Events
WHEN NATURE GOES BEYOND THE CENTRAL LIMIT THEOREM-FROM GENE CONTROL TO ANIMAL FORAGING
Simple chemical reactands 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 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
