Introduction - Logic Synthesis for Genetic Diseases - page 7

Networks [ 14 ], and Stochastic Gene Networks [ 15 ]. Our research focuses on Boolean
networks due to its significant adoption by the research community. A benefit of
using BNs is that they lend themselves to analysis using logic synthesis techniques.
Boolean networks are described in detail in the following subsection.
In addition to gene regulatory networks, RNA and protein regulatory networks
are also studied in genomics. RNA regulatory networks [ 16 ], [ 17 ] describe RNA
interactions such as splicing. After transcription, the RNA may undergo splicing
where portions of the RNA are kept, while other portions are removed. Some RNA
have alternative splicing, which allows RNA to produce different proteins. On the
other hand, protein regulatory networks [ 18 ] describe protein-protein interactions
such as protein binding (for example, hemo protein groups) or altering protein ac-
tivity. Protein networks are also important to study as most proteins perform various
cell functions through interactions with other proteins.

1.3.1 Boolean Network

We utilize the Boolean Network (BN) model that was proposed by Kauffman in
1969 [ 12 ]. In a Boolean Network, the expression activity of a gene is represented as
a binary value, where 1 indicates the gene is ON (expressed) and producing gene-
products, while 0 indicates it is OFF (not expressed). Such a model cannot capture the
continuous and stochastic biochemical properties of protein and RNA production.
However, it has been observed that genes can typically be modeled as ON or OFF in
any particular biochemical pathway [ 19 ].
A Boolean network is formally defined as a set of nodes

{ x 1 , x 2 , ... , x n } with

Boolean functions . In the context of genomics, each node x i is a

gene, and each gene is associated with a logic function g i . The value of a gene is a
binary variable, x i ∈{

{ g 1 , g 2 , ... , g n }

1 according to
its associated function g i () and the value of the genes ( x 1 , x 2 , ... , x n ) at the current
time point t . The state of a gene x i represents the expression of the gene, where
x i =

0, 1 } , and is updated at the next time point t +

0 indicates not expressed. In the BN, all genes
are assumed to updated synchronously, at each time step.
In general, each function g i () depends on a subset of genes s i ⊆

1 indicates expressed, and x i =

( x 1 , x 2 , ... , x n ).
In this sense, this subset of genes determine or “predict” the expression of a target
gene x i . The subset of genes s i is referred to as a predictor for gene i . In essence,
a predictor describes which genes directly interact with each other. The complete
set of all predictors in the GRN (for each of the genes in the GRN) is the predictor
set . The complete set of functions for each gene in the GRN in turn determine the
complete dynamic behavior of the GRN. The predictor set of the GRN determines
the structure or topology of the GRN.
Naturally, the Boolean network describes a dynamic system. The expression val-
ues of all the genes ( x 1 , x 2 , ... , x n ) at a particular time t is the state in the network at
t . At the next time point t

1, the network transitions to a new state as determined
by the functions and expressions of the genes at the current time step. For a BN

+