Biomedical Engineering Reference
In-Depth Information
to first find ways to accurately find the predictor set. This is the focus of this chapter.
Philosophically, our aim is to invest effort into accurate predictor set determination,
so that the results can be used to find high quality deterministic GRNs.
2.3
Background
This section describes our background and problem definition for inference of pre-
dictor sets using SAT. We begin with some GRN definitions and then explain some of
the biological constraints that will be used in our formation for the the next section.
Definition II.1:
A
predictor
f
i
={
g
j
,
g
k
,
···}
lists the set
{
g
j
,
g
k
,
···}
of genes
which regulate the activity of gene
g
i
.
Definition II.2:
The
predictor set
is the complete set of predictors {
f
1
,
f
2
,
···
,
f
n
}
for the GRN with
n
genes
g
1
,
g
2
,
,
g
n
.
Based on the gene products of one or more genes in a set
f
i
, a gene
g
i
can become
repressed or activated. In this case
f
i
is said to be predictor of gene
g
i
. A predictor
for target gene
g
i
is the collection of genes directly participating in the regulation of
gene
g
i
. As such, the predictor does not consider the type of regulation. Each gene
has a single predictor and the predictor set is the set consisting of predictors of each
gene.
Note, we can relate these terms to logic synthesis: the predictor is identical to
the logical support of a logic function, while the predictor set is akin to the set
representing the support of all variables. The Boolean network GRN then is the
complete logic circuit including function for each node.
···
Definition II.3:
Given a starting state, within a finite number of steps, the network
will transition as determined by the gene functions into a cycle of states, called an
attractor cycle
. States in an attractor cycle are called
attractor states
. The attractor
cycle represents the long term behavior of the network, and absent perturbation, a
network that has transitioned to an attractor cycle will continue to cycle thereafter.
There are several observations that impact the formulation of our GRN model and
predictor inference algorithm. First, the activity level (i.e. activation or repression)
of all genes at a particular time
t
represents the
state
of the GRN at that time
t
.
From our knowledge of biological systems, we observe that over time, cellular
processes converge to sequences of stable
attractor
states. Some of these attractor
states represent normal cellular phenomena in biology (i.e. cell cycle and division),
while other attractor states are consistent with disease (i.e. the metastasis of cancer).
Second, the GRN is often inferred by observing microarray-based experimental
data though which the activity level of genes is measured. The observations of gene
activity (or state) can be used to infer the gene regulation network. The disadvantage
of using microarray data is that such studies do not involve controlled time-series
experimental data. Hence the measurements are assumed to arise from cyclic se-
quences of gene expressions (attractor states) in steady state. Such a sequence is
referred to as an
attractor cycle
.
