Symmetric Folds Research Articles

Bursting mechanism in a time-delayed oscillator with slowly varying external forcing

This paper investigates the generation of complex bursting patterns in the Duffing oscillator with time-delayed feedback. We present the bursting patterns, including symmetric fold–fold bursting and symmetric Hopf–Hopf bursting when periodic forcing changes slowly. We make an analysis of the system bifurcations and dynamics as a function of the delayed feedback and the periodic forcing. We calculate the conditions of fold bifurcation and Hopf bifurcation as well as its stability related to external forcing and delay. We also identify two regimes of bursting depending on the magnitude of the delay itself and the strength of time delayed coupling in the model. Our results show that the dynamics of bursters in delayed system are quite different from those in systems without any delay. In particular, delay can be used as a tuning parameter to modulate dynamics of bursting corresponding to the different type. Furthermore, we use transformed phase space analysis to explore the evolution details of the delayed bursting behavior. Also some numerical simulations are included to illustrate the validity of our study.

Acoustic and perceptual effects of changes in body layer stiffness in symmetric and asymmetric vocal fold models

At present, it is not well understood how changes in vocal fold biomechanics correspond to changes in voice quality. Understanding such cross-domain links from physiology to acoustics to perception in the "speech chain" is of both theoretical and clinical importance. This study investigates links between changes in body layer stiffness, which is regulated primarily by the thyroarytenoid muscle, and the consequent changes in acoustics and voice quality under left-right symmetric and asymmetric stiffness conditions. Voice samples were generated using three series of two-layer physical vocal fold models, which differed only in body stiffness. Differences in perceived voice quality in each series were then measured in a "sort and rate" listening experiment. The results showed that increasing body stiffness better maintained vocal fold adductory position, thereby exciting more high-order harmonics, differences that listeners readily perceived. Changes to the degree of left-right stiffness mismatch and the resulting left-right vibratory asymmetry did not produce perceptually significant differences in quality unless the stiffness mismatch was large enough to cause a change in vibratory mode. This suggests that a vibration pattern with left-right asymmetry does not necessarily result in a salient deviation in voice quality, and thus may not always be of clinical significance.

A randomised trial of honey barrier cream versus zinc oxide ointment

In this single-blind multicentre, intervention study, 31 patients with symmetrical intertrigo in large skin folds were included to study the clinical effect of two topical treatments, i.e. standard therapy with zinc oxide ointment versus honey barrier cream. Patients were treated twice daily for 21 days, and the severity of intertrigo was scored in an observation period of 21 days. Patients were used as their own controls by treating symmetrical skin folds, on the left and right side. There was no significant difference in treatment effect between intervention groups. For the majority of patients, both treatments were effective. However, the use of honey barrier cream showed lower pruritus complaints (12.9% versus 29.0%). Honey barrier cream is a suitable alternative in the treatment of intertrigo, and promotes patient comfort.

Emergence of symmetric protein architecture from a simple peptide motif: evolutionary models.

Structural symmetry is observed in the majority of fundamental protein folds and gene duplication and fusion evolutionary processes are postulated to be responsible. However, convergent evolution leading to structural symmetry has also been proposed; additionally, there is debate regarding the extent to which exact primary structure symmetry is compatible with efficient protein folding. Issues of symmetry in protein evolution directly impact strategies for de novo protein design as symmetry can substantially simplify the design process. Additionally, when considering gene duplication and fusion in protein evolution, there are two competing models: "emergent architecture" and "conserved architecture". Recent experimental work has shed light on both the evolutionary process leading to symmetric protein folds as well as the ability of symmetric primary structure to efficiently fold. Such studies largely support a "conserved architecture" evolutionary model, suggesting that complex protein architecture was an early evolutionary achievement involving oligomerization of smaller polypeptides.

Review on Mathematical and Mechanical Models of the Vocal Cord

A review on mathematical and mechanical models of the vocal cords is given. The basic model is a two‐mass nonlinear oscillator system which is accepted to be the basic one for mechanical description in voice production. The model is not only extended into three, five, and more mass systems, systems with time variable parameters and three‐dimensional systems, but also simplified into one‐mass system with coupled two‐direction deflection and damping functions. The corresponding mathematical models are the systems of coupled second‐order differential equations which describe the vibrations of the symmetric and asymmetric vocal folds. The models give the conditions for the regular and irregular motions like bifurcation and deterministic chaos in vocal folds. The obtained results are of special interest for detecting the pathology of vocal cords, when there are no visual effects of disease. Based on the results given in the paper, the objectives for future investigation in this matter are given.

Caerin的二维HP折叠结构

采用标准化氨基酸疏水性指数将7种Caerins的氨基酸序列转换为28种疏水性(H)或极性(P)的序列，通过二维疏水性–极性(HP)模型分析其全部可能的折叠结构。结果显示Caerins有许多具有相同最小能量的天然形态，这些形态有各种各样对称的折叠结构，而且这些天然形态可以根据标准化的氨基酸疏水性指标进一步从数值上加以区分。这项研究从疏水性–极性角度揭示了Caerin折叠结构的多样性，有助于理解蛋白质的折叠过程，并提示通过工程学方法修改抗菌肽的可能途径。 The amino acid sequences of 7 Caerins were converted into 28 hydrophobic (H) or polar (P) sequences according to the normalized amino acid hydrophobicity index, and all of their possible folding structures were analyzed using 2D hydrophobic-polar (HP) model. The results showed that Caerins have many native states with the same mini- mal energy, which consist of various symmetric folding structures, and that the normalized amino acid hydrophobicity index can help furthermore distinguish native states numerically. The study demonstrates the diversity of Caerin folding structures from hydrophobic-polar (HP) angle, which can shed light on understanding folding process of protein and implying possible ways to modify antimicrobial peptides through engineering.

New Syndrome of Congenital Circumferential Skin Folds Associated with Multiple Congenital Anomalies

Congenital circumferential skin folds can be found in individuals with no additional defects, as well as in patients with multiple congenital anomalies and developmental abnormalities. Current data point to etiological heterogeneity of syndromic cases. We describe a 7-month-old girl with a novel combination of symmetrical congenital circumferential skin folds, dysmorphic features, and multiple congenital abnormalities. Examination of the patient revealed symmetrical congenital circumferential skin folds and dysmorphic features, as well as multiple congenital anomalies including nasal pyriform aperture stenosis, ventricular septal defect, absent spleen, camptodactyly, and severe psychomotor retardation. Skin biopsy demonstrated subcutaneous fat extending into the superficial and deep reticular dermis. Sequencing of the CDON, SHH, ZIC2, SIX3, and TGIF genes (associated with holoprosencephaly) did not disclose pathogenic alterations. Extensive review of previously described cases of syndromic congenital circumferential skin folds did not reveal a similar combination of clinical and histopathological findings.

Symmetric circular matchings and RNA folding

RNA secondary structures can be computed as optimal solutions of certain circular matching problems. An accurate treatment of this energy minimization problem has to account for the small — but non-negligible — entropic destabilization of secondary structures with non-trivial automorphisms. Such intrinsic symmetries are typically excluded from algorithmic approaches; however, because the effects are small, they play a role only for RNAs with symmetries at sequence level, and they appear only in particular settings that are less frequently used in practical application, such as circular folding or the co-folding of two or more identical RNAs. Here, we show that the RNA folding problem with symmetry terms can still be solved with polynomial-time algorithms. Empirically, the fraction of symmetric ground state structures decreases with chain length, so that the error introduced by neglecting the symmetry terms affects fewer and fewer predictions. We then explore the combinatorics of symmetric secondary structures in detail. Surprisingly, the singularities of the generating function coincide between symmetric and non-symmetric structures. Furthermore, generating functions and explicit asymptotic results for both the circular and the co-folding version are derived.

Experimental support for the evolution of symmetric protein architecture from a simple peptide motif

The majority of protein architectures exhibit elements of structural symmetry, and "gene duplication and fusion" is the evolutionary mechanism generally hypothesized to be responsible for their emergence from simple peptide motifs. Despite the central importance of the gene duplication and fusion hypothesis, experimental support for a plausible evolutionary pathway for a specific protein architecture has yet to be effectively demonstrated. To address this question, a unique "top-down symmetric deconstruction" strategy was utilized to successfully identify a simple peptide motif capable of recapitulating, via gene duplication and fusion processes, a symmetric protein architecture (the threefold symmetric β-trefoil fold). The folding properties of intermediary forms in this deconstruction agree precisely with a previously proposed "conserved architecture" model for symmetric protein evolution. Furthermore, a route through foldable sequence-space between the simple peptide motif and extant protein fold is demonstrated. These results provide compelling experimental support for a plausible evolutionary pathway of symmetric protein architecture via gene duplication and fusion processes.

Biosynthesis of Isoprenoids: Crystal Structure of the [4Fe–4S] Cluster Protein IspG

IspG protein serves as the penultimate enzyme of the recently discovered non-mevalonate pathway for the biosynthesis of the universal isoprenoid precursors, isopentenyl diphosphate and dimethylallyl diphosphate. The enzyme catalyzes the reductive ring opening of 2 C-methyl- d-erythritol 2,4-cyclodiphosphate, which affords 1-hydroxy-2-methyl-2-( E)-butenyl 4-diphosphate. The protein was crystallized under anaerobic conditions, and its three-dimensional structure was determined to a resolution of 2.7 Å. Each subunit of the c 2 symmetric homodimer folds into two domains connected by a short linker sequence. The N-terminal domain (N domain) is an eight-stranded β barrel that belongs to the large TIM-barrel superfamily. The C-terminal domain (C domain) consists of a β sheet that is flanked on both sides by helices. One glutamate and three cysteine residues of the C domain coordinate a [4Fe–4S] cluster. Homodimer formation involves an extended contact area (about 1100 Å 2) between helices 8 and 9 of each respective β barrel. Moreover, each C domain contacts the N domain of the partner subunit, but the interface regions are small (about 430 Å 2). We propose that the enzyme substrate binds to the positively charged surface area at the C-terminal pole of the β barrel. The C domain carrying the iron–sulfur cluster could then move over to form a closed conformation where the substrate is sandwiched between the N domain and the C domain. This article completes the set of three-dimensional structures of the non-mevalonate pathway enzymes, which are of specific interest as potential targets for tuberculostatic and antimalarial drugs.

Detecting internally symmetric protein structures

BackgroundMany functional proteins have a symmetric structure. Most of these are multimeric complexes, which are made of non-symmetric monomers arranged in a symmetric manner. However, there are also a large number of proteins that have a symmetric structure in the monomeric state. These internally symmetric proteins are interesting objects from the point of view of their folding, function, and evolution. Most algorithms that detect the internally symmetric proteins depend on finding repeating units of similar structure and do not use the symmetry information.ResultsWe describe a new method, called SymD, for detecting symmetric protein structures. The SymD procedure works by comparing the structure to its own copy after the copy is circularly permuted by all possible number of residues. The procedure is relatively insensitive to symmetry-breaking insertions and deletions and amplifies positive signals from symmetry. It finds 70% to 80% of the TIM barrel fold domains in the ASTRAL 40 domain database and 100% of the beta-propellers as symmetric. More globally, 10% to 15% of the proteins in the ASTRAL 40 domain database may be considered symmetric according to this procedure depending on the precise cutoff value used to measure the degree of perfection of the symmetry. Symmetrical proteins occur in all structural classes and can have a closed, circular structure, a cylindrical barrel-like structure, or an open, helical structure.ConclusionsSymD is a sensitive procedure for detecting internally symmetric protein structures. Using this procedure, we estimate that 10% to 15% of the known protein domains may be considered symmetric. We also report an initial, overall view of the types of symmetries and symmetric folds that occur in the protein domain structure universe.

A rapid Bézier curve method for shape analysis and point representation of asymmetric folds

Point representation of fold shapes is useful, in particular, for classification of a large number of folds into different geometric populations. The methods for shape analysis and point representation of asymmetric folds are a few and tedious, although several methods exist for the analysis of the individual fold limbs, or symmetric folds. This article gives a rapid method that uses the Bézier curve tool, available in any common computer graphics software, for the analysis of a complete asymmetric fold and its point representation in the two-dimensional frame. The new method is based on the reduction of variables in the parametric equations of a cubic Bézier curve. It makes the length of one Bézier handle zero, pins the end point of the other Bézier handle at the origin of the X– Y frame and drags its control point along the Y-axis to fit the Bézier curve on the given asymmetric fold. A Cartesian plot between normalised length of the Bézier handle and the lift, i.e., difference between the heights of the two inflection points, gives the unique point that represents the given asymmetric fold shape. We test the validity of the new method on several computer simulated asymmetric folds and demonstrate its usefulness with the help of a natural example.

Density Functional Theory Investigations of the Homoleptic Tris(dithiolene) Complexes [M(dddt)3]−q(q= 3, 2 ; M = Nd3+and U3+/4+) Related to Lanthanide(III)/Actinide(III) Differentiation

The structures of the homoleptic lanthanide and actinide tris(dithiolene) complexes [M(dddt)(3)](q-) (q = 3, M = Nd(3+) and q = 3 or 2, M = U(3+/4+)) have been investigated using relativistic Density Functional Theory (DFT) computations including spin-orbit corrections coupled with the COnductor-like Screening Model (COSMO) for a realistic solvation approach. The dithiolene ligands are known to be very efficient at stabilizing metal high oxidation states. The aim of the work is to explain the peculiar symmetric folding of the three Mdddt metallacycles in these complexes, some of them existing under a polymeric form, in relation with the Ln(III)/An(III) differentiation. In the [M(dddt)(3)(py)](q-) species, where an additional pyridine ligand is linked to the metal center, the Mdddt moieties appear to be almost planar. The study brings to light the occurrence of a M...C=C interaction explaining the Mdddt folding of the [U(dddt)(3)](q-) uranium species, the metal 5f electrons playing a driving role. No such interaction appears in the case of the Nd(III) complex, and the folding of the rather flexible dddt ligands in the polymeric structure of this species should be mainly due to steric effects. Moreover, the analysis of the normal modes of vibration shows that the U(III) complex [U(dddt)(3)](3-), which has not yet been isolated, is thermodynamically stable. It appears that the X-ray characterized U(IV) complex [U(dddt)(3)](2-) should be less stable than the calculated U(III) complex in a polar solvent.

Alternative to Homo-oligomerisation: The Creation of Local Symmetry in Proteins by Internal Amplification

The biologically active state of many proteins requires their prior homo-oligomerisation. Such complexes are typically symmetrical, a feature that has been proposed to increase their stability and facilitate the evolution of allosteric regulation. We wished to examine the possibility that similar structures and properties could arise from genetic amplifications leading to internal symmetrical repeats. For this, we identified internal structural repeats in a nonredundant Protein Data Bank subset. While testing if repeats in proteins tend to be symmetrical, we found that about half of the large internal repeats are symmetrical, most frequently around a rotation axis of 180°. These repeats were most likely created by genetic amplification processes because they show significant sequence similarity. Symmetrical repeats tend to have a fixed number of copies corresponding to their rotational symmetry order, that is, two for 180° rotation axis, whereas asymmetrical repeats are in longer proteins and show copy number variability. When possible, we confirmed that proteins with symmetrical repeats folding as an n-mer have homologues lacking the repeat with a higher oligomerisation number corresponding to the rotation symmetry order of the repeat. Phylogenetic analyses of these protein families suggest that typically, but not always, symmetrical repeats arise in one single event from proteins that are homo-oligomers. These results suggest that oligomerisation and amplification of internal sequences can interplay in evolutionary terms because they result in functional analogues when the latter exhibit rotational symmetry.

Bonding in titanocenyl complexes containing O,O′‐cyclic ligands

AbstractDensity functional theory calculations show that the formal 16‐electron count of d0 [Cp2TiIV(O,O′‐BID)]0/1 complexes containing a O,O′‐chelated bidentate ligand O,O′‐BID of different ring size, is increased via Ti←O π bonding when both the O donor atoms carry a formal negative charge. The Ti←O π bonding occurs by symmetry lowering of the complex by either symmetrical (Cs) or unsymmetrical (C2) folding of the O,O′‐BID ligand round the O···O axis. An NBO analysis confirms the Ti←O π charge transfer via back‐bonding. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

The NMR Structures of the Major Intermediates of the Two-domain Tick Carboxypeptidase Inhibitor Reveal Symmetry in Its Folding and Unfolding Pathways

There is a lack of experimental structural information about folding intermediates of multidomain proteins. Tick carboxypeptidase inhibitor (TCI) is a small, disulfide-rich protein consisting of two domains that fold and unfold autonomously through the formation of two major intermediates, IIIa and IIIb. Each intermediate contains three native disulfide bonds in one domain and six free cysteines in the other domain. Here we have determined the NMR structures of these two intermediates trapped and isolated at acidic pH in which they are stable and compared their structures with that of the native protein analyzed under the same conditions. Both IIIa and IIIb were found to contain a folded region that corresponds to the N- and C-terminal domains of TCI, respectively, with structures very similar to the corresponding regions of the native protein. The remainder of the polypeptide chains of the intermediates was shown to be unfolded in a random coil conformation. Solvent exchange measurements further indicated that the two protein domains are not completely independent, but affect each other in terms of dynamics and stability, in agreement with reported inhibitory activity data. The derived results provide structural evidence for symmetric TCI folding and unfolding mechanisms that converge in IIIa and IIIb and reveal the structural basis that accounts for the strong and simultaneous accumulation of both intermediates. Altogether, this work has important implications for a better understanding of the folding mechanisms of multidomain, disulfide-rich proteins.

Correction of Congenital Severe Ptosis by Suspension of a Frontal Muscle Flap Overlapped with an Inferiorly Based Orbital Septum Flap

This report introduces a new method for correction of congenital severe upper eyelid ptosis. The poor levator-function upper eyelid ptosis of 22 patients was corrected using suspension of the frontal muscle flap overlapped with an inferiorly based orbital septum flap as a motor unit, which substituted for the function of the levator muscle. The frontal muscle flap and orbital septum flap were formed in the frontal part and upper eyelid, respectively. Two flaps were overlapped and sutured to suspend the upper eyelid and to correct the congenital severe upper eyelid ptosis. This technique avoids the need for the linking structure necessary with the standard frontalis sling approach and improves the direction of pull to mimic that of a normal levator more closely than that of frontalis muscle advancement. The follow-up period ranged from 6 to 20 months (mean, 12 months). A total of 4 patients had bilateral surgery, whereas 18 patients underwent unilateral surgery (26 eyelids). In 22 cases (26 eyes), congenital severe upper eyelid ptosis was treated using suspension of the frontal muscle flap overlapped with an inferiorly based orbital septum flap. After the operation, 17 cases (19 eyes) were followed up and analyzed retrospectively. The average follow-up period was about 12 months (range, 6-20 months). The 17 corrected eyes had a symmetric redundant fold of preseptal skin according to the marginal reflex distance-1 (MRD-1) measurement used to judge efficacy. Two eyes in this series required reoperation for undercorrection. Complications such as ectropion and corneal exposure were avoided. Use of a frontalis muscle lap overlapped with an inferior based orbital septum flap to manage severe congenital upper eyelid ptosis is a useful procedure that results in substantial cosmetic and functional improvement with few complications.

The Anti-Atlas chain (Morocco): the southern margin of the Variscan belt along the edge of the West African craton

Abstract Broadly synchronous circum-Atlantic Variscan–Alleghanian orogenic belts developed during the Late Palaeozoic Gondwana–Laurentia collision. In the northern part of the West African craton (WAC), the Variscan orogeny produced basement-controlled structures in the Anti-Atlas, which represents the pericratonic foreland, now located south of the Variscan domains of Morocco and north of the Mauritanides belt. New structural field observations document the strong involvement of the basement and the inversion and folding of the Palaeozoic sedimentary basins at the edge the WAC. Two contrasting domains differently responding to regional NW–SE shortening are recognized: (1) a narrow belt along the Atlantic coast characterized by thin-skinned folding and ESE-vergent thrusting (para-autochthonous Anti-Atlas); (2) a large area between the WAC sensu stricto and the South Atlas front showing huge basement uplifts amidst a folded Palaeozoic cover with upright polyharmonic folds (autochthonous Anti-Atlas). The structural trend of the basement inliers is inherited at least in some case from previous Proterozoic fractures. Compressional reactivations led to basement uplift and concomitant folding of the Palaeozoic cover. Cover series are horizontally shortened by mostly upright symmetrical buckle folds of various wavelengths in response to thickness variations between abundant incompetent silt and shale horizons and rare competent carbonate and quartzite beds. Deformation is greatest near the borders of and between closely spaced basement uplifts. Regionally, deformation intensity decreases, either abruptly or progressively, towards the SE and it vanishes within the undeformed Tindouf basin.

The Carboniferous of Svoge Coalfield (Bulgaria)

The Svoge Coalfield Carboniferous is subdivided into Tsarichina Formation with Dalbochitsa Member (250 m – Namurian A), Svidnya Formation (220 m – Namurian C-Westphalian A), Dramsha Formation (180 m), Svoge Formation (500 m – Westphalian A), Berovdol Formation (280 m – Westphalian A-B) and Chibaovtsi Formation (420 m – Westphalian B-C). Except Dramsha Formation, that is built of claystones, the other formations consist mainly of sandstones, with few levels of claystones with or without coal seams. Conglomerates occur at the base of Tsarichina, Svidnya and Chibaovtsi Formation and are intercalated in the sequences of Svidnya, Svoge and Chibaovtsi Formation. The coal seams are superantracites (95—98% volatile) mainly thin, some are 0.6 to 2.0 m, but in place reach even 12 m most frequently in result of tectonic accumulation. Breaks in sedimentation are between Tsarichina and Svidnya Formation and at the base of Berovdol Formation. The basement is built of a continuous Ordovician, Silurian and Devonian sequence covered with erosive contact and angular (up to 30°) unconformity by the Carboniferous. The folded (in normal and reversed folds) Palaeozoic section is unconformably covered in the western part of the coalfield by Lower Triassic. Tectonically the Coalfield is a complex graben superimposed on the core of the Alpine Svoge anticline. The south parts are built of symmetric folds. The north parts are of recumbent folds which in the east half are north vergent, whereas in the west part are south vergent, being separated by a prominent wrench fault. The south part is folded in pre-Permian time, possibly during the Leonian Phase, when the sedimentation stopped, and the graben has been transformed in a horst structure, maybe during the Asturian Phase. Both parts are refolded during an Alpine (Late-Cretaceous) north-vergent folding. The western south vergent folds are separated from the Triassic cover by decollement whereas most probably the Svidnya Pluton has resisted to the north directed pressure.

Methodology of planar unsteady flow measurements in an excised larynx

A methodology to obtain phase locked planar unsteady flow of the near field of supraglottal flow in an excised larynx using particle image velocimetry (PIV) is presented. Different steps involved in obtaining 2D flow field at different instances of the EGG or microphone signal and the structural motion of the vocal fold are discussed. Real time signal processing of the sensor signal coupled with the synchronization of the PIV flow field and high speed imaging of the vocal fold is used to evaluate the relationship between acoustics‐structure and flow. Issues that can affect the accuracy of the flow field measurements and the reconstruction of the flow patterns at different instances during the EGG/microphone cycle were identified and suitable measures taken to resolve them are discussed. Some of these include simulating a symmetric vocal fold motion, maintaining a constant phonation frequency over the entire experimental run, preventing any spurious vectors that could arise due to reflection from the moist tissue surface or poor spatial or temporal resolution. Examples are also shown where the effect of these factors impact both the raw seeded image and correlation PIV algorithm used to extract the flow field vectors.