. 2016 Dec 12;17(4):440–447. doi: 10.1002/elsc.201600088

Table 1.

Model equations according to the three existing hypotheses for biomass segregation

Balances—biomass subpopulations

1. Viable cell concentration

\frac{d V C C}{d t} = (μ - k_{D}) \cdot V C C - D \cdot V C C

(1)

2. Dead cell concentrations

Hypothesis 1:

\frac{{d D C C}_{I}}{d t} = k_{D I} \cdot V C C - k_{D I L} \cdot {D C C}_{I} - D \cdot {D C C}_{I}

(1.1)

\frac{{d D C C}_{L}}{d t} = k_{D I L} \cdot D C C_{1} - D \cdot {D C C}_{L}

(1.2)

k_{D} = k_{D I}

(1.3)

Hypothesis 2:

\frac{d D C C_{I}}{d t} = k_{D I} \cdot V C C - D \cdot D C C_{I}

(2.1)

\frac{d D C C_{L}}{d t} = k_{D L} \cdot V C C_{I} - D \cdot D C C_{L}

(2.2)

k_{D} = k_{D I} + k_{D L}

(2.3)

Hypothesis 3:

\frac{d D C C_{I}}{d t} = k_{D I} \cdot V C C - k_{D I L} \cdot D C C_{I} - D \cdot D C C_{I}

(3.1)

\frac{d D C C_{L}}{d t} = k_{D L} \cdot V C C + k_{D I L} \cdot D C C_{I} - D \cdot D C C_{L}

(3.2)

k_{D} = k_{D I} + k_{D L}

(3.3)

VCC, viable cells; DCC_I, morphologically intact dead cells; DCC_L, morphologically not intact dead cells.