Modeling of Scale-Dependent Bacterial Growth by Chemical Kinetics Approach

Table 1

Kinetic setup of the CKA model. The parameters 𝑘₅ and 𝑘₆ are flow rate constants to simulate chemostat conditions or the inflow of CO₂ into the system. [B]₀, [O₂]₀, [CO₂]₀, and [N]₀ are the reactant inflow concentrations (B_an was not considered). The experimentally observed optical densities were taken as directly proportional to the total bacteria concentration [B]_𝑇 = [B] + [B_an].

Reaction fluxes	Differential equations
𝑟I=𝑘0 · [B] · [O2]	𝑑[B]/𝑑𝑡 = 𝑟I−𝑟II+𝑘5  ·  ([B]0−[B])
𝑟II=𝑘1 · [B]	𝑑[O2]/𝑑𝑡 = −𝑟I+𝑘5  ·  ([O2]0−[O2])
𝑟III=𝑘2/(𝑘4 · [CO2] + 1) · [Ban] · [N]	𝑑[Ban]/𝑑𝑡 = 𝑟II+𝑟III−𝑘5  ·  [Ban]
𝑟IV=𝑘3 · [CO2]	𝑑[CO2]/𝑑𝑡 = 𝑟III−𝑟IV+𝑘6  ·  ([CO2]0−[CO2])
	𝑑[N]/𝑑𝑡 = −𝑟III+𝑘5  ·  ([N]0−[N])