# Koch Lab:Protocols/Loading rate clamp

## Calculation of instantaneous stiffness correction factor (G)

The key to the "loading rate clamp" that Steve implemented for the dynamic force spectroscopy (DFS) of protein-DNA interactions by unzipping DNA (see PMID 12906513) was the ability to analyze the point-by-point data and calculate the instantaneous stiffness of the system. This was possible due to the good agreement between the force-extension curve of ssDNA and the extensible freely-jointed chain model (Smith, Bustamante et al. 1996).

The piezo (or AOD) stretch rate is scaled by the value of the instantaneous stiffness of the system.

### Picture of LabVIEW code

### LabVIEW VI

### Code documentation from early 2003

Here is the documentation from my LabVIEW sub-VI which calculates the "G" value, which is used in the loading rate clamp for unzipping DNA:

G is defined as "inverse of compliance per nm of ssDNA"...uh? say what?

G is basically stiffness multiplied by contour length, so that it has units of pN, and is independent of length of ssDNA.

The model is Smith, et al. FJC with stretch modulus.

I solved the equations by hand, but verified numerically that they are correct (to within a very small percentage, which is as careful as i was about numerical derivative)

I have added code so that it works above F = 5000 pN, but I'm not sure it's correct (who cares?)