Michaelis-Menten dynamics in protein subnetworks

TL;DR

This paper extends the projection method for modeling subnetwork dynamics to include Michaelis-Menten kinetics, enabling more accurate and efficient analysis of biochemical networks with enzymatic reactions.

Contribution

It introduces a novel approach to incorporate Michaelis-Menten kinetics into subnetwork dynamics models via a limiting process, broadening the method's applicability.

Findings

The extended method accurately captures enzyme effects in subnetworks.

It outperforms simpler enzyme representation methods in accuracy.

The approach is computationally more efficient.

Abstract

To understand the behaviour of complex systems it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves memory of the past, and that the memory functions can be calculated explicitly for biochemical reaction networks made up of unary and binary reactions. However, many established network models involve also Michaelis-Menten kinetics, to describe e.g. enzymatic reactions. We show that the projection approach to subnetwork dynamics can be extended to such networks, thus significantly broadening its range of applicability. To derive the extension we construct a larger network that represents enzymes and enzyme complexes explicitly, obtain the projected equations, and finally take the limit of fast enzyme reactions that gives back Michaelis-Menten kinetics. The crucial point is that this limit can be taken in closed form. The outcome is a simple procedure that allows one to obtain a description of subnetwork dynamics, including memory functions, starting directly from any given network of unary, binary and Michaelis-Menten reactions. Numerical tests show that this closed form enzyme elimination gives a much more accurate description of the subnetwork dynamics than the simpler method that represents enzymes explicitly, and is also more efficient computationally.