Journal articles: 'Helical lattices'

1

Carey, Seán, Ciarán McHale, Vincenzo Oliveri, and Paul M. Weaver. "Reconfigurable helical lattices via topological morphing." Materials & Design 206 (August 2021): 109769. http://dx.doi.org/10.1016/j.matdes.2021.109769.

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Pratap, J. V., B. F. Luisi, and C. R. Calladine. "Geometric principles in the assembly of α-helical bundles." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1993 (June 28, 2013): 20120369. http://dx.doi.org/10.1098/rsta.2012.0369.

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α-Helical coiled coils are usually stabilized by hydrophobic interfaces between the two constituent α-helices, in the form of ‘knobs-into-holes’ packing of non-polar residues arranged in repeating heptad patterns. Here we examine the corresponding ‘hydrophobic cores’ that stabilize bundles of four α-helices. In particular, we study three different kinds of bundle, involving four α-helices of identical sequence: two pack in a parallel and one in an anti-parallel orientation. We point out that the simplest way of understanding the packing of these 4-helix bundles is to use Crick's original idea that the helices are held together by ‘hydrophobic stripes’, which are readily visualized on the cylindrical surface lattice of the α-helices; and that the ‘helix-crossing angle’—which determines, in particular, whether supercoiling is left- or right-handed—is fixed by the slope of the lattice lines that contain the hydrophobic residues. In our three examples the constituent α-helices have hydrophobic repeat patterns of 7, 11 and 4 residues, respectively; and we associate the different overall conformations with ‘knobs-into-holes’ packing along the 7-, 11- and 4-start lines, respectively, of the cylindrical surface lattices of the constituent α-helices. For the first two examples, all four interfaces between adjacent helices are geometrically equivalent; but in the third, one of the four interfaces differs significantly from the others. We provide a geometrical explanation for this non-equivalence in terms of two different but equivalent ways of assembling this bundle, which may possibly constitute a bistable molecular ‘switch’ with a coaxial throw of about 12 Å. The geometrical ideas that we deploy in this paper provide the simplest and clearest description of the structure of helical bundles. In an appendix, we describe briefly a computer program that we have devised in order to search for ‘knobs-into-holes’ packing between α-helices in proteins.

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Lin, Zhiwei, Leticia C. Beltrán, Zeus A. De los Santos, Yinong Li, Tehseen Adel, Jeffrey A. Fagan, Angela R. Hight Walker, Edward H. Egelman, and Ming Zheng. "DNA-guided lattice remodeling of carbon nanotubes." Science 377, no. 6605 (July 29, 2022): 535–39. http://dx.doi.org/10.1126/science.abo4628.

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Covalent modification of carbon nanotubes is a promising strategy for engineering their electronic structures. However, keeping modification sites in registration with a nanotube lattice is challenging. We report a solution using DNA-directed, guanine (G)-specific cross-linking chemistry. Through DNA screening we identify a sequence, C 3 GC 7 GC 3 , whose reaction with an (8,3) enantiomer yields minimum disorder-induced Raman mode intensities and photoluminescence Stokes shift, suggesting ordered defect array formation. Single-particle cryo–electron microscopy shows that the C 3 GC 7 GC 3 functionalized (8,3) has an ordered helical structure with a 6.5 angstroms periodicity. Reaction mechanism analysis suggests that the helical periodicity arises from an array of G-modified carbon-carbon bonds separated by a fixed distance along an armchair helical line. Our findings may be used to remodel nanotube lattices for novel electronic properties.

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Matsumoto, Takao, Yeong-Gi So, Yuji Kohno, Hidetaka Sawada, Yuichi Ikuhara, and Naoya Shibata. "Direct observation of Σ7 domain boundary core structure in magnetic skyrmion lattice." Science Advances 2, no. 2 (February 2016): e1501280. http://dx.doi.org/10.1126/sciadv.1501280.

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Skyrmions are topologically protected nanoscale magnetic spin entities in helical magnets. They behave like particles and tend to form hexagonal close-packed lattices, like atoms, as their stable structure. Domain boundaries in skyrmion lattices are considered to be important as they affect the dynamic properties of magnetic skyrmions. However, little is known about the fine structure of such skyrmion domain boundaries. We use differential phase contrast scanning transmission electron microscopy to directly visualize skyrmion domain boundaries in FeGe1−xSix induced by the influence of an “edge” of a crystal grain. Similar to hexagonal close-packed atomic lattices, we find the formation of skyrmion “Σ7” domain boundary, whose orientation relationship is predicted by the coincidence site lattice theory to be geometrically stable. On the contrary, the skyrmion domain boundary core structure shows a very different structure relaxation mode. Individual skyrmions can flexibly change their size and shape to accommodate local coordination changes and free volumes formed at the domain boundary cores. Although atomic rearrangement is a common structural relaxation mode in crystalline grain boundaries, skyrmions show very unique and thus different responses to such local lattice disorders.

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Takeno, S. "Nonlinear modes in helical lattices: Localized modes and kinks." Physics Letters A 358, no. 5-6 (October 2006): 390–95. http://dx.doi.org/10.1016/j.physleta.2006.04.113.

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BISHOP, R. "ChemInform Abstract: Helical Host Lattices Formed by Alicyclic Diols." ChemInform 28, no. 2 (August 4, 2010): no. http://dx.doi.org/10.1002/chin.199702288.

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Tian, Yu, Huixi Violet Zhang, Kristi L. Kiick, Jeffery G. Saven, and Darrin J. Pochan. "Transition from disordered aggregates to ordered lattices: kinetic control of the assembly of a computationally designed peptide." Organic & Biomolecular Chemistry 15, no. 29 (2017): 6109–18. http://dx.doi.org/10.1039/c7ob01197k.

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8

Fang, Fang, Richard Clawson, and Klee Irwin. "The Curled Up Dimension in Quasicrystals." Crystals 11, no. 10 (October 14, 2021): 1238. http://dx.doi.org/10.3390/cryst11101238.

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Most quasicrystals can be generated by the cut-and-project method from higher dimensional parent lattices. In doing so they lose the periodic order their parent lattice possess, replaced with aperiodic order, due to the irrationality of the projection. However, perfect periodic order is discovered in the perpendicular space when gluing the cut window boundaries together to form a curved loop. In the case of a 1D quasicrystal projected from a 2D lattice, the irrationally sloped cut region is bounded by two parallel lines. When it is extrinsically curved into a cylinder, a line defect is found on the cylinder. Resolving this geometrical frustration removes the line defect to preserve helical paths on the cylinder. The degree of frustration is determined by the thickness of the cut window or the selected pitch of the helical paths. The frustration can be resolved by applying a shear strain to the cut-region before curving into a cylinder. This demonstrates that resolving the geometrical frustration of a topological change to a cut window can lead to preserved periodic order.

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9

Taylor, William R. "Exploring Protein Fold Space." Biomolecules 10, no. 2 (January 27, 2020): 193. http://dx.doi.org/10.3390/biom10020193.

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The model of protein folding proposed by Ptitsyn and colleagues involves the accretion of secondary structures around a nucleus. As developed by Efimov, this model also provides a useful way to view the relationships among structures. Although somewhat eclipsed by later databases based on the pairwise comparison of structures, Efimov’s approach provides a guide for the more automatic comparison of proteins based on an encoding of their topology as a string. Being restricted to layers of secondary structures based on beta sheets, this too has limitations which are partly overcome by moving to a more generalised secondary structure lattice that can encompass both open and closed (barrel) sheets as well as helical packing of the type encoded by Murzin and Finkelstein on small polyhedra. Regular (crystalline) lattices, such as close-packed hexagonals, were found to be too limited so pseudo-latticses were investigated including those found in quasicrystals and the Bernal tetrahedron-based lattice that he used to represent liquid water. The Bernal lattice was considered best and used to generate model protein structures. These were much more numerous than those seen in Nature, posing the open question of why this might be.

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10

Dixon, Maximillian D. X., Matthew P. O'Donnell, Alberto Pirrera, and Isaac V. Chenchiah. "Bespoke extensional elasticity through helical lattice systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2232 (December 2019): 20190547. http://dx.doi.org/10.1098/rspa.2019.0547.

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Nonlinear structural behaviour offers a richness of response that cannot be replicated within a traditional linear design paradigm. However, designing robust and reliable nonlinearity remains a challenge, in part, due to the difficulty in describing the behaviour of nonlinear systems in an intuitive manner. Here, we present an approach that overcomes this difficulty by constructing an effectively one-dimensional system that can be tuned to produce bespoke nonlinear responses in a systematic and understandable manner. Specifically, given a continuous energy function E and a tolerance ϵ > 0, we construct a system whose energy is approximately E up to an additive constant, with L ∞ -error no more that ϵ . The system is composed of helical lattices that act as one-dimensional nonlinear springs in parallel. We demonstrate that the energy of the system can approximate any polynomial and, thus, by Weierstrass approximation theorem, any continuous function. We implement an algorithm to tune the geometry, stiffness and pre-strain of each lattice to obtain the desired system behaviour systematically. Examples are provided to show the richness of the design space and highlight how the system can exhibit increasingly complex behaviours including tailored deformation-dependent stiffness, snap-through buckling and multi-stability.

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Bathla, Pranjal, and John Kennedy. "3D Printed Structured Porous Treatments for Flow Control around a Circular Cylinder." Fluids 5, no. 3 (August 14, 2020): 136. http://dx.doi.org/10.3390/fluids5030136.

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The use of porous coatings is one of the passive flow control methods used to reduce turbulence, noise and vibrations generated due to fluid flow. Porous coatings for flow stabilization have potential for a light-weight, cost-effective, and customizable solution. The design and performance of a structured porous coating depend on multiple control parameters like lattice size, strut thickness, lattice structure/geometry, etc. This study investigated the suitability of MSLA 3D printers to manufacture porous coatings based on unit cell designs to optimize porous lattices for flow control behind a cylinder. The Reynolds number used was 6.1×104–1.5×105 and the flow measurements were taken using a hotwire probe. Different experiment sets were conducted for single cylinder with varying control parameters to achieve best performing lattice designs. It was found that lattice structures with higher porosity produced lower turbulence intensity in the wake of the cylinder. However, for constant porosity lattice structures, there was negligible difference in turbulence and mean wake velocity levels. Coating thickness did not have a linear relationship with turbulence reduction, suggesting an optimal thickness value. For constant porosity coatings, cell count in coating thickness did not influence the turbulence or mean wake velocity. Partial coating designs like helical and spaced coatings had comparable performance to that of a full coating. MSLA printers were found capable of manufacturing thin and complex porous lattices.

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12

Kikkawa, M., T. Ishikawa, T. Nakata, T. Wakabayashi, and N. Hirokawa. "Direct visualization of the microtubule lattice seam both in vitro and in vivo." Journal of Cell Biology 127, no. 6 (December 15, 1994): 1965–71. http://dx.doi.org/10.1083/jcb.127.6.1965.

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Microtubules are constructed from alpha- and beta-tubulin heterodimers that are arranged into protofilaments. Most commonly there are 13 or 14 protofilaments. A series of structural investigations using both electron microscopy and x-ray diffraction have indicated that there are two potential lattices (A and B) in which the tubulin subunits can be arranged. Electron microscopy has shown that kinesin heads, which bind only to beta-tubulin, follow a helical path with a 12-nm pitch in which subunits repeat every 8-nm axially, implying a primarily B-type lattice. However, these helical symmetry parameters are not consistent with a closed lattice and imply that there must be a discontinuity or "seam" along the microtubule. We have used quick-freeze deep-etch electron microscopy to obtain the first direct evidence for the presence of this seam in microtubules formed either in vivo or in vitro. In addition to a conventional single seam, we have also rarely found microtubules in which there is more than one seam. Overall our data indicates that microtubules have a predominantly B lattice, but that A lattice bonds between tubulin subunits are found at the seam. The cytoplasmic microtubules in mouse nerve cells also have predominantly B lattice structure and A lattice bonds at the seam. These observations have important implications for the interaction of microtubules with MAPs and with motor proteins, and for example, suggest that kinesin motors may follow a single protofilament track.

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13

NANDI, SHUBHENDU, NEIL F. JOHNSON, and JOSHUA L. COHN. "PERSISTENT PATTERNS IN MICROTUBULE DIPOLE LATTICES." Advances in Complex Systems 16, no. 08 (December 2013): 1350033. http://dx.doi.org/10.1142/s0219525913500331.

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Microtubules (MTs) are cytoskeletal protein polymers orchestrating a host of important cellular functions including, but not limited to, cell support, cell division, cell motility and cell transport. We construct a toy-model of the MT lattice composed of classical vector Ising spins (dipole moments) representing the tubulin molecules, the building block of MTs. Nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions are considered within an anisotropic dielectric medium. As a consequence of the helical topology, certain spin orientations render the lattice frustrated with NN ferroelectric and NNN antiferroelectric bonds. Mapping the problem to a 2D Ising model and employing Monte Carlo methods we find that frozen clusters of spins exist at human physiological temperatures. This suggests a novel biological mechanism for storing information in living organisms, whereby the classical tubulin spin states become information bits and information gets stored in MTs in a way that is robust to thermal fluctuations.

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14

Liu, Xiuying, Frane Lunić, Daohong Song, Zhixuan Dai, Shiqi Xia, Liqin Tang, Jingjun Xu, Zhigang Chen, and Hrvoje Buljan. "Wavepacket Self‐Rotation and Helical Zitterbewegung in Symmetry‐Broken Honeycomb Lattices." Laser & Photonics Reviews 15, no. 7 (May 26, 2021): 2000563. http://dx.doi.org/10.1002/lpor.202000563.

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15

Nguyen, Henry C., Arthur A. Melo, Jerzy Kruk, Adam Frost, and Michal Gabruk. "Photocatalytic LPOR forms helical lattices that shape membranes for chlorophyll synthesis." Nature Plants 7, no. 4 (April 2021): 437–44. http://dx.doi.org/10.1038/s41477-021-00885-2.

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16

Fang, Chen, and Liang Fu. "New classes of topological crystalline insulators having surface rotation anomaly." Science Advances 5, no. 12 (December 2019): eaat2374. http://dx.doi.org/10.1126/sciadv.aat2374.

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We discover new types of quantum anomalies in two-dimensional systems with time-reversal symmetry (T) and discrete rotation symmetry with order of n = 2, 4, and 6 (Cn). The new anomalous states have n flavors of massless Dirac fermions protected by T and Cn, whereas any two-dimensional lattices having the two symmetries must have a multiple of 4, 8, and 12 Dirac cones for n = 2, 4, and 6, respectively. We show that these anomalous states are physically realized on the surface of new classes of topological crystalline insulators, normal to the rotation axis. Moreover, these topological crystalline insulators support n gapless one-dimensional helical mode on the otherwise fully gapped side surface, connecting the anomalous two-dimensional states on the top and bottom surfaces. The presence of these helical modes enables a new quantum device made from a topological crystalline insulator nanorod, a “helical nanorod,” which has a quantized longitudinal conductance of ne2/h.

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Shi, Zhiwei, Maowu Zuo, and Huagang Li. "Edge states supported by different boundaries of two helical lattices with opposite helicity." Results in Physics 24 (May 2021): 104191. http://dx.doi.org/10.1016/j.rinp.2021.104191.

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18

Shi, Zhiwei, Daryl Preece, Chensong Zhang, Yinxiao Xiang, and Zhigang Chen. "Generation and probing of 3D helical lattices with tunable helix pitch and interface." Optics Express 27, no. 1 (January 3, 2019): 121. http://dx.doi.org/10.1364/oe.27.000121.

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19

Tai, Jung-Shen B., and Ivan I. Smalyukh. "Three-dimensional crystals of adaptive knots." Science 365, no. 6460 (September 26, 2019): 1449–53. http://dx.doi.org/10.1126/science.aay1638.

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Starting with Gauss and Kelvin, knots in fields were postulated to behave like particles, but experimentally they were found only as transient features or required complex boundary conditions to exist and could not self-assemble into three-dimensional crystals. We introduce energetically stable, micrometer-sized knots in helical fields of chiral liquid crystals. While spatially localized and freely diffusing in all directions, they resemble colloidal particles and atoms, self-assembling into crystalline lattices with open and closed structures. These knots are robust and topologically distinct from the host medium, though they can be morphed and reconfigured by weak stimuli under conditions such as those in displays. A combination of energy-minimizing numerical modeling and optical imaging uncovers the internal structure and topology of individual helical field knots and the various hierarchical crystalline organizations that they form.

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20

Han, M. G., J. A. Garlow, Y. Kharkov, L. Camacho, R. Rov, J. Sauceda, G. Vats, et al. "Scaling, rotation, and channeling behavior of helical and skyrmion spin textures in thin films of Te-doped Cu2OSeO3." Science Advances 6, no. 13 (March 2020): eaax2138. http://dx.doi.org/10.1126/sciadv.aax2138.

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Topologically nontrivial spin textures such as vortices, skyrmions, and monopoles are promising candidates as information carriers for future quantum information science. Their controlled manipulation including creation and annihilation remains an important challenge toward practical applications and further exploration of their emergent phenomena. Here, we report controlled evolution of the helical and skyrmion phases in thin films of multiferroic Te-doped Cu2OSeO3 as a function of material thickness, dopant, temperature, and magnetic field using in situ Lorentz phase microscopy. We report two previously unknown phenomena in chiral spin textures in multiferroic Cu2OSeO3: anisotropic scaling and channeling with a fixed-Q state. The skyrmion channeling effectively suppresses the recently reported second skyrmion phase formation at low temperature. Our study provides a viable way toward controlled manipulation of skyrmion lattices, envisaging chirality-controlled skyrmion flow circuits and enabling precise measurement of emergent electromagnetic induction and topological Hall effects in skyrmion lattices.

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FORD, MATT, D. L. HUNTER, and NAEEM JAN. "INFLUENCE OF BOUNDARY CONDITIONS ON THE FRACTION OF SPANNING CLUSTERS." International Journal of Modern Physics C 10, no. 01 (February 1999): 183–88. http://dx.doi.org/10.1142/s0129183199000127.

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We use the Hoshen–Kopelman algorithm with the Nakanashi method of recycling redundant labels to measure the fraction of spanning configurations, R(pc), at and near pc, for random site percolation in two and three dimensions with different boundary conditions. For the square and cubic lattices we find that R(pc) is 0.50 and 0.28 for free edges and 0.64 (2-d) and 0.56 (3-d) for both helical and periodic boundary conditions. The error bars are of the order of ±0.01 for these results.

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Sepehri, Soroush, Mahmoud Mosavi Mashhadi, and Mir Masoud Seyyed Fakhrabadi. "Manipulation of wave motion in smart nonlinear phononic crystals made of shape memory alloys." Physica Scripta 96, no. 12 (November 25, 2021): 125527. http://dx.doi.org/10.1088/1402-4896/ac3959.

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Abstract Thanks to the functional role of shape memory alloys (SMAs) in controlling the mechanical behavior of structures, researchers have started investigating the possibility of manipulating wave motion in phononic crystals using SMAs. While SMAs were used before to tune the wave propagation in linear phononic crystals, in this work, we aim to extend their utilization to nonlinear lattices. For this purpose, SMA helical springs are used to manipulate the dispersion curves and the location of stop-bands in weakly nonlinear monoatomic and diatomic lattice chains. Using Brinson’s formulation to describe the thermo-mechanical behavior of SMA wires and Lindstedt-Poincaré method to solve the derived governing equations, closed-form nonlinear dispersion relations in monoatomic and diatomic lattice chains are obtained and the effects of temperature-induced phase transformation and stiffness nonlinearity on the wave propagation are investigated. The results reveal that the dispersion curves of a weakly nonlinear monoatomic chain are formed at lower frequencies through the austenite-to-martensite phase transformation. Similarly, both the acoustic and optical branches of a diatomic lattice are moved to lower frequencies during the phase transformation in the cooling process. Therefore, the generated stop-bands in nonlinear diatomic lattices are also moved to lower frequencies. In addition, using auxiliary SMA ground springs, new classes of nonlinear monoatomic and diatomic chains exhibiting additional low-frequency attenuation zones are introduced. These low-frequency stop-bands are tunable and their frequency range can be modulated by exploiting the temperature-induced phase transformation in the SMA springs. The results obtained from analytic formulations are verified by numerical calculations and an excellent agreement is observed. Such tunability and the potential for adding stop-bands in low frequencies reveal that SMAs can be very helpful in designing nonlinear phononic and acoustic devices, such as vibration mitigators and wave filters with pre-defined attenuation zones.

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Saczko-Brack, Dario, Ewa Warchol, Benoit Rogez, Markus Kröss, Sarah M. Heissler, James R. Sellers, Christopher Batters, and Claudia Veigel. "Self-organization of actin networks by a monomeric myosin." Proceedings of the National Academy of Sciences 113, no. 52 (December 12, 2016): E8387—E8395. http://dx.doi.org/10.1073/pnas.1612719113.

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The organization of actomyosin networks lies at the center of many types of cellular motility, including cell polarization and collective cell migration during development and morphogenesis. Myosin-IXa is critically involved in these processes. Using total internal reflection fluorescence microscopy, we resolved actin bundles assembled by myosin-IXa. Electron microscopic data revealed that the bundles consisted of highly ordered lattices with parallel actin polarity. The myosin-IXa motor domains aligned across the network, forming cross-links at a repeat distance of precisely 36 nm, matching the helical repeat of actin. Single-particle image processing resolved three distinct conformations of myosin-IXa in the absence of nucleotide. Using cross-correlation of a modeled actomyosin crystal structure, we identified sites of additional mass, which can only be accounted for by the large insert in loop 2 exclusively found in the motor domain of class IX myosins. We show that the large insert in loop 2 binds calmodulin and creates two coordinated actin-binding sites that constrain the actomyosin interactions generating the actin lattices. The actin lattices introduce orientated tracks at specific sites in the cell, which might install platforms allowing Rho-GTPase–activating protein (RhoGAP) activity to be focused at a definite locus. In addition, the lattices might introduce a myosin-related, force-sensing mechanism into the cytoskeleton in cell polarization and collective cell migration.

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Pal, Raj Kumar, Marshall Schaeffer, and Massimo Ruzzene. "Helical edge states and topological phase transitions in phononic systems using bi-layered lattices." Journal of Applied Physics 119, no. 8 (February 28, 2016): 084305. http://dx.doi.org/10.1063/1.4942357.

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25

Ganser-Pornillos, Barbie K., Uta K. von Schwedler, Kirsten M. Stray, Christopher Aiken, and Wesley I. Sundquist. "Assembly Properties of the Human Immunodeficiency Virus Type 1 CA Protein." Journal of Virology 78, no. 5 (March 1, 2004): 2545–52. http://dx.doi.org/10.1128/jvi.78.5.2545-2552.2004.

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ABSTRACT During retroviral maturation, the CA protein oligomerizes to form a closed capsid that surrounds the viral genome. We have previously identified a series of deleterious surface mutations within human immunodeficiency virus type 1 (HIV-1) CA that alter infectivity, replication, and assembly in vivo. For this study, 27 recombinant CA proteins harboring 34 different mutations were tested for the ability to assemble into helical cylinders in vitro. These cylinders are composed of CA hexamers and are structural models for the mature viral capsid. Mutations that diminished CA assembly clustered within helices 1 and 2 in the N-terminal domain of CA and within the crystallographically defined dimer interface in the CA C-terminal domain. These mutations demonstrate the importance of these regions for CA cylinder production and, by analogy, mature capsid assembly. One CA mutant (R18A) assembled into cylinders, cones, and spheres. We suggest that these capsid shapes occur because the R18A mutation alters the frequency at which pentamers are incorporated into the hexagonal lattice. The fact that a single CA protein can simultaneously form all three known retroviral capsid morphologies supports the idea that these structures are organized on similar lattices and differ only in the distribution of 12 pentamers that allow them to close. In further support of this model, we demonstrate that the considerable morphological variation seen for conical HIV-1 capsids can be recapitulated in idealized capsid models by altering the distribution of pentamers.

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Tashiro and Yamamoto. "Structural Evolution Mechanism of Crystalline Polymers in the Isothermal Melt-Crystallization Process: A Proposition Based on Simultaneous WAXD/SAXS/FTIR Measurements." Polymers 11, no. 8 (August 6, 2019): 1316. http://dx.doi.org/10.3390/polym11081316.

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Time-resolved simultaneous measurements of wide-angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS) (and FTIR spectra) were performed for various kinds of crystalline polymers in isothermal melt-crystallization processes, from which the common features of the structural evolution process as well as the different behaviors intrinsic to the individual polymer species were extracted. The polymers targeted here were polyethylene, isotactic polypropylene, polyoxymethylene, aliphatic nylon, vinylidene fluoride copolymer, trans-polyisoprene, and poly(alkylene terephthalate). A universal concept of the microscopically viewed structural evolution process in isothermal crystallization may be described as follows: (i) the small domains composed of locally regular but more or less disordered helical chain segments are created in the melt (this important information was obtained by the IR spectral data analysis); (ii) these domains grow larger as the length and number of more regular helical segments increase with time; (iii) the correlation among the domains becomes stronger and they approach each other; and (iv) they merge into the stacked lamellar structure consisting of the regularly arranged crystalline lattices. The inner structure of the domains is different depending on the polymer species, as known from the IR spectral data

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Gessmann, Renate, Danny Axford, Hans Brückner, Albrecht Berg, and Kyriacos Petratos. "A natural, single-residue substitution yields a less active peptaibiotic: the structure of bergofungin A at atomic resolution." Acta Crystallographica Section F Structural Biology Communications 73, no. 2 (January 27, 2017): 95–100. http://dx.doi.org/10.1107/s2053230x17001236.

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Bergofungin is a peptide antibiotic that is produced by the ascomycetous fungusEmericellopsis donezkiiHKI 0059 and belongs to peptaibol subfamily 2. The crystal structure of bergofungin A has been determined and refined to 0.84 Å resolution. This is the second crystal structure of a natural 15-residue peptaibol, after that of samarosporin I. The amino-terminal phenylalanine residue in samarosporin I is exchanged to a valine residue in bergofungin A. According to agar diffusion tests, this results in a nearly inactive antibiotic peptide compared with the moderately active samarosporin I. Crystals were obtained from methanol solutions of purified bergofungin mixed with water. Although there are differences in the intramolecular hydrogen-bonding scheme of samarosporin I, the overall folding is very similar for both peptaibols, namely 310-helical at the termini and α-helical in the middle of the molecules. Bergofungin A and samarosporin I molecules are arranged in a similar way in both lattices. However, the packing of bergofungin A exhibits a second solvent channel along the twofold axis. This latter channel occurs in the vicinity of the N-terminus, where the natural substitution resides.

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Hawkins, Stephen C., Roger Bishop, Donald C. Craig, Ian G. Dance, A. David Rae, and Marcia L. Scudder. "Syntheses and crystal structures of four alicyclic diols which crystallise in different lattices involving helical extensions." Journal of the Chemical Society, Perkin Transactions 2, no. 10 (1993): 1737. http://dx.doi.org/10.1039/p29930001737.

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Fraser, R. D. B., and T. P. MacRae. "Intermediate filament structure." Bioscience Reports 5, no. 7 (July 1, 1985): 573–79. http://dx.doi.org/10.1007/bf01117070.

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In a previous communication (Biosci. Rep. 3, 517–525, 1993) we described quantitative X-ray diffraction studies of α-keratin which were shown to be consistent with the presence of finite arrays of repeating units, successive arrays being set down at axial intervals of 470 Å. In addition the axial interval between repeating units in an array was shown to be 197.9 Å. It was suggested that this could most readily be explained by supposing that a surfacelattice was present which contained a dislocation along a helical path with unit height h = 470 Å and unit twist |t| = 49.1°. The number of repeating units was shown to be in the range 7–9. With 7 repeats the mismatch of the lattice along the dislocation is small and this choice was used to develop a detailed model for the filament. Subsequent studies of molecular interactions have shown however that the coiled-coil rope segments in the rod domain of the molecule are most probably oriented parallel to the dislocation, and so minimization of lattice mismatch may be less important than originally supposed. In the present communication it is shown that the choice of 8, rather than 7, for the number of repeating units yields a model which is more compatible with estimates of the linear density and also provides the basis for a general model for polymorphism in intermediate filament lattices.

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Nie, Simin, Gang Xu, Fritz B. Prinz, and Shou-cheng Zhang. "Topological semimetal in honeycomb lattice LnSI." Proceedings of the National Academy of Sciences 114, no. 40 (September 19, 2017): 10596–600. http://dx.doi.org/10.1073/pnas.1713261114.

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Recognized as elementary particles in the standard model, Weyl fermions in condensed matter have received growing attention. However, most of the previously reported Weyl semimetals exhibit rather complicated electronic structures that, in turn, may have raised questions regarding the underlying physics. Here, we report promising topological phases that can be realized in specific honeycomb lattices, including ideal Weyl semimetal structures, 3D strong topological insulators, and nodal-line semimetal configurations. In particular, we highlight a semimetal featuring both Weyl nodes and nodal lines. Guided by this model, we showed that GdSI, the long-perceived ideal Weyl semimetal, has two pairs of Weyl nodes residing at the Fermi level and that LuSI (YSI) is a 3D strong topological insulator with the right-handed helical surface states. Our work provides a mechanism to study topological semimetals and proposes a platform for exploring the physics of Weyl semimetals as well as related device designs.

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HAWKINS, S. C., R. BISHOP, D. C. CRAIG, I. G. DANCE, A. D. RAE, and M. L. SCUDDER. "ChemInform Abstract: Syntheses and Crystal Structures of Four Alicyclic Diols Which Crystallize in Different Lattices Involving Helical Extensions." ChemInform 25, no. 3 (August 19, 2010): no. http://dx.doi.org/10.1002/chin.199403119.

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Abasheeva, Ksenia D., Pavel A. Demakov, and Vladimir P. Fedin. "Diverse Hydrogen-Bonded Structural Motifs in 1,4-Diazabicyclo[2.2.2]octane N,N’-Dioxide Salts with Oxoanions." Molbank 2022, no. 4 (November 25, 2022): M1508. http://dx.doi.org/10.3390/m1508.

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Four new hybrid inorganic–organic salts of 1,4-diazabicyclo[2.2.2]octane N,N’-dioxide (odabco) with the formulae odabco·2HNO3 (1), odabco·HClO4 (2), odabco·H2SO4 (3) and odabco·2H2SO4 (4) were synthesized and characterized by single-crystal x-ray diffraction (XRD), powder XRD and infrared spectroscopy. Compound 1 is based on the isolated (H2odabco)2+ fragments, representing 0D structure. 2 is based on cationic 1D {Hodabco}nn+ hydrogen-bonded chains. Compound 3 comprising a strongly coordinated sulfate anion consists of two-component hydrogen-bonded {-H2odabco-SO4−} fragments forming uncharged 1D helical chains. 4 contains both {-HSO4-}nn– and {-HSO4-H2odabco-HSO4−} hydrogen bonding motifs, resulting in a 3D polymeric network. A comparative structural analysis of both the obtained and the previously reported cognate structures was performed to rationalize the impact of the degree of odabco protonation and the anion donor ability on the structural features and dimensionalities of odabco-based hydrogen-bonded lattices.

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33

Song, Y. H., and E. Mandelkow. "The anatomy of flagellar microtubules: polarity, seam, junctions, and lattice." Journal of Cell Biology 128, no. 1 (January 1, 1995): 81–94. http://dx.doi.org/10.1083/jcb.128.1.81.

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Although the overall structures of flagellar and cytoplasmic microtubules are understood, many details have remained a matter of debate. In particular, studies of the arrangement of tubulin subunits have been hampered by the low contrast of the tubulin subunits. This problem can now be addressed by the kinesin decoration technique. We have shown previously that the recombinant kinesin head domain binds to beta-tubulin, thus enhancing the contrast between alpha- and beta-tubulin in the electron microscope; this allows one to study the arrangement of tubulin dimers. Here we describe the lattices of the four different types of microtubules in eukaryotic flagellar axonemes (outer doublet A and B, central pair C1 and C2). They could all be labeled with kinesin head with an 8-nm axial periodicity (the tubulin dimer repeat), and all of them showed the B-surface lattice. This lattice is characterized by a 0.92-nm stagger between adjacent protofilaments. The B-lattice was observed on the axonemal microtubules as well as on extensions made by polymerizing porcine brain tubulin onto axonemal microtubules in the proximal and distal directions. This emphasizes that axonemal microtubules serve as high fidelity templates for seeding microtubules. The presence of a B-lattice implies that there must be a helical discontinuity ("seam") in the wall. This discontinuity is now placed near protofilaments A1 and A2 of the A-tubule, close to the inner junction between A- and B-microtubules. The two junctions differ in structure: the protofilaments of the inner junction (A1-B10) are staggered roughly by half a dimer, those of the outer junction (A10-B1) are roughly in register. Of the two junctions the inner one appears to have the stronger bonds, whereas the outer one is more labile and opens up easily, generating "composite sheets" with chevron patterns from which the polarity can be deduced (arrow in the plus direction). Decorated microtubules have a clear polarity. We find that all flagellar microtubules have the same polarities. The orientation of the dimers is such that the plus end terminates with a crown of alpha subunits, the minus end terminates with beta subunits which thus could be in contact with gamma-tubulin at the nucleation centers.

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Raimo, Maria. "An optical test to unveil twisting of birefringent crystals in spherulites." Royal Society Open Science 6, no. 1 (January 2019): 181215. http://dx.doi.org/10.1098/rsos.181215.

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Helical conformations and structures are frequently observed in materials. The presence of helices at points of the unit cell of a crystal, on a larger size scale in the crystalline lattice or even in the microscopic structure of crystals, affects the chemico-physical properties of a solid and, hence, also interactions with light. Here, attention has been drawn to the geometrical properties of helices produced by a hypothetical torque of a transparent crystal, and optical properties of twisted crystals easily observed by a polarizing microscope have been discussed. Radially grown spherulites are obtained by most substances crystallized from melt. The circular arrangement of elongated crystals reflects the optical behaviour of each crystal and, because of the larger dimensions of spherulites, allows investigations otherwise hardly feasible on separate crystals. According to the torsional analysis of elongated bodies and the birefringence theory, information on the existence of helically shaped crystals can be deduced, as hereinafter explained, from the microscopic appearance and birefringence pattern of spherulites. Indeed, twisting decreases the birefringence throughout an elongated crystal and, therefore, also the birefringence of spherulites formed by twisted radial crystals is reduced.

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35

Kicuntod, Jintawee, Sigrun Häge, Friedrich Hahn, Heinrich Sticht, and Manfred Marschall. "The Oligomeric Assemblies of Cytomegalovirus Core Nuclear Egress Proteins Are Associated with Host Kinases and Show Sensitivity to Antiviral Kinase Inhibitors." Viruses 14, no. 5 (May 11, 2022): 1021. http://dx.doi.org/10.3390/v14051021.

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The nucleo-cytoplasmic capsid egress of herpesviruses is a unique regulated process that ensures the efficiency of viral replication and release. For human cytomegalovirus (HCMV), the core of the nuclear egress complex (NEC) consists of the pUL50–pUL53 heterodimer that is able to oligomerize and thus to build hexameric lattices. These structures determine capsid binding and multicomponent protein interaction including NEC-associated host factors. The underlying characteristic of the core NEC formation is based on the N-terminal hook structure of pUL53 that binds into an alpha-helical groove of pUL50, and is thus described as a hook-into-groove interaction. This central regulatory element has recently been validated as a target of antiviral strategies, and first NEC-targeted prototypes of inhibitory small molecules were reported by our previous study. Here, we further analyzed the oligomerization properties of the viral NEC through an approach of chemical protein cross-linking. Findings were as follows: (i) a cross-link approach demonstrated the oligomeric state of the HCMV core NEC using material from HCMV-infected or plasmid-transfected cells, (ii) a Western blot-based identification of NEC-associated kinases using the cross-linked multicomponent NECs was successful, and (iii) we demonstrated the NEC-inhibitory and antiviral activity of specific inhibitors directed to these target kinases. Combined, the results strongly underline the functional importance of the oligomerization of the HCMV-specific NEC that is both phosphorylation-dependent and sensitive to antiviral kinase inhibitors.

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Häge, Sigrun, and Manfred Marschall. "‘Come together’—The Regulatory Interaction of Herpesviral Nuclear Egress Proteins Comprises Both Essential and Accessory Functions." Cells 11, no. 11 (June 4, 2022): 1837. http://dx.doi.org/10.3390/cells11111837.

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Herpesviral nuclear egress is a fine-tuned regulatory process that defines the nucleocytoplasmic release of viral capsids. Nuclear capsids are unable to traverse via nuclear pores due to the fact of their large size; therefore, herpesviruses evolved to develop a vesicular transport pathway mediating the transition across the two leaflets of the nuclear membrane. The entire process involves a number of regulatory proteins, which support the local distortion of the nuclear envelope. In the case of the prototype species of β-Herpesvirinae, the human cytomegalovirus (HCMV), the nuclear egress complex (NEC) is determined by the core proteins pUL50 and pUL53 that oligomerize, form capsid docking lattices and mediate multicomponent assembly with NEC-associated viral and cellular proteins. The NEC-binding principle is based on the hook-into-groove interaction through an N-terminal hook-like pUL53 protrusion that embraces an α-helical pUL50 binding groove. Thus far, the function and characteristics of herpesviral core NECs have been well studied and point to the groove proteins, such as pUL50, as the multi-interacting, major determinants of NEC formation and egress. This review provides closer insight into (i) sequence and structure conservation of herpesviral core NEC proteins, (ii) experimentation on cross-viral core NEC interactions, (iii) the essential functional roles of hook and groove proteins for viral replication, (iv) an establishment of assay systems for NEC-directed antiviral research and (v) the validation of NEC as putative antiviral drug targets. Finally, this article provides new insights into the conservation, function and antiviral targeting of herpesviral core NEC proteins and, into the complex regulatory role of hook and groove proteins during the assembly, egress and maturation of infectious virus.

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Kicuntod, Jintawee, Sewar Alkhashrom, Sigrun Häge, Benedikt Diewald, Regina Müller, Friedrich Hahn, Peter Lischka, Heinrich Sticht, Jutta Eichler, and Manfred Marschall. "Properties of Oligomeric Interaction of the Cytomegalovirus Core Nuclear Egress Complex (NEC) and Its Sensitivity to an NEC Inhibitory Small Molecule." Viruses 13, no. 3 (March 11, 2021): 462. http://dx.doi.org/10.3390/v13030462.

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Herpesviral nuclear egress is a regulated process shared by all family members, ensuring the efficient cytoplasmic release of viral capsids. In the case of human cytomegalovirus (HCMV), the core of the nuclear egress complex (NEC) consists of the pUL50-pUL53 heterodimer that builds hexameric lattices for capsid binding and multicomponent interaction, including NEC-associated host factors. A characteristic feature of NEC interaction is the N-terminal hook structure of pUL53 that binds to an alpha-helical groove of pUL50, thus termed as hook-into-groove interaction. This central regulatory element is essential for viral replication and shows structural–functional conservation, which has been postulated as a next-generation target of antiviral strategies. However, a solid validation of this concept has been missing. In the present study, we focused on the properties of oligomeric HCMV core NEC interaction and the antiviral activity of specifically targeted prototype inhibitors. Our data suggest the following: (i) transiently expressed, variably tagged versions of HCMV NEC proteins exert hook-into-groove complexes, putatively in oligomeric assemblies that are distinguishable from heterodimers, as shown by in vitro assembly and coimmunoprecipitation approaches; (ii) this postulated oligomeric binding pattern was further supported by the use of a pUL50::pUL53 fusion construct also showing a pronounced multi-interaction potency; (iii) using confocal imaging cellular NEC-associated proteins were found partly colocalized with the tagged core NECs; (iv) a small inhibitory molecule, recently identified by an in vitro binding inhibition assay, was likewise active in blocking pUL50–pUL53 oligomeric assembly and in exerting antiviral activity in HCMV-infected fibroblasts. In summary, the findings refine the previous concept of HCMV core NEC formation and nominate this drug-accessible complex as a validated antiviral drug target.

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38

Kwan, A. P., C. E. Cummings, J. A. Chapman, and M. E. Grant. "Macromolecular organization of chicken type X collagen in vitro." Journal of Cell Biology 114, no. 3 (August 1, 1991): 597–604. http://dx.doi.org/10.1083/jcb.114.3.597.

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The macromolecular structure of type X collagen in the matrices of primary cultures of chick hypertrophic chondrocytes was initially investigated using immunoelectron microscopy. Type X collagen was observed to assemble into a matlike structure with-in the matrix elaborated by hypertrophic chondrocytes. The process of self assembly was investigated at the molecular level using purified chick type X collagen and rotary-shadowing EM. It was shown that under neutral conditions at 34 degrees C, individual type X collagen molecules associate rapidly into multimeric clusters via their carboxy-terminal globular domains forming structures with a central nodule of carboxy-terminal domains and the triple helices radiating outwards. Prolonged incubation resulted in the formation of a regular hexagonal lattice by lateral association of the juxtaposed triple-helical domains from adjacent multimeric clusters. This extended lattice may play an important role in modifying the cartilage matrix for subsequent events occurring in endochondral bone formation.

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39

Mandelkow, E. M., R. Schultheiss, R. Rapp, M. Müller, and E. Mandelkow. "On the surface lattice of microtubules: helix starts, protofilament number, seam, and handedness." Journal of Cell Biology 102, no. 3 (March 1, 1986): 1067–73. http://dx.doi.org/10.1083/jcb.102.3.1067.

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The tubulin monomers of brain microtubules reassembled in vitro are arranged on a 3-start helix, irrespective of whether the number of protofilaments is 13 or 14. The dimer packing is that of the B-lattice described for flagellar microtubules. This implies that the tubulin core of microtubules contains at least one helical discontinuity. Neither 5-start nor 8-start helices have a physical significance and thus cannot be implicated in models of microtubule elongation, but the structure is compatible with elongation of protofilaments by dimers or protofilamentous oligomers. The inner and outer surfaces of the microtubule wall can be visualized by propane jet freezing, freeze fracturing, and metal replication, at a resolution of at least 4 nm. The 3-start helix is left-handed, in contrast to a previous study based on negative staining and shadowing. The reasons for this discrepancy are discussed.

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40

Hunyadi, Viktória, Denis Chrétien, Henrik Flyvbjerg, and Imre M. Jánosi. "Why is the microtubule lattice helical?" Biology of the Cell 99, no. 2 (February 2007): 117–28. http://dx.doi.org/10.1042/bc20060059.

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41

Prabhu, V. V., W. K. Schroll, L. L. Van Zandt, and E. W. Prohofsky. "Helical lattice vibrational modes in DNA." Physical Review Letters 60, no. 15 (April 11, 1988): 1587. http://dx.doi.org/10.1103/physrevlett.60.1587.

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42

Uchida, Masaya, Yoshinori Onose, Yoshio Matsui, and Yoshinori Tokura. "Real-Space Observation of Helical Spin Order." Science 311, no. 5759 (January 20, 2006): 359–61. http://dx.doi.org/10.1126/science.1120639.

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Helical spin order in magnetic materials has been investigated only in reciprocal space. We visualized the helical spin order and dynamics in a metal silicide in real space by means of Lorentz electron microscopy. The real space of the helical spin order proves to be much richer than that expected from the averaged structure; it exhibits a variety of magnetic defects similar to atomic dislocations in the crystal lattice. The application of magnetic fields allows us to directly observe the deformation processes of the helical spin order accompanied by nucleation, movement, and annihilation of the magnetic defects.

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43

Nye, J. F. "Dislocation lines in the hyperbolic umbilic diffraction catastrophe." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2072 (March 7, 2006): 2299–313. http://dx.doi.org/10.1098/rspa.2006.1683.

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The three-dimensional pattern of the hyperbolic umbilic diffraction catastrophe is computed from an integral representation. A detailed description is given of the geometrical arrangement of the wave dislocation lines (optical vortices) on which the diffraction pattern is based. From a crossed grid of nodal lines in the focal plane, two bundles of dislocation lines spring out symmetrically into the regions of 4-wave interference. Each dislocation line then follows a chain of curved segments which approximate successive steps along lattice vectors in the space group Fmmm . The result is a bundle of helices of non-circular cross-section that gradually straighten out until, far from the focal plane, they become the dislocations of the Pearcey diffraction pattern for the cusp catastrophe. A new phenomenon is the multiple puncturing of the caustic surface by a series of helical dislocations.

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44

Tan, Aaron, Alexander J. Pak, Dustin R. Morado, Gregory A. Voth, and John A. G. Briggs. "Immature HIV-1 assembles from Gag dimers leaving partial hexamers at lattice edges as potential substrates for proteolytic maturation." Proceedings of the National Academy of Sciences 118, no. 3 (January 4, 2021): e2020054118. http://dx.doi.org/10.1073/pnas.2020054118.

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The CA (capsid) domain of immature HIV-1 Gag and the adjacent spacer peptide 1 (SP1) play a key role in viral assembly by forming a lattice of CA hexamers, which adapts to viral envelope curvature by incorporating small lattice defects and a large gap at the site of budding. This lattice is stabilized by intrahexameric and interhexameric CA-CA interactions, which are important in regulating viral assembly and maturation. We applied subtomogram averaging and classification to determine the oligomerization state of CA at lattice edges and found that CA forms partial hexamers. These structures reveal the network of interactions formed by CA-SP1 at the lattice edge. We also performed atomistic molecular dynamics simulations of CA-CA interactions stabilizing the immature lattice and partial CA-SP1 helical bundles. Free energy calculations reveal increased propensity for helix-to-coil transitions in partial hexamers compared to complete six-helix bundles. Taken together, these results suggest that the CA dimer is the basic unit of lattice assembly, partial hexamers exist at lattice edges, these are in a helix-coil dynamic equilibrium, and partial helical bundles are more likely to unfold, representing potential sites for HIV-1 maturation initiation.

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45

Georgii, Robert, and Tobias Weber. "The Helical Magnet MnSi: Skyrmions and Magnons." Quantum Beam Science 3, no. 1 (February 21, 2019): 4. http://dx.doi.org/10.3390/qubs3010004.

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Since the late 1970s, MnSi has played a major role in developing the theory of helical magnets in non-centrosymmetric materials showing the Dzyaloshinsky-Moriya interaction (DMI). With a long helimagnetic pitch of 175 Å as compared to the lattice d-spacing of 4.55 Å, it was ideal for performing neutron studies, especially as large single crystals could be grown. A (B-T)-phase diagram was measured, and in these studies, under the application of a field of about 180 mT perpendicular to the scattering vector Q, a so-called A-phase in the B-T phase diagram was found and first interpreted as a re-orientation of the magnetic helix. After the surprising discovery of the skyrmion lattice in the A-phase in 2009, much interest arose due to the rigidity of the skyrmionic lattice, which is only loosely bound to the crystal lattice, and therefore only relatively small current densities can already induce a motion of this lattice. A very interesting approach to even better understand the complex structures in the phase diagram is to measure and model the spin excitations in MnSi. As the helimagnetic state is characterized by a long pitch of about 175 Å, the associated characteristic excitations form a band structure due to Umklapp scattering and can only be observed at very small Q with energies below 1 meV. Similarly, the excitations of the skyrmion lattice are very soft and low-energetic. We investigated the magnons in MnSi in the whole (B,T)-phase diagram starting in the single-k helimagnetic state by applying a small magnetic field, B = 100 mT. This way, the complexity of the magnon spectrum is significantly reduced, allowing for a detailed comparison of the data with theory, resulting in a full theoretical understanding of the spin system of MnSi in all its different magnetic phases.

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Vlieghe, Dominique, Johan P. Turkenburg, and Luc Van Meervelt. "B-DNA at atomic resolution reveals extended hydration patterns." Acta Crystallographica Section D Biological Crystallography 55, no. 9 (September 1, 1999): 1495–502. http://dx.doi.org/10.1107/s0907444999007933.

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Despite the importance of hydration around DNA in the understanding of its conformation and interactions with other molecules in many biological processes, only limited atomic resolution information is available. Crystal-engineering techniques, which were originally developed to mimic DNA base triplets in a crystal lattice, also eliminate the rotational disorder of oligonucleotides around their helical axis and thereby enhance the resolution of the structure analysis. The low-temperature crystal structure of the synthetic DNA decamer d(GGCCAATTGG) has been determined at atomic resolution (1.15 Å) using 17700 reflections and the highly organized hydration patterns in both grooves have been characterized. The narrow d(AATT) minor groove is occupied by an `extended hydration spine' alternately bridging base pairs and phosphate O1P atoms of opposite strands, while a distinctive pattern of parallel water ribbons is observed in the major groove. This analysis provides structural insight into the correlation found between narrow minor-groove width and occurrence of the BI conformation and can be used to design new minor-groove binders. By their location between adjacent helices, two fully hydrated magnesium ions further stabilize the crystal packing. The structure also provides details of the hydration and conformation of G·GC triple helices.

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BISHOP, R. F., P. H. Y. LI, D. J. J. FARNELL, and C. E. CAMPBELL. "MAGNETIC ORDERING OF ANTIFERROMAGNETS ON A SPATIALLY ANISOTROPIC TRIANGULAR LATTICE." International Journal of Modern Physics B 24, no. 25n26 (October 20, 2010): 5011–26. http://dx.doi.org/10.1142/s021797921005716x.

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We study the spin-1/2 and spin-1 [Formula: see text] Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice, using the coupled cluster method. With respect to an underlying square-lattice geometry the model contains antiferromagnetic (J1 > 0) bonds between nearest neighbours and competing [Formula: see text] bonds between next-nearest-neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry the model has two sorts of nearest-neighbour bonds, with [Formula: see text] bonds along parallel chains and with J1 bonds providing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one extreme (κ = 0) and a set of decoupled chains at the other (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For the spin-1/2 [Formula: see text] model, we find a weakly first-order (or possibly second-order) quantum phase transition from a Néel-ordered state to a helical state at a first critical point at κc1 = 0.80 ± 0.01, and a second critical point at κc2 = 1.8 ± 0.4 where a first-order transition occurs between the helical state and a collinear stripe-ordered state. For the corresponding spin-1 model we find an analogous transition of the second-order type at κc1 = 0.62 ± 0.01 between states with Néel and helical ordering, but we find no evidence of a further transition in this case to a stripe-ordered phase.

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48

Manning, Gerald S. "Counterion Condensation on a Helical Charge Lattice." Macromolecules 34, no. 13 (June 2001): 4650–55. http://dx.doi.org/10.1021/ma010159b.

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Ung, Alison T., Roger Bishop, Donald C. Craig, Ian G. Dance, and Marcia L. Scudder. "Stability of the helical tubuland inclusion lattice." Journal of the Chemical Society, Chemical Communications, no. 15 (1991): 1012. http://dx.doi.org/10.1039/c39910001012.

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Shikinaka, Kazuhiro, Saori Mori, Kiyotaka Shigehara, and Hiroyasu Masunaga. "Helical alignment inversion of microtubules in accordance with a structural change in their lattice." Soft Matter 11, no. 19 (2015): 3869–74. http://dx.doi.org/10.1039/c5sm00488h.

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Finely-regulated giant helical alignments of microtubules with centimeter order according to their lattice structure form over a temperature gradient during anisotropic spiral propagation via tubulin dimer addition in a capillary cell.

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Journal articles on the topic 'Helical lattices'

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