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TECHNICAL PAPERS

How Is a Tissue Built?

[+] Author and Article Information
Stephen C. Cowin

The Center for Biomedical Engineering and The Department of Mechanical Engineering, The School of Engineering of The City College and The Graduate School of The City University of New York, New York, NY 10031

J Biomech Eng 122(6), 553-569 (Jul 25, 2000) (17 pages) doi:10.1115/1.1324665 History: Received January 30, 2000; Revised July 25, 2000
Copyright © 2000 by ASME
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References

Figures

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Hierarchical structure of a tendon. Modified from 10.
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Five collagen molecules are in vivo wound together into a left-handed super-superhelix by electrostatic forces to form a microfibril (a). Recall that a superhelix is a helix of a structure that is itself a helix of opposite handedness, thus a super-superhelix is a helix of a structure with opposite handedness which is itself a helix of a structure with the original handedness. There are discrete gaps between the ends of the collagen molecules as shown in (a) and (b). That figure shows a high degree of order in the collagen molecules in the axial direction of a microfibril. On electron microradiographs collagen fibrils have a distinctive cross-striation with an apparent periodicity of 67 nm (not shown). This period of dimension length is denoted by the letter D and is used as a primary reference scale in describing structural levels. The true period is 5 D11. The helical length of a collagen molecule is 4.34 D∼291 nm and the discrete gaps are 0.66 D≈44 nm (some references give this as 35 nm) between two consecutive collagen molecules in a strand. At a gap there are only four collagen molecules in the strand, and the molecules tend to kink to fill the space uniformly as illustrated in (c). The actual gap is 0.6 D. In bone these gaps are the sites of nucleation for crystals of hydroxyapatite (the mineral component of bone tissue) to be deposited. The diameter of the microfibril is about 3.5 to 4 nm and its length is unknown. The microfibril is held together mainly by hydrophobic interactions and has very low mechanical strength by itself. The strength and stability during maturation of the microfibrils are achieved by the development of intermolecular cross-links. From 11 with permission.
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The Beloussov–Zhabotinskii or BZ reaction is an example of the diffusing patterns of reacting chemicals characterized by the Turing model. This figure is the image of this reaction at a particular time. The reaction proceeds in time in oscillating spirals. There are a number of web sites that contain movies of BZ reactions. These movies give a better impression of the oscillatory character of reaction than does this snapshot. This figure is the file liquidfire.gif downloaded from http://cochise.biosci.arizona.edu/∼art/graphics/liquidfire.gif. See the text for the location of recipes by Winfree 17 for recreating the BZ reaction illustrated above. Courtesy of Art Winfree.
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The patterns on the material surface of the epidermis formed by the reaction-diffusion mechanism. These results are model predictions and the differences (a) to (g) are associated with scale factor that is a measure of relative animal size. From 16 with permission.
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Patterns like those characteristic of trabecular bone are formed (right) from initially homogeneous and uniform material with a uniform density distribution (left) using the model of Mullender and Huiskes 18. The final equilibrium of the trabecular structure (right) is characterized by trabeculae that coincide with the orientation of the principal stresses of the applied loading. The applied loading is indicated by the arrowheads; the loading is maintained in direction and magnitude for the course of the structural adaptation process. Courtesy of Rik Huiskes.
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Beam on an elastic foundation. The beam is subjected to an axial compressive load and is supported by springs that are considered to be so close together that they can be treated as continuous elastic support. The lower sketch is the deflection curve of the beam. Large deflections are considered. Note the formation of pattern arising from a homogeneous field, in this case a sine wave curve arising from a straight line.
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A computer-generated ray-traced picture for Fibonacci leaf arrangement numbers (leaves per turn). The illustrations are the side view (upper left) and plan view (upper right) of one idealized leaf arrangement pattern and the plan view (lower left) and side view (lower right) of another. The Fibonacci numbers occur when counting both the number of times one goes around the stem, going from leaf to leaf, as well as counting the leaves one meets until one encounters a leaf directly above the starting one. If one counts in the other direction, one obtains a different number of turns for the same number of leaves. The number of turns in each direction and the number of leaves met are three consecutive Fibonacci numbers. For example, in the top plant in the picture above, 3 clockwise rotations are accomplished before one meets a leaf directly above the first, passing 5 leaves on the way. On the other hand, accomplishing an anti-clockwise path requires only 2 turns. Notice that 2, 3, and 5 are consecutive Fibonacci numbers. For the lower plant in the picture, one accomplishes 5 clockwise rotations passing 8 leaves, or just 3 rotations in the anti-clockwise direction. This time 3, 5, and 8 are consecutive numbers in the Fibonacci sequence. We can write this as, for the top plant, 3/5 clockwise rotations per leaf (or 2/5 for the anti-clockwise direction). For the second plant it is 5/8 of a turn per leaf (or 3/8). The illustration is the file fibflr1b.gif from the web site of Ron Knott R.Knott@altavista.net, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html. Courtesy of Brian Knott; copyrighted by Brian Knott.
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Spiral phyllotaxis illustrated by the marguerite, a European daisy. The florets of this marguerite are arranged in a pattern composed of two families of spirals called parastichies. The two families of parastichies differ in number and in pitch. The 21 parastichies on the left curl clockwise and the 34 on the right curl counterclockwise. The numbers of parastichies (here 21 and 34) associated with a spiral phyllotaxis are very often successive numbers in the Fibonacci series; that is so in this case. The illustration is the file marg.jpg from the web site 〈http://www.math.smith.edu/∼phyllo/〉; courtesy of Scott Hotton.
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Spiral phyllotaxis illustrated by the pinecone. The two families of parastichies on the pinecone have 8 green spirals going clockwise and 13 red ones counterclockwise. The numbers of parastichies (here 8 and 13) are successive numbers in the Fibonacci series. The illustration is the file pineconeSPRL.gif from the web site web site of Ron Knott, R.Knott@altavista.net, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html. Courtesy of Ron Knott; the copyright is held by Ron Knott.
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Plots of the radial (Nr) and circumferential (Nθ) tissue stresses for three stages of capitulum development (FS3-FS5). (A)–(C) Plots of Nr and Nθ as a function of distance from the center of the meristem (the plots stop at the radial distance corresponding to the approximate location of the youngest involucral bracts). For all three stages, the radial stress is positive (tension) over most of the capitulum surface. The region of negative circumferential stress (compression) moves from the periphery (FS3, FS4) to an intermediate position along the radius (FS5). (D)–(F) Color maps of the intensity of circumferential stress (Nθ) on the surface of the capitulum. Colors ranging from yellow to red indicate compressive circumferential stresses. The location of the compressive zone corresponds to the generative region. From 28, with permission.
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The progressive buckling of the circular plate model for the development of a flower of the spiral phyllotaxis. Solid lines show zero and positive contours. Depression contours are dotted. (A) A disk is provided, at its periphery, with the topography of humps in a (13, 21) Fibonacci pattern. The topography merges into noise of the inner region. One hump is marked by an arrow. (B) Progressive buckling occurs as a result of increased applied stress and the boundary topography is extended into the central noise region. (C) With only the positive contours shown, the spiral hump pattern is clearly extended toward the center of the disk as a result of increased applied stress. From 29 with permission.
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Scanning electron micrograph of a young sunflower capitulum (left) and simulation of the same structure based on mechanical buckling of a thin circular plate (right). One family of spirals is highlighted in yellow. This illustration was composed by Jacques Dumais (Department of Biological Sciences, Stanford) based on a micrograph he obtained and a computer buckling simulation of the sunflower capitulum using a thin circular plate model by Steven C. Rennich (Dept. of Aeronautics and Astronautics, Stanford University). A version of this figure appeared on the cover of the July 1999 issue American Journal of Botany as part of Green 27. Reproduced with permission.
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Flow diagram to show the “life” of a collagen molecule from synthesis to ultimate degradation back to amino acids. There is some controversy about whether collagen molecules are actually secreted through the Golgi apparatus. It is shown as occurring here but may not. From 11 with permission.
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Structure of liquid crystals made of rodlike structures such as molecules, microfibrils, or fibrils. Smectic liquid crystals are characterized by rods that lie parallel to one another in layers of equal thickness; they diffuse freely within the layers but not between the layers. Nematic liquid crystals are also characterized by rods that lie parallel to one another, but the layered structure of the smectic does not exist. The ordering is purely orientational and the distribution of the rods in the direction of the rod axis is random. Cholesteric liquid crystals lie parallel to one another in each plane, but each plane is rotated by a constant angle from the next plane of crystals. From 65 with permission.
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Illustration of natural and man-induced self-assembly. Diagram of a DNA–membrane complex, a material formed by mixing negatively charged DNA molecules with positively charged artificial versions of the membranes that form the protective coverings of cells. The DNA is an example of natural self-assembly and the entire complex is an example of man-induced self-assembly. These complexes, which are presently used as delivery vehicles in gene therapy, have a highly organized internal structure, which gives them many potential technological applications. The purple and blue ribbons represent the DNA double helices, which form a one-dimensional lattice between a double-layer sheet of the membrane. The green and white spheres represent the hydrophilic (“water-loving”) ends of the charged and neutral molecules that respectively make up the membrane. The yellow chains (two to each sphere) represent the hydrophobic (“water-fearing”) hydrocarbon “tails” in the molecules. These materials are molecularly aligned at mesoscopic length-scales (microns). The spaces between the DNA molecules can be tuned from 2.5–6.0 nm. The illustration is the file dna_memb.jpg from the web site (email physnews@aip.org) www.aip.org/physnews/graphics/html/dna_memb.htm. It appeared in 46 and it is reproduced by permission.
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The Waddington-Switching yard. The British embryologist C. H. Waddington liked the analogy of a railway switching yard for describing the progressive assignment of embryonic cells. Just as box cars can be shunted into different eventual sidings by throwing switches one way or the other, a series of genetic switches control whether a given cell turns on the set of genes appropriate for being a skin cell, or those appropriate for being a nerve cell, etc. Notice how often these epigenetic switch points correspond to physical rearrangements of cells. Gastrulation and neurulation are both good examples. From 47 with permission.
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Actin belt tightening. The barrel-shaped cell (left), a member of a sheet of cells, has circumferential arrays of microfilament bundles assembled into a “purse string” or “noose” around the apex of the cell. The contraction of this “purse string” distorts the barrel shape as shown (right).
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Mechanical model of actin belt: The vertical axis (L) represents the actual instantaneous length of the cell’s apical bundle. The horizontal axis (Lo) represents the equilibrium (rest) length of the bundle, i.e., the length it would assume in the absence of stretching forces. The apical bundle is stress-free only when the actual length equals the equilibrium length: L=Lo. In the simplest case, it is assumed that the apical bundle has only two stable equilibrium lengths: long (Lo1) and short (Lo2). Here stable means that following a small displacement in the actual length (L), the system returns to the same equilibrium point. For example, a dilation of the fiber bundle length from Lo1 to a point a, returns to Lo1 along trajectory T1. Separating the two stable equilibria is a “firing threshold.” A dilation from Lo1 to a point b, which exceeds the firing threshold, will not return to Lo1, but will contract along a trajectory T2 to the shorter equilibrium length Lo2. From 48 with permission.
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Odell gastrula: Computer simulation of gastrulation in the sea urchin. The frames (ordered, a, b, c,[[ellipsis]],f), were extracted from a computer-generated film obtained by solving the model’s equations. From 48 with permission.
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The blastula to gastrula transition. Gastrulation (Fig. 16) in the sea urchin egg. Courtesy of Jean-Paul Revel.
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Mesenchymal cells on an elastic substratum. The strong tractions generated deform the substratum and create compression and tension wrinkles. The tension wrinkles can extend several hundreds of cell diameters. Photograph by A. K. Harris, from 16 with permission.
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Cell Locomotion. The three principal stages in cell crawling: extension of the exploratory probe, attachment to the surface, and movement of the rear portion of cell forward. (Top) Extension of the exploratory probe. This entails the assembly of actin filaments. Free actin molecules move into the region of the advancing portion of the cell. (Middle) Attachment to the surface. Contact of the cell with a solid surface induces actin filaments to collect in that region. In cultured fibroblasts the membrane protein integrin, which has binding sites for several components of the extracellular matrix, accumulates at focal contacts. Rapidly locomoting cells form smaller, less permanent adhesions. (Bottom) Movement of the rear portion of the cell forward. Away from the exploratory probe of the cell, and especially in its tail region, the cortical network of actin contracts through the action of myosin. This has two important consequences. First, the contraction generates a polarized flow of cortical actin and a pulling of the cell as a whole toward points of anchorage. Second, it squeezes the cytoplasm, producing a hydrostatic pressure that drives cytoplasmic constituents to the front of the cell.
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Cell contact guidance. Phase contrast microscope views of the same cell type on flat surface (right) and on a surface with 10-μm-wide and 5-μm-deep grooves (left). The surface the cells are growing upon is silica but a similar result would be obtained with many other materials. The cells are epitenon cells. The epitenon is the connective tissue on the outside of the tendon. Courtesy of Adam Curtis.
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The twisted plywood model. The long axes of the molecules in each layer are rotated by a discrete angle from the long axes of the molecules in the layer above and in the layer below. Superposed series of nested arcs are visible on the sides of the stepped pyramid due to the regular variations in the directions of the long axes of the molecules. From Fig. 2 of 67 with permission.
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(a) In a planar twist, equidistant straight lines are drawn on horizontal planes, and the direction of the lines rotates regularly from plane to plane. (a′ ) In the conventional notation for a cholesteric geometry applied to a planar twist, lines represent molecules longitudinal to the drawing plane and dots represent molecules perpendicular to it; molecules in oblique position are represented by nails whose points are directed toward the observer. (b) In a cylindrical twist, equidistant helices are drawn on a series of coaxial cylinders, and the angle of the helices rotates regularly from one cylinder to the next. (b′ ) Conventional representation of a cholesteric geometry applied to a cylindrical twist. From Fig. 3 of 67 with permission.
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Possible relation between molecular conformation and angular rotation in collagen helicoids suggested by Neville. Collagen chains entwine to form triple helices. If these pack in a sheet with a stagger (out of register), they create a system of lined-up grooves. The next sheet of triple helices may then adopt either of two possible stable positions. These are (a) in parallel with the initial layer in the grooves between triple helices or (b) in the grooves lying at an angle across the initial layer. The position shown in part (b) could give the angular rotation required to generate a helicoid. The sense of twist changes from triple helix to helicoid, because the different levels in the hierarchy then pack together in a more stable manner. From 65 with permission.

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