1
Y x=s
¼
1
Y 0
þ
r 0
e
ð11:1Þ
where, Y 0 , is the maximal biomass yield and e = (g cm
-2 ) is an efficiency factor
inversely proportional to the ratio between maintenance (m) and growth (l)
coefficients. For example, r 0 /e µ m/l (Ortega-Sánchez et al. 2012). Thus, e corresponds to the maximal biomass surface density for a given culture. Correlations
between Eq. (11.1) and data for two separate reports (Favela-Torres et al. 1998 on
Amberlite beads, Ortega-Sánchez et al. 2012, on agar plates) are shown in
Fig. 11.3. The maximal yield was similar for both correlations (Y 0 & 0.5) and was
obtained when r 0 was very small. Whereas e = 0.015 g cm
-2 for agar plates and
e = 0.075 g cm
-2 for Amberlite beads, supporting the idea that coefficient e
depends on the culture conditions (strain, support, medium composition, etc.). On
the other hand, Y 0 = 0.5 is the accepted maximal yield for aerobic cultures grown
on glucose (Heijnen and Roels 1981).
Ortega-Sánchez et al. (2012) developed a mass balance model on the spherical
shell of biomass with depth, h, covering spherical particles of radius R and having
biomass volumetric density q v (see Fig. 11.1a) as shown in Eq. (11.2)
M ¼ ðK þ 1Þ
3 À 1
ð11:2Þ
y = 0.013x + 2.454
R² = 0.727
y = 0.067x + 1.999
R² = 0.950
0
1
2
3
4
5
6
7
0
20
40
60
80
100
120
140
160
1/YX/S
σ (m gcm -2
ο
Fig. 11.3 Plot of inverse biomass yield (1/Y X/S = gS gX
-1
) of Aspergillus niger grown with
various glucose concentrations and two different solid support. (h) Amberlite beads
(d = 0.06 cm; a = 100 cm
-1
) and (D) agar plates. Data from Favela-Torres et al. (1998) and
Ortega-Sánchez et al. (2012), respectively. Initial substrate availability was calculated as
r 0 = S 0 a
-1 (mg cm
-2
). In the case of agar plates, S 0 values, and a values, changed independently
of each other. For Amberlite beads, the values of a were fixed and S 0 had different values
11 New Horizons for the Production of Industrial Enzymes
323
Y x=s
¼
1
Y 0
þ
r 0
e
ð11:1Þ
where, Y 0 , is the maximal biomass yield and e = (g cm
-2 ) is an efficiency factor
inversely proportional to the ratio between maintenance (m) and growth (l)
coefficients. For example, r 0 /e µ m/l (Ortega-Sánchez et al. 2012). Thus, e corresponds to the maximal biomass surface density for a given culture. Correlations
between Eq. (11.1) and data for two separate reports (Favela-Torres et al. 1998 on
Amberlite beads, Ortega-Sánchez et al. 2012, on agar plates) are shown in
Fig. 11.3. The maximal yield was similar for both correlations (Y 0 & 0.5) and was
obtained when r 0 was very small. Whereas e = 0.015 g cm
-2 for agar plates and
e = 0.075 g cm
-2 for Amberlite beads, supporting the idea that coefficient e
depends on the culture conditions (strain, support, medium composition, etc.). On
the other hand, Y 0 = 0.5 is the accepted maximal yield for aerobic cultures grown
on glucose (Heijnen and Roels 1981).
Ortega-Sánchez et al. (2012) developed a mass balance model on the spherical
shell of biomass with depth, h, covering spherical particles of radius R and having
biomass volumetric density q v (see Fig. 11.1a) as shown in Eq. (11.2)
M ¼ ðK þ 1Þ
3 À 1
ð11:2Þ
y = 0.013x + 2.454
R² = 0.727
y = 0.067x + 1.999
R² = 0.950
0
1
2
3
4
5
6
7
0
20
40
60
80
100
120
140
160
1/YX/S
σ (m gcm -2
ο
Fig. 11.3 Plot of inverse biomass yield (1/Y X/S = gS gX
-1
) of Aspergillus niger grown with
various glucose concentrations and two different solid support. (h) Amberlite beads
(d = 0.06 cm; a = 100 cm
-1
) and (D) agar plates. Data from Favela-Torres et al. (1998) and
Ortega-Sánchez et al. (2012), respectively. Initial substrate availability was calculated as
r 0 = S 0 a
-1 (mg cm
-2
). In the case of agar plates, S 0 values, and a values, changed independently
of each other. For Amberlite beads, the values of a were fixed and S 0 had different values
11 New Horizons for the Production of Industrial Enzymes
323