Biomedical Engineering Reference
In-Depth Information
Figure 4
.
Cell fates as attractors
. The structure of the
N
-dimensional state space (
N
= number
of interacting genes in the network, e.g.,
N
= 10,000) is schematically shown as a three-
dimensional topographic "attractor landscape" that is conceptually equivalent to Waddington's
"epigenetic landscape" (Figure 5). Each point in the landscape represents a cell state
S
, defined
by the profile of the activation state
x
(measured as mRNA level) of all the
N
genes:
S
= [
x
1
(
t
),
x
2
(
t
), ...
x
N
(
t
)]. The pits in the landscape are the attractor states that represent the stable cell
fates, in this case the precursor cell and the differentiated neutrophil. Transition into the differ-
entiated state can be triggered by two pharmacologically distinct differentiation-inducing
agents that perturb the state of the precursor cell in different ways such that the cells takes two
different trajectories,
A
and
B
, respectively, to reach the neutrophil state. Monitoring the
change of
S
(
t
) along these two high-dimensional trajectories,
S
A
(
t
) and
S
B
(
t
), respectively, as the
change of gene expression profile using DNA microarrays would allow calculation of the inter-
trajectory distance
D
. The inset on top illustrates a case for the time course of
D
for a set of
2600 genes in a differentiation process. In this case, the course of
D
shows initial, rapid diver-
gence of the trajectory, followed by terminal convergence in more than 50% of the state di-
mensions as the cell reaches the differentiated state, indicating the approach to a high-
dimensional attractor state. Reprinted with permission from Huang (76).
down valleys (Figure 5) based on his observation that cells "switch between
distinct, well recognizable types" during development, and that intermediates are
rare and unstable (67,68). This picture captures the basic rules governing cell
fate dynamics, and we can now argue that, although proposed as an intuitive
representation, Waddington's epigenetic landscape is in principle the state space
of the molecular network that controls cell fates. Thus, the attractor landscape
represents the emergent properties of the interaction network.
