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Mathematical modelling of enzyme synthesis during fermentations: The Q-functions

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European journal of applied microbiology and biotechnology Aims and scope Submit manuscript

Summary

In modelling enzyme synthesis the Q-function has been generalized to describe ordinary induction and repression as well as mixed induction-repression. The practical use of the Q-function as found in the literature was considered, especially the implications of applying fractional exponents.

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Abbreviations

Co :

Binding constant of uncomplexed repressor protein to operator site

Ci :

Binding constant of REi to operator site

E:

Effector

Enz:

Enzyme

i:

Index (number of effector molecules)

k1 :

rate constant

k2 :

rate constant

Ki :

Formation constant of repressor protein with i effector molecules

mRNA:

Messenger ribonucleic acid

n:

Index (number of effector molecules)

O:

Operator site

[O]t :

Total concentration of operator sites

OR:

Uncomplexed repressor protein bound to operator site

OREi :

Repressor complexed with i effector molecules and bound to operator site

p:

The maximum number of effector molecules bound to repressor protein

Q:

The fraction of operons which can be transcripted

R:

Repressor protein

REi :

Repressor protein complexed with i effector molecules

[R]t :

Total concentration of repressor protein

X:

Biomass

[]:

Concentration

References

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Authors and Affiliations

  1. Department of Applied Biochemistry, The Technical University of Denmark, Block 223, DK-2800, Lyngby, Denmark

    Henrik K. Nielsen & Steen C. Martiny

Authors
  1. Henrik K. Nielsen
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  2. Steen C. Martiny
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Nielsen, H.K., Martiny, S.C. Mathematical modelling of enzyme synthesis during fermentations: The Q-functions. European J. Appl. Microbiol. Biotechnol. 13, 67–70 (1981). https://doi.org/10.1007/BF00499690

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  • DOI: https://doi.org/10.1007/BF00499690

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