The bacterial flagellum as an imperfect cylindrical crystal: flagellar geometry, movement and polymorphism, and the role of partial dislocations

A pairing attraction between helical turns of subunits in a cylindrical crystal, like that in the dahlemense strain of tobacco mosaic virus, can cause the axis of the rod or crystal to become helical. This is true only if the number of helices is odd. The shape of a bacterial flagellum can be accounted for then if, as Caspar &; Holmes and Klug have suggested, rows of its subunits exhibit such a pairing interaction. Klug's thoughts on bacterial flagella are developed and extended into a model that accounts qualitatively for geometry, movement and polymorphism of flagella. If the number of helices between which there is a pairing interaction is odd, then the crystal is an imperfect cylindrical crystal. The geometry of such crystals is described. They contain a line defect, termed here an antiphase boundary, across which the pairing interaction is reversed. The boundary is a line of expansion on the convex side of a curved filament. Movement of flagella is explained by circumferential displacement of the antiphase boundary. One polymorphic form can convert to another if a dislocation passes along it. Straight flagella are perfect cylindrical crystals with no antiphase boundary.     

Twinned Raphides of Calcium Oxalate in Grape (Vitis): Implications for Crystal Stability and Function

Among the higher plants that accumulate crystalline calcium oxalate, many taxa characteristically produce raphides, or needle-shaped crystals. Substantial evidence has accumulated indicating that raphides function in plant defenses against herbivory and that their acicular shape is a critical component in proposed mechanisms for these defenses. Previous observations have shown that raphides in members of the Vitaceae are twinned crystals. In this study, the fine structure of raphides in Vitis was examined in order to determine the nature of twinning. Rotation of isolated raphides under cross-polarized light revealed extinction patterns that indicated that raphides are twinned along their length. In cross sections of raphides, the twin plane extends across the raphides, parallel to their surfaces. The dissolution patterns observed in etched crystals indicate that the type of twinning is rotational. Parallels in other biomineralization systems indicate that the rotational nature of the twinning may increase mechanical strength. In addition, because twinning may affect crystal growth or enhance stability and persistence of crystals, it could be an important factor in allowing plant cells to produce the raphide morphology.     

Orientation by helical motion—II. Changing the direction of the axis of motion

We analyse the helical motion of organisms, concentrating on the means by which organisms change the direction in space of the axis of the helical trajectory, which is the net direction of motion. We demonstrate that the direction of the axis is determined largely by the direction of the organism's rotational velocity. Changes in direction of the rotational velocity, with respect to the organism's body, change the direction in space of the axis of the helical trajectory. Conversely, changes in direction of the translational velocity, with respect to the body of the organism, have little effect on the direction in space of the axis of the trajectory. Because the axis of helical motion is the net direction of motion, it is likely that organisms that move in helices change direction by pointing their rotational velocity, not their translational velocity, in a new direction.     

Role of the Z band in the mechanical properties of the heart

In striated muscle the mechanism of contraction involves the cooperative movement of contractile and elastic components. This review emphasizes a structural approach that describes the cellular and extracellular components with known anatomical, biochemical, and physical properties that make them candidates for these contractile and elastic components. Classical models of contractile and elastic elements and their underlying assumptions are presented. Mechanical properties of cardiac and skeletal muscle are compared and contrasted and then related to ultrastructure. Information from these approaches leads to the conclusion that the Z band is essential for muscle contraction. Our review of Z band structure shows the Z band at the interface where extracellular components meet the cell surface. The Z band is also the interface from cell surface to myofibril, from extra-myofibrillar to myofibril, and finally from sarcomere to sarcomere. Our studies of Z band in defined physiologic states show that this lattice is an integral part of the contractile elements and can function as an elastic component. The Z band is a complex dynamic lattice uniquely suited to play several roles in muscle contraction.     

Sequence dependence of translational positioning of core nucleosomes

The basis for the choice of translational position of a histone octamer on DNA is poorly understood. To gain further insights into this question we have studied the translational and rotational settings of core particles assembled on a simple repeating 20 bp positioning sequence. We show that the translational positions of the core particles assembled on this sequence are invariant with respect to the DNA sequence and occur at 20 bp intervals. Certain modifications of the original sequence reduce the spacing of possible dyads to 10 bp. At least one of these alters both the translational and rotational settings. We conclude that the translational position of a core particle is specified by sequence determinants additional to those specifying rotational positioning. The rotational settings on either side of the dyads of core particles assembled on the wild-type and a mutant sequence differ by +2 bp, corresponding to an overall helical periodicity of approximately 10.15 bp. The average helical periodicity of the central two to four turns is 10.5-11 bp whilst that of the flanking DNA is closer to 10 bp. The DNA immediately flanking the dyad is also characterised by a more extensive susceptibility to cleavage by hydroxyl radical.     

Hydrodynamic properties of a double-helical model for DNA.

The translational and rotational diffusion coefficients of very short DNA fragments have been calculated using a double-helical bead model in which each nucleotide is represented by one bead. The radius of the helix is regarded as an adjustable parameter. The translational coefficient and the perpendicular rotation coefficient agree very well with experimental values for oligonuclotides with 8, 12, and 20 base pairs, for a single value of the helical radius of about 10 A. We have also calculated a nuclear magnetic resonance relaxation time in which the coefficient for rotation about the main axis is involved. As found previously with cylindrical models, the results deviate from experimental values, indicating that the internal motion of the bases has a remarkable amplitude. An attempt to quantify the extent of internal motions is presented.     

Contraction of protoplasm. IV. Cinematographic analysis of the contraction of some peritrichs

The contraction and relaxation of Vorticella difficilis, V. campanula and Carchesium sp. were studied by high speed cinematography. In Vorticella it was shown that coiling of the stalk usually started near the zooid and spread downwards; the point of initiation bore no relation to the position of the stimulating electrodes. Contraction took about 5 msec to complete, and the fully contracted animals were 29 ± 3.9% of their original lengths. The zooids were 66 ± 5.0% and the stalks 14 ± 6.0% of their original lengths (V. difficilis). The shortening of the stalk was mostly in the form of coiling. Measurement of the myoneme length demonstrated that its real shortening was less than 10%. Thus the contraction is virtually isometric, producing a helical deformation of the stalk. As the stalk contracts it takes the form of a steeply pitched helix. This change in shape should produce rotational forces on the zooid (torque). Physical models of similar proportions produced about 1.5 revolutions of torque for similar changes in pitch. However during contraction no turning of the zooid was detected, though rotation did occur after the completion of contraction. In Carchesium the contraction is not so isometric, the myoneme apparently shortening by 20%. While the coiled shape of the contracted Vorticella stalk can be explained by its acentric structures, the stalk of Carchesium is much more symmetrical in cross-section, demonstrating that a high acentricity is not necessary for helical coiling. In all three species there seems to be some separation of the control of zooid and stalk contraction.     

Atomistic simulation of dislocation interactions in a model crystal subjected to shear

The interaction of edge dislocations in a two-dimensional (2D) model crystal subjected to “simple shear” is studied using molecular statics simulations. An initial point defect is introduced in the model to trigger the dislocation activities in a controlled manner. We consider dislocations gliding towards one another on parallel slip planes separated by various distances. The overall load-displacement response of the crystal is obtained from the simulations, which can be correlated with the nano-scale atomistic mechanisms. Although the crystal is inherently anisotropic, the incipient dislocation plasticity is such that slip is parallel to the primary shear direction as clearly demonstrated in this work. It is also illustrated that dislocation annihilation, as well as dislocation encounter which leaves behind a point defect, can be unambiguously modeled. Throughout the deformation history, more dislocations capable of gliding in the crystal tend to generate a weaker mechanical response and more pronounced plasticity. The present study also offers mechanistic insight into experimentally observed small-scale crystal plasticity.     

The cell envelope of Thermoproteus tenax: three-dimensional structure of the surface layer and its role in shape maintenance

The sulphur-dependent archaebacterium Thermoproteus tenax has a cylindrical cell shape variable in length, but constant in diameter. Its whole surface is covered by a regular protein layer (S-layer). The lattice has p6 symmetry and a lattice constant of 32.8 nm. The three-dimensional reconstruction from a tilt series of isolated and negatively stained S-layer shows a complex mass distribution of the protein: a prominent, pillar-shaped protrusion is located at the 6-fold crystallographic axis with radiating arms connecting neighbouring hexamers in the vicinity of the 3-fold axis. The base vectors of the S-layer lattice have a preferred orientation with respect to the longitudinal axis of the cell. The layer can be seen as a helical structure consisting of a right-handed, two-stranded helix, with the individual chains running parallel. Supposing that new S-layer protein is inserted at lattice faults (wedge disclinations) near the poles, growing of the layer would then proceed by moving a disclination at the end of the helix. The constant shape of the cell, as well as the particular structure of the layer, strongly suggest that this S-layer has a shape-maintaining function.     

Solution dimensions of the gramicidin dimer by dynamic light scattering

Gramicidin is thought to form dimeric helical rods in alcohol solutions. In addition, there is evidence that the rod dimensions change upon addition of potassium ions. The present work reports values for the translational and rotational diffusion coefficients of gramicidin in methanol and 95% ethanol and in these same solvents with added KSCN. Solution dimensions are calculated from the diffusion coefficients. The results suggest that gramicidin exists primarily as dimers in these solutions and that the gramicidin rod does indeed become shorter upon addition of potassium ion. These results are consistent with those obtained from X-ray studies on single crystals grown from alcohol solutions.     

Analysis of mitochondrial 3D-deformation in cardiomyocytes during active contraction reveals passive structural anisotropy of orthogonal short axes

The cardiomyocyte cytoskeleton, composed of rigid and elastic elements, maintains the isolated cell in an elongated cylindrical shape with an elliptical cross-section, even during contraction-relaxation cycles. Cardiomyocyte mitochondria are micron-sized, fluid-filled passive spheres distributed throughout the cell in a crystal-like lattice, arranged in pairs sandwiched between the sarcomere contractile machinery, both longitudinally and radially. Their shape represents the extant 3-dimensional (3D) force-balance. We developed a novel method to examine mitochondrial 3D-deformation in response to contraction and relaxation to understand how dynamic forces are balanced inside cardiomyocytes. The variation in transmitted light intensity induced by the periodic lattice of myofilaments alternating with mitochondrial rows can be analyzed by Fourier transformation along a given cardiomyocyte axis to measure mitochondrial deformation along that axis. This technique enables precise detection of changes in dimension of ～1% in ～1 μm (long-axis) structures with 8 ms time-resolution. During active contraction (1 Hz stimulation), mitochondria deform along the length- and width-axes of the cell with similar deformation kinetics in both sarcomere and mitochondrial structures. However, significant deformation anisotropy (without hysteresis) was observed between the orthogonal short-axes (i.e., width and depth) of mitochondria during electrical stimulation. The same degree of deformation anisotropy was also found between the myocyte orthogonal short-axes during electrical stimulation. Therefore, the deformation of the mitochondria reflects the overall deformation of the cell, and the apparent stiffness and stress/strain characteristics of the cytoskeleton differ appreciably between the two cardiomyocyte orthogonal short-axes. This method may be applied to obtaining a better understanding of the dynamic force-balance inside cardiomyocytes and of changes in the spatial stiffness characteristics of the cytoskeleton that may accompany aging or pathological conditions.     

Direct visualization of spruce budworm antifreeze protein interacting with ice crystals: basal plane affinity confers hyperactivity

Antifreeze proteins (AFPs) protect certain organisms from freezing by adhering to ice crystals, thereby preventing their growth. All AFPs depress the nonequilibrium freezing temperature below the melting point; however AFPs from overwintering insects, such as the spruce budworm (sbw) are 10-100 times more effective than most fish AFPs. It has been proposed that the exceptional activity of these AFPs depends on their ability to prevent ice growth at the basal plane. To test the hypothesis that the hyperactivity of sbwAFP results from direct affinity to the basal plane, we fluorescently tagged sbwAFP and visualized it on the surface of ice crystals using fluorescence microscopy. SbwAFP accumulated at the six prism plane corners and the two basal planes of hexagonal ice crystals. In contrast, fluorescently tagged fish type III AFP did not adhere to the basal planes of a single-crystal ice hemisphere. When ice crystals were grown in the presence of a mixture of type III AFP and sbwAFP, a hybrid crystal shape was produced with sbwAFP bound to the basal planes of truncated bipyramidal crystals. These observations are consistent with the blockage of c-axial growth of ice as a result of direct interaction of sbwAFP with the basal planes.     

Cell contraction caused by microtubule disruption is accompanied by shape changes and an increased elasticity measured by scanning acoustic microscopy

The state of crosslinking of microfilaments and the state of myosin-driven contraction are the main determinants of the mechanical properties of the cell cortex underneath the membrane, which is significant for the mechanism of shaping cells. Therefore, any change in the contractile state of the actomyosin network would alter the mechanical properties and finally result in shape changes. The relationship of microtubules to the mechanical properties of cells is still obscure. The main problem arises because disruption of microtubules enhances acto-myosin-driven contraction. This reaction and its impact on cell shape and elasticity have been investigated in single XTH-2 cells. Microtubule disruption was induced by colcemid, a polymerization inhibitor. The reaction was biphasic: a change in cell shape from a fried egg shape to a convex surface topography was accompanied by an increase in elastic stiffness of the cytoplasm, measured as longitudinal sound velocity revealed by scanning acoustic microscope. Elasticity increases in the cell periphery and reaches its peak after 30 min. Subsequently while the cytoplasm retracts from the periphery, longitudinal sound velocity (elasticity) decreases. Simultaneously, a two- to threefold increase of F-actin and alignment of stress fibers from the cell center to cell-cell junctions in dense cultures are induced, supposedly a consequence of the increased tension.     

Tubular arrays of spheres: Geometry,continuous and discontinuous contraction,and the role of moving dislocations

Microtubules, bacterial flagella, viral capsids, and other biological structures are tubular packings of subunits. The subunits form helical rows or parastichies. Such arrays are modeled as tubular packings of spheres. Parastichies along which spheres are in contact provide a symbol for a particular tubule. A tubule with hexagonal packing and k-fold rotational symmetry about its axis has the symbol k(m; m + n; n) where km, k(m + n), and kn represent the three sets of contact parastichies. A tubule with rhombic packing has two sets of contact parastichies and the symbol k(m; n). The symbol determines the chirality. Two processes are described by which tubules can be interconverted: continuous contraction and discontinuous contraction. In continuous contraction of a hexagonally packed tubule, contacts along km-, k(m + n)-, or kn-parastichies are broken uniformly throughout the tubule. The tubule becomes rhombic and undergoes twisting and change of length and radius. Continuation of the process converts the intermediate rhombic packing into a new hexagonal packing. Any tubule can be converted to any other having the same rotational symmetry k, by one or more steps of continuous contraction, but not to a tubule with different k. With respect to change in length, continuous contraction from one hexagonal packing to another may be either monotonic or non-monotonic. A step of discontinuous contraction of a hexagonally packed tubule is mediated by passage of an edge dislocation through the tubule, by glide or climb. The presence of a single edge dislocation in a tubule divides it into two parts with two different packings. Passage of the dislocation to one end or the other of the tubule converts the entire tubule into one packing or the other. Any tubule may be converted to any other, regardless of k, by one or more steps of discontinuous contraction. Maps showing possible paths of continuous and discontinuous contraction summarize the relationships among tubules. The analysis will provide a useful basis for studying particular biological cases of contraction.     

The bacterial linear motor of Spiroplasma melliferum BC3: from single molecules to swimming cells

Spiroplasma melliferum BC3 are wall-less bacteria with internal cytoskeletons. Spiroplasma, Mycoplasma and Acholeplasma belong to the Mollicutes, which represent the smallest, simplest and minimal free-living and self-replicating forms of life. The Mollicutes are motile and chemotactic. Spiroplasma cells are, in addition, helical in shape. Based on data merging, obtained by video dark-field light microscopy of live, swimming helical Spiroplasma cells and by cryoelectron microscopy, unravelling the subcellular structure and molecular organization of the cytoskeleton, we propose a functional model in which the cytoskeleton also acts as a bacterial linear motor enabling and controlling both dynamic helicity and swimming. The cytoskeleton is a flat, monolayered ribbon constructed from seven contractile fibrils (generators) capable of changing their length differentially in a co-ordinated manner. The individual, flat, paired fibrils can be viewed as chains of tetramers approximately 100 A in diameter composed of 59 kDa monomers. The cytoskeletal ribbon is attached to the inner surface of the cell membrane (but is not an integral part of it) and follows the shortest helical line on the coiled cellular tube. We show that Spiroplasma cells can be regarded, at least in some states, as near-perfect dynamic helical tubes. Thus, the analysis of experimental data is reduced to a geometrical problem. The proposed model is based on simple structural elements and functional assumptions: rigid circular rings are threaded on a flexible, helical centreline. The rings maintain their circularity and normality to the centreline at all helical states. An array of peripheral, equidistant axial lines forms a regular cylindrical grid (membrane), by crossing the lines bounding the rings. The axial and peripheral spacing correspond to the tetramer diameter and fibril width (100 A) respectively. Based on electron microscopy data, we assign seven of the axial grid lines in the model to function as contractile generators. The generators are clustered along the shortest helical paths on the cellular coil. In the model, the shortest generator coincides with the shortest helical line. The rest, progressively longer, six generators follow to the right or to the left of the shortest generator in order to generate the maximal range of lengths. A rubbery membrane is stretched over (or represented by) the three-dimensional grid to form a continuous tube. Co-ordinated, differential length changes of the generators induce the membranal cylinder to coil and uncoil reversibly. The switch of helical sense requires equalization of the generators' length, forming a straight cylindrical tube with straight generators. The helical parameters of the cell population, obtained by light microscopy, constitute several subpopulations related, most probably, to cell size and age. The range of molecular dimensions in the active cytoskeleton inferred from light microscopy and modelling agrees with data obtained by direct measurements of subunit images on electron micrographs, scanning transmission electron microscopy (STEM) and diffraction analysis of isolated ribbons. Swimming motility and chemotactic responses are carried out by one or a combination of the following: (i). reciprocating helical extension and compression ('breathing'); (ii). propagation of a deformation (kink) along the helical path; (iii). propagation of a reversal of the helical sense along the cell body; and (iv). irregular flexing and twitching, which is functionally equivalent to standard bacterial tumbling. Here, we analyse in detail only the first case (from which all the rest are derived), including switching of the helical sense.     

The effects of orientation, temperature, and displacement magnitude changes on the sonometrics system accuracy

The accuracy and reliability of a sonomicrometry system (Sonometrics Corporation, Ontario, Canada) was evaluated for its potential use in measuring 3-D in vivo joint kinematics. Distances between different sets of piezoelectric crystals were measured through a salt solution using ultrasound technology. We evaluated crystal-to-crystal distance under simulated in vivo conditions of changing crystal orientation and displacement magnitude. Crystal-to-crystal distance was also evaluated under changing solution temperature, since the crystals may be used at different temperatures. The 2 mm round and peg crystals were accurate to within 0.5mm for 0 through 180 degrees rotations, but the 2mm round suture loop crystals were only reliable at 0 degrees rotation. The speed of sound through a salt solution (and hence the distance between crystals) versus temperature was fit using a second order polynomial, C=1421.1+3.9808T-3.09x10(-2)T2, with an R2 value of 0.9998. The translational error was less than 0.072 mm for crystal displacements of 0.012, 0.2, 1.0, and 5.0 mm. The system was also accurate under dynamic conditions with translational errors that were less than 0.045 mm under 0.65 Hz motion. These results suggest that the Sonometrics crystals possess attributes (translational accuracy and rotational independence) that could provide the basis for a system capable of measuring joint kinematics.     

A test of improved force field parameters for urea: molecular-dynamics simulations of urea crystals

Molecular-dynamics (MD) simulations of urea crystals of different shapes (cubic, rectangular prismatic, and sheet) have been performed using our previously published force field for urea. This force field has been validated by calculating values for the cohesive energy, sublimation temperature, and melting point from the MD data. The cohesive energies computed from simulations of cubic and rectangular prismatic urea crystals in vacuo at 300 K agreed very well with the experimental sublimation enthalpies reported at 298 K. We also found very good agreement between the melting points as observed experimentally and from simulations. Annealing the crystals just below the melting point leads to reconstruction to form crystal faces that are consistent with experimental observations. The simulations reveal a melting mechanism that involves surface (corner/edge) melting well below the melting point, and rotational disordering of the urea molecules in the corner/edge regions of the crystal, which then facilitates the translational motion of these molecules.     

Interaction between cell shape and contraction pattern in the Physarum plasmodium

The relationship between cell shape and rhythmic contractile activity in the large amoeboid organism Physarum polycephalum was studied. The organism develops intricate networks of veins in which protoplasmic sol moved to and fro very regularly. When migrating on plain agar, the plasmodium extends like a sheet and develops dendritic veins toward the rear. After a particular stimulation, the vein organization changes into veinless or vein-network structures. In both structures, the mixing rate of the protoplasm, which is related to communication among contraction oscillators, decreased compared with that of the dendritic one. Accompanying these changes in vein structure, the spatio-temporal pattern of the rhythmic contraction changed into a small-structured pattern from a synchronized one. In the above process, cell shape affects the contraction pattern, but, conversely, the contraction pattern effects the cell shape. To demonstrate this, a phase difference in the rhythmic contraction was induced artificially by entraining the intrinsic rhythm to external temperature oscillations. New veins then formed along the direction parallel to the phase difference of the rhythm. Consequently, the vein organization of the cell interacts with the contractile activity to form a feedback loop in a mechanism of contraction pattern formation.