Simple Proofs of the Summation and Connectivity Theorems in Metabolic Control Analysis

TL;DR

This paper presents simplified, concise mathematical proofs of the summation and connectivity theorems in metabolic control analysis, making these foundational results more accessible.

Contribution

It offers straightforward, minimalistic proofs of key theorems in metabolic control analysis, improving understanding and accessibility compared to traditional, more complex proofs.

Findings

Simplified proofs of the summation theorem

Simplified proofs of the connectivity theorem

Enhanced clarity of foundational metabolic control analysis results

Abstract

In the early 1970s, the Kacser/Burns and the Heinrich/Rapoport groups independently discovered the important summation and connectivity theorems in metabolic control analysis. These theorems were derived originally by using thought experiments and proved mathematically later. The mathematical proofs are not easy for me to read and follow. But the proofs actually can be very simple and need only a couple of lines as I give here.