Oxygen management is a key cost for nitrogen fixers that we seek to quantitatively model. First consider the rate of change of the intracellular oxygen, QO2 (mol O2 per cell) in a spherical microbe:
Here, [O2] and [O2]C are the environmental and intracellular oxygen concentrations, respectively (mol O2 m−3). The first term on the right, PO2 (mol O2 per cell per s) represents a source from oxygenic photosynthesis. The second term is a source because of transfer across the membranes of cell with the cytoplasmic radius r (m per cell), governed by the oxygen gradient and the effective diffusivity across the membrane and external molecular boundary layer, κO2 (m2 s−1). The third term, in parentheses, represents consumption of intracellular oxygen by respiration associated with synthesis (RS) including the direct cost of nitrogen fixation, maintenance (Rm) and respiratory protection (RP) (mol O2 per cell per s). RS is related to the growth rate of the population, μ (s−1) by
where QC is the carbon quota (mol C per cell) of the species in question and YSO2:BIO is the growth yield with respect to oxygen (mol O2 consumed per mol C biomass synthesized), which can be evaluated from the overall stoichiometry of the reactions (Heijnen and Roels, 1981 ; Rittmann and McCarty, 2001 ; seeSupplementary Material S1 ).
As reducing intracellular oxygen concentration is critical for nitrogen fixers, consider the solution for the intracellular oxygen concentration [O2]C at steady state (dQO2/dt≈0):
Oxygenic photosynthesis, PO2, always acts to increase intracellular oxygen concentration along with invasion from the environment, if the external concentration is higher. In contrast, there are numerous strategies to reduce intracellular oxygen levels and protect nitrogenase, as mentioned in the introduction: living in a low-oxygen environment, reducing [O2] increasing the efficiency of respiratory oxygen consumption, YSO2:BIO; and creating thick membranes or mucus layers to reduce the effective diffusivity of oxygen, κO2 into the cell. As carbon quota, QC, increases with cell volume (r3), increasing cell radius will increase RS and reduce [O2]C, as will increasing growth rate μ also increase the respiratory oxygen demand. A high maintenance respiration or deliberate respiratory protection, RP, consumes oxygen. The investment in respiratory protection to reduce the intracellular oxygen concentration to very low levels can be estimated by setting [O2]C=0 inEquation (4) and re-arranging:
The required RP is the difference between sources due to oxygenesis and diffusive invasion, and the demand from growth and maintenance.
Here, [O2] and [O2]C are the environmental and intracellular oxygen concentrations, respectively (mol O2 m−3). The first term on the right, PO2 (mol O2 per cell per s) represents a source from oxygenic photosynthesis. The second term is a source because of transfer across the membranes of cell with the cytoplasmic radius r (m per cell), governed by the oxygen gradient and the effective diffusivity across the membrane and external molecular boundary layer, κO2 (m2 s−1). The third term, in parentheses, represents consumption of intracellular oxygen by respiration associated with synthesis (RS) including the direct cost of nitrogen fixation, maintenance (Rm) and respiratory protection (RP) (mol O2 per cell per s). RS is related to the growth rate of the population, μ (s−1) by
where QC is the carbon quota (mol C per cell) of the species in question and YSO2:BIO is the growth yield with respect to oxygen (mol O2 consumed per mol C biomass synthesized), which can be evaluated from the overall stoichiometry of the reactions (Heijnen and Roels, 1981 ; Rittmann and McCarty, 2001 ; see
As reducing intracellular oxygen concentration is critical for nitrogen fixers, consider the solution for the intracellular oxygen concentration [O2]C at steady state (dQO2/dt≈0):
Oxygenic photosynthesis, PO2, always acts to increase intracellular oxygen concentration along with invasion from the environment, if the external concentration is higher. In contrast, there are numerous strategies to reduce intracellular oxygen levels and protect nitrogenase, as mentioned in the introduction: living in a low-oxygen environment, reducing [O2] increasing the efficiency of respiratory oxygen consumption, YSO2:BIO; and creating thick membranes or mucus layers to reduce the effective diffusivity of oxygen, κO2 into the cell. As carbon quota, QC, increases with cell volume (r3), increasing cell radius will increase RS and reduce [O2]C, as will increasing growth rate μ also increase the respiratory oxygen demand. A high maintenance respiration or deliberate respiratory protection, RP, consumes oxygen. The investment in respiratory protection to reduce the intracellular oxygen concentration to very low levels can be estimated by setting [O2]C=0 in
The required RP is the difference between sources due to oxygenesis and diffusive invasion, and the demand from growth and maintenance.