Helical Substructures Research Articles

Homochiral boron imidazolate frameworks built from mixed Chiral and achiral ligands

Chiral metal-organic frameworks (MOFs) have been studied extensively because of the potential application. Based on the complexity of chiral structure, it is a great challenge to study the formation of novel chiral centers under self-assembly conditions. By mixing chiral and achiral ligands, five unusual homochiral BIFs materials were synthesized by using d-camphoric acid (D-H2cam) and KBH(mim)3 (mim = 2-methylimidazole) under solvothermal condition. The orientations of mim rings had been locked to a specific angle in these structures and freed tridentate BH(mim)3- ligands were separated into two enantiomers, S–BH(mim)3- and R–BH(mim)3-. BIF-123 and BIF-124 exhibited similar (3, 4)-connected pillared-layer chiral structures with a pair of opposite helical substructures. BIF-125, 126 and 127 exhibited a 4-connected chiral diamond structure, which incorporates the homochiral helical substructures containing only S–BH(mim)3- ligand. These homochiral BIFs showed high pore volume in gas adsorption measurements and good stability under different solvent environments. Furthermore, the obvious CD signals of BIF-126 proved the chirality of bulk samples.

Non-canonical helical transitions and conformational switching are associated with characteristic flexibility and disorder indices in TRP and Kv channels

ABSTRACT Structural evidence and much experimental data have demonstrated the presence of non-canonical helical substructures (π and 310) in regions of great functional relevance both in TRP as in Kv channels. Through an exhaustive compositional analysis of the sequences underlying these substructures, we find that each of them is associated with characteristic local flexibility profiles, which in turn are implicated in significant conformational rearrangements and interactions with specific ligands. We found that α-to-π helical transitions are associated with patterns of local rigidity whereas α-to-310 transitions are mainly leagued with high local flexibility profiles. We also study the relationship between flexibility and protein disorder in the transmembrane domain of these proteins. By contrasting these two parameters, we located regions showing a sort of structural discrepancy between these similar but not identical protein attributes. Notably, these regions are presumably implicated in important conformational rearrangements during the gating in those channels. In that sense, finding these regions where flexibility and disorder are not proportional allows us to detect regions with potential functional dynamism. From this point of view, we highlighted some conformational rearrangements that occur during ligand binding events, the compaction, and refolding of the outer pore loops in several TRP channels, as well as the well-known S4 motion in Kv channels.

Helical Substructures of Close-Packed Metals Determined by a Universal Building Unit (Tetrablock)

Helical Substructures of Close-Packed Metals Determined by a Universal Building Unit (Tetrablock)

Increased efficiency gyroid structures by tailored material distribution

The gyroid has been identified as a cellular topology suitable for engineering applications and, particularly in its solid-network form, for biomedical applications. Its solid-surface form has received less attention but offers additional benefits of a continuous surface that partitions space and provides large surface area for heat transfer or cell attachment. Through numerical methods it is shown for the first time that under uniaxial loading the solid-surface gyroid distributes loads predominantly within helical substructures. Furthermore, by adjusting the thickness of the load carrying helical regions, the mechanical response can be tuned in different directions. This novel discovery enables more efficient use of material distribution while taking advantage of the unique properties of the solid-surface gyroid.

Divergent topologies in luminescent and nitrobenzene-detecting zinc diphenate coordination polymers with flexible dipyridylamide ligands

Hydrothermal reaction of zinc nitrate, diphenic acid (H2dip), and one of the dipyridylamide ligands N,N′-(hexane-1,6-diyl)diisonicotinamide (hdin), N,N′-(pentane-1,5-diyl)diisonicotinamide (pedin), N,N′-(butane-1,4-diyl)diisonicotinamide (bdin), or N,N′-(ethane--1,2-diyl)diisonicotinamide (edin) resulted in coordination polymers whose dimensionalities depend on the aliphatic tether length within the coligand and the amount of base used in the synthesis. The five new phases were characterized by single crystal X-ray diffraction. {[Zn(dip)(hdin)]·2.5H2O}n (1) and {[Zn(dip)(pedin)]·2.5H2O}n (2) both possess undulating 2D coordination polymer layers with [Zn(dip)]n chains spanned by looped dipyridylamine ligands into a 2,4-connected self-penetrated (6)(648.10) topology. [Zn(dipH)2(bdin)]n (3) manifests a 1-D zig-zag chain topology, while {[Zn3(dip)3(bdin)3]·13H2O}n (4) and {[Zn(dip)(edin)]·3H2O}n (5) manifest helical substructures linked into a rare two-fold interpenetrated 6482nbo topology. Thermal and luminescent properties were also probed; compounds 1–5 showed ability to detect nitrobenzene in ethanol suspension with the 3D derivatives 4 and 5 manifesting the best “turn-off” luminescence quenching behavior.

Chiral behavior in rat tail tendon fascicles

Ex vivo tendon mechanical behavior has been well described under rotationally constrained uniaxial tensile testing. During standard loading of rat tail tendon (RTT) fascicles, apparent axial twist has been observed. To quantify this behavior, we designed a custom testing setup, utilizing magnetic suspension, to allow unconstrained axial rotation during tensile loading. We characterized the rotational behavior of single and paired RTT fascicles under cyclic loading. We also measured stress relaxation across loading cycles as well as “rotational relaxation”. Single fascicle nonlinear stretch-twist coupling is well described by the asymptotic function Δθ=A(1-e-Bε) in which fascicles rotated a mean ±51.1° within about 1% applied axial strain. On average, paired fascicles rotated just over 10° less. Specimen cross-sectional diameter had a noticeable effect on the measured mechanical properties, particularly effective elastic modulus. Such stretch-twist coupling and size dependence cannot be understood via classical elasticity but is predicted by Cosserat (micropolar) elasticity. The current study demonstrates RTT fascicles are chiral based on observed axial load-induced twist. Additionally, our findings support existing research that suggests a helical fascicle structure. Potential consequences of helical substructures, mechanical and biological, merit further investigation.

The relative compliance of energy-storing tendons may be due to the helical fibril arrangement of their fascicles.

A nonlinear elastic microstructural model is used to investigate the relationship between structure and function in energy-storing and positional tendons. The model is used to fit mechanical tension test data from the equine common digital extensor tendon (CDET) and superficial digital flexor tendon (SDFT), which are used as archetypes of positional and energy-storing tendons, respectively. The fibril crimp and fascicle helix angles of the two tendon types are used as fitting parameters in the mathematical model to predict their values. The outer fibril crimp angles were predicted to be 15.1° ± 2.3° in the CDET and 15.8° ± 4.1° in the SDFT, and the average crimp angles were predicted to be 10.0° ± 1.5° in the CDET and 10.5° ± 2.7° in the SDFT. The crimp angles were not found to be statistically significantly different between the two tendon types (p = 0.572). By contrast, the fascicle helix angles were predicted to be 7.9° ± 9.3° in the CDET and 29.1° ± 10.3° in the SDFT and were found to be statistically highly significantly different between the two tendon types (p < 0.001). This supports previous qualitative observations that helical substructures are more likely to be found in energy-storing tendons than in positional tendons and suggests that the relative compliance of energy-storing tendons may be directly caused by these helical substructures.

Chlorophyl mutations in haricot plants treated with mutagens

Ex vivo tendon mechanical behavior has been well described under rotationally constrained uniaxial tensile testing. During standard loading of rat tail tendon (RTT) fascicles, apparent axial twist has been observed. To quantify this behavior, we designed a custom testing setup, utilizing magnetic suspension, to allow unconstrained axial rotation during tensile loading. We characterized the rotational behavior of single and paired RTT fascicles under cyclic loading. We also measured stress relaxation across loading cycles as well as “rotational relaxation”. Single fascicle nonlinear stretch-twist coupling is well described by the asymptotic function Δθ=A(1-e-Bε) in which fascicles rotated a mean ±51.1° within about 1% applied axial strain. On average, paired fascicles rotated just over 10° less. Specimen cross-sectional diameter had a noticeable effect on the measured mechanical properties, particularly effective elastic modulus. Such stretch-twist coupling and size dependence cannot be understood via classical elasticity but is predicted by Cosserat (micropolar) elasticity. The current study demonstrates RTT fascicles are chiral based on observed axial load-induced twist. Additionally, our findings support existing research that suggests a helical fascicle structure. Potential consequences of helical substructures, mechanical and biological, merit further investigation.

Synthesis and Structural Features of Quadruple Helicenes: Highly Distorted π Systems Enabled by Accumulation of Helical Repulsions.

Quadruple helicenes, bearing dithia[6]helicene and [5]helicene substructures, were prepared by a well-controlled Scholl reaction. The 4-fold helicity provides 9 stereoisomers including 4 pairs of enantiomers and 1 meso isomer. Among them, differently distorted structures of a propeller-shaped isomer (QH-A) and a saddle-shaped isomer (QH-B) were unambiguously determined by X-ray crystallography. Especially in the latter isomer, a proper accumulation of repulsions on the helical substructures twisted the naphthalene core to the limit (69.5°), the highest degree of twisting deformation per benzene unit (35.3° at the most). Photophysical and electrochemical studies showed a broadened HOMO-LUMO gap and a HOMO of QH-B lying lower compared to those of QH-A. These results together with the density functional theory (DFT) calculations have clearly demonstrated the electronic state dependency on the molecular geometry. Additionally, kinetic studies of the isomerization between these isomers using (1)H NMR, circular dichroism, and DFT calculations shed light on the interconversion pathways among the stereoisomers. The height of barriers in the inversion of a certain helical substructure may be affected by the neighboring helical substructures.

A new strain energy function for modelling ligaments and tendons whose fascicles have a helical arrangement of fibrils

A new strain energy function for the hyperelastic modelling of ligaments and tendons whose fascicles have a helical arrangement of fibrils is derived. The stress–strain response of a single fascicle whose fibrils exhibit varying levels of crimp throughout its radius is calculated and used to determine the form of the strain energy function. The new constitutive law is used to model uniaxial extension test data for human patellar tendon and is shown to provide an excellent fit, with the average relative error being 9.8%. It is then used to model shear and predicts that the stresses required to shear a tendon are much smaller than those required to uniaxially stretch it to the same strain level. Finally, the strain energy function is used to model ligaments and tendons whose fascicles are helical, and the relative effects of the fibril helix angle, the fascicle helix angle and the fibril crimp variable are compared. It is shown that they all have a significant effect; the fibril crimp variable governs the non-linearity of the stress–strain curve, whereas the helix angles primarily affect its stiffness. Smaller values of the helix angles lead to stiffer tendons; therefore, the model predicts that one would expect to see fewer helical sub-structures in stiff positional tendons, and more in those that are required to be more flexible.

Synthesis, Structures, and Properties of π-Extended Double Helicene: A Combination of Planar and Nonplanar π-Systems

The synthesis, structures, and properties of a π-extended double helicene 1 are described. This double helicene 1 was synthesized by a four-fold oxidative C-H biphenylation of naphthalene followed by the Scholl reaction or via five steps including the Suzuki-Miyaura cross-coupling reaction and the Scholl reaction. Due to the two helical substructures, 1 has three isomers, i.e., two enantiomers in a twisted form [(P,P) and (M,M)] and one diastereoisomer in a meso form. X-ray crystallographic analysis of the twisted isomers (twisted-1) revealed a tightly offset packing pattern of (P,P)- and (M,M)-twisted isomers, affording a three-dimensional lamellar stacking structure. A high isomerization barrier (43.5 kcal mol(-1)) and the relative thermal stability of twisted-1 isomer over meso-1 by 0.9 kcal mol(-1) were estimated by DFT calculations. The three isomers were successfully separated by chiral HPLC and characterized by circular dichroism spectroscopy as well as by TD-DFT studies. Electronic state variation resulting from the molecular geometry difference between the two diastereoisomers (twisted-1 and meso-1) was observed by UV-vis absorption and fluorescence spectra.

Effect of fatigue loading on structure and functional behaviour of fascicles from energy-storing tendons

Tendons can broadly be categorized according to their function: those that act purely to position the limb and those that have an additional function as energy stores. Energy-storing tendons undergo many cycles of large deformations during locomotion, and so must be able to extend and recoil efficiently, rapidly and repeatedly. Our previous work has shown rotation in response to applied strain in fascicles from energy-storing tendons, indicating the presence of helical substructures which may provide greater elasticity and recovery. In the current study, we assessed how preconditioning and fatigue loading affect the ability of fascicles from the energy-storing equine superficial digital flexor tendon to extend and recoil. We hypothesized that preconditioned samples would exhibit changes in microstructural strain response, but would retain their ability to recover. We further hypothesized that fatigue loading would result in sample damage, causing further alterations in extension mechanisms and a significant reduction in sample recovery. The results broadly support these hypotheses: preconditioned samples showed some alterations in microstructural strain response, but were able to recover following the removal of load. However, fatigue loaded samples showed visual evidence of damage and exhibited further alterations in extension mechanisms, characterized by decreased rotation in response to applied strain. This was accompanied by increased hysteresis and decreased recovery. These results suggest that fatigue loading results in a compromised helix substructure, reducing the ability of energy-storing tendons to recoil. A decreased ability to recoil may lead to an impaired response to further loading, potentially increasing the likelihood of injury.

Complex superstructures in chiral liquid crystals: surface-induced helix destruction.

The influence of surface anchoring in thin chiral ferroelectric liquid crystals on helical superstructures imposed onto smectic layers is studied by means of a simple model allowing surface anchoring through the self-depolarization effect. It is shown that, for narrow temperature ranges close to temperatures of tilting phase transitions, these interactions can destroy helices, leading to the emergence of complex, intertwined undulatory, and helical substructures with different, mainly short, pitches. Regions with both undulated and helical orderings are demonstrated to reveal different sizes and random distributions along the smectic layer normal. Assuming values of material model parameters, typical for liquid crystals being close to tilting phase transitions, the free energy of thin helical smectic liquid crystal systems is determined as a function of two variables. One of them specifies the helix period of the appropriate bulk system (unperturbed by surfaces), while the second describes the interplay between the surface anchoring and the liquid crystal elasticity. It is shown that the free energy exhibits a very complicated behavior within variable regions for which the regular helices or complex superstructures occur. The resulting sensitivity of the free energy on changes of these variables corresponds to the appearance of a large variety of complex superstructures with coexisting helices of different periods. This gives an explanation of the occurrence of intricate superstructures and provides new insight into the interplay between molecular and surface interactions near the tilting phase transitions.

Helical sub-structures in energy-storing tendons provide a possible mechanism for efficient energy storage and return

The predominant function of tendons is to position the limb during locomotion. Specific tendons also act as energy stores. Energy-storing (ES) tendons are prone to injury, the incidence of which increases with age. This is likely related to their function; ES tendons are exposed to higher strains and require a greater ability to recoil than positional tendons. The specialized properties of ES tendons are thought to be achieved through structural and compositional differences. However, little is known about structure–function relationships in tendons. This study uses fascicles from the equine superficial digital flexor (SDFT) and common digital extensor (CDET) as examples of ES and positional tendons. We hypothesized that extension and recoil behaviour at the micro-level would differ between tendon types, and would alter with age in the injury-prone SDFT. Supporting this, the results show that extension in the CDET is dominated by fibre sliding. By contrast, greater rotation was observed in the SDFT, suggesting a helical component to fascicles in this tendon. This was accompanied by greater recovery and less hysteresis loss in SDFT samples. In samples from aged SDFTs, the amount of rotation and the ability to recover decreased, while hysteresis loss increased. These findings indicate that fascicles in the ES SDFT may have a helical structure, enabling the more efficient recoil observed. Further, the helix structure appears to alter with ageing; this coincides with a reduction in the ability of SDFT fascicles to recoil. This may affect tendon fatigue resistance and predispose aged tendons to injury.

Lanthanide-Thiophene-2,5-dicarboxylate Frameworks: Ionothermal Synthesis, Helical Structures, Photoluminescent Properties, and Single-Crystal-to-Single-Crystal Guest Exchange

Eight three-dimensional lanthanide-thiophene-2,5-dicarboxylate frameworks, [Ln(TDC)(2)]·(choline) (1-6; Ln = Gd, Nd, Eu, Er, Tb, Dy; TDC = thiophene-2,5-dicarboxylate), [Yb(TDC)(2)(e-urea)]·(choline)·H(2)O (7; e-urea = ethyleneurea), [Nd(2)(TDC)(3)(e-urea)(4)]·3(e-urea) (8) have been successfully prepared in deep eutectic solvents (choline chloride/e-urea), respectively. Compounds 1-7 are anionic frameworks with 8-connected bcu topology, while compound 8 features a neutral 6-connected rob-type framework with guest e-urea molecules. In these structures, lanthanide ions show dicapped trigonal prism, pentagonal bipyramid, and tricapped trigonal prism coordination configurations, respectively, and the TDC ligands exhibit different coordination modes. Versatile helical substructures are presented in these compounds. The photoluminescent properties of compounds 3 (Eu) and 8 (Nd) were studied. Moreover, compound 8 can perform single-crystal-to-single-crystal guest exchange. The ethanol-exchange mechanism of 8 can be ascribed to the kinetically controlled flexibility (KCF).

Nickel(II) Coordination Polymers – 4,4′‐Bipyridine‐Connected Six‐ and Four‐Fold Metal–Succinate Helices and Their Corresponding Chiral and Achiral Networks

AbstractThe reaction of equimolar amounts of Ni(NO3)2·6H2O, Na2(suc)·6H2O (suc = succinate) and 4,4′‐bipyridine (bipy) under different conditions yield the coordination polymers [Ni(suc)(bipy)(H2O)2]n·2nH2O (1) and [Ni(suc)(bipy)(H2O)2]n·nH2O (2). The complexes were characterized by elemental analysis, spectroscopic, thermogravimetric, and magnetic susceptibility measurements. Crystal structures reveal that the metal centers in both complexes are in a distorted octahedral N2O4 coordination sphere assembled by mutually trans pairs of 4,4′‐bipyridine, succinate, and water molecules. The helical metal–succinate chains have a right‐handed sixfold configuration in 1, with guest water molecules inside the helix, and both right‐ and left‐handed fourfold configurations in 2, with guest water molecules outside the helix. The parallel helical substructures are connected by 4,4′‐bipyridine and provide 3D chiral 75.9 and achiral 65.8 networks in 1 and 2, respectively.

Graphical Abstract: Eur. J. Inorg. Chem. 6/2011

AbstractThe cover picture shows the porous metal‐organic polymer [(Cp°2Mo2P4S)CuI)4]n, which is composed of helical substructures with opposite handedness. The compound incorporates CH2Cl2 molecules when it is stored under the solvent. This process is reversible under high vacuum without loss of crystallinity of the material and resembles, therefore, the reversible stretching of an elastic spring. Details of the synthesis and characterization of this and related compounds are given in the article by J. Wachter et al. on p. 785 ff.

Novel Metal‐Organic Frameworks Incorporating [Cp°2Mo2P4S] (Cp° = 1‐tBu‐3,4‐Me2C5H2), P4S3 and Cu2I2 Building Blocks (Eur. J. Inorg. Chem. 6/2011)

AbstractThe cover picture shows the porous metal‐organic polymer [(Cp°2Mo2P4S)CuI)4]n, which is composed of helical substructures with opposite handedness. The compound incorporates CH2Cl2 molecules when it is stored under the solvent. This process is reversible under high vacuum without loss of crystallinity of the material and resembles, therefore, the reversible stretching of an elastic spring. Details of the synthesis and characterization of this and related compounds are given in the article by J. Wachter et al. on p. 785 ff.

Novel Metal‐Organic Frameworks Incorporating [Cp°2Mo2P4S] (Cp° = 1‐tBu‐3,4‐Me2C5H2), P4S3 and Cu2I2 Building Blocks

AbstractThe synthesis and characterization of [Cp°2Mo2P4S] (1) and [Cp°2Mo2P2S3] (2) (Cp° = 1‐tBu‐3,4‐Me2C5H2) has been described. The reaction of 1 in CH2Cl2 with 2 equiv. of CuI in MeCN under diffusion conditions gave [(Cp°2Mo2P4S)3(CuI)4]n (6a). The crystal structure of 6a consists of helical substructures of opposed chirality which are formed by the coordination of two Cu2I2 rings to three phosphorus atoms of the cyclo‐P4S middle deck of 1. The resulting helix is connected with four helices of the same chirality by front‐backside P coordination of another 1 unit. Compound 6a can reversibly include or release CH2Cl2 molecules without loosing its crystalline character. Thus, storing crystals of 6a under CH2Cl2 results in the formation of 6a·0.55CH2Cl2 (6b), the unit cell volume increasing by 113.6 Å3 per formula unit, while in high vacuum the unit cell volume of 6b decreases to the value of 6a. The reaction of 1 with CuI in the presence of P4S3 gave a mixture of two isomeric polymers 7 and 8 of composition [(Cp°2Mo2P4S)(P4S3)(CuI)2]n. The crystal structures of both compounds 7 and 8 contain linear strands of [1(CuI)2]n and [(P4S3)(CuI)2]n with planar Cu2I2 rings as common interface. A two‐dimensional framework is formed by interpenetration of both types of strands. The analogous reaction of the mixture of [Cp*2Mo2P4S] (Cp* = C5Me5) and P4S3 with CuI gave [(Cp*2Mo2P4S)(P4S3)(CuI)2]n (9). Contrary to the structures of 7 and 8 in this compound coordination of adjacent P atoms of the η3‐P3 ligand and the η2‐PS dumbbell leads to the formation of one‐dimensional ribbons.

A lvt-type framework material [Pb3Cl3(OH)(succinate)]n with helical sub-structures and incomplete cubane-like clusters

Abstract Presented here are the hydrothermal synthesis, single crystal XRD characterization and physical property of a polymeric lead(II) compound, [Pb3Cl3(OH)(succinate)]n ( 1 ). In the structure of 1 , the succinate ligands bridge the trinuclear incomplete cubane-like Pb3O3Cl clusters to form a non-interpenetrating three-dimensional framework with lvt (4284) topology. Single helices with the same ratio of different orientation are found in this unusual network.