WHEN NATURE GOES BEYOND THE CENTRAL LIMIT THEOREM-FROM GENE CONTROL TO ANIMAL FORAGING

00:00 25-12-2007

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

central  limit  theorem,   lead  to