Table 1 Symbolic notations used and corresponding units

R:

Response as inhibition of bacterial growth. Dimensionless

D:

Dose. Dimensions: mg/l

b:

Position parameter. Dimensions: mg/l

a:

Shape parameter. Dimensionless

m:

Dose for semi-maximum response (ED₅₀). Dimensions: mg/l

K:

Maximum inhibition response. Dimensionless

Logistic equation and biomass dynamic

X:

Biomass. Dimensions: mg/l

t:

Time. Dimensions: h

v _x :

Biomass production rate. Dimensions: mg l^-1 h^-1

X _m :

Maximum biomass. Dimensions: mg/l

r ₀ :

Specific maximum rate without effector action. Dimensions: h^-1

r:

Specific maximum rate with effector action. Dimensions: h^-1

Q ₀ :

Initial effector concentration. Dimensions: mg/l

Q _H :

Concentration of effector retained by dead biomass (X _H ). Dimensions: mg/l

q _H :

First order kinetic constant. Dimensionless

v _Q :

Rate of available effect dynamic. Dimensions: mg l^-1 h^-1

Q _S :

Concentration of effector metabolically deactivated by living biomass (X _S ). Dimensions: mg/l

q _S :

Second order kinetic constant. Dimensions: l mg^-1 h^-1

D*:

Dose:Biomass ratio. Dimensionless

Subscript meaning

H:

Death

S:

Survival

m:

Maximum