Physics-Biology interface seminar: Denis Grebenkov

Inferring anomalous diffusion from single particle trajectories

Denis Grebenkov (PMC, École polytechnique)

SPECIAL LOCATION

Transport of macromolecules, organelles and vesicles in living cells
is a very complicated process that essentially determines and controls
many biochemical reactions, growth and functioning of cells. The passive
thermal diffusion through the overcrowded cytoplasm is combined with
the active transport by motor proteins attached to microtubules. This
intricate mechanism results in anomalous diffusions that found abundant
experimental evidences but no consensus on the physical mechanism and
the appropriate mathematical model is achieved so far. Single-particle
tracking (SPT) experiments survey random trajectories of individual
tracers inside living cells and can thus provide the missing information
on the intracellular transport in order to discriminate between different
physical mechanisms and to identify the appropriate theoretical model
of anomalous diffusion. In SPT, an ensemble average of the quantities
of interest (e.g., diffusivity, viscosity, first passage times, etc.)
is often unavailable or even undesired, as tracers move in spatially
heterogeneous and time evolving media such as living cells. One faces
therefore a challenging problem of inferring dynamical, structural and
functional properties of living cells from a limited (small) number of
individual random realizations of an unknown stochastic process.

After a short introduction to theoretical aspects of the intracellular
transport, we discuss the recent progress onto probing ergodicity of
the tracer dynamics from a single particle trajectory. The proposed
estimators are first investigated for several models of anomalous
diffusion. In the case of nonergodic continuous time random walks,
we show analytically that both estimators do not vanish even for
infinitely long trajectories. The estimators are then applied to
two sets of earlier published trajectories: mRNA molecules inside
live E. coli cells and Kv2.1 potassium channels in the plasma membrane.
These tests suggest that the former set exhibits ergodic behavior
while the latter reveals both ergodic and nonergodic features.


Date/Time : 25/01/2016 - 11:00 - 12:15

Location : LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay

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