Toolbox: microbe

Micro-organisms in reactors: 1 reserve, 1 structure, V1-morph

microbe

Demo that runs:

The microbe is decomposed in:
structure (V) and general reserves (E)

Organic compounds:
X = substrate, V = structure, E = reserve, P = product(s)
Mineral compounds:
C = carbon dioxide, H = water, O = dioxygen, N = ammonia

Uptake is proportional to surface area, which is taken to be proportional to the structural volume: V1-morph. This removes the distinction between the individual and the population level.

The simplification k_J = k_M*(1 - kap)/kap is implemented, which makes this energy-structured model also size-structured. The microbe divides when the structural mass exceeds a threshold value

In a generalized reactor, the specific supply and draining rates can be set independently for all compounds. If they are chosen to be equal, we have a chemostat. If the specific draining rates are set to zero, we have a fed-batch reactor; if the specific supply rate set to zero as well, we have a batch-reactor.

Example of use after (optionally) editing file pars_microbe.m: microbe


pars_microbe

Set the parameters by editing file pars_microbe.m in toolbox microbe.

shbatch

Batch reactor; Initial conditions can be changed by editing file shbatch.m. See pages 315 ff of the DEB-book.
Four figures are shown of variables against time

fig 1
Living (green, drawn) and and dead (green, stippled) structure; living (red, drawn) and dead (red, stippled) reserve. All in Molar.

fig 2
Living (brown, drawn) and dead (brown, stippled) biomass (so structure plus reserve) in gram per litre.

fig 3
Substrate (green, drawn) in Molar

fig 4
Product (red, drawn) in Molar. Think, for instance of penicillin, or acetate. It is not difficult to extend the routine to include more types of product.

Example of use after editing pars_microbe.m: clear all; pars_microbe; shbatch.
The command clear; pars_microbe; shbatch (4) will only plot fig 4.


shchemostat

Chemostat reactor in equilibrium. See pages 147, 312 ff of the DEB-book.
Six figures are shown of variables against throughput rate

fig 1
Living (green, drawn) and dead (green, stippled) structure; living (red, drawn) and dead (red, stippled) reserve, all in Molar

fig 2
Living (brown, drawn) and dead (brown, stippled) biomass (so structure plus reserve) (red, drawn) in gram per litre.

fig 3
Fraction of dead structure (brown) in M/M.

fig 4
Substrate (green) in the medium in Molar.

fig 5
Product (brown) in the medium in Molar.

fig 6
Heat production (red) in kJ/d by the biomass in the reactor.

Example of use after editing pars_microbe.m: clear all; pars; shchemostat.
The command clear; pars; shchemostat(5) will only plot fig 5.


shflux_microbe

This routine is similar to shchemostat, but presents scaled fluxes, rather than states: the ratio of the fluxes and the flux of substrate, or the flux of structure, or the total weight (living plus dead biomass).

fig 1
Scaled flux of structure (green), reserve (red), product (black)

fig 2
Scaled flux of carbon dioxide (black) and water (blue)

fig 3
Scaled flux of dioxygen (black) and ammonia (blue)

fig 4
Scaled flux of dissipating heat (red)

fig 5-8
Similar to figs 1-4, but the fluxes are divided by the flux of (living) structure, rather than that of substrate. Fig 5 shows the scaled flux of substrate rather than the scaled flux of structure (cf fig 1), for obvious reasons.

fig 9-12
Similar to figs 1-4, but the fluxes are divided by the weight of biomass (living plus dead), rather than the scaled flux of substrate.

Example of use after editing pars_microbe.m: clear all; pars_microbe; shflux_microbe.
The command clear; pars_microbe; shflux_microbe (2) will only plot fig 2.


chemostat

Calculates states, powers, organic and mineral fluxes. (Used by shchemostat and shflux_microbe)

Input:

Output: 4 matrices (throughput rates in rows). In columns:

Example of use:
clear; pars; [Xh, ph, JOh, JMh] = chemostat ([.1 .2], 1);


shratio_microbe

Routine that produces three plots that show ratios of mineral fluxes as functions of the specific growth rate. All fluxes are in terms of mol per time; the ratio's are dimensionless. See pages 143 and 167 of the DEB-book. Contrary to the similar routine in toobox animal, the contribution of assimilation is here taken into account, and no changes in signs are made. (The signs depend on the composition of substrate and biomass, but the substrate can here be chosen from a wide range.)

fig 1
Respiration Quotient: ratio of carbon dioxide and dioxygen fluxes

fig 2
Watering Quotient: ratio of water and dioxygen fluxes

fig 3
Urination Quotient: ratio of nitrogen waste and dioxygen fluxes

Example of use after editing pars_microbe.m: clear all; pars; shratio_microbe.
The command clear; pars; shratio_microbe (2) will only plot fig 2.


batch

Subroutine that specifies nutrient limited growth in a batch culture. The special case of no-maintenance and a very small saturation constant has been coded, which results in expo-logistic growth (see DEB book page 355).

The script file mydata_batch illustrates the application of this subroutine in parameter estimation and plotting routines.

Input:

Ouput:

Running mydata_batch shows 2 plots of the potassium concentration and of the biomass of Escherichia coli against time. Notice the continuation of growth in absence of potassium, which reflects the presence of intracellular storage of potassium.


adapt

Subroutine that specifies slow adaptation to substrate availability and mutual inhibition of the uptake of two substrates in a batch culture. The special case of 2 substrates and 4 batch cultures has been coded. The theory is given in
Brandt, B. W., Kelpin, F. D. L., Leeuwen, I. M. M. van, Kooijman, S. A. L. M. 2004. Modelling microbial adaptation to changing availability of substrates. Water Res. 38: 1003--1013

The script file mydata_adapt illustrates the application of this subroutine in parameter estimation and plotting routines.

Input:

The output is 4 vectors with predictions of biomasses. The number of cultures can easily be adapted.

Running mydata_adapt shows 4 plots of biomass of Klebsiella oxytoca against time in 4 batch cultures with different initial concentrations of glucose and xylose; in g/l: (1) 5.8, 0 (2) 0, 4.7 (3) 0.5, 2.5 (4) 0.33, 2.0. The bacteria were precultured on glucose. Data and model predictions are shown. Diauxic growth is clearly visible (in the last two cultures).


yield

Calculates the yield coefficients for mineral and organic compounds, given the chemical indices of the organic compounds.

Input: (4,4)-matrix with chemical indices for energy and carbon substrate, reserve, structure in the columns, and chemical element C, H, O, N in the rows.

Output: (8,5)-matrix with yield coefficients with mineral and organic compounds in the rows (CO2, H2O, O2, NH3, energy and carbon substrate, reserve, structure) and processes in the columns (catabolic and anabolic aspects of assimilation, maintenance, catabolic and anabolic aspects of growth).

Example of use: see mydata_reaction_eq


flux_5

Calculates the specific fluxes for catabolic and anabolic aspects of assimilation, maintenance, catabolic and anabolic aspects of growth.

Input:

Output: (n,5)-matrix with fluxes in the columns (catabolic and anabolic aspects of assimilation, maintenance, catabolic and anabolic aspects of growth).

Example of use: see mydata_reaction_eq


entropy

Calculates the entropy of a CHON compound under aerobic conditions in J/mol.K, on the basis of the entropies 214.70 J/mol.K for CO2, 72.331 J/mol.K for H2O, 205.80 J/mol.K for O2 and 112.34] J/mol.K for NH3.

Input: 4-vector with chemical indices for elements C, H, O, N.

Output: scalar with entropy of CHON-compound in J/mol.K


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