Polymorphism of Sickle Cell Hemoglobin Aggregates: Structural Basis for Limited Radial Growth

Makowski, Lee; Magdoff-Fairchild, Beatrice

doi:10.1126/science.3775381

Cited by 34 publications

(26 citation statements)

References 16 publications

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“…There are at least two possible explanations for the constancy of pitch as a function of the radius of these fibers (6). (i) Interactions within individual protofibrils are constant for all fibers, but interactions among protofibrils vary with changing conditions, causing differences in radius.…”

Section: Resultsmentioning

confidence: 99%

“…Simple geometric considerations (6) (E) Such molecules will form protofibrils with a very long helical pitch. (F) When two twisted protofibrils interact with one another side-by-side, to maintain specific interactions over an extended length, it is necessary for them to twist around one another.…”

Section: Resultsmentioning

confidence: 99%

“…When the energy required to stretch a protofibril exceeds the binding energy of a protofibril to a fiber, then the growth of the fiber ceases. This mechanism has been proposed as being responsible for the determination of diameter in sickle cell hemoglobin aggregates (6), and a similar mechanism may apply to fibrin.…”

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confidence: 88%

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Twisting of fibrin fibers limits their radial growth.

Weisel

Nagaswami

Makowski

1987

Proc. Natl. Acad. Sci. U.S.A.

122

109

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Electron microscopy of freeze-dried, shadowed fibrin fibers has demonstrated that these structures are twisted. The pitch and radius of many fibers were measured from the micrographs. Although there is some variability, the average pitch of 1930 ± 280 (SD) nm is independent of radius. The distribution of observed radil of fibers assembled in vitro is highly skewed, suggesting that individual fibers grow to a maximum radius of about 50 nm, except when both pH and ionic strength are high; fibers aggregate to form thicker fiber bundles under some conditions. The observed twisting may be responsible for limiting the lateral growth of individual fibers. Protofibrils near the surface of a twisted fiber are stretched relative to those near the center. Consequently, the degree to which a protofibril can be stretched limits the radius of a fiber; protofibrils can be added to a growing fiber until the energy required to stretch an added protofibril exceeds the energy of binding. These properties of assembly arise directly from the intrinsic twist of the fibrinogen molecule determined from structural evidence. Simple geometric considerations lead to conclusions regarding the locations of the binding sites for assembly of the protofibril and the flexibility of the fibrin molecule.The physical properties of blood clots are determined to a large extent by properties of fibrin fibers, such as diameter, degree ofaggregation, stability, and resistance to proteolysis. Fibrinogen is the soluble precursor of the fibrin clot. It has a molecular weight of 340,000 and is made up of three pairs of polypeptide chains, (AaBI3y)2. The molecule is 45 nm in length and consists of globular domains connected by rodlike, a-helical coiled-coil domains (1, 2). All amino termini are linked together in the central domain, the disulfide knot.The carboxyl-terminal ends of the BP and y chains form the proximal and distal end domains, respectively. The carboxylterminal ends of both of the Aa chains appear to interact to form a domain adjacent to the central domain.Fibrin fibers with an axial repeat of 22.5 nm form from fibrinogen upon removal of the fibrinopeptides by thrombin. Cleavage of the fibrinopeptides in the central domain of the molecule exposes binding sites that are complementary to sites always present at each end of the molecules (1). These specific interactions result in the half-staggering of molecules to form two-stranded protofibrils, which then aggregate laterally to yield fibers. The characteristic 22.5-nm band pattern seen in electron micrographs of fibrin fibers indicates that the protofibrils align in register axially. Electron micrographs of cross sections offibers indicate that the side-to-side packing of protofibrils is disordered, although the average distance between neighboring protofibrils exhibits some regularity (ref. 3; J.W.W. and J. G. White, unpublished data).The diameter of fibrin fibers is an important component in determining the physical properties of the fibrin clot. Diameters of fibers from clots made un...

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Twisting of fibrin fibers limits their radial growth.

Weisel

Nagaswami

Makowski

1987

Proc. Natl. Acad. Sci. U.S.A.

122

109

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“…7(a)) from bacteria, to plants and animals. 72 The self-twisted architecture of chiral filament assemblies has been a key aspect of structural models of a broad range biological [73][74][75][76][77][78][79][80][81][82][83] and synthetic [84][85][86] assemblies. Here, I describe models of frustrated chiral assemblies of rods, focussing on long filaments, and again separate the discussion into models that consider chiral frustration of orientational and positional ordering.…”

Section: B Chirality Vs Long-range Order In Filamentous Assembliesmentioning

confidence: 99%

Perspective: Geometrically frustrated assemblies

Grason

2016

The Journal of Chemical Physics

117

149

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This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems. Published by AIP Publishing. [http://dx

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“…Helically twisted assemblies of multiple filaments or strands are not only key structural elements in macroscopic materials-cables, ropes, yarns, and textile fibers-but they also constitute an important class of macromolecular assemblies in biological materials at the nanoscopic scale. Fibers of extracellular proteins like collagen (10) and fibrin (11) are well-known to organize into twisted assemblies, and the helical twist of multifiber cables has been implicated in the assembly thermodynamics of sickle-hemoglobin macrofibers (12). Whereas the helical twist of human-made ropes is built in to optimize mechanical properties-such as bending compliance (13) and tensile strength (14)-the twist of selfassembled ropes of biomacromolecules derives from torques generated by interactions between helical (i.e., chiral) molecules (15,16).…”

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confidence: 99%

Non-Euclidean geometry of twisted filament bundle packing

Bruss

Grason

2012

Proc. Natl. Acad. Sci. U.S.A.

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Densely packed and twisted assemblies of filaments are crucial structural motifs in macroscopic materials (cables, ropes, and textiles) as well as synthetic and biological nanomaterials (fibrous proteins). We study the unique and nontrivial packing geometry of this universal material design from two perspectives. First, we show that the problem of twisted bundle packing can be mapped exactly onto the problem of disc packing on a curved surface, the geometry of which has a positive, spherical curvature close to the center of rotation and approaches the intrinsically flat geometry of a cylinder far from the bundle center. From this mapping, we find the packing of any twisted bundle is geometrically frustrated, as it makes the sixfold geometry of filament close packing impossible at the core of the fiber. This geometrical equivalence leads to a spectrum of close-packed fiber geometries, whose low symmetry (five-, four-, three-, and twofold) reflect non-Euclidean packing constraints at the bundle core. Second, we explore the ground-state structure of twisted filament assemblies formed under the influence of adhesive interactions by a computational model. Here, we find that the underlying non-Euclidean geometry of twisted fiber packing disrupts the regular lattice packing of filaments above a critical radius, proportional to the helical pitch. Above this critical radius, the ground-state packing includes the presence of between one and six excess fivefold disclinations in the cross-sectional order.self-assembly | topological defects | geometric frustration P acking problems arise naturally in a multitude of contexts, from models of crystalline and amorphous solids to structure formation in tissues of living organisms. Though often easy to state, packing problems are notoriously difficult to solve. The cannonball stacking of spheres, for example, conjectured by Kepler to be the densest packing in three-dimensional space (1), was only proven so in 1999, and even then with the aid of a computer algorithm (2). In some cases, like the densest packing of spheres, the face-centered cubic lattice-or its two-dimensional analogue, the densest packing of discs, the hexagonal lattice-the optimal structure is a regular, periodic partition of space. In many problems, however, perfect lattice packings are prohibited, and optimal structures necessarily lack the translational and rotational symmetry of periodic order. A well-known example is the problem of finding the densest packing of N discs on a sphere of a given radius, known alternately as the Tammes or the generalized-Thomson problem (3). In this problem, spherical topology requires a variation in the local packing symmetry: All states possess at minimum 12 discs whose nearest-neighbor geometry is fivefold coordinated (4). Beyond its relevance to structural studies of such diverse materials as spherical viral capsids (5) and colloid-stabilized emulsions (6, 7), the problems involving point or disc packing on spheres serve as an important example of systems where topological de...

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Polymorphism of Sickle Cell Hemoglobin Aggregates: Structural Basis for Limited Radial Growth

Cited by 34 publications

References 16 publications

Twisting of fibrin fibers limits their radial growth.

Twisting of fibrin fibers limits their radial growth.

Perspective: Geometrically frustrated assemblies

Non-Euclidean geometry of twisted filament bundle packing

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