Anomalous stochastic processes and biological relevance
Many processes in Nature deviate from the standard laws of Brownian
motion or exponential relaxation. I will introduce the continuous
time random walk and the related fractional Fokker-Planck equation
as general tools to model such dynamic anomalies.
Four examples from cellular biology are introduced:
(1) Due to the superdense environment of a variety of biomacromolecules (molecular
crowding), it has been claimed from experiments and simulations that the
diffusion of proteins and polynucleotides in the cell is subdiffusive.
I will show that, e.g. for transcription factors, this will give rise
to a weak ergodicity breaking, whose potentially beneficial effects to
the stability and efficiency of gene regulation are discussed. Similar
effects would be expected for larger molecules that intermittently bind
to the cell membrane or pass through membrane channels
(2) The passage of longer biomolecules through membrance pores as such is also reported
to be subdiffusive. Some recent models will be introduced.
(3) The opening time of certain ion channels was reported to follow logarithmic oscillations
around a general power-law trend. A model taking these oscillations into
account by a scaling of characteristic times and amplitudes of single
exponential contributions is presented.
(4) Finally, the rebinding dynamics of ligands to proteins such as myoglobin are discussed.