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Effect of fluid dispersion on cybernetic control of microbial growth on substitutable substrates

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Abstract

Many fermentation media contain two or more substrates, which a microorganism utilizes for similar purposes. Depending on the conditions prior to and during a fermentation, the substrates may be utilized in succession or simultaneously. Since it is difficult to portray this behavior through mechanistic models, a cybernetic method was proposed earlier. Here the microorganism chooses the mode of substrate utilization that maximizes its own survival, usually expressed by the growth rate. In a fully dispersed bioreactor, simultaneous utilization generates higher growth rates but leads to low biomass concentrations since this utilization pattern is preferred at low concentrations of the substrates. In this study it has been shown that by allowing less than complete dispersion in the broth it is possible to shift from sequential to simultaneous utilization at high concentrations, thereby enabling both high growth rates and large biomass concentrations. This strategy thus allows the natural incomplete dispersion in large bioreactors to be gainfully exploited.

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Abbreviations

c :

concentration of biomass

D e :

effective dispersion coefficient

\( e_{m_i m_j } \) :

concentration of enzyme \( E_{m_i m_j } \)

\( e_{m_i m_j }^{\max } \) :

maximum value of \( e_{m_i m_j } \)

\( e_{s_i m_j } \) :

concentration of enzyme \( E_{s_i m_j } \)

\( e_{s_i m_j }^{\max } \) :

maximum value of \( e_{s_i m_j } \)

\( K_{Gm_i } \) :

saturation constant for precursor M i

\( K_{s_i m_j } \) :

saturation constant for \( r_{s_i m_j } \)

\( K_{s_i m_j }^E \) :

saturation constant for \( r_{s_i m_j }^E \)

L :

characteristic dimension of bioreactor

m i :

concentration of precursor M i

Pe :

Peclet number=wL/D e

r ij :

rate of formation of jth product from ith substrate

r G :

rate of formation of biomass

\( r_G^{\max } \) :

maximum value of r G

\( r_{s_i m_j } \) :

rate of formation of precursor M j from substrate S i

\( r_{s_i m_j }^{\max } \) :

maximum value of \( r_{s_i m_j } \)

\( r_{s_i m_j }^E \) :

induced rate of synthesis of enzyme \( E_{s_i m_j } \)

\( r_{s_i m_j }^{E,\max } \) :

maximum value of \( r_{s_i m_j }^E \)

\( r_{s_i m_j }^{E,*} \) :

constitutive rate of synthesis of enzyme \( E_{s_i m_j } \)

\( r_{m_i m_j } \) :

rate of formation of precursor M j from M i

\( r_{m_i m_j }^E \) :

induced rate of synthesis of enzyme \( E_{m_i m_j } \)

\( r_{m_i m_j }^{E,\max } \) :

maximum value of \( r_{m_i m_j }^E \)

\( r_{m_i m_j }^{E,*} \) :

constitutive rate of synthesis of enzyme \( E_{m_i m_j } \)

s i :

concentration of ith substrate S i

t :

elapsed time

:
u ij :

cybernetic variable for enzyme synthesis relating jth product from ith substrate

\( u_{m_i m_j } \) :

cybernetic variable for the synthesis of enzyme \( E_{m_i m_j } \)

\( u_{s_i m_j } \) :

cybernetic variable for the synthesis of enzyme \( E_{s_i m_j } \)

v ij :

cybernetic variable for enzyme activity relating jth product from ith substrate

\( v_{m_i m_j } \) :

cybernetic variable for the activity of enzyme \( E_{m_i m_j } \)

\( v_{s_i m_j } \) :

cybernetic variable for the activity of enzyme \( E_{s_i m_j } \)

w :

fluid velocity in the bioreactor

\( Y_{s_i c} \) :

yield coefficient for biomass from substrate S i

\( Y_{s_i m_j } \) :

yield coefficient for precursor M j from substrate S i

\( \beta _{m_i m_j } \) :

degradation rate constant for enzyme \( E_{m_i m_j } \)

τ :

dimensionless time=\( t/\bar t \)

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  1. Sector 39-A, Institute of Microbial Technology, 160 036, Chandigarh, India

    P. R. Patnaik

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Patnaik, P.R. Effect of fluid dispersion on cybernetic control of microbial growth on substitutable substrates. Bioprocess Biosyst Eng 25, 315–321 (2003). https://doi.org/10.1007/s00449-002-0306-9

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