Electronic Journal of Biotechnology ISSN: 0717-3458
  © 2001 by Universidad Católica de Valparaíso -- Chile
Vol. 4 No. 1, Issue of April 15, 2001
 


APPENDIX

  1. Polyols and oxygen yields and rates

Polyols. For macroscopic analysis a simple process representation was obtained by substitution of the overall set of excreted polyols (Röhr et al., 1987) for an unique formula equivalent. The mean composition used was [CH2.54O]n, n=3.72 since the average composition of polyols showed minor variations among the different idiophase stages (data not shown). This expression is a weighted average of the elementary composition of all polyols involved, considering as weight factor their own excretion rate. However, when the balance of intracellular fluxes was done, individual polyols were considered. Macroscopic rates were calculated by means equation (A.1) where f stands for fluxes (in C-moles. g-1. h-1) of medium exchanged compounds .

(A.1)


Oxygen. Reductance balance was used to the determination of the oxygen yields at the idiophase stages considered in the model: early, medium (A.2) and late (A.3). In these equations f stands for fluxes (in C-moles.g-1.h-1) between cell and medium, while g stands for the reductance grade.

(A.2)


(A.3)

II. Determination of the rate of GABA cycle

At the early idiophase the NH3/NH4+ pool is considered at steady state (free diffusion). This fact, together with the absence of nitrogen at the culture medium allows us to write down the following mass balance equation:

(A.4)

 

The balance equations for the extracellular (A5), cytoplasmic (A6) and mitochondrial compartments (A7) are the followings:

(A.5)

(A.6)

(A.7)


By summation of equations A5-A7 we obtain (A.8), suitable for the R14 reaction.

(A.8)


Following the same procedure we can write the corresponding equation for NH3 in each compartment:

(A.9)


(A.10)


(A.11)


From equations (A.9) to (A.11) we obtain (A.12):

(A.12)


By substitution of A.12 in A.8 we finally obtain:

(A.13)


III. Energy Balances

Assuming a steady state the H+ balance equation

(1/3) R13 - b R20 - R21 + 2 R22 = 0

 


allows us to write equation A.14:

0.30133 + 2 R22 = R21 + 1.1669 R20
(A.14)


Analogously, the mitochondrial ATP balance

(1/3) R13 + 3 R15 + 2 R16 - (R20 + R21) = 0  


allows us to write equation A.15:

R21 = 2.7412 - R20
(A.15)


By substituting equation A.15 into A14 we obtain the uptake rate of mitochondrial Pi:

R22 = 0.08345 R20 + 1.21996
(A.16)


From the mass balance for cytoplasm Pi, we obtain A.17:

R19 - R22=(1/3) R8 - [(1/6) R2+(1/10) R3+(1/5) R4+(1/6) R6+(1/3) R11+(1/6) R12]  



R19 - R22 = 0.7435
(A.17)


By substitution in A.17 of A.16 we obtain A.18:

R19 - 0.08345 R20 = 1.9635
(A.18)


That together equation 6 (see Energy balance section in the main text) we finally obtain A.19, that allow us the determination of the H+-ATPase rates.

R19 + R20 = 3.662
(A.19)


After evaluation of R19 and R20 it can be determined the values for R21 and R22.

IV. Energy and reductive balance relations


The alternative respiration fraction can be envisaged as a consequence of an imbalance between the energy and reductive mechanisms. Only if the oxygen demand based in ATP is equal to the oxygen demand from the reductive equivalents, all the respiration rate would be ATP associated. Hence, for conservation of ATP equation A.20 must be fulfilled, ao, ax, ap standing for ATP yields of respiration, biomass and citric acid respectively; f being the corresponding specific productivity respectively and m the ATP cellular maintenance as defined in equation (6) in the text.

(A.20)

(A.21)

On the other hand, equation A.21 must be satisfied by the reductive equivalents. The subindex i refers to any product different but biomass that consume or produce NADH, NADPH or FADH. aoH, axH refers to yields in reduction equivalents for oxygen and biomass respectively.

Accordingly the following expression (A.22) is derived for the ratio of the alternative respiration system rate, which equivalent to the previously presented for the alternative respiration ratio [R17/(R15+R16+R17].

(A.21)

 

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