Theoretical Analysis of Molecular Motor mechanico-chemical processes

The cellular environment is an out of equilibrium system in which there is a continuous transduction of matter and energy. The mechanisms driving this processes are the molecular motors. There are many different Molecular Motors with many different functions. For instance, kinesin, which can transport cargos along microtubules track along the cell, or BFM, which rotates the flagella of bacteria allowing them to propel in the extracellular media. What is even more interesting is that Molecular Motors are able to achieve its goal despite the high noise media in which the live. The origin of this fluctuations are two: Thermal fluctuations, which are comparable to typical energies of Molecular Motors; and the discretness of molecules in the system. One particular molecular motor is the F1-ATPase, part of the ATPsyntase holoenzyme. F1-ATPase is a rotatory motor that uses the hydrolysis energy of ATP to rotate its central shaft. F1-ATPase is reversible and can also synthesize ATP out of its hydrolysis products when the shaft is mechanically rotated in the proper direction. The rotation trajectories can be experimentally studied by attaching a load to the shaft. The aim of our work is to analyze such trajectories studying the mechanico-chemical properties of the motor and the biochemical information available. The result is a flashing ratchet model that is able to reproduce the stepping trajectories observed and predict the velocity of the motor and its dependence on external parameters such as the ATP concentration, the friction of the load, ATP hydrolysis energy or thermal fluctuations. The model is also able to predict the complete substep phenomenology observed in recent experiments.

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