Information Technology Reference
In-Depth Information
Every product
x
has a corresponding promoter “
f
,” which samples the concen-
tration of
x
and accordingly regulates the genes associated with product
x
. The pro-
moter modulates the gene's expression
y
based on function
x
f
.
The tight association creates a situation where the only way a gene can be fully
promoted by a promoter, say
f
1
, is if it is the only active gene that affects product
x
1
(reducing
f
1
)
/
. Each promoter maintains equilibrium of its product regardless
of the state of other promoters. However, multiple promoters can affect a gene's
expression.
If several genes affect the same product, no gene will be fully promoted by the
amount the product is consumed. For example, if two genes affect the same product,
the promoters each uses will not be available for the other. In this way they “inhibit”
each other through the product's promoter, forcing these genes' promotion to be
mediated through other promoters from other processes.
The more products two genes mutually interact with, the more they will blunt
each other's promoters. The less products genes mutually affect, the less their pro-
moters will mutually interfere, and the more “parallel” or independent these genes
can be.
The network dynamically evaluates gene expression by
1. Determining promoter activity based on product concentration.
2. Modifying gene expression based on the promoter.
3. Redetermining promoter activity based on new product concentration.
Steps 1-3 are continuously cycled through expression, promoters, and products.
7.2.3 Model Equations
This section introduces the nonlinear equations governing this network. For any
gene
y
denoted by index
a
,let
N
a
denote all products that gene
y
a
affects. Let
n
a
denote the number of products gene
y
a
affects. For any product
x
denoted by index
b
,let
M
b
denote all genes that affect
x
b
. The total amount of expression of product
x
b
is
Y
b
, which is the sum of expression from all genes that affect product
x
b
.
Y
b
=
∑
j
y
j
(
t
)
(7.1)
∈
M
b
Efficacy of promoter
f
b
is determined by consumption of
x
b
and the overall pro-
duction of
x
b
:
Y
b
. This is determined by
x
b
Y
b
f
b
=
(7.2)
The expression of
y
a
is dependent on its previous expression and its promoters.
The equations are designed so that gene expression is proportional to the amount of
product consumed and inversely proportional to their promoters based on product
consumption and also depends on their previous expression levels [2, 1]. Describing
