Lecture
11
Introduction to signaling pathways
Glycolytic
Oscillation
Reverse Engineering of biological networks
Signaling networks involves the transduction of “signal”
usually from outside to the inside of the cell
On molecular level signaling involves the same type of
processes as metabolism such as production and degradation
of substances, molecular modifications (mainly
phosphorylation
but also
methylation
and
acetylation
) and
activation or inhibition of reactions.
But signaling pathways serve for information processing or
transfer of information while metabolism provide mainly
mass transfer
Introduction to signaling pathways
Introduction to signaling pathways
Signal transduction often involves:
•
The binding of a
ligand
to an extracellular receptor
•
The subsequent
phosphorylation
of an intra cellular
enzyme
•
Amplification and transfer of the signal
•
The resultant change in the cellular function e.g. increase
/decrease in the expression of a gene
Signaling
paradiam
Usually a signaling network has three principal parts:
Events around the membrane
Reactions that link sub

membrane events to the nucleus
Events that leads to transcription
Source: Systems biology in practice by E.
klipp
et. al.
Schematic representation of receptor activation
Source: Systems biology in practice by E.
klipp
et. al.
Steroids
Not always a receptor exists at
the membrane for example the
steroid receptors.
Sterol lipids include hormones
such as
cortisol
, estrogen,
testosteron
and
calcitriol
.
These steroids simply cross the
membrane of the target cell and
then bound the intracellular
receptor which results in the
release of the inhibitory
molecule from the receptor.
The receptor then traverses the
nuclear membrane and binds to
its site on the DNA to trigger the
transcription of the target gene.
Source: Systems biology by Bernhard O.
Palsson
G

protein signaling
G

protein coupled receptor (GPCR)
represents important components of
signal transduction network
This class of receptor comprises
5
% of
the genes in C.
elegans
The G

protein complex consists of
three subunits (α, β and λ) and in its
inactive state bound to
guanosine
diphosphate
(GDP)
When a
ligand
binds to the GPCR, the
G

protein exchanges its GDP for a
guanosine
trihosphate
(GTP)
This exchange leads to the dissociation
of the G

protein from the receptor and
its split into a
βλ
complex and a GTP

bound α subunit which is its active
state initiating other downstream
processes
Source: Systems biology by Bernhard O.
Palsson
G

protein signaling model
Source: Systems biology in practice by E.
klipp
et. al.
G

protein signaling model
Time course of G protein activation. The total number of
molecules is
10000
. The concentration of GDP

bound
Gα
is low
for the whole period due to its fast complex formation with the
heterodimer
Gβλ
Source: Systems biology in practice by E.
klipp
et. al.
The JAK

STAT network
A cell surface receptor often
dimerizes
upon binding to a cytokine
The
monomeric
form of the receptor is associated with a
kinase
called
JAK
When the receptor
dimerizes
the JAKs induce
phosphorylation
of
themselves and the receptor which is the active state of the receptor.
The active complex
phosphorylates
the STAT(signal transducer and
activator of transcription) molecules
STAT molecules then
dimerizes
, go to nucleus and trigger transcription
The JAK

STAT signaling
system is an important two

step process that is involved
in multiple cellular functions
including cell growth and
inflammatory response
Source: Systems biology in practice by E.
klipp
et. al.
Schematic representation of the MAP
kinase
cascade. An
upstream signal causes
phosphorylation
of the MAPKKK. The
phosphorylation
of the MAPKKK in turn
phosphorylates
the
protein at the next level.
Dephosphorylation
is assumed to occur
continuously by
phosphatases
or
autodephosphorylation
Source: Systems biology in practice by E.
klipp
et. al.
Signaling pathways in Baker’s yeast
HOG pathway
activated by osmotic shock,
pheromone pathway
activated by pheromones from cells of opposite mating type and
pseudohyphal
growth pathway
stimulated by starvation condition
A MAP
kinase
cascade is a particular part of many
signalling
pathways . In this figure its components are indicated by bold
border
Source: Systems biology in practice by E.
klipp
et. al.
Glycolytic
Oscillation
In living organism we see many periodic changes or oscillations:
Pulse of the heart
Respiration
Ovulation in mammals
Annual flowering of the plants
Sleeping at night
Lifecycle of cells
Actually after starting or being affected by some perturbation
many systems go through oscillations before becoming stable or
unstable (collapsing)
Glycolytic
Oscillation
Phosphofructokinase

1
(PFK

1
) catalyzes the important step
of
glycolysis
, the conversion of fructose
6

phosphate and
ATP to fructose
1
,
6

bisphosphate and ADP.
The ADP then exert a positive feedback on PFK

1
This system can be represented as follows:
For a large range of parameter values the system moves to a
stable steady state but beyond a critical parameter value the
system becomes unstable.
Glycolytic
Oscillation
The Temporal behavior of the concentration of substrate
and product can be described as follows:
Here the supply rate of S is v
0
and k
1
and k
2
are mass action rate
constants.
The function R(p) represents the autocatalytic effect of the
product P on its own production
Glycolytic
Oscillation
Glycolytic
Oscillation
Assuming
r(P) = P
2
,
The Temporal behavior of the
concentration of substrate and product can be described
as follows:
Glycolytic
Oscillation
The dynamic behavior of the above system with a particular set
of parameter values is represented as follows:
The above solution corresponds to v
0
=
1
, and k
1
=
1
, and k
2
=
1.00001
S(
0
)=
2
, P(
0
)=
1
in
arbitrary unit
By using
dS
/
dt
=
0
and
dP
/
dt
=
0
, The steady state solutions
for the above system can be determined as follows:
However the steady state is achievable or not depends on
the parameter values
Glycolytic
Oscillation
The stability of the steady state can be analyzed by inspection of the
Jacobian
matrix J.
The character of the steady state is determined by the value and signs
(positive, negative , zero etc.) of trace and the determinant of the
Jacobian
matrix
Glycolytic
Oscillation
Glycolytic
Oscillation
The stability analysis of the above system for fixed value of k
1
=
1
and variable values of V
0
and k
2
Glycolytic
Oscillation
The stability analysis of the above system for fixed value of k
1
=
1
and variable value of
vo
and k
2
With v
0
=
1
, k
1
=
1
, and k
2
=
1.00001
the system is in the stable focus region which
means it gradually goes to steady state through decaying oscillation
Reverse Engineering of biological networks
The task of reverse engineering of a genetic network is the
reconstruction of the interactions among biological entities (
genes, proteins, metabolites etc.) in a qualitative way from
experimental data using algorithm that weight the nature of
the possible interactions with numerical values.
In forward modeling network is constructed with known
interactions and subsequently its topological and other
properties are analyzed
In reverse engineering the network is estimated from
experimental data and then it is used for other predictions
Reverse Engineering of gene regulatory network
By clustering the gene expression data, we can determine co

expressed genes.
Co

expressed genes might have similar regulatory characteristics
but it is not possible to get the information about the nature of
the regulation.
Here we discuss a reverse engineering method of estimating
regulatory relation between genes based on gene expression
data from the following paper:
Reverse engineering gene networks using singular value
decomposition and robust regression
M. K. Stephen
Yeung
,
Jesper
Tegne
´
r†, and James J. Collins‡
Proc. Natl. Acad. Sci. USA
99
:
6163

6168
It is assumed that the dynamics i.e. the rate of change of a gene

product’s abundance is a function of the abundance of all other
genes in the network.
For all N genes the system of equations are as follows:
In Vector notation
Where f(X) is a vector valued function
Reverse Engineering of gene regulatory network
Under linear assumption i.e. has linear relation with X
i
s we
can write
Here
A
ij
is the coupling parameter that represents the
influence of
X
j
on the expression rate of X
i
. In other words
A
ij
represents a network showing the regulatory relation among
the genes.
Target of reverse engineering is to determine A. Solving A
requires a large number of measurements of and X
Reverse Engineering of gene regulatory network
Measurement of is difficult and hence can be estimated in
several ways.
First, if time series data can be obtained then can be
approximated by using the profiles of the expression values for
fixed time intervals
Alternatively a cellular system at steady state can be perturbed
by external stimulation and then can be determined by
comparing the gene expression in the perturbed cellular
population and the unperturbed reference population.
Reverse Engineering of gene regulatory network
Now using any method if we can
produce
matrices and
then we can write
Or, (if external perturbation is used)
Here
B
NxM
is the matrix representing the effect of
perturbation
The goal of reverse engineering is to use the measured
data
B
,
X
, and
to deduce
A
i.e. the connectivity matrix of
the regulatory relation among the genes.
Reverse Engineering of gene regulatory network
By taking transpose the system can be rewritten as
A
is the unknown. If
M
=
N
and
X
is full

ranked, we can simply
invert the matrix
X
to find
A
. However, typically
M<<N
mainly
because of the high cost of perturbations and measurements.
We therefore have an underdetermined problem.
Underdetermined problem means the number of linearly
independent equations is less than the number of unknown
variables. Therefore there is no unique solution One way to
get around this is to use SVD to decompose
X
T
into
Reverse Engineering of gene regulatory network
where
U
and
V
are each orthogonal which means:
with
I
being the identity matrix, and
W
is diagonal:
Without loss of generality, we may assume that all nonzero
elements of
w
k
are listed at the end, i.e.,
w
1
,
w
2
, . . . ,
wL
=
0
and
w
L
+
1
,
w
L
+
2
,. . . ,
w
N
≠
0
, where
L
:=dim(
ker
(
X
T
)). Then one
particular solution for
A
is:
Reverse Engineering of gene regulatory network
the general solution is given by the affine space
with
C
= (
c
ij
)
N
×
N
, where
c
ij
is zero if
j
>
L
and is otherwise an
arbitrary scalar coefficient. This family of solutions in Eq.
3
represents all the possible networks that are consistent with the
microarray data. Among these solutions, the particular solution
A
0
is the one with the smallest
L
2
norm.
Now, the question is which one of the solutions of equation
3
is
the best.
Reverse Engineering of gene regulatory network
In such cases, we may rely on insights provided by earlier
works on gene regulatory networks and bioinformatics
databases, which suggest that naturally occurring gene
networks are sparse, i.e., generally each gene interacts with
only a small percentage of all the genes in the entire genome.
Imposing sparseness on the family of solutions given by Eq.
3
means that we need to choose the coefficients
c
ij
to maximize
the number of zero entries in
A
.
This is a nontrivial problem.
Reverse Engineering of gene regulatory network
The task is equivalent to the problem of finding the exact

fit
plane in robust statistics, where we try to fit a
hyperplane
to a
set of points containing a few outliers.
Here they have chosen
L
1
regression where the figure of merit
is the minimization of the sum of the absolute values of the
errors, for its efficiency.
In short, this method of reverse engineering can produce
multiple solutions (gene networks) that are consistent with a
given microarray data. This paper says among them the
sparsest one is the best solution and used L
1
regression to
detect the best solution.
Reverse Engineering of gene regulatory network
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