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Fig. 1.5
Two semi-complete liposome aggregations that provide a membrane by joining their
tail-uncovered borders
explaining the difference between the spherical and bilinear shapes is given by the
symmetric nature of double monomers with respect to their head-head axis, in op-
position with the asymmetric nature of the head-tail monomers which are catenated
in the two lines. DNA monomers, as will be explained in the next chapter, are asym-
metric with respect to the head-tail axis, and along this direction can be established
a pairing only with another monomer. Therefore, the double DNA arrangement is
a “bilinear concatenation”, in opposition to the liposome arrangement which is a
“bilayer (closed) convolution”. As will be explained in the next chapter, under very
general hypotheses, bilinear catenative arrangements will provide helical shapes.
Another crucial difference between phospholipid and DNA aggregations is due
to the kind of molecules that they aggregate. In the phospholipid case, there is only
one type of head-tail monomers, while in the DNA case there are four different
head-tail monomers. This is the reason for the enormous number of combinatorial
possibilities for DNA molecules.
We conclude with the following statement.
Both aggregations of phospholipids and DNA molecules are based on asym-
metric monomers. Phospholipid aggregation is based on homogeneous bilayer
double monomers, which are symmetric with respect to the head-head axis.
DNA aggregation is based on heterogeneous double linear concatenation of
monomers, which are asymmetric with respect to the head-tail axis.
1.6
Populations and Hypermultisets
Chemistry deals with multisets at two different levels. In fact
CO
2
is a multiset over
the set
{
C
,
O
}
, while 6
CO
2
+
6
H
2
O
is a multiset over the set
{
CO
2
,
H
2
O
}
.Inother
words:
+
=
(
+
)+
(
+
)
.
6
CO
2
6
H
2
O
6
C
2
O
6
2
H
O
