Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride.

When two-dimensional crystals are brought into close proximity, their interaction results in reconstruction of electronic spectrum and crystal structure. Such reconstruction strongly depends on the twist angle between the crystals, which has received growing attention due to interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Here we study two insulating crystals of hexagonal boron nitride stacked at small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential. The observation is attributed to interfacial elastic deformations that result in out-of-plane dipoles formed by pairs of boron and nitrogen atoms belonging to opposite interfacial surfaces. This creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modeling. These findings open up possibilities for designing van der Waals heterostructures and offer an alternative probe to study moiré-superlattice electrostatic potentials.

Composite super-moiré lattices in double-aligned graphene heterostructures.

When two-dimensional (2D) atomic crystals are brought into close proximity to form a van der Waals heterostructure, neighbouring crystals may influence each other's properties. Of particular interest is when the two crystals closely match and a moiré pattern forms, resulting in modified electronic and excitonic spectra, crystal reconstruction, and more. Thus, moiré patterns are a viable tool for controlling the properties of 2D materials. However, the difference in periodicity of the two crystals limits the reconstruction and, thus, is a barrier to the low-energy regime. Here, we present a route to spectrum reconstruction at all energies. By using graphene which is aligned to two hexagonal boron nitride layers, one can make electrons scatter in the differential moiré pattern which results in spectral changes at arbitrarily low energies. Further, we demonstrate that the strength of this potential relies crucially on the atomic reconstruction of graphene within the differential moiré super cell.

Assessment of inner dynein arm structure and possible function in ciliary and flagellar axonemes.

The construction and assessment of a three-dimensional computer-generated model of inner dynein arms on a 96-nm repeat unit of an axonemal doublet is described. The model is based on published electron micrographs of axonemes from Tetrahymena cilia and eel sperm, which were prepared using several different techniques: negative stain, freeze etch, and thin section. The inner arm structure is represented as three inner dynein arm complexes containing four inner dynein arms (IDAs), three dyads, and one single-headed arm, each capable of bridging the interdoublet gap. The IDA structures in the model have been correlated with the domains containing dynein heavy-chain isoforms mapped by several authors using genetic analyses of Chlamydomonas mutants. The model is consistent with micrographic evidence from axonemes of cilia and flagella from other organisms that led previously to conflicting structural interpretations. In this reconciling interpretation, the different alignments of the IDAs relative to the corresponding outer dynein arms observed in micrographs of differently prepared samples, result from the IDAs being arrested at different stages of their cycles of activity in each preparation. By interpolating between these positions of arrest, cycles of activity are proposed for each of the IDAs during which the arms attach to the neighbouring doublet microtubule and drive it tipwards.

Mechanochemical aspects of axonemal dynein activity studied by in vitro microtubule translocation.

We have determined the relationship between microtubule length and translocation velocity from recordings of bovine brain microtubules translocating over a Paramecium 22S dynein substratum in an in vitro assay chamber. For comparison with untreated samples, the 22S dynein has been subjected to detergent and/or to pretreatments that induce phosphorylation of an associated 29 kDa light chain. Control and treated dyneins have been used at the same densities in the translocation assays. In any given condition, translocation velocity (v) shows an initial increase with microtubule length (L) and then reaches a plateau. This situation may be represented by a hyperbola of the general form v = aL/(L+b), which is formally analogous to the Briggs-Haldane relationship, which we have used to interpret our data. The results indicate that the maximum translocation velocity Vo(= a) is increased by pretreatment, whereas the length constant KL(= b), which corresponds to Km, does not change with pretreatment, implying that the mechanochemical properties of the pretreated dyneins differ from those of control dyneins. The conclusion that KL is constant for defined in vitro assays rules out the possibility that the velocity changes seen are caused by changes in geometry in the translocation assays or by the numbers of dyneins or dynein heads needed to produce maximal translocational velocity. From our analysis, we determine that f, the fraction of cycle time during which the dynein is in the force-generating state, is small--roughly 0.01, comparable to the f determined previously for heavy meromyosin. The practical limits of these mechanochemical changes imply that the maximum possible ciliary beat frequency is about 120 Hz, and that in the physiological range of 5-60 Hz, beat frequency could be controlled by varying the numbers of phosphorylated outer arm dyneins along an axonemal microtubule.

Biophysical aspects and modelling of ciliary motility.

The dominance of viscous forces in the generation of propulsive thrust by cilia is emphasised. Fourier analysis indicates that ciliary bends consist of circular arcs joined by linear segments; this arc-line shape appears to be a property associated with the molecular mechanism responsible for bending the cilium and is unchanged by variations in the external viscous loading on the organelle. The flexibility of a computer-generated model of axonemal structure is demonstrated by the incorporation of recent data concerning the surface lattice of the microtubules. Computer simulations using the model show that predictions based on stochastic, rather than co-ordinated, dynein arm activity provide a qualitative match to experimental observations of microtubules gliding over fields of dynein molecules.

Physical model of axonemal splitting.

A physical model developed to explain microtubule sliding patterns in the trypsin-treated ciliary axoneme has been extended to investigate the generation of bending moments by microtubules sliding in an axoneme in which the doublets are anchored at one end. With sliding restricted, a bending moment is developed by the polarized shearing interaction between neighbouring doublets, effected by the activity of dynein arms on doublet N pushing N + 1 in a tipward (+) direction. In arrested axonemes in which arms on several contiguous doublets are active, the bending moment causes splitting of the 9 + 2 microtubule array into two or more sets of doublets. In the absence of special constraints, splitting depends only on breaking the circumferential interdoublet links most distorted by the bending moment. The analysis, which permits assignment of arm activity to specific microtubules in each of the observed patterns of splitting, indicates that the axoneme will split between doublet N and N + 1 if arms on doublet N are inactive and arms on either N + 1 or N-1 are active. To produce the observed major splits, dynein arms on the microtubules of roughly one-half of the axoneme are predicted to be active, in a manner consistent with the switch-point hypothesis of ciliary motion. Electron microscopic examination indicates that virtually every set of doublets in the split axonemes retains its cylindrical form. Maintenance of cylindrical symmetry can be ascribed to the mechanical properties of the unbroken links, which may resist both tensile and compressive stress, and to active dynein arms.

Structural and geometrical constraints on the outer dynein arm in situ.

This study considers the relationship between two structural forms of the 22S dynein arm of Tetrahymena thermophila: the bouquet and the compact arm. The compact arm differs from the bouquet and from other proposed forms (e.g., the "toadstool") in that the globular domains are situated transversely across the interdoublet gap with one globular subunit, the head, proximal to the adjacent doublet microtubule. The other models place all three globular domains proximal to the neighboring doublet microtubule. When sliding of an isolated axoneme is induced, at least 57% of total attached arms on exposed doublets are in the compact form within dimensions of 24 x 24 x 12 nm, and only about 2% of the arms are bouquets. Toadstools are incompatible with the images seen. Bouquets are not found in regions of the doublet protected by a neighboring doublet. When axonemes with exposed doublets are treated with 0.5 M KCl for 30 min, the compact arms and the dynein heavy (H)-chains disappear, while isolated bouquets and dynein H-chains appear in the medium, suggesting that the compact arms give rise to the bouquets as they are solubilized. The bouquet is the predominant form of isolated 22S dynein molecules, which are found in two apparently enantiomorphic forms, within dimensions 45 x 39 x 13 nm; bouquets attached to doublets have dimensions similar to those of isolated bouquets. Computer modeling indicates that in an intact standard-diameter axoneme, these dimensions are incompatible with the interdoublet volume available for an arm; the bouquet therefore represents an unfolded compact arm. A plausible sequence of changes can be modeled to illustrate the conversion of an attached compact arm to an attached and then free bouquet. The toadstool is probably an artifact that arises after unfolding. Consistent with the conformational difference, H-chains of attached compact arms differ from those of isolated bouquets in their susceptibility to limited proteolysis. These results suggest that the compact arm, rather than the unfolded bouquet or the toadstool, is the functional form of the outer arm in the intact axoneme.

Computer modelling of Tetrahymena axonemes at macromolecular resolution. Interpretation of electron micrographs.

A computer-generated model of the structural arrangement of the complete 9+2 ciliary axoneme of Tetrahymena at macromolecular resolution (4 nm) is presented. The model reconciles detailed information about subcomponents from negative-stained, thin-section and freeze-fracture electron micrographs, integrating the images into a consistent three-dimensional picture. This illuminates problems such as the requirement for compaction of dynein to form the arm, difficulties in visualization of the circumferential links, construction of the central sheath, and the comparative periodicities of the inner and outer arms. The model is pragmatic in that it is flexible and easily changed, as new information becomes available. It is also useful in the development of dynamic concepts, such as a spatial description of the dynein cross-bridge cycle, which is illustrated, or relationships between adjacent doublets during sliding and bending.

A physical model of microtubule sliding in ciliary axonemes.

Ciliary movement is caused by coordinated sliding interactions between the peripheral doublet microtubules of the axoneme. In demembranated organelles treated with trypsin and ATP, this sliding can be visualized during progressive disintegration. In this paper, microtubule sliding behavior resulting from various patterns of dynein arm activity and elastic link breakage is determined using a simplified model of the axoneme. The model consists of a cylindrical array of microtubules joined, initially, by elastic links, with the possibility of dynein arm interaction between microtubules. If no elastic links are broken, sliding can produce stable distortion of the model, which finds application to straight sections of a motile cilium. If some elastic links break, the model predicts a variety of sliding patterns, some of which match, qualitatively, the observed disintegration behavior of real axonemes. Splitting of the axoneme is most likely to occur between two doublets N and N + 1 when either the arms on doublet N + 1 are active and arms on doublet N are inactive or arms on doublet N - 1 are active while arms on doublet N are inactive. The analysis suggests further experimental studies which, in conjunction with the model, will lead to a more detailed understanding of the sliding mechanism, and will allow the mechanical properties of some axonemal components to be evaluated.

Flagellar wave reversal in the kinetoplastid flagellate Crithidia oncopelti.

Living Crithidia oncopelti cells swim through their environment by means of tip-to-base waves on their single flagellum. The cells are able to re-orient themselves by using a short burst of asymmetrical base-to-tip waves. All points on a flagellum are capable of initiating waves. Placing a population of cells in a medium of high viscosity initially produces a large number of organisms beating in the reverse mode. An individual cell has a random "switching" behavior. Viscosity affects the frequency of forward and reverse waves in different ways. The concentration of free Ca++ ions determines the direction of wave propagation in reactivated axonemes. Calmodulin may play a role in mediating the Ca++ dependence of wave direction.

Structures attached to doublet microtubules of cilia: computer modeling of thin-section and negative-stain stereo images.

With a single set of positional coordinates for longitudinal and transverse attachment of the inner and outer rows of dynein arms with respect to the doublet microtubules of Tetrahymena ciliary axonemes, a computer model has been constructed at 4-nm resolution that reconciles negative-stain en face stereo images of arm and spoke positions to traditional images of tannic acid/glutaraldehyde-fixed sections. In this model, inner and outer arms correspond in substructure; both repeat with a 24-nm periodicity without stagger between rows, and a pair of arms is in exact alignment with the first spoke (S1) in each doublet spoke group. The model and the supporting micrographs suggest that each arm cycles in three dimensions and that, during cycling, the inner and outer arms move in opposite directions with respect to the center of subfiber A of the doublet (N). Attachment is off-center with respect to subfiber B of the adjacent doublet (N + 1), causing the sliding doublets to skew with respect to one another.

Motile flagellar axonemes with a 9 + 1 microtubule configuration.

Electron microscope (EM) studies of the eukaryotic flagellum reveal that the organelle contains a 9 + 2 arrangement of microtubules, the axoneme, with nine doublets surrounding two singlets enveloped by a membrane which is continuous with that of the cell; various linkages and projections are associated with the microtubules. Strong experimental evidence supports the idea that the forces required for bend formation on eukaryotic flagella are derived from active relative sliding of the peripheral doublets. Dynein arms, which project from each peripheral microtubule and possess ATPase activity, interact with a neighbouring doublet and undergo conformational changes which induce sliding. To form and propagate coordinated bends along a flagellum the sliding must be resisted in a controlled manner by structures within the axoneme. The regulatory mechanism responsible for the control of inter-doublet sliding is not known in detail, but ultrastructural studies suggest that interactions between the radial spokes attached to each doublet and the central complex of the axoneme may be involved. We report here the treatment of flagella with a 9 + 2 microtubular structure from the trypanosomid flagellate Crithidia oncopelti to produce motile axonemes with only one central microtubule. We conclude that the complete central complex is not involved in the conversion of microtubule sliding into axonemal bending, but may be both associated with the control of wave propagation and essential for bend initiation.

A sliding microtubule model incorporating axonemal twist and compatible with three-dimensional ciliary bending.

1. Equations are developed to calculate the relative displacements of the doublet microtubules at the tip of a cilium when the microtubules twist about the axis of the organelle. 2. Displacements measured from electron micrographs show asymmetry (or skew) which can be matched quantitatively by the theoretical model with the appropriate selection of twist angle and orientation of the axoneme with respect to the plane of beat. 3. For Elliptio cilia the experimental results are consistent with a planar effective stroke and a recovery stroke involving a three-dimensional bend. The plane of the effective stroke is not normal to a surface containing the central pair of microtubules but contains microtubule 2 to produce the observed skew. 4. This model for the beat also explains the range of orientations of axoneme observed in sections through the metachronal wave.

Effects of calcium on flagellar movement in the trypanosome Crithidia oncopelti.

1. The effects of calcium on the motility of different preparations of flagella from Crithidia oncopelti were studied using stroboscopic and high-speed cine photographic techniques. 2. By varying the concentration of calcium in suspensions of chemically treated samples of the organism it was found that changes occurred in bend shape, wave direction and frequency. 3. Waves on the flagellum of the organisms in vivo possess the unusual ability to propagate from tip to base, but reverse in direction during an avoiding response. In chemically extracted and reactivated preparations tip to base propagation was observed only at low concentrations (less than 10(-4) mol m-3) of calcium ion; at high concentrations base to tip propagation only was seen. In cells treated with ion across membranes, tip to base propagation was seen only in the presence of EGTA; when calcium was added the majority of organisms propagated waves from base to tip. 4. At certain values (ca. 10(-3) mol m-3) of the calcium concentration the wave shape had meander-like characteristics, whereas at higher and lower concentrations it was more sinsoidal. At high calcium concentrations only one wave appeared on the flagellum whereas at low values two or three were observed. 5. A reduction in frequency at high calcium concentrations was probably due to competitive inhibition of magnesium ions. 6. The results suggest that wave reversal in living Crithidia is induced by the release of calcium ions within the flagellum following stimulation of the membrane. In terms of the sliding filament model of flagellar activity the effects of calcium suggest that the ion is effective in modifying the interaction between the spoke head and central sheath and may control the relative direction of microtubular sliding.

Dynamics of the hispid flagellum of Ochromonas danica. The role of mastigonemes.

High speed cinephotographic techniques were used to determine the pattern of fluid flow about the hispid flagellum of Ochromonas danica and to investigate the behavior of this flagellum in media of increased viscosity. The fluid currents are consistent with the hypothesis that the mastigonemes are passive, rigid, remain normal to the flagellar surface, and lie in the plane of flagellar undulation during motility.