Crystalline structure of the gas vesicle wall from Anabaena flos-aquae.

The gas vesicles isolated from Anabaena flos-aquae have been studied by X-ray diffraction. Electron microscopy has previously shown that the gas vesicles are elongated shapes, with a thin wall having regular striations (ribs) at right-angles to the long axis. The X-ray diffraction pattern from a specimen of oriented, intact vesicles includes a number of sharp reflections which are attributed to regular structure in the plane of the wall. After correcting for the imperfect alignment of the long axes of the vesicles, the in-plane reflections are all seen to lie on a few, regularly spaced lines parallel to the long axis. This result shows for the first time that there are subunits regularly spaced along each rib, one subunit every 11 Å. The spacing of the in-plane reflections along each line is consistent with a rib periodicity of 46 Å. The 11 Å repeat, together with the 46 Å repeating distance from rib to rib and the average wall thickness of about 20 Å, define a volume for the subunit. Assuming a reasonable value for the density of the protein making up the wall, the molecular weight of the subunit indicated is about 8000 g/mol.The X-ray data also indicate that a large part of the protein is in the β-sheet conformation. In this structure there are parallel, or anti-parallel, polypeptide chains which are hydrogen-bonded to one another in a regular way to form a thin sheet. Assuming the wall contains β-sheet in two layers, one on top of the other and with the chains in each layer tilted at 35 ° to the long axis of the vesicle, we can explain a number of the X-ray observations: (1) oriented arcs with a Bragg spacing of 4.7 Å, which is the distance between the axes of neighbouring chains in each layer; (2) diffraction oriented in the direction of the chains at a spacing of 6 to 7 Å, which is the repeating distance of the dipeptide unit along the chain; (3) the 11 Å repeat, which is the repeating distance of pairs of chains along each rib; and (4) a broad band of diffraction at right-angles to the plane of the wall and centred at a spacing of 10 Å, which is a reasonable value for the distance between the mid-planes of the two sheets. Moreover, we can also find the remaining lattice parameter, the angle relating the centres of the subunits in neighbouring ribs. Thus the shortest line joining the centres makes an angle of 86 ° with the direction of the ribs.     

An analysis of possible movements of human upper rib cage

A geometrically realistic mathematical model of the first six ribs and vertebrae of the human rib cage is described. Under the assumption that the individual elements of the rib cage do not deform significantly, the possible range of movements of the model are determined subject to the constraint that the joint surfaces remain in contact. It is shown that normal movements of the ribs cannot be described as a rotation about a single fixed axis. The possible movements of the ribs are analyzed in terms of the misfit incurred at the costovertebral joint surfaces. This analysis shows that there is a movement, corresponding to lateral expansion of the rib for an increase in anteroposterior diameter, in which the misfit at the joint is minimized and also that small deviations from this movement involve only very small degrees of misfit at the joint surfaces. It is concluded that many observed "deformations" of the chest wall can be explained by rigid ribs and normal movements at the costovertebral joints. The interaction between the ribs and the spine is analyzed. It is shown that there can be considerable independent movement of the sternum and the spine, thus allowing mobility of the spine without forcing concomitant movements of rib cage.     

Molecular weight of gas-vesicle protein from the planktonic cyanobacterium Anabaena flos-aquae and implications for structure of the vesicle

The gas vesicle of the planktonic cyanobacterium Anabaena flos-aquae is a cylindrical shell made of protein enclosing a gas-filled space. Protein sequence analysis shows that the vesicle is made from a single protein. By gel electrophoresis and amino acid analysis its molecular weight was estimated to be 20 600. Taken with previously obtained X-ray data, a simple interpretation of its molecular structure is of the polypeptide snaking in six pairs of antiparallel chains, three in each layer. The molecule would repeat along the ribs of the vesicle at intervals of 3.4 nm.     

Gas vesicles.

The gas vesicle is a hollow structure made of protein. It usually has the form of a cylindrical tube closed by conical end caps. Gas vesicles occur in five phyla of the Bacteria and two groups of the Archaea, but they are mostly restricted to planktonic microorganisms, in which they provide buoyancy. By regulating their relative gas vesicle content aquatic microbes are able to perform vertical migrations. In slowly growing organisms such movements are made more efficiently than by swimming with flagella. The gas vesicle is impermeable to liquid water, but it is highly permeable to gases and is normally filled with air. It is a rigid structure of low compressibility, but it collapses flat under a certain critical pressure and buoyancy is then lost. Gas vesicles in different organisms vary in width, from 45 to > 200 nm; in accordance with engineering principles the narrower ones are stronger (have higher critical pressures) than wide ones, but they contain less gas space per wall volume and are therefore less efficient at providing buoyancy. A survey of gas-vacuolate cyanobacteria reveals that there has been natural selection for gas vesicles of the maximum width permitted by the pressure encountered in the natural environment, which is mainly determined by cell turgor pressure and water depth. Gas vesicle width is genetically determined, perhaps through the amino acid sequence of one of the constituent proteins. Up to 14 genes have been implicated in gas vesicle production, but so far the products of only two have been shown to be present in the gas vesicle: GvpA makes the ribs that form the structure, and GvpC binds to the outside of the ribs and stiffens the structure against collapse. The evolution of the gas vesicle is discussed in relation to the homologies of these proteins.     

Gas vesicles.

The gas vesicle is a hollow structure made of protein. It usually has the form of a cylindrical tube closed by conical end caps. Gas vesicles occur in five phyla of the Bacteria and two groups of the Archaea, but they are mostly restricted to planktonic microorganisms, in which they provide buoyancy. By regulating their relative gas vesicle content aquatic microbes are able to perform vertical migrations. In slowly growing organisms such movements are made more efficiently than by swimming with flagella. The gas vesicle is impermeable to liquid water, but it is highly permeable to gases and is normally filled with air. It is a rigid structure of low compressibility, but it collapses flat under a certain critical pressure and buoyancy is then lost. Gas vesicles in different organisms vary in width, from 45 to > 200 nm; in accordance with engineering principles the narrower ones are stronger (have higher critical pressures) than wide ones, but they contain less gas space per wall volume and are therefore less efficient at providing buoyancy. A survey of gas-vacuolate cyanobacteria reveals that there has been natural selection for gas vesicles of the maximum width permitted by the pressure encountered in the natural environment, which is mainly determined by cell turgor pressure and water depth. Gas vesicle width is genetically determined, perhaps through the amino acid sequence of one of the constituent proteins. Up to 14 genes have been implicated in gas vesicle production, but so far the products of only two have been shown to be present in the gas vesicle: GvpA makes the ribs that form the structure, and GvpC binds to the outside of the ribs and stiffens the structure against collapse. The evolution of the gas vesicle is discussed in relation to the homologies of these proteins.     

Geometry and kinematics of dog ribs

Five anesthetized supine beagle dogs were scanned using a fast, multislice computed tomographic X-ray technique to determine the orientation of the ribs at total lung capacity (TLC) and functional residual capacity (FRC). A plane was fit to each rib using a coordinate system in which the z-axis was aligned approximately cephalocaudally and the x-z-plane coincided with the sagittal midplane. The orientation of each plane was described by "pump-handle" and "bucket-handle" angles. The ribs rotated downward and inward during a passive deflation of the lungs from TLC to FRC. Rib displacement was not uniform: bucket-handle motion was predominant in the upper ribs, and pump- and bucket-handle motions were equal in the lower ribs. The change in the pump-handle angles between TLC and FRC was approximately 6 degrees for ribs 3-8, and the change in the bucket-handle angles decreased with rib number from 16 degrees for rib 3 to 6 degrees for rib 8. Rib shape was described by fitting an ellipse to the data for each rib; the ribs became larger and more circular with increasing rib number.     

Geometry and respiratory displacement of human ribs

The three-dimensional coordinates of points in the ribs of two supine relaxed males, holding their breath at functional residual capacity (FRC) and with their glottis closed at total lung capacity (TLC), were obtained from volumetric X-ray computed tomographical images. The orientation of planes that best fit the data for each rib at each lung volume and the circular arcs that fit the points in the planes of the ribs were determined, and average values of these geometrical parameters for ribs 3-7 are reported. The planes of the ribs at TLC can be described as displaced from the planes at FRC by a rotation about an axis that passes near the spine. The pump handle and bucket handle components of rotation are 11 and 13 degrees, respectively, for rib 3 and both decrease with increasing rib number to 7 and 10 degrees at rib 7. The angles between the axes of rotation and the midplane are approximately 35 degrees for all 5 ribs. The radii of the circular arcs fit to the data at TLC are slightly larger than those at FRC, and this suggests that there is a small component of rotation normal to the plane of the rib.     

Conical tomography II: A method for the study of cellular organelles in thin sections

We have used conical electron tomography in order to reconstruct neuronal organelles in thin sections of plastic embedded rat somato-sensory cortical tissue. The conical tilt series were collected at a 55 degrees tilt and at 5 degrees rotations, aligned using gold particles as fiduciary markers, and reconstructed using the weighted back projection algorithm. After a refinement process based on projection matching, the 3D maps showed the "unit membrane pattern" along the entire reconstructed volume. This pattern is indicative of the bilayer arrangement of phospholipids in biological membranes. Based on Fourier correlation methods as well as the visualization of the "unit membrane" pattern, we estimated resolutions of approximately 4 nm. To illustrate the prospective advantages of conical tomography, we segmented "coated" vesicles in the reconstructed volumes. These vesicles were comprised of a central core enclosing a small lumen, and a protein "coating" extending into the cytoplasm. The "coated" vesicle was attached to the plasma membrane through a complex structure shaped as an arch where the ends are attached to the membrane and the crook is connected to the vesicle. We concluded that conical electron tomography of thin-sectioned specimens provides a powerful experimental approach for studying thin-sectioned neuronal organelles at resolution levels of approximately 4 nm.     

Adaptive modeling of the human rib cage in median sternotomy

This paper describes a limited computer-analyzed kinematic model of the rib cage that can be adapted to individual subjects. Also described is its validation and use in assessing the changes in chest wall shape after coronary artery bypass graft (CABG) surgery in 12 patients. The positions of a small number of anatomic locations on the thoracic spine, ribs, manubrium, and sternum are measured from lateral and posterior-anterior chest radiographs. The computer program puts these two views together removing the magnification and reconstructs any missing points to give a three-dimensional picture of the rib cage to which mathematical models of the bones are scaled. The patients had chest radiographs taken at total lung capacity (TLC) and residual volume (RV) to investigate the source of the restrictive ventilatory defect that follows CABG. The predictions from the model were tested by comparing full-sized computer plots with the actual chest radiographs. The estimates of the bony structures were accurate to +/- 3 degrees for orientations and +/- 6 mm for positions. We found reduced rib motion both "pump-handle" (theta) and "bucket handle" (psi) going from theta, psi left, psi right = 9 degrees, 10 degrees, 14 degrees to 4 degrees, 10 degrees, 9 degrees, respectively, after surgery with P less than 0.025, 0.42, 0.07. The angles were measured from the horizontal and increased caudally. There was also reduction in the range of angles subtended by the arc of the thoracic vertebrae between TLC and RV, which went from 12 degrees to -1 degrees (P less than 0.015). These data explain the fall in lung volumes that follow CABG and provide insight into the contribution made by the ribs and spine in full inspiration and full expiration.     

Analysis of the intrinsic bend in the M13 origin of replication by atomic force microscopy

Atomic force microscopy (AFM) has been used to image a 471-bp bent DNA restriction fragment derived from the M13 origin of replication in plasmid LITMUS 28, and a 476-bp normal, unbent fragment from plasmid pUC19. The most probable angle of curvature of the 471-bp DNA fragment is 40-50 degrees, in reasonably good agreement with the bend angle determined by transient electric birefringence, 38 degrees +/- 7 degrees. The normal 476-bp DNA fragment exhibited a Gaussian distribution of bend angles centered at 0 degrees, indicating that this fragment does not contain an intrinsic bend. The persistence length, P, was estimated to be 60 +/- 8 and 62 +/- 8 nm for the 471- and 476-bp fragments, respectively, from the observed mean-square end-to-end distances in the AFM images. Since the P-values of the normal and bent fragments are close to each other, the overall flexibility of DNA fragments of this size is only marginally affected by the presence of a stable bend. The close agreement of AFM and transient electric birefringence results validates the suitability of both methods for characterizing DNA bending and flexibility.     

Chromatin fibers are left-handed double helices with diameter and mass per unit length that depend on linker length

Four classes of models have been proposed for the internal structure of eukaryotic chromosome fibers--the solenoid, twisted-ribbon, crossed-linker, and superbead models. We have collected electron image and x-ray scattering data from nuclei, and isolated chromatin fibers of seven different tissues to distinguish between these models. The fiber diameters are related to the linker lengths by the equation: D(N) = 19.3 + 0.23 N, where D(N) is the external diameter (nm) and N is the linker length (base pairs). The number of nucleosomes per unit length of the fibers is also related to linker length. Detailed studies were done on the highly regular chromatin from erythrocytes of Necturus (mud puppy) and sperm of Thyone (sea cucumber). Necturus chromatin fibers (N = 48 bp) have diameters of 31 nm and have 7.5 +/- 1 nucleosomes per 10 nm along the axis. Thyone chromatin fibers (N = 87 bp) have diameters of 39 nm and have 12 +/- 2 nucleosomes per 10 nm along the axis. Fourier transforms of electron micrographs of Necturus fibers showed left-handed helical symmetry with a pitch of 25.8 +/- 0.8 nm and pitch angle of 32 +/- 3 degrees, consistent with a double helix. Comparable conclusions were drawn from the Thyone data. The data do not support the solenoid, twisted-ribbon, or supranucleosomal particle models. The data do support two crossed-linker models having left-handed double-helical symmetry and conserved nucleosome interactions.     

The tetrameric form of ribosomal protein L7/L12 from Escherichia coli

A tetrameric form of the ribosomal protein L7/L12 has been prepared and its structure studied by using hydrodynamic methods, photon correlation spectroscopy, and small angle x-ray scattering. The tetrameric nature of the protein preparation is confirmed by three independent determinations of its molecular weight, with analysis of accurate sedimentation equilibrium data giving the most reliable estimate. The species has a Stokes radius of 4.0 +/- 0.1 nm and an absolute frictional ratio of 1.7. Taken together, the hydrodynamic measurements suggest the possibility of a flat structure, and this is consistent with the x-ray scattering results. The molecule has a radius of gyration of 3.6 +/- 0.05 nm and a maximum dimension of 11-12 nm. A geometric model consisting of four elongated monomers, arranged in a plane, is proposed.     

A model for studies of the deformable rib cage.

An earlier model for the study of rib cage mechanics was modified so that rib deformity in scoliosis could be better represented. The rigid ribs of that model were replaced by five-segment deformable ribs. Literature data on cadaver rib mechanical behavior were used to assign stiffnesses to the new individual model ribs so that experimental and model rib deflections agreed. Shear and tension/compression stiffnesses had little effect on individual rib deformation, but bending stiffnesses had a major effect. Level-to-level differences in mechanical behavior could be explained almost exclusively by level to level differences in the rib shape. The model ribs were then assembled into a whole rib cage. Computer simulations of whole rib cage behaviors, both in vivo and in vitro, showed a reasonable agreement with the measured behaviors. The model was used to study rib cage mechanics in two scolioses, one with a 43 degrees and the other with a 70 degrees Cobb angle. Scoliotic rib cage deformities were quantified by parameters measuring the rib cage lateral offset, rib cage axial rotation, rib cage volume and rib distortion. Rib distortion was quantified both in best-fit and simulated computer tomography (CT) scan planes. Model rib distortion was much smaller in best-fit planes than in CT planes. The total rib cage volume changed little in the presence of the scolioses, but it became asymmetrically distributed.     

AFM for structure and dynamics of biomembranes

We review structure and dynamic measurements of biomembranes by atomic force microscopy (AFM). We focus mainly on studies involving supported lipid bilayers (SLBs), particularly formation by vesicle rupture on flat and corrugated surfaces, nucleation and growth of domains in phase-separated systems, anesthetic-lipid interactions, and protein/peptide interactions in multicomponent systems. We show that carefully designed experiments along with real-time AFM imaging with superior lateral and z resolution (0.1 nm) have revealed quantitative details of the mechanisms and factors controlling vesicle rupture, domain shape and size, phase transformations, and some model biological interactions. The AFM tip can also be used as a mechanical transducer and incorporated in electrochemical measurements of membrane components; therefore, we touch on these important applications in both model and cell membranes.     

X-ray diffraction evidence for the existence of 102.0- and 230.0-nm transverse periodicities in striated muscle

Synchrotron radiation techniques have enabled us to record meridional x-ray diffraction patterns from frog sartorius muscle at resolutions ranging from approximately 2,800 to 38 nm (i.e., overlapping with the optical microscope and the region normally accessible with low angle diffraction cameras). These diffraction patterns represent the transform of the low resolution structure of muscle projected on the sarcomere axis and sampled by its repeat. Altering the sarcomere length results in the sampling of different parts of this transform, which induces changes in the positions and the integrated intensities of the diffraction maxima. This effect has been used to determine the transform of the mass projection on the muscle axis in a quasicontinuous fashion. The results reveal the existence of maxima arising from long-range periodicities in the structure. Determination of the zeroes in the transforms has been used to obtain phase information from which electron density maps have been calculated. The x-ray diffraction diagrams and the resulting electron density maps show the existence of a series of mass bands, disposed transversely to the sarcomere axis and distributed at regular intervals. A set of these transverse structures is associated with thin filaments, and their 102.0-nm repeat suggests a close structural relationship with their known molecular components. A second set, spaced by approximately 230.0 nm, is also present; from diffraction theory one has to conclude that this repeat simultaneously exists in thick and thin filament regions.     

AFM for structure and dynamics of biomembranes

We review structure and dynamic measurements of biomembranes by atomic force microscopy (AFM). We focus mainly on studies involving supported lipid bilayers (SLBs), particularly formation by vesicle rupture on flat and corrugated surfaces, nucleation and growth of domains in phase-separated systems, anesthetic-lipid interactions, and protein/peptide interactions in multicomponent systems. We show that carefully designed experiments along with real-time AFM imaging with superior lateral and z resolution (0.1 nm) have revealed quantitative details of the mechanisms and factors controlling vesicle rupture, domain shape and size, phase transformations, and some model biological interactions. The AFM tip can also be used as a mechanical transducer and incorporated in electrochemical measurements of membrane components; therefore, we touch on these important applications in both model and cell membranes.     

Crystallization of Acanthamoeba profilin-I

Profilin-I, a protein that inhibits actin polymerization in Acanthamoeba castellanii, has been crystallized in a form suitable for high resolution x-ray analysis. The crystals have the symmetry of the space group C2 with lattice constants a = 110.4 +/- 0.2, b = 31.7 +/- 0.1, c = 33.5 +/- 0.1 A, beta = 112.2 degrees. They diffract to at least 2.0-A resolution. The asymmetric unit contains one 12,800-dalton monomer of profilin-I.     

Projection structure of P-glycoprotein by electron microscopy. Evidence for a closed conformation of the nucleotide binding domains

The structure of P-glycoprotein (Pgp) from mouse has been studied by electron microscopy and image analysis. Two-dimensional crystals of Pgp in a lipid bilayer were generated by reconstituting pure, detergent-solubilized protein containing a C-terminal six-histidine tag using the lipid monolayer technique. The crystals belong to plane group P1 with a = b = 104 +/- 2 A and gamma = 90 +/- 4 degrees. The projection structure of Pgp calculated at a resolution of 22 A shows two closely interacting protein domains that can be interpreted as the N- and C-terminal halves of the protein. The projection structure of Pgp is consistent with the recently published x-ray structure of MsbA, a lipid A flippase from Escherichia coli with high sequence homology to Pgp but only when the two MsbA subunits are rotated to bring their nucleotide binding domains together.     

Sensitivity of the knee joint kinematics calculation to selection of flexion axes

Various flexion axes have been used in the literature to describe knee joint kinematics. This study measured the passive knee kinematics of six cadaveric human knee specimens using two widely accepted flexion axes; transepicondylar axis and the geometric center axis. These two axes were found to form an angle of 4.0 degrees +/- 0.8 degrees. The tibial rotation calculated using the transepicondylar axis was significantly different than the rotation obtained using the geometric center axis for the same knee motion. At 90 degrees of flexion, the tibial rotation obtained using the transepicondylar axis was 4.8 degrees +/- 9.4 degrees whereas the rotation recorded using the geometric center axis at the same flexion angle was 13.8 degrees +/- 10.2 degrees. At 150 degrees of knee flexion, the rotations obtained from the transepicondylar and the geometric center axes were 7.2 degrees +/- 5.7 degrees and 19.9 degrees +/- 6.9 degrees, respectively. The data suggest that a clear definition of the flexion axis is necessary when reporting knee joint kinematics.     

GvpCs with reduced numbers of repeating sequence elements bind to and strengthen cyanobacterial gas vesicles

We have previously shown that the gas-vesicle protein GvpC is present on the outer surface of the gas vesicle, can be reversibly removed and rebound to the surface, and increases the critical collapse pressure of the gas vesicle. The GvpC molecule, which contains five partially conserved repeats of 33 amino acids (33-RR) sandwiched between 18 N-terminal and 10 C-terminal amino acids, is present in a ratio of 1:25 with the GvpA molecule, which forms the ribs of the gas vesicle. By using recombinant techniques we have now made modified versions of GvpC that contain only the first two, three or four of the 33-amino-acid repeats. All of these proteins bind to and strengthen gas vesicles that have been stripped of their native GvpC. Recombinant proteins containing three or four repeats bind in amounts that give the same ratio of 33-RR:GvpA (i.e. 1:5) as the native protein, and they restore much of the strength of the gas vesicle; the protein containing only two repeats binds at a lower ratio (1:7.7), however, and restores less of the strength. Ancestral proteins with only two, three or four of the 33-amino-acid repeats would have been functional in strengthening the gas vesicle but the progressive increase in number of repeats would have provided strength with increased efficiency.