Biology Reference
In-Depth Information
The Toggle-Switch as an Example for a Gene Regulatory Network
In the following we present a simplifed, qualitative introduction to network dynamics using
the well-known example of
N
2-gene network to demonstrate key concepts of network
dynamics, attractors and landscape. The mutual inhibition of two opposing transcription
factors (TFs), which we call X
1
and X
2
, is one of the simplest GRNs (
Fig. 5.1A
). We are now
interested in how the network state
S
, which is defined by the measurable gene expression
5
(A)
X
1
X
2
Gene regulatory
network
State space &
vector field
Quasi-potential
landscape
(B)
84
X
1
X
2
Cell type1
(C)
Multi-potent
progenitor cell
Cell type 1
binary cell fate
decision
Cell type 2
Cell type 3
State space
coordinate
( ~ X2/X1 )
Differentiated
(mature) cells
X
1
X
2
Cell type 2
Cell type 3
X
1
X
2
X
1
X
2
FIGURE 5.1
Topology, state spaces with the vector field and quasi-potential landscapes of gene-regulatory networks (circuits). For the two gene circuits (A) and (B), various
representations are given from left to right: The gene circuit topology, the state space with the vector field, and the quasi-potential landscape. Circuit (A)
represents the cross-inhibition and bistability, with two attractors S
1
and S
2
which are separated by a saddle point S
0
. Circuit (B) has two positive-feedback
loops which stabilize the central steady-state S
0
, converting it from unstable to stable. The latter can serve to represent a metastable progenitor state which can
differentiate to two differentiated cell fates, represented by attractors S
1
ð
X
2
Þ and S
2
ð
X
1
c
X
2
c
X
1
Þ, as shown in (C).
