SUPPORTING INFORMATION
In this section, large tables are provided as a compliment to the main manuscript. A detailed
discussion of the content of some of the tables is also provided to complement and facilitate the
interpretation of the results in the tables.
S1 Description of the parameters of the model and their nominal values
Table S1.1 Input parameters related to the biological processes of the model
Definition
Symbol
Value
Unit
Biomass growth yield on substrate
YSX
0.46
C-mmol X/C-mmol S
Inert particulate content of biomass
fXI
0.09
g/g DW
Nitrogen content of biomass
iNX
0.21
N-mmol /C-mmol X
Phosphorus content of biomass
iPX
0.0094
P-mmol /C-mmol X
Molecular weight of biomass
MWx
25.065
mg/C-mmol X
Molecular weight of substrate
MWs
30.0
mg/C-mmol S
Degree of reduction of biomass
x
4.035
mmol e-/C-mmol X
Degree of reduction of substrate
s
4.0
mmol e-/C-mmol S
Maximum growth rate of biomass
max
0.135
1/h
Maintenance coefficient
ms
0.0375
C-mmol S/(C-mmol X·h)
Biomass decay coefficient
kd
0.02
1/h
Lag time prior to onset of biomass growth
tlag
29.2
h
Monod half-saturation coefficient for substrate
KS
33.33
C-mmol/L
Monod half-saturation coefficient for oxygen
KO
3.1E-5
O-mmol/L
Monod half-saturation coefficient for ammonia
KNH3
1E-4
N-mmol /L
Monod half-saturation coefficient for phosphate
KPO
1.05
P-mmol/L
Actinorhodin (ACT) yield on substrate
YSACT
0.17
C-mmol Act/C-mmol S
Growth associated ACT production constant
ACT
0.014
C-mmol Act/C-mmol X
Non-growth associated ACT production rate
ACT
0.001
C-mmol Act/(C-mmol X·h)
Maximum level of ACT production
max
S ACT
1.3
C-mmol/L
1
Molecular weight of ACT
MWact
19.81
g/C-mmol ACT
Degree of reduction of ACT
ACT
3.94
mmol e-/C-mmol ACT
Undecylprodigiosin (RED) yield on substrate
YSRED
0.0954
C-mmol RED/C-mmol S
Growth associated RED production constant
RED
1E-04
C-mmol RED/C-mmol X
Non-growth associated RED production rate
 RED
4.42E-05 C-mmol RED/(C-mmol X·h)
Maximum level of RED production
max
S RED
0.2
C-mmol RED/L
Molecular weight of RED
MWred
15.72
g/C-mmol RED
Degree of reduction of RED
 RED
4.96
mmol e-/C-mmol RED
Nitrogen content of RED
iNRED
0.12
N-mmol/C-mmol RED
Table S1.2 Input parameters related to the physical-chemical processes of the model
Definition
Symbol
Value
Unit
Temperature of the fermenter
T
25.0
0C
Negative logarithm of hydrogen ions
pH
7.02
-
Apparent equilibrium constant for NH4 dissociation
pKNH
9.25
-
Apparent equilibrium constant for CO2 dissociation
pKHCO3
6.35
-
Apparent equilibrium constant for H2PO4 dissociation
pKH2PO4
7.20
-
Apparent equilibrium constant for water dissociation
pKw
14.0000
-
Apparent forward rate constant for NH4 dissociation
kf,NH
3.6E+10
1/h
Apparent forward rate constant for CO2 dissociation
kf,CO2
3.6E+10
1/h
Apparent forward rate constant for H2PO4 dissociation
kf,H2PO4
3.6E+10
1/h
Apparent forward rate constant for water dissociation
kf,W
3.6E+10
1/h
Universal gas constant
R
0.082057
L·atm /(K·mol)
Diffusion coefficient of O2 in water at 25 0C
DO2
2.42E-05
cm2/s
Diffusion coefficient of CO2 in water at 25 0C
DCO2
1.91E-05
cm2/s
Diffusion coefficient of N2 in water at 25 0C
DN2
2.00E-05
cm2/s
Henry’s gas-liquid equilibrium constant for O2
KHO2
0.0013
mmol/ (L ·atm)
Henry’s gas-liquid equilibrium constant for CO2
KHCO2
0.045
mmol/ (L·atm)
2
Henry’s gas-liquid equilibrium constant for N2
KHN2
0.00065
mmol/ (L ·atm)
Saturation concentration of O2 in liquid
S*O2
0.27
mmol/L
Saturation concentration of CO2 in liquid
S*CO2
0.027
mmol/L
Saturation concentration of N2 in liquid
S*N2
1.02
mmol/L
Equilibrium/saturation concentration of NH3 in liquid
S*NH3
1E-6
mmol/L
Mass transfer rate coefficient for O2
KLaO2
121.9
1/h
Mass transfer rate coefficient for CO2
KLaCO2
107.5
1/h
Mass transfer rate coefficient for N2
KLaN2
110
1/h
Mass transfer rate coefficient for NH3
KLaNH3
0.125
1/h
Liquid volume in the fermenter
VL
3
L
Gas-phase volume in the fermenter
VG
0.5
L
Gas (air) inflow rate to the fermenter
QGin
180
L/h
Total pressure in the inflow gas
Pin
1.2
atm
Partial pressure of oxygen in the inflow gas
PO2
0.2097
atm
Partial pressure of CO2 in the inflow gas
PCO2
0.0003
atm
Total pressure in the outflow gas (off-gas)
Pout
1.0
atm
3
S2 Results of Latin Hypercube Sampling of the input parameters with correlation control
The correlation matrix available for some of the model parameters was obtained from non-linear least
square model identification results, and is shown in Table 2.1 (Sin et al., 2008). As there is no
information available, no correlation was assumed between the remaining input parameters.
Examples from the results of the Latin Hypercube Sampling with 500 total samples are shown in Figure
S2.1 for some input parameters. In the same figure, one can also observe the effectiveness of the
correlation control induced with the Iman-Conover (IC) method. Overall, the IC method was successful
in imposing the correlation between the inputs as required by the correlation matrix of the input
parameters in Table S2.1.
Table S2.1 The available correlation matrix for 10 input parameters of the model
YSX
iNX
iPX
max
KP
ACT
RED
tlag
Pin
YSX
1.00
iNX
-0.36
1.00
iPX
-0.25
0.66
1.00
max
-0.12
-0.05
-0.33
1.00
KP
-0.18
-0.03
-0.34
0.98
1.00
ACT
-0.30
0.04
-0.26
0.60
0.68
1.00
RED
-0.25
0.07
-0.12
0.32
0.38
0.36
1.00
tlag
-0.08
0.01
-0.16
0.84
0.73
0.33
0.17
1.00
Pin
-0.54
-0.11
-0.27
0.19
0.19
0.20
0.15
0.19
1.00
KLaO2
-0.01
0.02
0.00
0.00
0.00
0.00
0.00
0.00
-0.24
KLaO2
1.00
4
Figure S2.1 Examples of Latin Hypercube Sampling results for some input parameters. The rank
correlation was imposed by the Iman-Conover method.
5
S3 Morris sampling results
We performed the Morris sampling following the suggestion of Campolongo et al (2007). The latter
authors advice to first perform a large number of sampling, e.g. r equal to 1000 and then to select a
smaller subset among them, e.g. 35 that has the highest Euclidean distance.
The Morris sampling results with r equal to 1000 and the improved Morris sampling results with r equal
to 35 are shown in Figure 3. The figure shows the scatter plots of 3 Morris-sampled input parameters to
assess the performance of the sampling. One observes that each input parameter took values from 4 (p)
distinct levels within their corresponding range (as imposed by the Morris sampling algorithm). Further,
the mean of the sampled inputs from both sampling scheme were rather close to their corresponding
nominal values indicating both sampling schemes covered the input space uniformly. Hence the
improved Morris sampling results with r equal to 35 were used for this study as it required a much lower
number of model simulations (compare 1995 (35*(56+1)) versus 57000 (1000*(56+1)) respectively).
6
Figure S3 Comparison of the effect of sampling number in the Morris method: Original Morris
sampling with r equal to 1000 (top) and improved Morris sampling with r equal to 35 (bottom).
7