Modeling DNA unzipping in the presence of bound proteins

Unzipping force analysis of protein association is a technique to investigate protein-DNA interactions by mechanically unzipping DNA. We computationally investigate the limits of this technique under quasistatic conditions. We find the minimum binding energy of a protein for which the protein can be detected using this technique and the minimum distance between the binding sites of two proteins of varying binding energies that can be resolved unambiguously with this technique.

Figure 1

A cartoon illustrating DNA being unzipped using optical tweezers.

Figure 2

A plot showing the (unnormalized) contribution of each index $m$ toward the partition function at a fixed extension $R=1400\mathrm{nm}$ and a DNA length of 2000 basepairs.

Figure 3

(Color online) A series of calculated force-extension curves obtained with a DNA sequence with proteins of progressively less binding energy attached to the DNA molecule at the same position. The dotted line shows the mean unzipping force for a DNA strand in the absence of proteins. The solid lines indicate one standard deviation above and below the mean. The energies labeled are the binding energies of the protein for the highest and lowest curves. The lowest curve coincides with the curve for bare DNA.

Figure 4

(Color online) The average variation in the height of the force-extension curve peak above the unzipping force for bare DNA for DNA strands with varying GC:AT ratios. The heights were averaged over 15 random sequences each for a given GC:AT ratio.

Figure 5

(Color online) The surface formed by force-extension curves of a DNA molecule having two proteins of equal binding energy of $100\mathrm{kJ}∕\mathrm{mol}$ attached to it as the protein binding positions are separated further apart. Only a single peak is seen until the proteins are separated by a distance of roughly 35 basepairs. Thus UFAPA will not be able to resolve two proteins closer than this distance.

Figure 6

(Color online) Force-extension curves from a DNA strand having two bound proteins initially separated by 64 basepairs. The series of curves are obtained by bringing the proteins closer in steps of 16 basepairs until they are at the same position. As can be seen, the peaks from the two proteins merge while the proteins are still separated by more than 30 basepairs.

Figure 7

(Color online) The minimum resolvable distance between two proteins on a DNA strand using UFAPA. The number after each curve gives the ratio between the second protein to be unbound and the first protein to be unbound. The $x$ axis indicates the strength of the first protein. The resolvable distances are averaged over 15 random sequences.