabolic rate and growth rate of actively growing microbes are driven by the changeable rate of their rate-limiting enzymes and concluded that natural logarithmic microbial metabolism (lnλ) and growth (or biomass) (lnM) are both dependent on limiting resources, and then developed novel models with interdependence between lnλ and lnM. We tested the models using the data obtained from the literature. We explain how and why the scaling is usually curved with the difference between microbial metabolic and growth (or biomass's) half-saturation constants (K_M, K_λ) in the active state and agree that the linear relationship of the power law is a particular case under the given condition: K_M = K_λ, which means that the enzyme dynamics may drive active and basal metabolic scaling relationships. Our interdependent model is more general than the power law, which is important for integrating the ecology and biochemical processes.