Biology Reference
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Fig. 15.8 The “Tree-Ring-And-Landscape” (TRAL) model of the EvoDevo duality of life (in
analogy to the wave/particle duality of light). Each circle has 2 N cells, where N is the number of
circles starting from the center which is assigned the value of N ¼ 0. Each node has 2 n possible
internal states, where n ¼ the number of genes in the cell
applied to morphogenesis (one of the three branches of developmental biology, the
other two being growth and differentiation ), has the following characteristics:
1. Each circle represents one cell generation which is exposed to an environment
that may or may not change with time.
2. The number of cells (represented as nodes or vertices) on the Nth circle is 2 N ,
where N is the number of cell generations. When N
¼
0, there is one cell (at the
¼
center of the tree rings); when N
1, there are two cells (or nodes) on the first
2, there are four cells on the second circle, etc.
3. The cells/nodes on any concentric circle carry a set of n genes in their DNA.
The set of n genes can be represented in terms of a string of n 0 0 s and 1 0 s,
enabling the functional state of the cell to be characterized by the patterns of the
distribution of 0 0 s (inactive genes) and 1 0 s (activated genes). The total number
of possible cell states is 2 n . In other words, each node on a circle has a set of 2 n
possible internal states (not shown) that can be represented as a string of n 1 0 s
and 0 0 s. (The n genes are renormalized as a node.)
4. Thus the TRAL model provides a convenient visual method for representing
one (stem) cell growing into a system of 2 N cells, each cell occupying one of
the 2 n cell states compatible with the prevailing environmental conditions:
2 N
circle; when N
¼
¼
cell number
2 n
¼
cell states
5. The Nth circle (or ring) of the TRAL model can be described as an N-
dimensional hypercube with 2N nodes, each node having characteristics
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