Scaling Exponents and Probability Distributions of DNA End-to-End Distance

Abstract

The scaling of the average gyration radius of polymers as a function of their length can be experimentally determined from ensemble measurements, such as light scattering, and agrees with analytical estimates. Ensemble techniques, yet, do not give access to the full probability distributions. Single molecule techniques, instead, can deliver information on both average quantities and distribution functions. Here we exploit the high resolution of atomic force microscopy over long DNA molecules adsorbed on a surface to measure the average end-to-end distance as a function of the DNA length, and its full distribution function. We find that all the scaling exponents are close to the predicted 3D values ($\nu =0.589\pm 0.006$ and $\delta =2.58\pm 0.77$). These results suggest that the adsorption process is akin to a geometric projection from 3D to 2D, known to preserve the scaling properties of fractal objects of dimension $d_f<2$.