ecoli command

Syntax

fix ID group-ID nufeb/growth/ecoli suc-ID suc-Ks o2-ID o2-Ks co2-ID keyword value ...

ID = user-assigned name for the fix
group-ID = ID of the group atoms to apply the fix to
suc-ID = substrate ID for sucrose
suc-Ks = half-velocity constant (Ks) for sucrose
o2-ID = substrate ID for oxygen
o2-Ks = half-velocity constant (Ks) for oxygen
co2-ID = substrate ID for carbon dioxide
zero or more keyword/value pairs may be appended

keyword = growth or yield or decay or maintain

growth value = maximum growth rate
yield value = yield coefficient
decay value = decay rate
maintain value = maintenance coefficient

Examples

#--- examples/Pub-J.Sakkos-2023-Phototroph ---#

group ecoli type 1
grid_style nufeb/chemostat 3 suc o2 co2 4e-6

fix f_gecoli aob nufeb/growth/ecoli suc 3.6 o2 0.001 co2 growth 2.7e-4 yield 0.43 maintain 9.5e-7 decay 2e-5

Description

Perform microbial growth to the atoms defined in group-ID. The affected atoms are considered as Escherichia coli (E.coli). The model assumes that E.coli can utilise sucrose and oxygen to produce co2. Additionally, the model takes into account microbial decay and endogenous respiration processes.

The fix is called at each biological step (see run_style nufeb) to update atom and grid attributes. The value of the substrate ID keyword XX-ID must be consistent with the name defined in the grid_style chemostat command. The following forward Euler method is implemented to update the mass (m) of each atom in the group:

\[ \begin{align}\begin{aligned}m' & = m + \mu \cdot \Delta t\\\hfill\end{aligned}\end{align} \]

The specific growth rates \(\mu\) is calculated based on the equations described in (Sakkos, J., et al, 2023):

\[ \begin{align}\begin{aligned}\mu & = r1 - r2 - b_{decay}\\r1 & = \mu_{max} \cdot \frac{S_{suc}}{S_{suc} + Ks_{suc}} \cdot \frac{S_{o2}}{S_{o2} + Ks_{o2}}\\r2 & = b_{maint} \cdot \frac{S_{o2}}{S_{o2} + Ks_{o2}}\end{aligned}\end{align} \]

where:

\(b_{decay}\) is the decay rate (decay)
\(\mu_{max}\) is the maximum growth rate (growth)
\(S_{suc}, S_{o2}\) are the local concentrations of sucrose and oxygen, respectively, at the grid cell in which atom resides
\(Ks_{suc}, Ks_{o2}\) are the half-velocity constants for sucrose (suc-Ks) and oxygen (o2-Ks), respectively
\(b_{maint}\) is the maintenance coefficient (maintain)

The new mass is then used to update atom attributes. In the case of atom_style coccus is used, the diameter changes accordingly. For atom_style bacillus, update affects the length of the bacilli.

If fix nufeb/diffusion_reaction is applied, the fix also updates substrate utilisation (reaction) rates in all the affected grid cells:

\[ \begin{align}\begin{aligned}R_{suc} & = -\frac{1}{Y} \cdot r1 \cdot X\\R_{o2} & = -0.399 \cdot (r1 + r2) \cdot X\\R_{co2} & = -0.2 \cdot (r1 + r2) \cdot X\end{aligned}\end{align} \]

where:

\(R_{suc}, R_{o2}, R_{co2}\) are the utilisation rates of sucrose, oxygen, carbon dioxide in the affected grid cells, respectively
\(Y\) is the yield coefficient (yield)
\(X\) is the E.coli biomass density in grid cell

(Sakkos, J., et al, 2023) Sakkos, J., et al., Predicting partner fitness based on spatial structuring in a light-driven microbial community. PLoS Comput. Biol. (2023)