On a class of sigmoidal growth models induced by reaction networks

Authors

  • Milen Kolev Borisov Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
  • Svetoslav Markov*

Abstract

We formulate and study a class of sigmoidal growth models induced by catalytic reaction network via the mass action law. The proposed reaction network, called “pre-logistic”, is based on the autocatalytic logistic reaction inducing the familiar logistic growth model. The pre-logistic reaction network consists of two catalytic reactions. We show that the dynamics of the pre-logistic network is close to the dynamics of either the logistic, or the first-order  saturation reaction depending on the ratio of  the rate constants. In particular we show that the autocatalytic logistic reaction can be obtained as a limit case of the pre-logistic reaction network whenever one of the rate constants tends to infinity while the other is kept fixed. Hence the pre-logistic reaction can be considered as a generalization of both the logistic and the saturation reactions and thus can be used in a number of real-world situations when modeling growth processes in life sciences. A generalization of the pre-logistic network involving more intermediate steps is also discussed. The proposed growth models possess clear physic-chemical mechanisms and are suitable for fitting a variety of measurement data. Numerical examples of the proposed growth models using experimental measurement data from the field of microbial cultivation are presented and graphically visualized.

References

Anguelov R., Borisov M., Iliev A., Kyurkchiev N., Markov S., On the chemical meaning of some growth models possessing Gompertzian-type property, Math Meth Appl Sci. 2017;1–2 https://doi.org/10.1002/mma.4539

Iliev A., Kyurkchiev N., Markov S., On the Approximation of the step function by some sigmoid functions, Mathematics and Computers in Simulation 2017; 133:223--234.

Lente G. Deterministic Kinetics in Chemistry and Systems Biology, Briefs in Molecular Science, Springer 2016.

Chellaboina V., Bhat P., Haddat M., Bernstein S., Modeling and Analysis of Mass-Action Kinetics, IEEE Control Systems Magazine 2009; 60--78.

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Published

2018-03-17

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Conference Contributions