Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures

The design of complex, competing effects in magnetic systems—be it via the introduction of nonlinear interactions1–4, or the patterning of three-dimensional geometries5,6—is an emerging route to achieve new functionalities. In particular, through the design of three-dimensional geometries and curvature, intrastructure properties such as anisotropy and chirality, both geometry-induced and intrinsic, can be directly controlled, leading to a host of new physics and functionalities, such as three-dimensional chiral spin states7, ultrafast chiral domain wall dynamics8–10 and spin textures with new spin topologies7,11. Here, we advance beyond the control of intrastructure properties in three dimensions and tailor the magnetostatic coupling of neighbouring magnetic structures, an interstructure property that allows us to generate complex textures in the magnetic stray field. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality and magnetic coupling are jointly exploited. By reconstructing the three-dimensional vectorial magnetic state of the double helices with soft-X-ray magnetic laminography12,13, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. Micromagnetic simulations reveal that the magnetization configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetization and antivortices in free space, which together form an effective B field cross-tie wall14. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials15, unconventional computing2,16, particle trapping17,18 and magnetic imaging19.

Simulative Analysis of a Family of DNA Tetrahedrons Produced by Changing the Twisting Number of Each Double Helix

In this paper, three tetrahedral nanocages, composed of six DNA double helix edges with all having the twist number 1, 2 or 3, have been characterized using classical molecular dynamics simulation to measure the specific structural and conformational features produced by only changing the twisting number of each double helix. The simulation result indicates that three tetrahedral cages are relatively stable and are maintained along the entire trajectory. Each double helix is more inclined to behave as a whole in the 2TD and 3TD cages than in the 1TD cage according to the cross-correlation maps for three nanocages, and also their local motions are more easily induced by the conformational variability of the thymidine linkers due to the increased flexibility of each helix. Hence, the double helices become the important factors on the structural stability of total cages with the DNA twisting number, and also give the signification contributions to the sizes of these cages conferring the larger spaces of the 2TD and 3TD cages than the 1TD cage. Our result provides an insight into which roles the double helix edges play in assembling DNA polyhedron, and also contribute to improving the loading capacity of DNA tetrahedron in drug delivery.

Cryo-EM structure of MukBEF reveals DNA loop entrapment at chromosomal unloading sites

The ring-like structural maintenance of chromosomes (SMC) complex MukBEF folds the genome of Escherichia coli and related bacteria into large loops, presumably by active DNA loop extrusion. MukBEF activity within the replication terminus macrodomain is suppressed by the sequence specific unloader MatP. Here we present the complete atomic structure of MukBEF in complex with MatP and DNA as determined by electron cryomicroscopy (cryo-EM). The complex binds two distinct DNA double helices corresponding to the arms of a plectonemic loop. MatP-bound DNA threads through the MukBEF ring, while the second DNA is clamped by the kleisin MukF, MukE and the MukB ATPase heads. Combinatorial cysteine cross-linking confirms this topology of DNA loop entrapment in vivo. Our findings illuminate how a class of near-ubiquitous DNA organizers with important roles in genome maintenance interacts with the bacterial chromosome.

Folds induced by multiple parallel or antiparallel double-helices: (pseudo)knotting of single-stranded RNA

ABSTRACTWe develop tools to explore and catalogue the topologies of knotted or pseudoknotted circular folds due to secondary and tertiary interactions within a closed loop of RNA which generate multiple double-helices due (for example) to strand complementarity. The fold topology is captured by a ‘contracted fold’ which merges helices separated by bulges and removes hairpin loops. Contracted folds are either trivial or pseudoknotted. Strand folding is characterised by a rigid-vertex ‘polarised strand graph’, whose vertices correspond to double-helices and edges correspond to strands joining those helices. Each vertex has a plumbline whose polarisation direction defines the helical axis. That polarised graph has a corresponding circular ribbon diagram and canonical alphanumeric fold label. Key features of the ‘fully-flagged’ fold are the arrangement of complementary domains along the strand, described by a numerical bare fold label, and a pair of binary ‘flags’: a parity flag that specifies the twist in each helix (even or odd half-twists), and an orientation flag that characterises each double-helix as parallel or antiparallel. A simple algorithm is presented to translate an arbitrary fold label into a polarised strand graph. Any embedding of the graph in 3-space is an admissible fold geometry; the simplest embeddings minimise the number of edge-crossings in a planar graph drawing. If that number is zero, the fold lies in one of two classes: (a)-type ‘relaxed’ folds, which contain conventional junctions and (b)-type folds whose junctions are described as meso-junctions in H. Wang and N.C. Seeman, Biochem, vol. 34, pp920-929. (c)-type folds induce polarised strand graphs with edge-crossings, regardless of the planar graph drawing. Canonical fold labelling allows us to sort and enumerate all ‘semi-flagged’ folds with up to six contracted double-helices as windings around the edges of a graph-like fold skeleton, whose cyclomatic number - the ‘fold genus’ - ranges from 0 – 3, resulting in a pair of duplexed strands along each skeletal edge. Those semi-flagged folds admit both even and odd double-helical twists. Appending specific parity flags to those semi-flagged folds gives fully-flagged (a)-type folds, which are also enumerated up to genus-3 cases. We focus on all-antiparallel folds, characteristic of conventional ssRNA and enumerate all distinct (a), (b) and (c)-type folds with up to five double-helices. Those circular folds lead to pseudoknotted folds for linear ssRNA strands. We describe all linear folds derived from (a) or (b)-type circular folds with up to four contracted double-helices, whose simplest cases correspond to so-called H, K and L pseudoknotted folds, detected in ssRNA. Fold knotting is explored in detail, via constructions of so-called antifolds and isomorphic folds. We also tabulate fold knottings for (a) and (b)-type folds whose embeddings minimise the number of edge-crossings and outline the procedure for (c)-type folds. The inverse construction - from a specific knot to a suitable nucleotide sequence - results in a hierarchy of knots. A number of specific alternating knots with up to 10 crossings emerge as favoured fold designs for ssRNA, since they are readily constructed as (a)-type all-antiparallel folds.

Asymmetric Metal-Organic Frameworks with Double Helices for Enantioselective Recognition

A pair of homochiral metal-organic frameworks are elaborated by employing flexible enantiopure ligands. They possess interesting double helical chains and rich hydrogen-bonding environment, exhibiting excellent chiral recognition ability to carvone.

Single- and double-helices of α,α′-dibenzylaminotripyrrin: solution and solid state studies

α,α′-Di(benzylamino)tripyrrin was synthesized, which exhibited an equilibrium between single- and double-helical forms in solution. XRD analysis showed its co-crystal structure including both forms.