# Properties of the Michaelis-Menten Mechanism in Phase Space

Source: [Properties of the Michaelis-Menten Mechanism in Phase Space](<https://www.sota2.com/research/paper/68fa4eaa1e209131ce95d2ca>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T09:53:49.546Z

Authors: Matt S. Calder, David Siegel

Published: 2006-11-05T16:51:23.000Z

## Abstract

We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of all solutions in the first quadrant. Third, we establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we determine the asymptotic behaviour of the slow manifold at infinity.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0611119>)

[PDF](<https://arxiv.org/pdf/math/0611119.pdf>)