Page 327 - Fiber Fracture
P. 327

FRACTURE OF NATURAL POLYMERIC FIBRES                                 309

          Primary and Secondary Bonds Can Have Direct, Distinguishable, Complementary
          Effects on Fibre Mechanical Properties

             The charge distribution involved in  stabilising a bond  can be used to compute the
          bond energy, from which the force needed to break the bond can in turn be derived.
          Crystallographic information can be used to determine how many such bonds must be
          broken per unit area of  simple fracture surface. The intrinsic strength of  any material
          can  therefore be  calculated from  first principles  (Kelly and  Macmillan,  1986). This
          fundamental contribution  to  strength  is  often  modified  at  higher  length  scales.  For
          example, we have noted in the section ‘A Traditional View of Natural Fibres’ that the
          extrinsic properties of  conventional textile  yams  are  not  related  in  a  simple way  to
          the intrinsic properties of  the  constituent polymers; mechanical interactions between
          filaments  are  especially  challenging  to  quantify  accurately.  In  contrast,  if  we  are
          concerned with individual filaments that have been produced entirely by  self-assembly,
          then the properties of the chemical bonds between subunits (at whatever length scale)
           will be directly reflected in the properties of the filament.
             As  an  example  that  will  recur  throughout  this  paper,  consider  the  case  of  actin
           (Fig.  2).  The  many  roles  of  this  protein  include  load  transmission  (muscle  fibres),
           contributions to  cell  structure  and  motility  (microfilaments) and  barrier  penetration
           (sperm acrosomes) (Oster et  al.,  1982; Tilney  and  InouC,  1982; Lodish et  al.,  1995;
           Stryer,  1995). Actin  has  a  well  defined molecular weight  (41.8  kDa:  Alberts et  al.,
           1989), and is constructed from a specific sequence of amino acid monomers. Each actin
           chain naturally folds into a non-spherical globular conformation, that can fit into a space
           approximately 5.5 x 5.5 x 3.5 nm (Kabsch and Vandekerckhove, 1992). In deference to
          their shape, these globular molecules are conventionally referred to as G-actin. G-actin
           self-assembles into a right-handed, double-helical, elongated aggregate (Fig. 2) that is
          called F-actin to  acknowledge its  fibrous  structure. From the  point of  view  of  these
           fibrous aggregates, the  G-actin molecules act  as monomers,  so the  term  ‘monomer’
           always has to be interpreted in context.
             Two distinct domains can be identified in  each G-actin molecule; the gap between



                      - 5.5 nm
                      U
                       ..<.::...  G-actin molecule
                       .....  ,....
                       ..,.,.,.,...   (both domains within the circular outline,
                       .,.\. ..>.,.
                             and the two chain segments that link them,
                       $$$  are formed by a single protein molecule)
                          \                               Self-assembly

                                                  F-actin
                                    (right-handed double-helical arrangement of  G-actin;
                                    there are 13 G-actin molecules per turn of  each helix)
           Fig. 2.  Molecular  and  supramolecular features  in  the  hierarchical  structure  of  F-actin.  Each  circle  cor-
           responds  to  one  G-actin  molecule.  In  the  depiction  of  F-actin,  the  empty  and  filled  circles  represent
           distinguishable  helical strands. Self-assembly  and stability require the presence of water.
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