Respiration predicted from an Enzyme Kinetic Model and the Metabolic Theory of Ecology in two species of marine bacteria

Abstract

Respiratory oxygen consumption is the result of a cell's biochemistry. It is caused by enzymatic activity of the respiratory electron transfer system (ETS). However, in spite of this understanding, respiration models continue to be based on allometric equations relating respiration to body size, body surface, or biomass. The Metabolic Theory of Ecology (MTE) is a current example. It is based on Kleiber's law relating respiration ( R) and biomass ( M) in the form, R = C M 3 4 e − E a k T , where C is a constant, E a is the Arrhenius activation energy, k is the Boltzmann constant for an atom or molecule, and T is the temperature in Kelvin. This law holds because biomass packages the ETS. In contrast, we bypass biomass and model respiration directly from its causal relationship with the ETS activity, R = f (ETS). We use a biochemical Enzyme Kinetic Model (EKM) of respiratory oxygen consumption based on the substrate control of the ETS. It postulates that the upper limit of R is set by the maximum velocity, V max , of complex I of the ETS and the temperature, and that the substrate availability, S, modulates R between zero and this upper limit. Kinetics of this thermal-substrate regulation is described by the Arrhenius and Michaelis–Menten equations. The EKM equation takes the form R = E T S [ S ] e − E a R g T K + [ S ] where R g is the molar gas constant and K is the Michaelis–Menten constant. Here, we apply the EKM and the MTE to predict a respiration time-profile throughout the exponential, steady state, and nutrient-limited phases of the marine bacteria Pseudomonas nautica and Vibrio natriegens in acetate-based cultures. Both models were tested by comparing their output with the measured R O 2 time-profile. The MTE predicted respiration accurately only in the exponential growth phase, but not during the nutrient limitation part of the stationary phase. In contrast, the EKM worked well throughout both physiological phases as long as the modeled substrates fall with the declining carbon source. Results support the theoretical bases of the EKM. We conclude that the EKM holds promise for predicting respiration at the different physiological states and time-scales important to microbiological studies.