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1, the cells settle on a binary solution
(1, 0, 1). Thus simple solutions can be found as long as there is an even number of
products consumed. Cases with
N
When all products are consumed, all
x
s
=
4 genes become progressively complicated to
solve and beyond the scope of this chapter (Fig. 7.6).
>
2-Product Genes Only
y
4
y
2
y
3
x
1
x
2
x
3
x
4
Fig. 7.6: Example 4b.
7.3.4 Subchains
If a product in the chain is not consumed, this can break the chain into independent
components composed of the right and left parts of the chain from the unconsumed
product. These chains can function as smaller chains. For example, if product
x
6
=
0,
the chains involving genes
y
1
−
6
and
y
6
−
N
become independent. Thus gene expres-
sion patterns are determined by distributed product-promoter dynamics involving
consumption and gene structures. Further analysis remains for future research.
7.4 Discussion
This theory shows that highly regulated genes can affect one another and form a
classification system. The recognition system configures the expression of multiple
genes to efficiently minimize extraneous products. This chapter serves as a demon-
stration of this concept. Though details of the molecular mechanisms have been
abstracted, this model suggests methods to control gene expression by artificially in-
troducing products. Genetic data indicating shared promoter regions between genes
may predict which genes compete.
Suppose a patient has a deleterious gene. Though still highly speculative, this
model suggests that introducing artificial products which match a gene's regulation
pattern may change the deleterious gene's expression. Through gene competition,
artificial products may be introduced to favor other native genes which share the
same production pathway and will turn off the deleterious gene.
