When Nature goes beyond the central limit theorem: From gene control to animal foraging – Niels Bohr Institute - University of Copenhagen

When Nature goes beyond the central limit theorem: From gene control to animal foraging

Prof Dr Ralf Metzler,
Physik Department (T30g), Technical University of Munich, Garching, Germany

Simple chemical reactants search for each other by three-dimensional
diffusion until encounter, as originally described by Smoluchowski.
At low concentrations of reactands, pure 3D search is quite inefficient.
Nature has therefore come up with various active and passive solutions
to speed up search. I will discuss two examples: facilitated diffusion
as observed in gene regulation on a molecular scale; and the search of
animals for food based on search principles that appear to be shared
by many biological species.

Facilitated diffusion of regulatory proteins for a specific binding site
on a DNA molecule consisting of megabases of base-pairs combines 3D volume
diffusion with 1D motion along the DNA. The latter is mediated by so-called
non-specific binding, a finite binding affinity to DNA also at segments,
that are not the specific binding site. The combination of these two
mechanisms significantly speeds up the search. In addition, intersegmental
transfers that occur at contact points of chemically remote segments of the
DNA due to looping gives rise to Levy flights along the DNA that further
optimise the search.  While this model holds for diluted in vitro solutions,
in the cell molecular crowding occurs, leading to the subdiffusion of larger
molecules. Consequences of this effect to the search process will be
discussed, in particular, due to the resulting weak ergodicity breaking.

Bacteria or higher animals perform an active search for food. In cases
of sparse food distribution their search needs to be optimized in order
to be able to efficiently compete for the food. I will present empirical
evidence for long-tailed distributions of relocation events during the
search, and discuss some simplified models for search strategies. It
turns out that long-tailed distributions, that help avoiding the spell
of the central limit theorem, lead to significantly higher search