Tuesday, September 15, 2009

Ratcheting up my understanding

Something I have never quite understood has been discussions of ratchets which are driven by thermal fluctuations. Today in PHYS3170 we discussed these in the context of molecular motors. In Chapter 10 of Biological Physics, Nelson considers:

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.

1 comment:

  1. 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.