Biology Reference
In-Depth Information
parameters, including global binding affinities and noise
levels.
Extensions of the simple cooperativity-based bistable
model described by Eqs
1and3
may include a unilateral
repression of the core circuit's members by one or more
repressors (see scenario in
Figure 22.3
B). In the context of
the core network such unilateral repression results in oscil-
latory behavior. In the case of two or more repressors their
oscillations may or may not synchronize, depending on the
relative strength of linkage between the core factors involved
in the unilateral repression (see
Figure 22.6
C, D). This
supports the possibility for strange attractor-like steady
states and/or limit cycles for the core pluripotency network.
tags attached to antibodies using metal-chelating labeling
reagents, and allow reading of 30 channels (proteins) and
more in a large number of cells.
Improper balance between the number of open
(unknown) parameters in the system and the amount of
available experimental data (such as single cell readings)
may be a serious issue. If few data are available, over-
whelming numbers of parameters may result in data over-
fitting, when the available data fit almost any model. The
presence of overfitting may be displayed by deletion or
over-expression in silico, as described above. In the case of
BRN-based models, the number of parameters may be
reduced by learning the relative values of binding constants
from promoter and enhancer DNA sequences (see above) or
using global parameters for most of the reaction compo-
nents. For instance, degradation and synthesis constants as
well as constants for gene expression noise may be
considered identical for all network components regulated
in a similar manner. Indeed, biological networks typically
have sufficient robustness to tolerate significant changes in
component concentrations. The described strategies may
help to minimize the number of open parameters to three to
five in the case of models for single kernels (such as the
core circuit alone), and 10
Model Validation and Overfitting
A simple way to validate quantitative models is to perform
a series of deletion or over-expression in silico to test the
consistency between predictive behavior from the quanti-
tative simulations and biological outcomes from experi-
mental gene perturbations. For example, in the Boolean
formalism the predictive results could be steady states/
attractors of a network after in-silico simulations of gene
knockdown by forcing that gene to be constantly 'off'.
Gene expression pattern of the steady states after such
perturbation can then be examined by RNA interference-
mediated gene knockdown followed by real-time PCR of
the network genes. Approximate distribution of dynamic
attractors and the presence of limit cycles is a more chal-
lenging problem. Mapping phase spaces such as those
shown in
Figure 22.6
may be explored based on single-cell
gene expression data. A major experimental challenge here
is to obtain reliable protein level readouts in single cells for
as many network components as possible. Tools available
for such measurements include transgenic cell lines
expressing GFP under the control of regulatory elements
for the core pluripotency factors Nanog or Oct4
[10]
.
These cell lines provide the power to measure gene
expression in live cells and record gene expression
dynamics. However, these measurements can be done in
a single channel only for either Nanog or Oct4. Routine
immunostaining in combination with flow cytometry will
allow an increase in the number of channels to three or four
(1
e
transgenic Nanog
þ
2
e
3 channels for immunostan-
ing)
[129]
. This number of channels will entirely satisfy
elementary models, such as the core circuit model (see
preliminary results), but will be insufficient for larger
models. Methods based on high-throughput real-time
PCR assays (BioMark System, Fluidigm Corporation) are
able to deliver readings for up to 96 genes (mRNA) in
a single cell, but the number of cells (96) in this method
requires the use of multiple chips to achieve statistically
sound cell numbers. Recently emerging mass cytometry-
based methods
[130]
read the stable lanthanide isotope
20 in the case of larger, inte-
e
grated networks
[113]
.
INFORMATION FLOW AND EPIGENETIC
LANDSCAPES IN DIFFERENTIATION
Information Flow and Epigenetic Memory
One interesting problem emerging from quantitative anal-
ysis of stem cell gene networks is informational flow in the
system during self-renewal and differentiation. The infor-
mation content of any pluripotent cell state and each tran-
sient or terminally differentiated state can be characterized,
for instance, by a genome-wide set of gene expression
levels. This rather trivial representation is supported by
frequently observed specific 'molecular signatures' char-
acterizing pluripotent and differentiated cell types in
microarray studies
[14]
. During transition between two
(rather arbitrary defined) neighboring cell states n and n
þ
1,
genes specific to n
þ
1 are activated, whereas some genes
specific to n are shut down and some genes specific to n
maintain or slightly change their activity levels
(
Figure 22.7
A). One can see that the new information,
required to achieve state n
1 from state n, has been read
from the genome. Intuitively, the amount of new informa-
tion may not exceed the amount of binary information
contained in the DNA encoding the newly activated genes,
with the account of their transcription regulatory regions as
well. In the case of differentiation, the genome plays a role
similar to that of a storage device on a computer, such as
þ
