Biomedical Engineering Reference
In-Depth Information
Wheatley observes that ''as many as 4000 reactions may be occurring simulta-
neously in a cell (
) and every one has to be harmoniously controlled. There is
no factory on earth that comes anywhere near this complexity and, at the same
time, gives the fidelity or replicative performances while remaining flexible and
adaptable to its environment'' [38].
...
1.1.2
Growth of Living Organisms
It is supposed from the works of Braun, Schimper, brothers Bravais, Schwendener,
Wulff, and Lewis that the crystallization and growth of a living tissue are similar
[39-46]. The dislocations' gliding and climbing is the basis for such similarity. In
two-dimensional packing, it is realized by the motion of pentagons and heptagons
(five to seven) among crystalline hexagons.
One of the most striking aspects of symmetry in plants is in phyllotaxis - the
arrangement of leaves on a stem or of flowers in the inflorescences. It is an
interdisciplinary study involving mathematics, botany, and crystallography among
others. The phyllotaxis should be properly studied at the shoot apical meristem
(SAM). It is at the meristemic apex that the organs of shoot such as primordia of
leaves, buds, or flowers originate, cf. also [47]. A
primordium
, in embryology, is
defined as an organ or tissue in its earliest recognizable stage of development.
Biological systems are the best prototypes of genuine smart structures. A unique
example is provided by considering the important and mysterious phenomenon
of spiral phyllotaxis - leaf primordia packing with Fibonacci differences between
nearest neighbors, Figure 1.4. For the Fibonacci spiral, in polar coordinates
r
and
φ
,the
n
th primordium has the position
r
n
=
A
√
n
,
ϕ
n
=
C
(
√
5
360
◦
5
◦
,and
u
where
A
is a constant,
C
=
·
u
≈
222
.
=
−
1)
/
2, or, what is
5
◦
. The golden symmetry
ratio
u
is typical for quasicrystals, and for the icosahedron dimensions.
As they grow, older primordia are displaced radially away from the center of the
circular meristem. The newest primordium initiates in the least crowded space at
the edge of the meristem. The growth process is accomplished in an exceptional
order. Phyllotaxis compromises local interactions giving rise to long range order
and assures the best way of optimal close packing.
Meristems are classified according to their location in the plant as apical (located
at the root and shoot tips), lateral (in the vascular and cork cambia), and intercalary
(at internodes, or stem regions between the places at which leaves attach, and leaf
bases). Lateral meristems, found in all woody plants and in some herbaceous ones,
consist of the vascular cambium and the cork cambium. They produce secondary
tissues from a ring of vascular cambium in stems and roots. The lateral meristems
surround the stem of a plant and cause it to grow laterally, cf. Figure 1.5. Nature
uses the same pattern to place seeds on a seedhead, to arrange petals around the
edge of a flower, and to place leaves around a stem.
360
◦
equivalent for structural form
C
=
/
(2
+
u
)
≈
137
.
