Bone and Cartilage – its Structure and Physical Properties - Biomechanics of Hard Tissues - page 58

The force F WLC becomes divergent for the straightened chain, when r → L

[245-247].
Stretching individual biomolecules are now achieved by a variety of techniques
including flow stress, microneedles, optical tweezers, and magnetic tweezers that
allow measurement of forces from 10 fN to hundreds of piconewtons.
Different biological molecules have now been analyzed and the accuracy of these
techniques has sufficiently improved so that the theoretical models used to analyze
force-extension curves must be refined. In particular, Bustamante et al .haveshown
that the force-extension diagram of a DNA molecule is well described by a WLC
model [248, 249], and DNA has persistence length 50 nm.

The TC molecules have lengths of L ≈ 300 nm, and are roughly 1.5 nm in diam-
eter. Hydrodynamic methods and TEM permitted us to show that TC molecules
exhibit some flexibility. Hydrodynamic methods suggested a persistence length of
130-180 nm; and TEM-based methods estimated the range between 40 and 60 nm.
Experiments using optical tweezers suggested a much lower persistence length,
between 11 and 15 nm.
Buehler and Wong reported molecular modeling of stretching single molecule
of TC, the building block of collagen fibrils and fibers that provide mechanical
support in CTs. For small deformation, they observed a dominance of entropic
elasticity. At larger deformation, they have found a transition to energetic elasticity,
which is characterized by first stretching and breaking of hydrogen bonds, followed
by deformation of covalent bonds in the protein backbone, eventually leading
to molecular fracture. Their force-displacement curves obtained at small forces
show excellent quantitative agreement with optical tweezer experiments. Their
model predicts a persistence length

ξ ≈

16 nm, confirming experimental results
suggesting the flexible elastic nature of TC molecules [241].

ξ ≈

1.3.9.4 Architecture of Biological Fibers
Most biological tissues are built with polymeric fibers. Two of the most important
and abundant fibers found in nature are cellulose and collagen. Cellulose is the
structural component of the cell walls of green plants, many forms of algae, and the
oomycetes. Some species of bacteria secrete it to form biofilms. As a constituent
of the plant cell wall, it is responsible for the rigidity of the plant stems. One of
the questions deals with the relation between the arrangement of cellulose fibrils
inside the cell wall and its mechanical properties, and the way in which the cellulose
architecture is assembled and controlled by the cell.
Similar problems arise with the structure of collagen fibrils. The TC molecules are
arranged in microfibrils, which are seen under an electron microscope. Microfibrils
are arranged into fibrils visible under a light microscope, and fibrils built connective
tissues (CTs). The TC molecules and microfibrils are also cross-linked. Examples
of fibrous system that achieves high tensile strength by a lateral bonding of
macromolecular polymers are the materials such as skin, tendon, and other forms
of CTs containing the protein collagen. The tensile strength is about 700 MPa; it is
of the order of greatness observed for silk and stainless steel. The tensile strength
of a bone is about 100 MPa [17, 250].