monod command

Syntax

fix ID group-ID nufeb/growth/monod sub-ID sub-Ks keyword value ...

ID = user-assigned name for the fix
group-ID = ID of the group atoms to apply the fix to
sub-ID = ID of the substrate for atom growth
sub-Ks = half-velocity constant (Ks) for the substrate
zero or more keyword/value pairs may be appended

keyword = growth or yield or decay

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

Examples

group bac type 1
grid_style nufeb/chemostat 1 glucose 0.001

fix f_monod bac nufeb/growth/monod glucose 3.5e-5 growth 4e-4 yield 0.61 decay 2e-5 maintain 1e-5
fix f_monod bac nufeb/growth/monod glucose 3.5e-5 growth 4e-4 yield 0.61

Description

Impose a Monod-like growth process to the atoms defined in group-ID. 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 sub-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 rate \(\mu\) is calculated based on the Monod equation:

\[\mu = \mu_{max} \cdot \frac{S_{sub}}{S_{sub} + Ks_{sub}} - b_{decay}\]

where:

\(\mu_{max}\) is the maximum growth rate (growth)
\(S_{sub}\) is the local substrate concentration at the grid cell in which atom resides
\(Ks_{sub}\) is the half-velocity constant for the substrate (sub-Ks)
\(b_{decay}\) is the decay rate (decay)

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 update substrate utilisation (reaction) rate R in all the affected grid cells:

\[R = \frac{1}{Y} \cdot \mu \cdot X\]

where:

\(Y\) is the yield coefficient (yield)
\(X\) is the biomass density of the affected atoms in grid cell