# Validity of the Michaelis-Menten Approximation for the Stability Analysis in Regulatory Reaction Networks

### Takashi Naka

#### Abstract

Cellular signalling systems are comprised of enzymatic reaction cascades and organized as regulatory reaction networks. The primary building block of the network is an enzymatic activation-inactivation cyclic reaction such as phosphoryl modifications. We have investigated the effects of the network architectures and kinetic parameter values on the stability such as the emergence of bi-stability or oscillations employing the canonical Michaelis-Menten equation as the approximation for Michaelis-Menten-type reaction mechanisms in each of enzymatic cyclic reaction. Although the Michaelis-Menten approximation has known to work well under an assumption of a large excess of substrate over enzyme which is usually satisfied for metabolic pathways, the approximation might not suit to regulatory reaction networks in which the required assumption might be violated. In this study, comparing the predicted stabilities from the model with the Michalis-Menten approximation and with the full set of reaction equations derived only from the law of mass action, the validity of the Michaelis-Menten approximation was examined for the regulatory reaction networks over the possible network architectures and kinetic parameter values elucidating that employing the Michalis-Menten approximation might not be valid even in the analysis for the steady states such as the stability analysis.

Download#### Paper Citation

#### in Harvard Style

Naka T. (2020). **Validity of the Michaelis-Menten Approximation for the Stability Analysis in Regulatory Reaction Networks**.In *Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS,* ISBN 978-989-758-398-8, pages 176-182. DOI: 10.5220/0009093001760182

#### in Bibtex Style

@conference{bioinformatics20,

author={Takashi Naka},

title={Validity of the Michaelis-Menten Approximation for the Stability Analysis in Regulatory Reaction Networks},

booktitle={Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS,},

year={2020},

pages={176-182},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0009093001760182},

isbn={978-989-758-398-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS,

TI - Validity of the Michaelis-Menten Approximation for the Stability Analysis in Regulatory Reaction Networks

SN - 978-989-758-398-8

AU - Naka T.

PY - 2020

SP - 176

EP - 182

DO - 10.5220/0009093001760182