%0 DATA
%A J. koch, Steven
%8 2011/12/30
%T 2003 Loading Rate Clamp Flow Chart supp to Koch and Wang PRL 2003
%U http://figshare.com/articles/2003_Loading_Rate_Clamp_Flow_Chart_supp_to_Koch_and_Wang_PRL_2003/148
%1 http://dx.doi.org/10.6084/m9.figshare.148
%2 http://files.figshare.com/147/Koch__Wang_PRL_2003_Supp_Loading_Rate_Clamp_Flow_Chart.png
%K freely-jointed chain
%K dynamic force spectroscopy
%K polymer physics
%K loading rate clamp
%K optical tweezers
%X This flow chart may help explain the "loading rate clamp" optical tweezers system used in the publication "Dynamic Force Spectroscopy of Protein-DNA Interactions by Unzipping DNA" by Koch and Wang, Phys. Rev. Lett. (2003). http://link.aps.org/doi/10.1103/PhysRevLett.91.028103
I was always disappointed that since we published in PRL we could not explain the loading rate clamp effectively because of page limits. I had drawn this figure to expalin to my advisor how the feedback system worked, but I never published it. The key to the system is that we know we are unzipping DNA and the polymer stiffness is dominated by the single-stranded DNA. Knowing the properties of the ssDNA (freely-jointed chain model), allowed me to calculate in real-time the number of nucleotides that had been unzipped. It also allowed for calculation of the instantaneous stiffness of the system, by taking analytical derivatives of the extensible freely-jointed chain model.
I'll want to publish the derivatives someday, but they're not complicated. I did something like this:
R = ( -B/((sinh(F*B))**2) + 1 / (B*F*F) );
G =(1 + 1 / (F*F*B))*(1+F/K) +
(1 - 1 / (F*B) ) * (1 + 1 / K);
Gp = (1-2/(F*F*F*B))*(1+F/K) +
2*(1+1/(F*F*B))*(1+1/K);
where B is persistence length scaled by kT, F is force (pN), and K is stretch modulus for FJC model. The instantaneous length was calculated something like
cotf = 1/tanh(f1);
Lss = (x / (1+f2))
*( 1 / (cotf - 1/f1));
tp = (Lss) / a;
/*tp is length of ssDNA in nucleotides*/