Ralf Metzler
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.