DOI: 10.1002/cphc.200900655 Diffusion of Circular DNA in Two-Dimensional Cavity Arrays Dmytro Nykypanchuk, [a] David A. Hoagland, [b] and Helmut H. Strey* [c] Dedicated to Erich Sackmann on the occasion of his 75th birthday. 1. Introduction We previously investigated by fluorescence imaging the diffu- sion of linear DNA through a medium of precisely controlled (and known) pore structure. This structure was a periodic, two- dimensional hexagonal array of spherical cavities interconnect- ed by short circular holes. Tracking many single-molecule tra- jectories, we found that, for DNA radius of gyration R g ap- proaching cavity diameter D c , diffusion is dominated by the sporadic “hopping” of DNA between cavities, a mechanism predicted by the entropic barriers transport theory. [1] Hopping corresponds to configurational fluctuations that allow passage of a flexible polymer through a pore constriction smaller than the average coil size. For the same pore geometry, we now ad- dress this passage in more detail. Does a polymer “thread” by one of its ends or “loop” by one of its mid-segments? Do both processes occur with equal facility? Several scenarios are illus- trated in Figure 1 for polymers of different topology. Answers to these questions obviously depend not just on R g , D c , and topology but also on chain persistence length l p and cavity-to- cavity hole diameter d h . In this first attack on the passage problem, we stick to pa- rameter ranges relevant to previous experiments, d  D/6, l p  25 nm, R g = 100 nm (2.69kb), 130 nm (4.36kb), 166 nm (7.25kb), and D c = 920 nm. Since hopping events are too small and too fast to deconstruct from images, these events are probed indirectly, by comparing the diffusion coefficients D of linear and circular molecules in the same pore structure. Loop- ing is the sole passage mechanism allowing diffusion of circu- lar molecules, while looping and threading are both possibili- ties for linear molecules. By gaining knowledge of D for linear and circular DNA, we are assessing the effect of molecular top- ology on chain dynamics. Loop (hernia) formation is important not just to fundamental diffusion studies but also to the design of improved media for the separation of flexible polymer molecules. Under some con- ditions, for example, the migration of linear DNA in electropho- resis gels is governed by looping. [2–6] An open technological challenge is to separate flexible polymers more strongly by their topology than by their average coil size. The isolation of circular DNA from linear DNA is relatively straightforward, but analysis of circular DNA mixtures remains difficult due to a poor understanding of transport. The same problems are en- countered in the realm of synthetic polymers, where separa- tion of branched molecules from linear molecules is technolog- Through a two-dimensional cavity array with connecting pores of submolecular size, diffusion of relaxed circular and linear DNA molecules is visualized by fluorescence microscopy. Across the entropic barriers transport regime, associated with spatially heterogeneous confinement of flexible polymers, cir- cular DNA diffuses slower than linear DNA of the same length, a trend indicating that linear DNA preferably moves through connecting pores by the threading of an end rather than the looping of a midsection. Figure 1. Modes of polymer diffusion through a pore for molecules of vari- ous topologies. A) and B) are showing linear molecule diffusion through the pore; A) “end first” mechanism and B) “loop first” mechanism. C) and D) show circular and branched molecule diffusion through a pore. [a] Dr. D. Nykypanchuk Center for Functional Nanomaterials Brookhaven National Laboratories, Upton NY 11973-5000 (USA) [b] Prof. D. A. Hoagland Polymer Science and Engineering Department University of Massachusetts, Amherst MA, 01003 (USA) [c] Prof. H. H. Strey Department of Biomedical Engineering Stony Brook University, Stony Brook NY 11794-2580 (USA) Fax: (+ 1) 631-632-8577 E-mail : hstrey@notes.cc.sunysb.edu ChemPhysChem 2009, 10, 2847 – 2851  2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 2847