Biomedical Engineering Reference
In-Depth Information
Table 5.3
Drug Selection
Count and Fault Coverage
Drug vector
Count
Coverage
(%)
Drug vector
Count
Coverage
(%)
000001
3
23
000111
13
100
000010
2
15
001011
6
46
000100
2
15
001101
6
46
001000
1
8
001110
10
77
010000
2
15
010011
7
54
100000
3
23
010101
7
54
000011
5
38
010110
10
77
000101
3
23
011001
6
46
000110
10
77
011010
5
38
001001
4
31
011100
5
38
001010
3
23
100011
8
62
001100
3
23
100101
8
62
010001
5
38
100110
10
77
010010
4
31
101001
7
54
010100
4
31
101010
6
46
011000
3
23
101100
6
46
100001
6
46
110001
6
46
100010
5
38
110010
5
38
100100
5
38
110100
5
38
101000
4
31
111000
4
31
110000
3
23
5.5
Sequential and Feedback Circuits
In this section, we discuss the generalization of our approach to sequential circuits.
Thus far, the SAT-based ATPG algorithm has been described for and applied to
purely combinational circuits, wherein the primary output of the circuit is dependent
only on the primary inputs. We observe that the output of the GF signaling pathway
from the experiment is fixed based on the primary inputs, where the drug vector is
technically also an input. In general though, the circuit representation of the BN can
be sequential, where the primary output is determined by current state in addition to
the input. The local GRN for mammalian cell-cycle [
19
] is one such example of a
sequential circuit where gene expression updates based on the current gene state. If
we consider a directed graph where the genes are nodes and edges are regulations
upon other genes, then a combinational circuit (such as the GF signaling pathway)
is acyclic. However, for a directed graph of a sequential circuit, a subset of genes
will be inter-regulated forming directed cycles. As such, in the BN, a gene takes its
current input (state of its regulatory genes and/or external inputs) and outputs a new
state or value for the next time point. We assume in the BN that all genes update
synchronously. In other words, for each primary input and current state, the resulting
primary output and next state are determined for all genes, and that the next state
becomes the new current state. Since the time constants of the updates of individual
genes are not known, the synchronous update assumption is the only recourse we
have. While a synchronous update is biologically unrealistic, it allows us to have
deterministic state transitions and simplifies the analysis for our ATPG algorithm.
