DEBtool Toolbox: degrad

Biodegradation of chemical compounds in batch cultures.

The theory for the models can be found in the DEB-book.

pirt

The Marr-Pirt model is a special case of the DEB model, and has the Monod model as special case. It concerns V1-morphs in a batch culture. Two data sets are required to estimate all parameters using routines nmregr, or nrregr: time-substrate-weight and time-biomass-weight matrices. The weight coefficients can be suppressed, in which case value one is inserted for all weight coefficients. The single data set time-substrate-weight is sufficient if the initial biomass concentration, the yield and maintenance rate coefficients are kept fixed.

Input:

  • 6-vector with parameters:
    1. initial concentration of substrate
    2. initial concentration of biomass
    3. saturation constant
    4. max spec uptake rate
    5. yield of substrate on biomass
    6. maintenance rate coefficient
  • (n,k)-matrix with times for concentrations of substrate in column 1
  • (m,k)-matrix with times for biomass in column 1

Output:

  • n-vector with concentrations of substrate
  • m-vector with biomass

An example of application of pirt in regression and plotting routines is given in the script-file mydata_pirt.

DEB

The DEB model concerns 1-structure, 1-reserve V1-morphs in a batch culture. The reserve density is treated as a hidden variable, and the measured biomass is taken to quantify structure. Two data sets are required to estimate all parameters using routines nmregr, or nrregr: time-substrate-weight and time-biomass-weight matrices. The weight coefficients can be suppressed, in which case value one is inserted for all weight coefficients.

Input:

  • 6-vector with parameters:
    1. initial concentration of substrate
    2. initial concentration of structure
    3. saturation constant
    4. max spec uptake rate
    5. yield of substrate on structure
    6. reserve turnover rate
    7. maintenance rate coefficient
  • (n,k)-matrix with times for concentrations of substrate in column 1
  • (m,k)-matrix with times for biomass in column 1

Output:

  • n-vector with concentrations of substrate
  • m-vector with biomass

An example of application of DEB in regression and plotting routines is given in the script-file mydata_deb.