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A biological cell is a system of mesoscopic length scale that is truly out of equilibrium. This non- equilibrium nature of the dynamics arises due to the processes happening inside that do not follow detailed balance, being fuelled by the energy released owing to chemical reactions, 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 can be referred to as the dynamics of an active agent or a probe in a crowded environment. One interesting aspect of the dynamics of these probes is their persistent motion. More recently, experiments have also been performed, where the active biomolecules are replaced by synthetic probes, such as self-propelled colloids or polymer chains. It is obvious that the 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 an active probe in a crowded medium (passive). Our analytically solvable statistical mechanical models and model computer simulations reveal interesting aspects of the probe dynamics, sometimes counter-intuitive. Most importantly, our theoretical predictions go hand in hand with experiments and some of our predictions are verified later by experiments. |