It is also possible to divide the biomass into living and dead biomass and to
include equations for temperature-related death. Arrhenius-type relationships
can be used to describe the effect of temperature on both the specific growth
rate and the specific death rate, giving a net growth rate [99]:
–E g
–E d
m T = m To exp 61 – k do exp 61
(9)
RT
RT
In this case both of the rates increase with temperature, but the death rate is
negligible below the optimal temperature. Above the optimal temperature the
death term increases faster than the growth term, so the net specific growth rate
falls. In this case the equation was fitted to data collected using the isothermal
approach using non-linear regression.
A slightly different approach was taken by Smits et al. [100]. Rather than
describing the death of biomass itself, they incorporated an inactivation term
into their equation relating oxygen uptake to growth. This corresponds to a
decrease in specific respiration activity as a result of aging processes. The inactivation term was expressed as an Arrhenius function of temperature:
E a 1
1
m d = m d0 + k md exp ΄ – 31 21 – 7 ΅
(10)
R T T max
where m d0 is the basal specific inactivation rate.
As mentioned above, to date the effect of temperature on growth and death
kinetics has been based on data obtained using the isothermal method.
However, recent work indicates that the growth and death kinetics of a microorganism which starts growing at the optimum temperature for growth and is
later subjected to a rise in temperature is not adequately described by the equations obtained using this isothermal approach. In the bioreactor model of
Saucedo-Casteneda et al. [96], the model could not describe the experimental
temporal temperature profiles if the specific growth rate was allowed to
decrease as the temperature rose above the optimum temperature according to
the expression obtained from isothermal approach data. Good agreement with
the experimental results could only be obtained if the growth rate was assumed
to remain constant as the temperature increased. Ikasari et al. [101] mimicked
the temporal temperature profile in SSF of Rhizopus oligosporus by making a
step upshift in temperature from 37 °C to 50 °C after 20 h of fermentation and a
downshift back to 37 °C 10 h later. Growth rates close to the growth rate before
the temperature upshift were maintained for several hours at the higher temperature. Furthermore, the upshift had delayed deleterious effects which were
not reversed by returning the culture to 37 °C. More work needs to be done with
a wider range of organisms and various temporal temperature profiles to obtain
sufficient kinetic data to allow the effect of a varying temperature on growth to
be modeled adequately.
Biochemical Engineering Aspects of Solid State Bioprocessing
87
include equations for temperature-related death. Arrhenius-type relationships
can be used to describe the effect of temperature on both the specific growth
rate and the specific death rate, giving a net growth rate [99]:
–E g
–E d
m T = m To exp 61 – k do exp 61
(9)
RT
RT
In this case both of the rates increase with temperature, but the death rate is
negligible below the optimal temperature. Above the optimal temperature the
death term increases faster than the growth term, so the net specific growth rate
falls. In this case the equation was fitted to data collected using the isothermal
approach using non-linear regression.
A slightly different approach was taken by Smits et al. [100]. Rather than
describing the death of biomass itself, they incorporated an inactivation term
into their equation relating oxygen uptake to growth. This corresponds to a
decrease in specific respiration activity as a result of aging processes. The inactivation term was expressed as an Arrhenius function of temperature:
E a 1
1
m d = m d0 + k md exp ΄ – 31 21 – 7 ΅
(10)
R T T max
where m d0 is the basal specific inactivation rate.
As mentioned above, to date the effect of temperature on growth and death
kinetics has been based on data obtained using the isothermal method.
However, recent work indicates that the growth and death kinetics of a microorganism which starts growing at the optimum temperature for growth and is
later subjected to a rise in temperature is not adequately described by the equations obtained using this isothermal approach. In the bioreactor model of
Saucedo-Casteneda et al. [96], the model could not describe the experimental
temporal temperature profiles if the specific growth rate was allowed to
decrease as the temperature rose above the optimum temperature according to
the expression obtained from isothermal approach data. Good agreement with
the experimental results could only be obtained if the growth rate was assumed
to remain constant as the temperature increased. Ikasari et al. [101] mimicked
the temporal temperature profile in SSF of Rhizopus oligosporus by making a
step upshift in temperature from 37 °C to 50 °C after 20 h of fermentation and a
downshift back to 37 °C 10 h later. Growth rates close to the growth rate before
the temperature upshift were maintained for several hours at the higher temperature. Furthermore, the upshift had delayed deleterious effects which were
not reversed by returning the culture to 37 °C. More work needs to be done with
a wider range of organisms and various temporal temperature profiles to obtain
sufficient kinetic data to allow the effect of a varying temperature on growth to
be modeled adequately.
Biochemical Engineering Aspects of Solid State Bioprocessing
87