Biomedical Engineering Reference
In-Depth Information
The function T[.] is the sign function. T
he
output of interest is the steady-state
levels of gene expre
s
sion in the network
S
as a function of the initial conditions
of gene expression (0
S
and network connectivity. Whereas duplication (dupli-
cation function Q) of one or more genes (
k
) creates a network in a higher dimen-
sional state space, deletion (deletion function E) creates a network in a lower
dimensional state space:
Q: {-1,1}
N
{-1,1}
N+k
,
[2]
and hence
(
S
1
, ...,
S
k
,
S
k+1
, ...,
S
N
) (
S
1
,
S
1
, ...,
S
k
,
S
k
,
S
k+1
, ...,
S
N
)
[3]
and for deletions
E: {-1,1}
N+k
{-1,1}
N
,
[4]
and hence
(
S
1
,
S
1
, ...,
S
k
,
S
k
,
S
k
+1
, ...,
S
N
) (
S
1
, ...,
S
k
,
S
k
+1
, ...,
S
N
).
[5]
Wagner compa
re
s the wild-type equilibrium states (
S
) an
d
the state f
o
llowing
duplication (Q:
S
) using the Hamming distance between (
S
) and (Q:
S
) as the
robustness metric. It is observed that small duplications and large duplications
have the least impact on phenotypic change. And hence small and large dele-
tions are likely to have the least impact on phenotype. Intermediate sized dupli-
cations (around 40% of genes) have the greatest impact on phenotype. In a
region of the genome made up from sets of duplicate genes, perturbations in-
volving deletions of just under half of the genome are expected to have the
greatest effect on the phenotype, whereas genotypes are expected to be robust
against perturbations involving a few or almost all genes.
Redundancy in this model does not refer to the duplicate genes, but the
phenotypic invariance relating to epistasis in the transcriptional network. The
explanation for this result is fairly obvious. Duplicating all the genes leaves the
network effectively unchanged. Small numbers of duplications proportionately
influence a small number of connected pairs. Intermediate sized duplications are
likely to be most disruptive.
4.2. Modularity in Genetic Regulatory Networks
In
Drosophila
the anterior-posterior body axis is segmented. Segmentation
is initiated by maternal factors at the embryo stage. Those factors initiating seg-
