The length and viscosity dependence of end-to-end collision rates in single-stranded DNA

Intramolecular dynamics play an essential role in the folding and function of biomolecules and, increasingly, in the operation of many biomimetic technologies. Thus motivated we have employed both experiment and simulation to characterize the end-to-end collision dynamics of unstructured, single-stranded DNAs ranging from 6 to 26 bases. We find that, because of the size and flexibility of the optical reporters employed experimentally, end-to-end collision dynamics exhibit little length dependence at length scales <11 bases. For longer constructs, however, the end-to-end collision rate exhibits a power-law relationship to polymer length with an exponent of -3.49 +/- 0.13. This represents a significantly stronger length dependence than observed experimentally for unstructured polypeptides or predicted by polymer scaling arguments. Simulations indicate, however, that the larger exponent stems from electrostatic effects that become important over the rather short length scale of these highly charged polymers. Finally, we have found that the end-to-end collision rate also depends linearly on solvent viscosity, with an experimentally significant, nonzero intercept (the extrapolated rate at zero viscosity) that is independent of chain length--n observation that sheds new light on the origins of the "internal friction" observed in the dynamics of many polymer systems.