In her provocative (and informative) article on recent research into power laws in biology, Evelyn Fox Keller implies that this work has not led to research that is self-generating and, above all, that it has not produced significant insights. A refutation of this particular criticism might be based on the work of several groups, including our own. Specifically we can look at the potential insights into cell division and periodic behaviour, evolution, and a thermodynamic approach to networks that attempts to extract macroscopic descriptors from statistical data.
Our entree to the power law scene was made in 1999 when we envisaged looking at the distribution of delta Gs in metabolic reactions for evidence of self-organised criticality. This concept (to which Keller does not allude) was advanced by Bak to describe the many systems that, in response to a flow of energy through them, exhibit a power law pattern of organisation over several orders of magnitude. He argues that 'complex behaviour in nature reflects the tendency of large systems with many components to evolve into a poised, ''critical'' state, way out of balance, where minor disturbances may lead to events, called avalanches, of all sizes. The state is established solely because of the dynamical interactions among individual elements of the system: the critical state is self-organised'. In the classical example of avalanches from the unstable pile that sand forms when it is trickled onto a table, the distribution of avalanche sizes is characterised by a power law that holds over decades. Independently of the Barabasi group, we found evidence of self-organised criticality in the connectivity of the charts of metabolic pathways and presented this at the NECSI conference in 2000. In the regulatory network of Saccharomyces cerevisiae, the in-degree connections (the number of regulating proteins per regulated gene) and out-degree connections (the number of regulated genes per regulating protein) have distributions with exponential and power-law characteristics, respectively. The observed power law distributions of mRNA abundance are compatible with this observation if the production of mRNAs is correlated with the out-degree connectivity (Grondin & Raine, unpublished data). On the face of it, this seems teleological because the production machinery for a regulator appears to 'know' what the regulator is being produced for. The implication is that evolutionary processes must be responsible in some way for the power law distribution. Such a connection between evolution and power laws then suggests a way in which coevolving systems might be associated with critical (or 'poised') states. Power laws also appear in the distribution of periods of periodic regulatory networks in realistic parameter regimes