# A linear elimination framework

Source: [A linear elimination framework](<https://www.sota2.com/research/paper/68fa5ea21e209131ce9e403c>)

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

Data updated: 2025-10-25T18:54:48.646Z

Authors: Jeremy Gunawardena

Published: 2011-09-28T15:04:51.000Z

## Abstract

Key insights in molecular biology, such as enzyme kinetics, protein allostery and gene regulation emerged from quantitative analysis based on time-scale separation, allowing internal complexity to be eliminated and resulting in the well-known formulas of Michaelis-Menten, Monod-Wyman-Changeux and Ackers-Johnson-Shea. In systems biology, steady-state analysis has yielded eliminations that reveal emergent properties of multi-component networks. Here we show that these analyses of nonlinear biochemical systems are consequences of the same linear framework, consisting of a labelled, directed graph on which a Laplacian dynamics is defined, whose steady states can be algorithmically calculated. Analyses previously considered distinct are revealed as identical, while new methods of analysis become feasible.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1109.6231>)

[PDF](<https://arxiv.org/pdf/1109.6231.pdf>)