Biological question: How does a molecular motor convert chemical energy, a scalar quantity, into directed motion, a vector?
Physical idea: Mechanochemical cuoupling arises from a free energy landscape with a direction set by the geometry of the motor and its track. The motor executes a biased random walk on this landscape.
The figure below shows a protein (i.e., chain of amino acids) being irreversibly dragged to the right through a membrane.
Nelson considers the mechanical model below.
[We thought the S-ratchet and G-ratchet were from some profound nomenclature. But they are G&S = Gilbert and Sullivan!, who Nelson often uses for Socratic dialogues.]
This can be described by the potential energy curve below. On top of this random thermal motion (i.e, Brownian motion) occurs. One can see that this will lead to a nett motion to the right because the random thermal motion leads to small reversible displacements, except near the steps.
I did a web search for a simulation (e.g., a Java applet) of such a ratchet but could not find anything. Please let me know if you are aware of something like that.
I did a web search for a simulation (e.g., a Java applet) of such a ratchet but could not find anything. Please let me know if you are aware of something like that.
Here is a straightforward MATLAB program to simulate the evolution of a ratcheted system. The potential is defined by this file and the code to run is here. It's not pretty but it demonstrates the concept.
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