The restoration of electron micrographs blurred by drift and rotation

We have investigated the restoration of electron micrographs exhibiting blurring due to drift and rotation. Blurring due to drift arises in micrographs taken of a specimen which is moving relative to the image plane. A related problem is that of rotational blurring which arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. Restoration algorithms were evaluated by applying them to the restoration of blurred model images degraded by additive Gaussian noise. Model images were also used to investigate how an incorrect estimate of the point spread function describing the blur would effect the restoration. Images were, if necessary, geometrically transformed to a space in which the point spread function of the blur can be considered as linear and space invariant as, under these conditions, the restoration algorithms are greatly simplified. In the case of the rotationally blurred images this procedure was accomplished by transforming the image to polar coordinates. The restoration techniques were successfully applied to blurred micrographs of bacteriophage T4 and crystals of catalase. The quality of the restoration was judged by comparisons of the restored images to undegraded images. Application to micrographs of rotationally blurred cross sections of helical macrofibers of sickle hemoglobin resulted in a reduction in the amount of rotational blurring.     

On the assembly of sickle hemoglobin fascicles

Deoxyhemoglobin S fibers associate into bundles, or fascicles, that subsequently crystallize by a process of alignment and fusion. We have used electron microscopy to study the formation of fascicles and the changes in fiber packing that occur during the conversion of fascicles to crystals. The first event in crystallization involves fibers forming fascicles that are initially small and poorly ordered but, with time, become progressively larger and more highly ordered. After six to eight hours, the fibers in a fascicle form a crystalline lattice. The three-dimensional unit cell parameters of this lattice are a = 1300 A, b = 365 A, and c = 210 A (the a axis is parallel to the fiber axis). Fibers have an elliptical cross-section whose major and minor axes are 250 A and 185 A, respectively. When projected on to the unit cell vectors, these dimensions are 210 A and 155 A, so the unit cell dimension of 365 A implies that there are two fibers per unit cell. Theoretically, fibers could pair so that each member of the unit cell is oriented in the same direction (parallel) or opposite directions (antiparallel). Fourier transforms of electron micrographs (or models) cannot distinguish between these alternatives, since the two arrangements produce very similar intensity distributions. The orientation of the fibers was determined from cross-sections of the fascicles in which the fibers are seen end-on. In this view the images of the fibers are rotationally blurred because the fibers twist 30 degrees to 40 degrees about their helical axis through the 300 A to 400 A thick section. We have been able to remove the rotational blur from each of the fibers in the unit cell using the procedures described by Carragher et al. The deblurred images of the two fibers in the unit cell are related by mirror symmetry. This relationship means that the fibers are antiparallel. These observations suggest that crystallization of fibers in fascicles is mediated by assembly of the fibers into antiparallel pairs that contain equal numbers of double strands running in each direction.     

Artificial neural networks for blur identification and restoration of nonlinearly degraded images.

In this paper, an image restoration algorithm is proposed to identify noncausal blur function. Image degradation processes include both linear and nonlinear phenomena. A neural network model combining an adaptive auto-associative network with a random Gaussian process is proposed to restore the blurred image and blur function simultaneously. The noisy and blurred images are modeled as continuous associative networks, whereas auto-associative part determines the image model coefficients and the hetero-associative part determines the blur function of the system. The self-organization like structure provides the potential solution of the blind image restoration problem. The estimation and restoration are implemented by using an iterative gradient based algorithm to minimize the error function.     

Three-dimensional reconstruction of the 14-filament fibers of hemoglobin S.

The supramolocular structure of hemoglobin S has been studied by electron microscopy and computer-based image reconstruction. Negatively stained fibers prepared by the lysis of sickled cells or the stirring of hemoglobin S hemolysates have been observed to be almost exclusively of the 20-nm diameter form. These fibers have a periodic variation in diameter between the extremes of 18 nm and 23 nm. Computed Fourier transforms of the fibers show a, highly complex pattern of reciprocal space maxima, with 30 maxima on 20 layer-lines clearly resolved. The Bessel orders of the maxima were assigned with the aid of a newly developed technique, a combined real-space Fourier-space reconstruction method (REFORM). This method utilizes the filtered image produced by the inverse Fourier transform of the low-resolution maxima to calculate in real space the crosssection of a helical fiber. The REFORM analysis indicated that the fibers have an elliptical cross-section and are composed of 14 hexagonally packed filaments with 10 outer filaments surrounding four inner filaments. On the basis of this cross-section, the Bessel orders of all the maxima were assigned, permitting the calculation of three-dimensional reconstructions by Fourier Bessel synthesis. From these reconstructions details of the location of hemoglobin S molecules of each filament were obtained. Hemoglobin S molecules are staggered in adjacent filaments to produce a closely packed helical structure. Reconstructions of fibers at various stages of disassembly revealed a stable intermediate containing 10 filaments which could be characterized in terms of the loss of two pairs of specific outer filaments. A partially disassembled fiber with only six filaments at positions corresponding to three inner and three outer filaments of the parent structure was also identified. The six-filament structure appears to be produced from the 10-filament structure by the loss of two specific pairs of filaments. Thus pairs of filaments are evidently significant structural units in the stabilization of the complete fibers and the orientation of the molecules in these pairs may be related to the filament pairs known to occur in crystals of hemoglobin S.     

Structural analysis of polymers of sickle cell hemoglobin. II. Sickle hemoglobin macrofibers

Sickle cell hemoglobin macrofibers are an important intermediate in the low pH crystallization pathway of deoxygenated hemoglobin S that link the fiber to the crystal. Macrofibers are a class of helical particles differing primarily in their diameters but are related by a common packing of their constituent subunits. We have performed three-dimensional reconstructions of three types of macrofibers. These reconstructions show that macrofibers are composed of rows of Wishner-Love double strands in an arrangement similar to that in the crystal. We have measured the orientation and co-ordinates of double strands in macrofibers using cross-correlation techniques. In this approach, the electron density projections of double strands calculated from the known high-resolution crystal structure are compared with regions along the length of the particles in which the distinct pattern of double strands in c-axis projection may be observed. Contrary to assertions by Makinen & Sigountos (1984), our results unambigously demonstrate that adjacent rows of double strands in macrofibers are oriented in an antiparallel manner, as in the Wishner-Love crystal. Adjacent rows of antiparallel double strands are displaced along the helical axis relative to their co-ordinates in the crystal. Electron density models of macrofibers based on the crystallographic structure of the sickle hemoglobin double strand are in good agreement with the projections of macrofibers observed in electron micrographs. We have studied the structure of a closely related crystallization intermediate, the sickle hemoglobin paracrystal. The arrangement of double strands in paracrystals is similar to that in Wishner-Love crystals, except that they are displaced along the a-axis of the crystal. Measurements of the double strand co-ordinates reveal that the distribution of strand positions is bimodal. These results further establish the close structural relationship between macrofibers and paracrystals as intermediates in the crystallization of deoxygenated sickle hemoglobin.     

Crystallization of deoxyhemoglobin S by fiber alignment and fusion.

Fibers of deoxyhemoglobin S obtained directly from lysed sickled red blood cells have been compared with fibers from chromatographically pure deoxyhemoglobin S solutions of known chemical composition. Electron micrographs of negatively stained specimens reveal that the molecular packing within the fibers remains largely invariant with changes in pH, ionic strength, Mg²⁺ concentration, 2,3-diphosphoglycerate concentration, temperature or the method of deoxygenation.When solutions of chromatographically pure deoxyhemoglobin S are stirred, the fibers align into well defined fascicles. After several hours of stirring, long needles and twisted ribbons develop and in a relatively short time replace the fascicles in solution. With continued stirring all forms are replaced by small crystals. By use of electron microscopy and low-angle X-ray diffraction we have found these crystals to have cell parameters indistinguishable from those of crystals grown in polyethylene glycol and citrate/phosphate buffer at pH 5 to 6 (Wishner et al., 1975a).Our evidence indicates that crystal formation in stirred solutions of deoxyhemoglobin S is the result of a progressive alignment and fusion of the fibers, and that the molecular arrangement within the fibers is closely related to that within the crystal. The remarkable pH invariance of the molecular packing within the fiber and crystal structures is consistent with the dominance of hydrophobic bonding between molecules. The β6-valine contact observed by Wishner et al. (1975b) is apparently the pathological contact responsible for the polymerization of deoxyhemoglobin S in vivo. On the basis of our observations and knowledge of the crystal structure we propose that the deoxyhemoglobin S fiber consists of eight molecular double strands, four of which run in each direction along the length of the fiber.     

Neural adjustments to chromatic blur

The perception of blur in images can be strongly affected by prior adaptation to blurry images or by spatial induction from blurred surrounds. These contextual effects may play a role in calibrating visual responses for the spatial structure of luminance variations in images. We asked whether similar adjustments might also calibrate the visual system for spatial variations in color. Observers adjusted the amplitude spectra of luminance or chromatic images until they appeared correctly focused, and repeated these measurements either before or after adaptation to blurred or sharpened images or in the presence of blurred or sharpened surrounds. Prior adaptation induced large and distinct changes in perceived focus for both luminance and chromatic patterns, suggesting that luminance and chromatic mechanisms are both able to adjust to changes in the level of blur. However, judgments of focus were more variable for color, and unlike luminance there was little effect of surrounding spatial context on perceived blur. In additional measurements we explored the effects of adaptation on threshold contrast sensitivity for luminance and color. Adaptation to filtered noise with a 1/f spectrum characteristic of natural images strongly and selectively elevated thresholds at low spatial frequencies for both luminance and color, thus transforming the chromatic contrast sensitivity function from lowpass to nearly bandpass. These threshold changes were found to reflect interactions between different spatial scales that bias sensitivity against the lowest spatial grain in the image, and may reflect adaptation to different stimulus attributes than the attributes underlying judgments of image focus. Our results suggest that spatial sensitivity for variations in color can be strongly shaped by adaptation to the spatial structure of the stimulus, but point to dissociations in these visual adjustments both between luminance and color and different measures of spatial sensitivity.     

Blurred Palmprint Recognition Based on Stable-Feature Extraction Using a Vese–Osher Decomposition Model

As palmprints are captured using non-contact devices, image blur is inevitably generated because of the defocused status. This degrades the recognition performance of the system. To solve this problem, we propose a stable-feature extraction method based on a Vese–Osher (VO) decomposition model to recognize blurred palmprints effectively. A Gaussian defocus degradation model is first established to simulate image blur. With different degrees of blurring, stable features are found to exist in the image which can be investigated by analyzing the blur theoretically. Then, a VO decomposition model is used to obtain structure and texture layers of the blurred palmprint images. The structure layer is stable for different degrees of blurring (this is a theoretical conclusion that needs to be further proved via experiment). Next, an algorithm based on weighted robustness histogram of oriented gradients (WRHOG) is designed to extract the stable features from the structure layer of the blurred palmprint image. Finally, a normalized correlation coefficient is introduced to measure the similarity in the palmprint features. We also designed and performed a series of experiments to show the benefits of the proposed method. The experimental results are used to demonstrate the theoretical conclusion that the structure layer is stable for different blurring scales. The WRHOG method also proves to be an advanced and robust method of distinguishing blurred palmprints. The recognition results obtained using the proposed method and data from two palmprint databases (PolyU and Blurred–PolyU) are stable and superior in comparison to previous high-performance methods (the equal error rate is only 0.132%). In addition, the authentication time is less than 1.3 s, which is fast enough to meet real-time demands. Therefore, the proposed method is a feasible way of implementing blurred palmprint recognition.     

Enzyme-ligand complexes of pyridoxine 5'-phosphate synthase: implications for substrate binding and catalysis

Pathogenesis in sickle cell disease depends on polymerization of deoxyhemoglobin S into rod-like fibers, forming gels that rigidify red cells and obstruct the systemic microvasculature. Fiber structure, polymerization kinetics and equilibria are well characterized and intimately related to pathogenesis. However, data on gel rheology, the immediate cause of obstruction, are limited, and models for structure and rheology are lacking. The basis of gel rheology, micromechanics of individual fibers, has never been examined. Here, we isolate fibers by selective depolymerization of gels produced under photolytic deliganding of CO hemoglobin S. Using differential interference contrast (DIC) microscopy, we measure spontaneous, thermal fluctuations in fiber shape to obtain bending moduli (kappa) and persistence lengths (lambda(p)). Some fibers being too stiff to decompose shape accurately into Fourier modes, we measure deviations of fiber midpoints from mean positions. Serial deviations, sufficiently separated to be independent, exhibit Gaussian distributions and provide mean-squared fluctuation amplitudes from which kappa and lambda(p) can be calculated. Lambda(p) ranges from 0.24 to 13 mm for the most flexible and stiffest fibers, respectively. This large range reflects formation of fiber bundles. If the most flexible are single fibers, then lambda(p) =13 mm represents a bundle of seven single fibers. Preliminary data on the bending variations of frozen, hydrated single fibers of HbS obtained by electron microscopy indicate that the value 0.24 mm is consistent with the persistence length of single fibers. Young's modulus is 0.10 GPa, less than for structural proteins but much larger than for extensible proteins. We consider how these results, used with models for cross-linking, may apply to macroscopic rheology of hemoglobin S gels. This new technique, combining isolation of hemoglobin S fibers and measurement of micromechanical properties based on thermal fluctuations and midpoint deviations, can be used to study fibers of mutants, hemoglobin A/S, and mixtures and hybrids of hemoglobin S.     

Intermolecular contacts within sickle hemoglobin fibers

By combining X-ray crystallographic co-ordinates of sickle hemoglobin (HbS) molecules with three-dimensional reconstructions of electron micrographs of HbS fibers we have synthesized a model for the structure of the clinically relevant HbS fiber. This model largely accounts for the action of 55 point mutations of HbS whose effect on fiber formation has been studied. In addition, it predicts locations at which additional point mutations are likely to affect fiber formation. The number of intermolecular axial contacts decreases with radius until, at the periphery of the fiber, there are essentially no axial contacts. We suggest that this observation accounts for the limited radial growth of the HbS fiber and that a similar mechanism may be a factor in limiting the size of other helical particles. The methodology for the synthesis of the fiber model is applicable to other systems in which X-ray crystallographic and electron microscopic data are available.     

Proportions of slow myosin heavy chain-positive fibers in muscle spindles and adjoining extrafusal fascicles, and the positioning of spindles relative to these fascicles.

Chicken leg muscles were examined to calculate the percentages of slow myosin heavy chain (MHC)-positive fibers in spindles and in adjacent extrafusal fascicles, and to clarify how the encapsulated portions of muscle spindles are positioned relative to these fascicles. Unlike mammals, in chicken leg muscles slow-twitch MHC and slow-tonic MHC are expressed in intrafusal fibers and in extrafusal fibers, suggesting a close developmental connection between the two fiber populations. In 8-week-old muscles the proportions of slow MHC-positive extrafusal fibers that ringed muscle spindles ranged from 0-100%. In contrast, proportions of slow MHC-positive intrafusal fibers in spindles ranged from 0-57%. Similar proportions in fiber type composition between intrafusal fibers and surrounding extrafusal fibers were apparent at embryonic days 15 and 16, demonstrating early divergence of extrafusal and intrafusal fibers. Muscle spindles were rarely located within single fascicles. Instead, they were commonly placed where several fascicles converged. The frequent extrafascicular location of spindles suggests migration of intrafusal myoblasts from developing clusters of extrafusal fibers toward the interstitium, perhaps along a neurotrophic gradient established by sensory axons that are advancing in the connective tissue matrix that separates adjoining fascicles.     

Dependence on pH of formation and oxygen affinity of hemoglobin S fibers in the presence and absence of phosphates and polyphosphates

This paper presents data on the effect of phosphates and polyphosphates on the formation of hemoglobin S fiber, and on the Bohr effect of hemoglobin S samples whose concentration was high enough (near 5 mM) in order to form fibers upon deoxygenation. The experiments were performed in 0.2 M Bistris or Tris buffers at 30 degrees C in the presence and absence of inositol hexakisphosphate and of 2,3-diphosphoglycerate. Alternatively, 0.2 M phosphate buffers were used without addition of effectors. Under these conditions, few fibers were formed in Tris or Bistris buffers, while extensive fiber formation occurred in the presence of phosphates and polyphosphates. In all cases, increasing pH strongly inhibited fiber formation. At pH 7.5 and above, fibers were not formed in our samples. In the presence of phosphates and polyphosphates fiber formation reduced the oxygen affinity of hemoglobin S with respect to either hemoglobin A or soluble hemoglobin S under similar experimental conditions. The fiber-polyphosphate complexes showed a larger Bohr effect than that in hemoglobin A. In the presence of inositol hexakisphosphate fiber-forming solutions of hemoglobin S liberated as much as six protons per tetramer upon oxygen binding. The increased liberation of protons was probably due to a higher affinity of the effectors for the fibers of hemoglobin S. Very likely the higher affinity was supported by a conformational change of hemoglobin S specific for the fibers.     

Distribution and innervation of short, interdigitated muscle fibers in parallel-fibered muscles of the cat hindlimb

The cat hindlimb contains several long, biarticular strap muscles composed of parallel muscle fascicles that attach to short tendons. Three of these muscles--sartorius, tenuissimus, and semitendinosus--were studied by dissecting individual gold-stained fibers and determining the surface distribution of acetylcholinesterase-stained end-plate zones. In each muscle, fascicles were composed of muscle fibers that ran only part of the fascicle length and tapered to end as fine strands that interdigitated with other tapering fibers within the muscle mass. Most muscle fibers measured 2-3 cm in length. Fascicles of muscle fibers were crossed by short transverse bands of endplates (1 mm wide by 1-5 mm long) that were spaced at fairly regular intervals from the origin to the insertion of the muscle. The endplate pattern suggested that the fiber fascicles were organized into multiple longitudinal strips. In the sartorius, the temporospatial distribution of electromyographic (EMG) activity evoked by stimulating fine, longitudinal branches of the parent nerve confirmed that each strip was selectively innervated by a small subset of the motor axons. These axons appeared to distribute their endings throughout the entire length of the fascicles, providing for synchronous activation of their in-series fibers.     

Morphology and histochemistry of the ambiens muscle of the red-eared turtle (Pseudemys scripta)

Six fiber types have been described in the ambiens muscle of red-eared turtles. These include one slow oxidative type, two fast oxidative types, two fast oxidative and glycolytic types, and one fast glycolytic type. Fiber types are non-randomly distributed throughout cross sections of the muscle. There is a decreasing gradient of oxidative staining and an increasing gradient of glycolytic staining along an axis from the superficial to deep regions of the muscle. The slow oxidative fibers are predominantly located within one or two fascicles of the superficial surface of the muscle. The fast glycolytic fibers are predominant in deep fascicles. In contrast to previous reports of histochemically monotypic intrafusal fibers in turtle muscle, ambiens muscle spindles have been observed containing one to eleven intrafusal fibers, including two fiber types. Fiber diameter and area are consistently smaller than observed in most extrafusal fibers. Spindles are predominantly located in superficial and cranial fascicles of the ambiens muscle and are located in regions characterized by extrafusal fibers with high oxidative activity.     

Using Pattern Classification to Measure Adaptation to the Orientation of High Order Aberrations

Background

The image formed by the eye''s optics is blurred by the ocular aberrations, specific to each eye. Recent studies demonstrated that the eye is adapted to the level of blur produced by the high order aberrations (HOA). We examined whether visual coding is also adapted to the orientation of the natural HOA of the eye.

Methods and Findings

Judgments of perceived blur were measured in 5 subjects in a psychophysical procedure inspired by the “Classification Images” technique. Subjects were presented 500 pairs of images, artificially blurred with HOA from 100 real eyes (i.e. different orientations), with total blur level adjusted to match the subject''s natural blur. Subjects selected the image that appeared best focused in each random pair, in a 6-choice ranked response. Images were presented through Adaptive Optics correction of the subject''s aberrations. The images selected as best focused were identified as positive, the other as negative responses. The highest classified positive responses correlated more with the subject''s Point Spread Function, PSF, (r = 0.47 on average) than the negative (r = 0.34) and the difference was significant for all subjects (p<0.02). Using the orientation of the best fitting ellipse of angularly averaged integrated PSF intensities (weighted by the subject''s responses) we found that in 4 subjects the positive PSF response was close to the subject''s natural PSF orientation (within 21 degrees on average) whereas the negative PSF response was almost perpendicularly oriented to the natural PSF (at 76 degrees on average).

Conclusions

The Classification-Images inspired method is very powerful in identifying the internally coded blur of subjects. The consistent bias of the Positive PSFs towards the natural PSF in most subjects indicates that the internal code of blur appears rather specific to each subject''s high order aberrations and reveals that the calibration mechanisms for normalizing blur also operate using orientation cues.     

The hand of the helix of deoxyhemoglobin S fibers.

Electron micrographs of deoxyhemoglobin S fiber cross sections provide an end-on view of the fiber whose appearance is sensitive to small changes in orientation. We have developed a procedure to exploit this sensitivity in order to determine the hand of these particles. In a sickle hemoglobin fiber the hemoglobin molecules form long pitch helical strands which twist about the particle axis with a pitch of about 3000 A. Tilting a 400-A-thick cross section by a few degrees aligns one of the long pitch helices so that it is nearly parallel to the direction of view. When a strand of hemoglobin molecules in a fiber is aligned in this manner it appears as a strongly contrasted bright spot. It is this spot, rather than the fiber axis, which appears to be the apparent center of rotation of the cross section. The direction of the displacement of the spot from the particle axis depends upon the particle hand and tilt direction. We have used this property to determine that sickle hemoglobin fibers are right-handed particles. This method may be applicable to other particles with long pitch helices as well.     

Mechanisms of nascent fiber formation during avian skeletal muscle hypertrophy

This study examined two putative mechanisms of new fiber formation in postnatal skeletal muscle, namely longitudinal fragmentation of existing fibers and de novo formation. The relative contributions of these two mechanisms to fiber formation in hypertrophying anterior latissimus dorsi (ALD) muscle were assessed by quantitative analysis of their nuclear populations. Muscle hypertrophy was induced by wing-weighting for 1 week. All nuclei formed during the weighting period were labeled by continuous infusion of 5-bromo-2'-deoxyuridine (BrdU), a thymidine analog, and embryonic-like fibers were identified using an antibody to ventricular-like embryonic (V-EMB) myosin. The number of BrdU-labeled and unlabeled nuclei in V-EMB-positive fibers were counted. Wing-weighting resulted in significant muscle enlargement and the appearance of many V-EMB+ fibers. The majority of V-EMB+ fibers were completely independent of mature fibers and had a nuclear density characteristics of developing fibers. Furthermore, nearly 100% of the nuclei in independent V-EMB+ fibers were labeled. These findings strongly suggest that most V-EMB+ fibers were nascent fibers formed de novo during the weighting period by satellite cell activation and fusion. Nascent fibers were found primarily in the space between fascicles where they formed a complex anastomosing network of fibers running at angles to one another. Although wing-weighting induced an increase in the number of branched fibers, there was no evidence that V-EMB+ fibers were formed by longitudinal fragmentation. The location of newly formed fibers in wing-weighted and regenerating ALD muscle was compared to determine whether satellite cells in the ALD muscle were unusual in that, if stimulated to divide, they would form fibers in the inter- and intrafascicular space. In contrast to wing-weighted muscle, nascent fibers were always found closely associated with necrotic fibers. These results suggest that wing-weighting is not simply another model of regeneration, but rather produces a unique environment which induces satellite cell migration and subsequent fiber formation in the interfascicular space. De novo fiber formation is apparently the principal mechanism for the hyperplasia reported to occur in the ALD muscle undergoing hypertrophy induced by wing-weighting.     

Triclinic crystals associated with fibers of deoxygenated sickle hemoglobin.

Triclinic crystals have been found in capillaries that initially contained deoxygenated sickled erythrocytes, and in solutions of sickle hemoglobin that were stirred during deoxygenation. In both cases these crystals occur as a phase transition from fibers. They have been observed only as twins; the a-axis of one member is related to that of its twin by 180 degrees rotation about the b* direction. The volume of the triclinic crystal unit cell is half that of the monoclinic crystals that have also transformed from fibers. Analysis of X-ray diffraction data indicates that the two molecules in the triclinic unit cell that repeat at an interval of 64 A form double filaments similar to those found in the monoclinic crystals and in the fiber. The existence of the triclinic crystals which contain only one double filament per unit cell removes a postulated requirement that antipolar double filament pairs be the sole unit of the fiber architecture.     

Molecular topology in crystals and fibers of hemoglobin S

Several lines of evidence indicate a close correspondence between the linear double filaments in the crystal form of hemoglobin S grown from solutions containing polyethylene glycol and the seven pairs of helical filaments that occur in the 14-filament fibers of hemoglobin S. An analysis of the adjustments to the intermolecular contacts required to convert the double filaments from crystals to fibers is presented here. In addition, postulated contacts between the helical double filaments, which are distinct from any of the contacts of the crystals, are specified for the first time. The movements from crystals to fibers are described in terms of three rotation angles: α, the inclination of the filaments with respect to the fiber axis; δ, the tilt of successive molecules along the filaments; and ω, the rotation of successive molecules along the filaments. On the basis of the fiber structure determined by three-dimensional reconstruction of electron micrographs and the assignment of filament pairs from data on incomplete fibers, the various angles have been evaluated. For the filaments at various radii in the fibers, a varies from 3 ° to 12 °, δ varies from 1 ° to 4 ° and ω is constant at 9 °. The effects of the rotations on the contacts between molecules of hemoglobin S at various positions in the fibers are characterized using surface maps based on polar coordinates. For each residue on the surface of hemoglobin the centroid position of its side-chain is located by a longitude, a latitude and an altitude. Locations on the maps are assigned for the contacts within the helical double filaments, as well as 11 classes of new contacts describing the potential interaction sites between double filaments. The resulting maps (1) deduce roles for the various α mutants of hemoglobin known to influence fiber formation that have been identified by the Benesches; (2) distinguish effects for the α chain mutants on the same (cis) or opposite (trans) α₁β₁ dimer as the β6 Val in asymmetric tetramers; (3) propose new sites where effects of mutations on fiber formation may be found; and (4) suggest why some mutants may inhibit, while others enhance, fiber formation. Concerning the last point, the possibility of certain mutants “correcting” the effects of other mutants is proposed as a test of contact assignments.     

Blind Image Blur Assessment Using Singular Value Similarity and Blur Comparisons

The increasing number of demanding consumer image applications has led to increased interest in no-reference objective image quality assessment (IQA) algorithms. In this paper, we propose a new blind blur index for still images based on singular value similarity. The algorithm consists of three steps. First, a re-blurred image is produced by applying a Gaussian blur to the test image. Second, a singular value decomposition is performed on the test image and re-blurred image. Finally, an image blur index is constructed based on singular value similarity. The experimental results obtained on four simulated databases to demonstrate that the proposed algorithm has high correlation with human judgment when assessing blur or noise distortion of images.