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Stoichiometric and Energetic Considerations of Yield Coefficients and Pathway Selectivity under Different Conditions

The yield of 1,3-PD from glycerol depends significantly on the selectivity of pathways involved in the pyruvate metabolism and on the regulation of the reducing equivalent balance (33,38). This is illustrated below by the glycerol fermentation of C. butyricum. Similar analysis can be done for the glycerol fermentation of K. pneumoniae. For the glycerol fermentation of C. butyricum we first consider the situation in which the redu­ced ferredoxin (Fdred) is cleaved into hydrogen and oxidized ferredoxin (Fdox) (reaction 3 in Fig.2). The main reactions involved in the glycerol fermentation by C butyricum under these conditions can be written as follows:

(1) biomass formation

C3H803+3NH3 + 3-^-ATP -> 3C4H702N + 8[H] + 6H20 (la) yatp

Where C4H702N denotes the elemental composition of biomass and corresponds to a molecular biomass weight (MG) of 101 g/mol (38). The same formula for biomass has been used for the analysis of glycerol fermentation by K. pneumoniae (33). YATP is the energetic yield of biomass (g biomass/mol ATP) which was found to be about 8.5 g/mol ATP for C. butyricum (8). For simplicity YATP is taken here as 8.6 g/mol ATP. In Eq. 1 [H] represents one g atom available hydrogen which is equivalent to 1/2 mole NADH2. Thus, Eq. (la) becomes

C3H803 + 3NH3 + 35ATP -► 3C4H702N + 4NADH2 + 6H20 (lb)

(2) acetate formation

C3H803 -> C2H402 + 2NADH2 + 2ATP + C02 + H2 — H20 (2)

(3) butyrate formation

2C3H803 C4H802 + 2NADH2 + 3ATP + 2C02 + 2H2 (3)

(4) 1,3-propanediol formation

C3H803 + NADH2 ->C3H802 + 2H20 (4)

From Eqs. 2 and 3 it is obvious that the formation of acetate and/or butyrate is necessary for the generation of energy (ATP) for biosynthesis. These two pathways are also associated with the generation of reducing equivalent which is regenerated by the 1,3-PD pathway. Thus, the overall energetic and product yields depend on the degree of involvement of the acetic acid and butyric acid pathways. Two extreme cases can be considered.

Case I assumes that only the acetate pathway is used for energy generation. Un­der the prerequisite of ATP and NADH2 balances a fermentation equation can be obtai­ned through the operation 17.5 x Eq.2 + Eq. lb + 39 x Eq.4:

60.5C3H8O3 + 3NH3 -> 3C4H702N +39C3H802 + 17.5C2H402 + 17.5COz + 17.5H2 (5)

According to this reaction, the yield coefficients on glycerol can be calculated for bio­mass, ATP, acetic acid and propanediol which are given in row I of Table I.

Case II assumes that only the butyrate pathway is used for the energy genera­tion. Under the prerequisite of ATP and NADH2 balances it follows from Eqs. (1-4) (11.7 x Eq.3 + Eq. lb + 27.4 x Eq.4):

54.8C3H803 + 3NH3 -> 3C4H702N + 27.4C3H802 +11.7C4H802 + 23.4C02 + 23.4H2 (6)

The yield coefficients on glycerol according to this fermentation equation are calculated and given in row II of Table I. It can be seen that the butyrate pathway renders higher ATP and biomass yields than the acetic acid pathway under these conditions. Thus, for the biosynthesis of cell material the butyrate pathway is more efficient than the acetate pathway. The maximum ATP and biomass yields on glycerol would be 0.64 mol/mol and 5.52 g/mol, respectively. The involvement of the acetic acid pathway results in re­duced yields of ATP and biomass. However, acetic acid formation involves a 1,3-PD yield which is about 30% higher than butyric acid formation. Thus, for the production of 1,3-PD the acetic acid pathway is more attractive. According to the above calcula­tions the theoretical maximum 1,3-PD yield would be 0.65 mol PD/mol glycerol. It will be reduced as soon as butyric acid is produced.

Table I. Theoretical maximum yields of growth and metabolism of C. butyricum under different conditions

Conditions

Ypo/S

mol/mol

Yhac/S

mol/mol

YhBu/S

mol/mol

Yx/s

g/mol

Yatp/s

mol/mol

Case I

No butyrate Maximum H2

0.65

0.29

0.00

5.05

0.56

Case II

No acetate Maximum H2

0.50

0.00

0.21

5.53

0.64

Case III

No butyrate No H2

0.72

0.22

0.00

3.84

0.45

Case IV

No acetate No H2

0.65

0.00

0.15

3.84

0.45

S: Glycerol; PD: 1,3-propanediol; HBu: butyric acid; HAc: acetic acid; X: biomass

Table II shows typical experimental data of glycerol fermentation by C. butyri­cum. Both the two fermentation cases considered above have been experimentally en­countered under low residual glycerol conditions. The steady-state at D = 0.052 h’1 un­der conditions of low residual glycerol in glycerol-limited culture represents the case of no acetate formation (case II of Table I). Under these conditions the experimental buty­ric acid yield reached exactly the theoretical maximum (0.21 mol/mol) as calculated above. The propanediol and ATP yields are also very close to the theoretical values. The steady-state at D = 0.60 h’1 approximately approached the case of no butyric acid formation (case I of Table I). These results confirm the general approach used for the theoretical calculation of yields.

Inspection of data in Table II shows that at similar growth rate (= dilution rate) the energetic yield YATp/s and biomass yield are generally higher under low residual glycerol conditions than under glycerol-excess conditions. This applies also to the for­mation of butyric acid. Furthermore, at low residual glycerol the yield of butyric acid decreases with increasing dilution rate. In contrast, the yield of acetic acid increases with growth rate and is lower under low residual glycerol conditions than under glycerol-excess conditions. Ypd/s is less dependent on growth rate. Significant differen­ce is however observed for cultures under glycerol limitation and glycerol excess: YPD/S is generally higher under glycerol excess than under glycerol limitation. It is noted that the highest Ypd/s value (0.71 mol/mol) achieved under glycerol excess is distinctively higher than the theoretical maximum value (0.65 mol/mol) as calculated above for ace­tic acid formation alone. Values of YPD/S in the range 0.70-0.71 mol/mol have been fre­quently obtained in continuous culture of C butyricum (18,24). Similar high values of YPD/s (0.68 — 0.73 mol/mol) were also obtained for glycerol fermentation by K. pneumo­niae (55; see also Menzel, K.; Zeng, A.-P.; Deckwer, W.-D. Enzyme Microbiol Tech — nol. in press). It was found that the increase of 1,3-PD yield in both the cultures of C. butyricum and K. pneumoniae is due to an altered regulation and balance of reducing equivalents released from the oxidation of pyruvate into acetyl-CoA under conditions of glycerol excess. As pointed out above, reducing equivalents of the reduced ferredoxin formed during the oxidation of pyruvate by C. butyricum can be either released as H2 or transferred to NAD+ under formation of NADH2:

H2 + Fdrcd о Fdred + (2H+ or NAD+) о NADH2 + Fdoxd (7)

Table II. Experimental yields of growth and metabolism of C. butyricum under different culture conditions

Culture

D

h’1

Residual

glycerol

mmol/1

Ypo/S

mol/mol

YhAc/S

mol/mol

YhBu/S

mol/mol

Yx/s

g/mol

Yatp/s

mol/mol

Low

0.052

0.98

0.51

0.00

0.21

4.48

0.62

residual

0.098

1.63

0.56

0.009

0.19

6.01

0.59

glycerol

0.20

1.63

0.55

0.028

0.18

7.63

0.59

0.29

2.99

0.60

0.099

0.11

6.84

0.54

0.39

1.21

0.52

0.13

0.077

6.80

0.49

Glycerol

0.06

27

0.71

0.092

0.12

0.92

0.54

excess

0.1

30.5

0.69

0.068

0.14

3.32

0.56

0.11

34.5

0.70

0.088

0.14

3.20

0.59

0.23

134

0.61

0.13

0.074

3.91

0.47

0.35

237

0.66

0.14

0.072

4.63

0.50

0.45

254

0.60

0.10

0.10

4.94

0.50

0.56

409

0.65

0.13

0.14

8.70

0.67

0.60

139.7

0.67

0.22

0.06

4.85

0.62

The distribution of reducing equivalents of Fd^ to NADH2 and H2 has signifi­cant influence on the metabolic pathways and maximum yields of the fermentation. It is obvious from reaction (7) that the maximum 1,3-PD yield will be obtained if H2 is not produced at all. In the following the maximum possible propanediol yields are calcula­ted for the two fermentation pathways under ideal conditions. For the case of the acetate pathway (Case III) the following reaction can be written:

C3H803 -> C2H402 + 3NADH2 + 2ATP + C02 — H20 (8)

Under the prerequisite of ATP and NADH2 balances it follows

78C3H803 + 3NH3 3C4H702N +56.5C3H802 + 17.5C2H402 + 17.5C02 (9)

The yield coefficients on glycerol under these conditions are calculated and given in row III of Table I. A propanediol yield as high as 0.72 mol/mol is calculated. This me­ans an increase of propanediol yield of 12.3 % compared with the case of maximal hy­drogen evolution. In contrast, the biomass and ATP yields would be reduced by about 22%.

For the case of the butyrate pathway (Case IV) the reaction can be written as:

2C3H803 -► C4H802 + 4NADH2 + 3ATP + 2C02 (11)

Under the prerequisite of ATP and NADH2 balances it follows

78.2C3H803 + 3NH3 -> 3C4H702N + 50.8C3H8O2 +11.7C4H802 + 23.4C02 (12)

The yield coefficients on glycerol under these conditions are given in row IV of Table I. The calculations indicate an increase of PD yield of 30 % compared with the case of maximum hydrogen evolution. This is more significant than in the acetate pathway. The biomass and ATP yields would also be reduced by about 30%. It is interesting to note that the ATP and biomass yields of these two pathways under conditions of no hydro­gen production are exactly the same. The selectivity of the two pathways under these conditions would be determined by the toxicity of the products. The theoretical maxi­mum propanediol yield (0.72 mol/mol) calculated above for the acetic acid pathway is slightly higher than the experimental maximum value. It can be seen in Table 2 that un­der conditions of low dilution rate and high residual concentration glycerol fermenta­tion by C butyricum can proceed with nearly theoretical maximum PD yield.

The formation rate of hydrogen in the glycerol fermentation of C. butyricum was measured in continuous culture at different dilution rate (28). This enabled the cal­culation of distribution of reducing equivalents produced during glycerol degradation to acetyl-CoA and biomass formation to the NADH2-dependent products (i. e., 1,3-PD, butyric acid and H2). Figs. 3a and 3b show the distribution of reducing equivalents for substrate-limited and product inhibited cultures, respectively. It can be seen that a pro­portion of as high as 40-60% of the total reducing equivalents is allocated to the forma­tion of butyric acid and hydrogen under conditions of substrate limitation, whereas it accounts for about only 25-40% of the total reducing equivalents under conditions of substrate excess (product inhibition). The relatively higher level of reducing equivalent allocation to butyric acid under conditions of substrate limitation may be explained by the higher energy and biomass yields of the butyric pathway (see Table I). The energe­tic consideration gives also a possible explaination for the relatively high allocation of reducing equivalents to H2 formation under these conditions. Comparing the cases I — IV in Table I it is obvious that an increased formation of H2 enhances both the energy and biomass yields. However, under conditions of substrate excess the energetics of the cell machinery may no longer have the highest priority due to energy excess, leading to a diminished allocation of reducing equivalents to the formation of hydrogen. Simulta­neously, the allocation of reducing equivalents to the formation of butyric acid is also slightly reduced, propabaly due to its strong toxicity to growth (34). It should be men­tioned that the experimentally measured formation rates of butyric acid and hydrogen under substrate excess are somewhat higher than one would expect from the stoichio-

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metry and the high 1,3-PD yield under these conditions. It is possible that more redu­cing equivalents than assumed in eq. (1) might have been released during biomass for­mation. Theoretically, an 1,3-PD yield higher than 0.72 mol/mol would be thus possible if the formation of butyric acid and/or hydrogen can be further reduced. Efforts have been made in obtaining mutants without butryric acid and hydrogen formation (see be­low).

Dilution rate [h1 ] Dilution rate [h’1 ]

Fig.3. Distribution of reducing equivalents produced during glycerol catabolism to acety-CoA and biomass formation to the NADH-dependent products. Values normali­zed to Rh = 1.0. Data from Solomon et al. (8). (A) Substrate limited culture. (B) Product limited culture.