Information Technology Reference
In-Depth Information
7.3.3.1 Chain of Genes Including A 1-Product Gene
Consider the case where there are
N
two-product genes that are connected in a
chain shown in Fig. 7.5. This configuration includes a 1-product gene similar to
Examples 1 and 3. Suppose all products are consumed equally, for example, all
have the value 1. The network will find the most efficient configuration of expression
where no extraneous products are created. These configurations may change based
on the properties of the links. For example, suppose there are
N
gene links. If
N
is
an
odd
number then gene
y
1
will express its single product and every second gene
will express their products. The genes interspersed in between will be turned off (0).
If
N
is
even
,
y
1
will be turned off and the
even
genes expressed (1) and
odd
ones
turned off. If
i
and
j
represent gene indexes the general solution becomes
∑
j
x
j
, ··· ,
(
x
1
,
x
i
, ··· ,
x
N
)
→
N
(
−
1
)
x
N
i
≤
j
≤
With a 1-Product Gene (y
1
)
y
2
y
n
y
…
x
1
x
2
x
n-1
x
n
Fig. 7.5: Example 4a.
For example, with four genes chained,
N
=
4:
(
1
,
1
,
1
,
1
)
→
(0,1,0,1).With
five genes chained
N
=
5:
(
1
,
1
,
1
,
1
,
1
)
→
(1, 0, 1, 0, 1). If the concentrations of
x
are such that
y
0, the chain breaks at that gene and the rest of the links behave as
smaller independent chains from that point (
see
Section 7.3.4).
<
7.3.3.2 Chain of Genes Without A 1-Product Gene
If a one product gene is not available, then the network does not have a favorable set
of genes to resolve an odd number of products. Two-product genes cannot produce
an odd number of products. The configuration with three products was presented in
Example 2. In case of four inputs (even) distributed over three genes the solution
becomes
x
1
(
Σ
X
)
)
,
−
(
Σ
X
)(
x
1
x
4
−
x
3
x
2
)
x
4
(
Σ
X
)
,
where
Σ
X
=
x
1
+
x
2
+
x
3
+
x
4
.
2
(
x
1
+
x
3
2
(
x
1
+
x
3
)(
x
2
+
x
4
)
2
(
x
2
+
x
4
)
