Abstract Ring origami has emerged as a robust strategy for designing foldable and deployable structures due to its impressive packing abilities achieved from the snap-folding mechanism. In general, polygonal rings with rationally designed geometric parameters can fold into compacted three-loop configurations with curved segments, which result from the internal bending moment in the folded state. Inspired by the internal bending moment-induced curvature in the folded state, we explore how this curvature can be tuned by introducing initial natural curvature to the segments of the polygonal rings in their deployed stress-free state, and study how this initial curvature affects their folded configurations. Taking a clue from straight-segmented polygonal rings that fold into overlapping curved loops, we find it is possible to reverse the process by introducing curvature into the ring segments in the stress-free initial state such that the rings fold into a straight-line looped pattern with “zero” area. This realizes extreme packing. In this work, by a combination of experimental observation, finite element analysis, and theoretical modeling, we systematically study the effect of segment curvature on folding behavior, folded configurations, and packing of curved ring origami with different geometries. It is anticipated that curved ring origami can open a new avenue for the design of foldable and deployable structures with simple folded configurations and high packing efficiency.
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Protamine loops DNA in multiple steps
Abstract Protamine proteins dramatically condense DNA in sperm to almost crystalline packing levels. Here, we measure the first step in the in vitro pathway, the folding of DNA into a single loop. Current models for DNA loop formation are one-step, all-or-nothing models with a looped state and an unlooped state. However, when we use a Tethered Particle Motion (TPM) assay to measure the dynamic, real-time looping of DNA by protamine, we observe the presence of multiple folded states that are long-lived (∼100 s) and reversible. In addition, we measure folding on DNA molecules that are too short to form loops. This suggests that protamine is using a multi-step process to loop the DNA rather than a one-step process. To visualize the DNA structures, we used an Atomic Force Microscopy (AFM) assay. We see that some folded DNA molecules are loops with a ∼10-nm radius and some of the folded molecules are partial loops—c-shapes or s-shapes—that have a radius of curvature of ∼10 nm. Further analysis of these structures suggest that protamine is bending the DNA to achieve this curvature rather than increasing the flexibility of the DNA. We therefore conclude that protamine loops DNA in multiple steps, bending it into a loop.
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- Award ID(s):
- 1653501
- NSF-PAR ID:
- 10206835
- Date Published:
- Journal Name:
- Nucleic Acids Research
- Volume:
- 48
- Issue:
- 11
- ISSN:
- 0305-1048
- Page Range / eLocation ID:
- 6108 to 6119
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract DNA in cells is organized in negatively supercoiled loops. The resulting torsional and bending strain allows DNA to adopt a surprisingly wide variety of 3-D shapes. This interplay between negative supercoiling, looping, and shape influences how DNA is stored, replicated, transcribed, repaired, and likely every other aspect of DNA activity. To understand the consequences of negative supercoiling and curvature on the hydrodynamic properties of DNA, we submitted 336 bp and 672 bp DNA minicircles to analytical ultracentrifugation (AUC). We found that the diffusion coefficient, sedimentation coefficient, and the DNA hydrodynamic radius strongly depended on circularity, loop length, and degree of negative supercoiling. Because AUC cannot ascertain shape beyond degree of non-globularity, we applied linear elasticity theory to predict DNA shapes, and combined these with hydrodynamic calculations to interpret the AUC data, with reasonable agreement between theory and experiment. These complementary approaches, together with earlier electron cryotomography data, provide a framework for understanding and predicting the effects of supercoiling on the shape and hydrodynamic properties of DNA.
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Abstract Several strategies are recently exploited to transform 2D sheets into desired 3D structures. For example, soft materials can be morphed into 3D continuously curved structures by inducing nonhomogeneous strain. On the other hand, rigid materials can be folded, often by origami/kirigami‐inspired approaches (i.e., flat sheets are folded along predesigned crease patterns). Here, for the first time, combining the two strategies, composite sheets are fabricated by embedding rigid origami/kirigami skeleton with creases into heat shrinkable polymer sheets to create novel 3D structures. Upon heating, shrinkage of the polymer sheets is constrained by the origami/kirigami patterns, giving rise to laterally nonuniform strain. As a result, Gaussian curvature of the composite sheets is changed, and flat sheets are transformed into 3D curved structures. A series of 3D structures are folded using this approach, including cones and truncated pyramids with different base shapes. Flat origami loops are folded into step structures. Tessellation of origami loops is transformed into 3D checkerboard pattern.
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Abstract The structures and functions of proteins are embedded into the loop scaffolds of structural domains. Their origin and evolution remain mysterious. Here, we use a novel graph-theoretical approach to describe how modular and non-modular loop prototypes combine to form folded structures in protein domain evolution. Phylogenomic data-driven chronologies reoriented a bipartite network of loops and domains (and its projections) into ‘waterfalls’ depicting an evolving ‘elementary functionome’ (EF). Two primordial waves of functional innovation involving founder ‘
p -loop’ and ‘winged-helix’ domains were accompanied by an ongoing emergence and reuse of structural and functional novelty. Metabolic pathways expanded before translation functionalities. A dual hourglass recruitment pattern transferred scale-free properties from loop to domain components of the EF network in generative cycles of hierarchical modularity. Modeling the evolutionary emergence of the oldest P-loop and winged-helix domains with AlphFold2 uncovered rapid convergence towards folded structure, suggesting that a folding vocabulary exists in loops for protein fold repurposing and design. -
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Abstract Protein loops make up a large portion of the secondary structure in nature. But very little is known concerning loop closure dynamics and the effects of loop composition on fold stability. We have designed a small system with stable β‐sheet structures, including features that allow us to probe these questions. Using paired Trp residues that form aromatic clusters on folding, we are able to stabilize two β‐strands connected by varying loop lengths and composition (an example sequence: R
W ITVTI – loop – KKIRVW E). Using NMR and CD, both fold stability and folding dynamics can be investigated for these systems. With the 16 residue loop peptide (sequence: RW ITVTI‐(GGGGKK)2GGGG‐KKIRVW E) remaining folded (ΔGU = 1.6 kJ/mol at 295K). To increase stability and extend the series to longer loops, we added an additional Trp/Trp pair in the loop flanking position. With this addition to the strands, the 16 residue loop (sequence: RW ITVRIW ‐(GGGGKK)2GGGG‐W KTIRVW E) supports a remarkably stable β‐sheet (ΔG U = 6.3 kJ/mol at 295 K,T m = ∼55°C). Given the abundance of loops in binding motifs and between secondary structures, these constructs can be powerful tools for peptide chemists to study loop effects; with the Trp/Trp pair providing spectroscopic probes for assessing both stability and dynamics by NMR.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/nar/gkaa365
