Lecture 11 (pptx)

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Dec 14, 2012 (4 years and 6 months ago)

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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


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