Rigid Folding Research Articles

Designing of self-deploying origami structures using geometrically misaligned crease patterns.

Usually, origami-based morphing structures are designed on the premise of 'rigid folding', i.e. the facets and fold lines of origami can be replaced with rigid panels and ideal hinges, respectively. From a structural mechanics viewpoint, some rigid-foldable origami models are overconstrained and have negative degrees of freedom (d.f.). In these cases, the singularity in crease patterns guarantees their rigid foldability. This study presents a new method for designing self-deploying origami using the geometrically misaligned creases. In this method, some facets are replaced by 'holes' such that the systems become a 1-d.f. mechanism. These perforated origami models can be folded and unfolded similar to rigid-foldable (without misalignment) models because of their d.f. focusing on the removed facets, the holes will deform according to the motion of the frame of the remaining parts. In the proposed method, these holes are filled with elastic parts and store elastic energy for self-deployment. First, a new extended rigid-folding simulation technique is proposed to estimate the deformation of the holes. Next, the proposed method is applied on arbitrary-size quadrilateral mesh origami. Finally, by using the finite-element method, the authors conduct numerical simulations and confirm the deployment capabilities of the models.

The refraction phenomenon of singularities in thin elastic shells with developable mid-surface in presence of rigid folds: Case of parabolic shells

Abstract This paper deals with the refraction phenomenon that appears in the theory of thin shells of which the mid-surface is developable in presence of rigid folds when the thickness e tends to zero. Roughly speaking we talk about thin parabolic shells. On each side of the fold, the nature of the mid-surface of the shell is developable and boundary conditions ensure the geometric rigidity. The limit problem ( e = 0) which is also parabolic has some peculiarities that induce singularities. These singularities propagate along the asymptotic curves also called characteristics. When these singularities encounter a fold on which transmission conditions are given, they pass through the fold and they continue to propagate along the characteristic curves of the opposite part of the shell corresponding to the adjacent parts of the fold. A theoretical approach is proposed in order to study the refraction phenomenon in thin parabolic shells. Numerical simulations have been constructed to illustrate and observe the refraction phenomenon. The main result is that, once the singularities have crossed the fold, they continue to propagate along the characteristic curves of the other side of the fold without any loss or gain of regularity but with a variation in amplitude.

Rigid folding representation by the Stereographic Projection

The Stereographic Projection machinery is applied to the qualitative and quantitative description of the folding problem of an origami-like structure: the facets of a creased rigid sheet undergo successive rotation about several creases arbitrarily located in the three-dimensional space. The theoretical apparatus is revisited and some basic problems are depicted to emphasize both the simplicity and the great efficiency of the representation. Several original results, useful to simplify the trajectory tracing of the facet, are derived. The Representation of the Pole Path around a corner is finally presented as an alternative synthetic description of the folded configuration. An application to a multi-folded carton erection demonstrates the effectiveness of the proposed formulation.

Linearly diverging vocal folds and the Coanda effect

We would like to verify whether the Coanda effect has a significant impact when incorporated into theoretical vocal fold models that assume a piecewise linear shape of the vocal fold walls, as many do. We model the intraglottal flow with the equations of Thwaites. Thwaites boundary layer theory gives simple criteria for the glottal jet separation point if the vocal folds diverge linearly, and even validates well-known empirical observations for the jet width at flow separation. We test this criteria against flow experiments with rigid vocal fold replicas. The experiments involve symmetric and asymmetric vocal fold configurations, as well as steady and unsteady flow. We then validate the significance of the predicted Coanda effect on several numerical models of human vocal folds. We test the significance of the effect both on mechanically symmetric vocal fold models and on ones with mechanical asymmetries. We find limited effects on symmetric vocal folds and varying degrees of impact on asymmetric vocal folds.

New Deployable Structures Based on an Elastic Origami Model

Traditionally, origami-based structures are designed on the premise of “rigid folding,” However, every act of folding and unfolding is accompanied by elastic deformations in real structures. This study focuses on these elastic deformations in order to expand origami into a new method of designing morphing structures. The authors start by proposing a simple model for evaluating elastic deformation in nonrigid origami structures. Next, these methods are applied to deployable plate models. Initial strain is introduced into the elastic parts as actuators for deployment. Finally, by using the finite element method (FEM), it is confirmed that the proposed system can accomplish the complete deployment in 3 × 3 Miura-or model.

Molecular dynamics simulations of apocupredoxins: insights into the formation and stabilization of copper sites under entatic control

Cupredoxins perform copper-mediated long-range electron transfer (ET) in biological systems. Their copper-binding sites have evolved to force copper ions into ET-competent systems with decreased reorganization energy, increased reduction potential, and a distinct electronic structure compared with those of non-ET-competent copper complexes. The entatic or rack-induced state hypothesis explains these special properties in terms of the strain that the protein matrix exerts on the metal ions. This idea is supported by X-ray structures of apocupredoxins displaying "closed" arrangements of the copper ligands like those observed in the holoproteins; however, it implies completely buried copper-binding atoms, conflicting with the notion that they must be exposed for copper loading. On the other hand, a recent work based on NMR showed that the copper-binding regions of apocupredoxins are flexible in solution. We have explored five cupredoxins in their "closed" apo forms through molecular dynamics simulations. We observed that prearranged ligand conformations are not stable as the X-ray data suggest, although they do form part of the dynamic landscape of the apoproteins. This translates into variable flexibility of the copper-binding regions within a rigid fold, accompanied by fluctuations of the hydrogen bonds around the copper ligands. Major conformations with solvent-exposed copper-binding atoms could allow initial binding of the copper ions. An eventual subsequent incursion to the closed state would result in binding of the remaining ligands, trapping the closed conformation thanks to the additional binding energy and the fastening of noncovalent interactions that make up the rack.

Rigid Folding in Robotic Multi-agent Systems

The paper seeks to investigate the potential of biologically inspired multi-agent systems for architectural applications. The generation of ‘form’ through the process of ‘rigid folding’ represents a complex architectural procedure, which we seek to perform by employing a number of simple collaborative agents. Through a prototypic approach, closely matched with the constraints of a real world application, we want to demonstrate that the central architectural needs of form adaptability and resilience can be increased with this method. The established prototype is intended to serve as the ‘embodiment’ for different codes and strategies to test. Its shape transitions are based on the principal of folding, in which the triangle mesh topology serves as the basis for its folding patterns.

New experimental model of gastric carcinogenesis in rats with the use of formaldehyde and hydrogen peroxide mixture

This study was designed to develop an animal model of gastric cancer by using a mixture of formaldehyde and hydrogen peroxide. Thirty‐five outbred rats were used. In experimental group, 1.0 ml of the formaldehyde (0.4%) and hydrogen peroxide (0.4%) mixture (1:1) were administered to 30 rats by intragastric gavage on the 1st and 3rd day every 2 weeks for 6 months. Five non‐treated rats served as a control. The mortality rate among treated rats was 13.3%. We found that 6 months after the onset of treatment the 4 of 5 rats had gastric tumor, while after 7.5 months all survived 21 rats showed malignant tumors of the stomach. The tumors were primarily localized within the gastric mucosa, though the invasion of individual tumor cells and their clusters in the muscularis propria and serosa as well as in the lymphatic and blood vessels were also seen. In most cases, the infiltrated gastric mucosa areas (2 to 3) had rigid gastric folds and were 0.7×1.0cm to 1.5×3.0cm in size. We observed signet‐ring cell carcinomas in 80.9% of rats, well‐differentiated tubular adenocarcinoma in 66.6% of rats and moderately differentiated tumors in 23.8% of rats. Metastasis in regional lymph nodes were noted in 3 rats (14.3 %), while 6 animals (28.6%) revealed peritoneal dissemination of the small intestine. In addition, 19.0% of rats showed tumors of the lungs. Therefore, these data demonstrate that our animal model can be used to study gastric carcinogenesis.

Patterns of cerebral and cerebellar herniation

Anatomically the brain is compartmentalized by rigid folds of dura such as the falx cerebri which the lies between the cerebral hemispheres, and the tentorium cerebelli that separates the inferior portions of the occipital lobes from the cerebellum. When intracranial pressure increases, brain tissue may be compressed resulting in characteristic flattening of gyri and protrusion of tissue from one compartment into another. This may be caused by a diffuse increase in brain volume from edema due to trauma, or by a focal space occupying lesion such as hemorrhage, tumor or abscess [1]. Intracranial pressure may rapidly increase following hemorrhage or trauma [2]. The resultant herniations may be subfalcine, transtentorial (uncal), tonsillar or transcalvarial (Fig. 1) and may compress blood vessels resulting in critical compromise of circulation with local areas of infarction. The following provides a description and illustration of the major forms of herniation that may be encountered in forensic practice, with a discussion of possible secondary effects. Although the underlying lesions in the reported cases did not necessarily cause sudden and/ or unexpected deaths, they have been selected as they clearly demonstrate characteristic features of typical herniations.

816 弾性折りを利用した展開構造の設計

As represented by Miura-ori, origami has inspired various types of deployable structures. Usually, these Origami structures are designed under the assumption of "rigid folding", which means each plane is undeformable and connected with ideal joints. In this study, a new strategy for designing deployable structures are proposed by using partially elastic origami models. These new origami structures take into account the elastic deformation. It enables us to estimate the elastic energy through folding and unfolding process and to design self-deploying origami structures.

A Case of Mantle Cell Lymphoma Exhibiting Features of Gastric Linitis Plastica Type of Advanced Gastric Cancer

Mantle cell lymphoma has a broad spectrum of endoscopic presentations, such as thick, rigid folds that are indispensible on air insufflation, superficial confluent ulceration, or a polypoidal mass protruding into the lumen. The exact diagnosis is difficult to make because the lesion is in the submucosal layer and inaccessible by biopsy. Lesions will often exfoliate necrotic cells which make interpretation difficult, or they may be too small in number and size and thus indistinguishable from anaplastic carcinoma. We report a case of mantle cell lymphoma with diffuse wall thickening of the whole stomach in a 51-year-old man. The series of endoscopic findings in this case support the role of differential diagnosis of linitis plasica type of advanced gastric cancer with mantle cell lymphoma. (Korean J Helicobacter Up Gastrointest Res 2012;12:42-46)

Can a Proton be Encapsulated in Tetraamido/Diamino Quaternized Macrocycles in Aqueous Solution and Electric Field?

The proton-binding behavior of solvated tetraamido/diamino quaternized macrocyclic compounds with rigid phenyl and flexible phenyl bridges in the absence or presence of an external electric field is investigated by molecular dynamics simulation. The proton can be held through H-bonding interactions with the two carbonyl oxygen atoms in macrocycles containing rigid (phenyl) and flexible (propyl) bridges. The solute-solvent H-bonding interactions cause the macrocyclic backbones to twist to different extents, depending on the different bridges. The macrocycle with the rigid phenyl linkages folds into a cuplike shape due to π-π interaction, while the propyl analogue still maintains the ellipsoidal ringlike shape with just a slight distortion. The potential energy required for proton transfer is larger in the phenyl-containing macrocycle than in the compound with propyl units. When an external electric field with a strength of 2.5 V nm(-1) is exerted along the carbonyl oxygen atoms, a difference in proton encircling is exhibited for macrocycles with rigid and flexible bridges. In contrast to encapsulation of a proton in the propyl analogue, the intermolecular solute-solvent H-bonding and intramolecular π-π stacking between the two rigid phenyl spacers leads to loss of the proton from the highly distorted cuplike macrocycle with phenyl bridges. The competition between intra- and intermolecular interactions governs the behavior of proton encircling in macrocycles.

A solution for folding rigid tall shopping bags

Rigid origami is concerned with the folding of rigid thin-walled structures. The materials from which the structures are made are not allowed to deform or bend, but can rotate freely about pre-arranged creases. One of the challenges in rigid origami is the flat folding of a shopping bag with a rectangular base if the bag is made of rigid materials. The problem is not only mathematically interesting but also has practical implications as many consumer goods are packaged in box-shaped cartons or cardboard boxes. In this paper, a new crease pattern has been proposed that allows a tall box-shaped bag with a rectangular base to be rigidly folded flat. Rigid folding conditions are established, and solutions that meet these conditions are found numerically. Simulations and experiments carried out demonstrate that the solution works. The new pattern represents the first practical solution for tall bags and can lead to direct applications in the packaging industry. Moreover, the folding analysis can be used to design an automated packaging process for folding box-shaped stiff cartons.

Sequence Diversity in the Lasso Peptide Framework: Discovery of Functional Microcin J25 Variants with Multiple Amino Acid Substitutions

Microcin J25 (MccJ25) is a ribosomally synthesized antimicrobial peptide that has an unusual threaded lasso structure in which the C-terminal "tail" of the peptide is fed through a macrocyclic "ring" formed by the N-terminal residues. Production of MccJ25 in Escherichia coli is dependent upon a four-gene cluster encoding the structural gene mcjA, two maturation enzymes mcjB and mcjC, and an immunity factor, mcjD, in the form of an MccJ25 export pump. Here we have developed a system for orthogonal control of the expression of mcjA and mcjD, thus permitting independent control of MccJ25 production and export/immunity in E. coli. We used this system to screen saturation mutagenesis libraries targeted to either the ring or tail portions of MccJ25 and discovered nearly 100 new MccJ25 variants that retain antimicrobial function. While multiple amino acid substitutions in the tail portion of the peptide are well-tolerated, mutagenesis of the ring portion of the peptide is detrimental to the antimicrobial function of MccJ25. We demonstrated that the decreased function of the ring variants is due to the inability of these variants to be transported to the cytoplasm of susceptible strains. Additionally, we found several MccJ25 variants from the tail library with improved efficacy toward the MccJ25-sensitive strains E. coli and Salmonella enterica serovar Newport with the best variants exhibiting a nearly 5-fold increase in potency. The results described here provide further evidence that diverse amino acid sequences can be tolerated by the rigid lasso peptide fold.

The glmS ribozyme: use of a small molecule coenzyme by a gene-regulatory RNA.

The glmS ribozyme is the first known example of a natural ribozyme that has evolved to require binding of an exogenous small molecule for activity. In Gram-positive bacteria, this RNA domain is part of the messenger RNA (mRNA) encoding the essential enzyme that synthesizes glucosamine-6-phosphate (GlcN6P). When present at physiologic concentration, this small molecule binds to the glmS ribozyme and uncovers a latent self-cleavage activity that ultimately leads to degradation of the mRNA. Biochemical and structural studies reveal that the RNA adopts a rigid fold stabilized by three pseudoknots and the packing of a peripheral domain against the ribozyme core. GlcN6P binding to this pre-organized RNA does not induce conformational changes; rather, the small molecule functions as a coenzyme, providing a catalytically essential amine group to the active site. The ribozyme is not a passive player, however. Active site functional groups are essential for catalysis, even in the presence of GlcN6P. In addition to being a superb experimental system with which to analyze how RNA catalysts can exploit small molecule coenzymes to broaden their chemical versatility, the presence of the glmS ribozyme in numerous pathogenic bacteria make this RNA an attractive target for the development of new antibiotics and antibacterial strategies.

A record of ductile syn-intrusional fabrics to post solidification cataclasis: Magnetic fabric analysis of neoproterozoic Mirpur and Mt. Abu Granitoids, NW India

The Mirpur granite body represents a relatively small (10 km2) pluton intruded along the northern margin of the adjacent Mt. Abu batholith (∼125 km2) in NW India. It is a visibly undeformed alkali feldspar rich pink granite; in contrast, the Mt. Abu is a composite granitoid body and variably deformed. Both are intruded by rhyolitic dykes and the terminal magmatic events in both the cases are mafic dykes. The AMS (Anisotropy of Magnetic Susceptibility) data identify the Mt. Abu with SE-dipping foliations and subvertical lineations as a single structural domain while the Mirpur granite body shows two domains characterized by predominantly E — W trend of magnetic foliation in the eastern part (domain I) and N — S orientations in the western part (domain II). The domain I shows magmatic fabrics, typical for the peraluminous granites of Malani Igneous Suite (MIS). Change in fabric orientation in the domain II has resulted from cataclasis wherein the samples show destruction of the original E — W fabric and complete transposition by N — S trends. The foliations in the Mt. Abu granites have been related to SE orientation of maximum horizontal stress. The same maximum stress direction can be inferred from dyke orientation in the Mirpur granite, which is interpreted as continuation of the tectonic imprint in this region during emplacement of both the granites. Age of the cataclastic overprint with a predominant N — S orientation is not yet constrained but corresponds with the trend of the nearby Sindreth basin within the Malani Igneous Suite. The Neoproterozoic tectonic scenario for the region has been interpreted in terms of an ongoing crustal convergence and granitic magma emplacement against the back stop offered by the rigid Delhi Fold Belt.

Theoretical simulation and experimental validation of inverse quasi-one-dimensional steady and unsteady glottal flow models

In physical modeling of phonation, the pressure drop along the glottal constriction is classically assessed with the glottal geometry and the subglottal pressure as known input parameters. Application of physical modeling to study phonation abnormalities and pathologies requires input parameters related to in vivo measurable quantities commonly corresponding to the physical model output parameters. Therefore, the current research presents the inversion of some popular simplified flow models in order to estimate the subglottal pressure, the glottal constriction area, or the separation coefficient inherent to the simplified flow modeling for steady and unsteady flow conditions. The inverse models are firstly validated against direct simulations and secondly against in vitro measurements performed for different configurations of rigid vocal fold replicas mounted in a suitable experimental setup. The influence of the pressure corrections related to viscosity and flow unsteadiness on the flow modeling is quantified. The inversion of one-dimensional glottal flow models including the major viscous effects can predict the main flow quantities with respect to the in vitro measurements. However, the inverse model accuracy is strongly dependent on the pertinence of the direct flow modeling. The choice of the separation coefficient is preponderant to obtain pressure predictions relevant to the experimental data.

Biochemical Studies on Mycobacterium tuberculosis UreG and Comparative Modeling Reveal Structural and Functional Conservation among the Bacterial UreG Family

Nickel is a fundamental micronutrient for cellular life, but it is toxic in soluble form at nonphysiological concentrations. Such potentially contradictory features required living organisms to develop efficient systems for nickel utilization and homeostasis. This is the case for incorporation of nickel into the active site of urease, a multistep, tightly regulated process, requiring the interplay of various accessory proteins. The understanding of this activation mechanism may find medical applications against ureolytic bacteria, among which Mycobacterium tuberculosis is a deadly pathogen for humans. The topic of this study is UreG, an essential chaperone in the in vivo activation of urease upon insertion of Ni2+ into the active site. The protein was examined using both experimental and computational approaches. In particular, the soluble M. tuberculosis UreG (MtUreG) was overexpressed in Escherichia coli and purified to homogeneity. The identity of the isolated protein was established by mass spectrometry. On-line size-exclusion chromatography and light scattering indicated that MtUreG exists as a dimeric form in solution. Determination of the free thiol concentration revealed that a disulfide bond is present in the dimer. The isolated MtUreG shows low GTPase activity under native conditions, with a kcat of 0.01 min-1. Circular dichroism spectroscopy demonstrated the presence of a well-defined secondary structure (8% alpha-helices, 29% beta-strands) in MtUreG, whereas NMR spectroscopy indicated that this protein does not behave as a rigid three-dimensional fold and thus can be assigned to the class of intrinsically unstructured polypeptides. The molecular model of MtUreG in the fully folded and functional form was built using fold recognition algorithms. An extensive similarity search was performed to determine conservation patterns in all known bacterial UreG sequences. The generation of a multiple-sequence alignment and the related phylogenetic tree allowed us to recognize key residues and motifs that are likely important for protein function. A structural database containing the homology-built models of the most representative UreG proteins was created, confirming the structural analogies among the UreG family. A flexible region, likely to be important for protein function, is identified. The structural conservation among this class of GTPases is discussed on the basis of their function in the urease assembly process.

Structure of DDB1 in Complex with a Paramyxovirus V Protein: Viral Hijack of a Propeller Cluster in Ubiquitin Ligase

The DDB1-Cul4A ubiquitin ligase complex promotes protein ubiquitination in diverse cellular functions and is reprogrammed by the V proteins of paramyxoviruses to degrade STATs and block interferon signaling. Here we report the crystal structures of DDB1 alone and in complex with the simian virus 5 V protein. The DDB1 structure reveals an intertwined three-propeller cluster, which contains two tightly coupled beta propellers with a large pocket in between and a third beta propeller flexibly attached on the side. The rigid double-propeller fold of DDB1 is targeted by the viral V protein, which inserts an entire helix into the double-propeller pocket, whereas the third propeller domain docks DDB1 to the N terminus of the Cul4A scaffold. Together, these results not only provide structural insights into how the virus hijacks the DDB1-Cul4A ubiquitin ligase but also establish a structural framework for understanding the multiple functions of DDB1 in the uniquely assembled cullin-RING E3 machinery.

Unfolding-resistant Translocase Targeting: A NOVEL MECHANISM FOR OUTER MITOCHONDRIAL MEMBRANE LOCALIZATION EXEMPLIFIED BY THE Bβ2 REGULATORY SUBUNIT OF PROTEIN PHOSPHATASE 2A

Heterotrimeric serine/threonine protein phosphatase 2A (PP2A) consists of scaffolding (A), catalytic (C), and variable (B, B', and B'') subunits. Variable subunits dictate subcellular localization and substrate specificity of the PP2A holoenzyme. The Bbeta regulatory subunit gene is mutated in spinocerebellar ataxia type 12, and one of its splice variants, Bbeta2, targets PP2A to mitochondria to promote apoptosis in PC12 cells (Dagda, R. K., Zaucha, J. A., Wadzinski, B. E., and Strack, S. (2003) J. Biol. Chem. 278, 24976-24985). Here, we report that Bbeta2 is localized to the outer mitochondrial membrane by a novel mechanism, combining a cryptic mitochondrial import signal with a structural arrest domain. Scanning mutagenesis demonstrates that basic and hydrophobic residues mediate mitochondrial association and the proapoptotic activity of Bbeta2. When fused to green fluorescent protein, the N terminus of Bbeta2 acts as a cleavable mitochondrial import signal. Surprisingly, full-length Bbeta2 is not detectably cleaved and is retained at the outer mitochondrial membrane, even though it interacts with the TOM22 import receptor, as shown by luciferase complementation in intact cells. Mutations that open the C-terminal beta-propeller of Bbeta2 facilitate mitochondrial import, indicating that this rigid fold acts as a stop-transfer domain by resisting the partial unfolding step prerequisite for matrix translocation. Because hybrids of prototypical import and beta-propeller domains recapitulate this behavior, we predict the existence of other similarly localized proteins and a selection against highly stable protein folds in the mitochondrial matrix. This unfolding-resistant targeting to the mitochondrial translocase is necessary but not sufficient for the proapoptotic activity of Bbeta2, which also requires association with the rest of the PP2A holoenzyme.