  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.
