Renormalization group approach to power-law modeling of complex metabolic networks

TL;DR

This paper uses renormalization group analysis to explain why power-law models accurately describe complex metabolic networks across wide concentration ranges, showing that power-laws are invariant solutions under scale transformations.

Contribution

It demonstrates that power-law rate-laws are critical, invariant solutions of the renormalization group, explaining their success in modeling biological systems over multiple scales.

Findings

Power-law rate-laws are renormalization group invariant solutions.

Results explain the broad accuracy of power-law models in biological systems.

Power-laws are invariant under concentration scaling.

Abstract

In the modeling of complex biological systems, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations.