Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, R 2 g , was found to scale as N 4/5 for an intermediate regime and N 2/3 for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper 1 . Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.

Molecular dynamics simulations were conducted to investigate the dynamic properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. The ring melts were found to diffuse faster than their linear counterparts, with both architectures approximately obeying a D ∼ N −2.4 scaling law for large N . The mean-square displacement of the center-of-mass of the rings follows a sub-diffusive behavior for times and distances beyond the ring extension R 2 g , neither compatible with the Rouse nor the reptation model. The rings relax stress much faster than linear polymers and the zero-shear viscosity was found to vary as η 0 ∼ N 1.4±0.2 which is much weaker than the N 3.4 behavior of linear chains, not matching any commonly known model for polymer dynamics when compared to the observed mean-square displacements. These findings are discussed in view of the conformational properties of the rings presented in the preceding paper 1 .

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.

Ring polymers remain a challenge to our understanding of polymer dynamics. Experiments are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and nonequilibrium molecular dynamics simulations we have investigated the structure, dynamics, and rheology of perfectly controlled ring-linear polymer blends of chains of up to about 14 entanglements per chain, comparable to experimental systems. Linear contaminants increase the zero-shear viscosity of a ring polymer melt by about 10% around one-fifth of their overlap concentration. For equal concentrations of linear and ring polymers, the blend viscosity is about twice that of the pure linear melt. The diffusion coefficient of the rings decreases dramatically, while the linear polymers are mostly unaffected. Our results are supported by a primitive path analysis.

The science of self-assembly has undergone a radical shift from asking questions about why individual components self-organize into ordered structures, to manipulating the resultant order. However, the quest for far-reaching nanomanufacturing requires addressing an even more challenging question: how to form nanoparticle (NP) structures with designed architectures without explicitly prescribing particle positions. Here we report an assembly concept in which building instructions are embedded into NPs via DNA frames. The integration of NPs and DNA origami frames enables the fabrication of NPs with designed anisotropic and selective interactions. Using a pre-defined set of different DNA-framed NPs, we show it is possible to design diverse planar architectures, which include periodic structures and shaped meso-objects that spontaneously emerge on mixing of the different topological types of NP. Even objects of non-trivial shapes, such as a nanoscale model of Leonardo da Vinci's Vitruvian Man, can be self-assembled successfully.