Activity and crowding, two major players in single probe dynamics
A biological cell is probably the best example of a medium in the mesoscopic length scale that is truly out of equilibrium. This non-equilibrium arises due the processes occurring inside that do not follow detailed balance and are commonly fuelled by the energy released due to some chemical reaction, such as ATP hydrolysis. In other words, the constituents of biological cells are "active". Apart from its constituents being active, the cell is highly packed or crowded. Therefore, dynamics of a biomolecule inside a cell is an example of the dynamics of an active probe in a crowded environment. Motivated by these, physical scientists have come up with biomimetic environments, where the true biomolecules are replaced by probes, such as active or self-propelled colloids or single polymer chains, fuelled by some chemical reaction or by some other means [2, 3]. One interesting aspect of the dynamics of these probes is their persistent motion  like bacteria. Another direction in which experimentalists have recently ventured into, is the dynamics of a passive probe in an active medium such as bacteria bath [3, 5]. One motivation is to build highly efficient micron sized heat engines in a non-equilibrium active bath.
These processes occurring inside a cell or in a biomimetic environment cannot be modelled in the framework of equilibrium statistical mechanics. In this talk I plan to discuss our recent attempts to model the dynamics of a probe (passive or active) in a crowded medium (passive) using non equilibrium statistical mechanics and computer simulations. The probe is either a single self-propelled colloid [6, 7, 8] or a single polymer chain [9, 10] and the medium is either viscoelastic or non-viscoelastic. Our analytically solvable models and computer simulations reveal interesting aspects of the probe dynamics, sometimes counter intuitive. Most importantly, our theoretical predictions are either predicted by experiments in the recent past [2, 4, 5] or later confirmed by new experiments .
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