WOLFRAM|DEMONSTRATIONS PROJECT

Lag Time in Microbial Growth

​
shifted logistic model data generation parameters
y
asym
10.
k
0.2
t
c
30.
pts. to generate
6
data scatter ϵ
0.
seed
0
Gompertz fitting model initial parameter values
y
asym
G
9.
b
16.
c
0.1
Weibull fitting model initial parameter values
y
asym
W
8.
Ï„
35.
m
2.
fit selected model to data and plot results
before next fit, set initial parameters to
default values
last fitted values
axes maxima
time axis max.
60.
growth axis max.
12.
data generation model:
y
logisticshifted
(t) =
y
asym
S
1
k(
t
c
-t)
e
+1
-
1
k
t
c
e
+1
Gompertz fitting model:
y
Gompertz
(t) =
y
asym
G
-b
-ct
e
e
Weibull fitting model:
y
Weibull
(t) =
y
asym
W
1-
-
m
t
Ï„
e
Gompertz model fit
Weibull model fit
2
r
= 0.9976
MSE = 0.2051
2
r
= 1.000
MSE = 0.00904
y
asym
G
= 10.6
y
asym
W
= 9.87
b = 16.1
Ï„ = 32.8
c = 0.104
m = 4.23
t
inflec
G
= 26.8
t
inflec
W
= 30.7
μ
max
G
= 0.405
μ
max
W
= 0.483
λ
G
= 17.1
λ
W
= 19.8
λ
G
= 8.05 at
y
G
(t) = 0.01
λ
W
= 6.42 at
y
W
(t) = 0.01
Frequently, when a microbial population is transferred into a new habitat, noticeable cell division only commences after what is known as a "lag time". According to the food microbiology literature, this lag time can be determined by extrapolating the tangent to the growth curve at its inflection point to the line
N(t)=
N
0
, where
N
0
is the inoculum's original size. In this Demonstration, simulated growth ratio data, with or without random scatter, is fitted to the Gompertz or stretched exponential (Weibullian) models using nonlinear regression. The tangent method is then used to calculate the lag time with the fitted parameters. It is shown that the lag time so calculated can depend on the growth model chosen and be substantially longer than that marking the time where growth can first be observed.