Bioinformatics tools as JAWB (Just another Western Blot)

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2 Οκτ 2013 (πριν από 4 χρόνια και 13 μέρες)

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Analyzing the systemic
function of genes and proteins

Rui Alves

Organization of the talk


From networks to physiological behavior


Network representations


Mathematical formalisms


Studying a mathematical model

In silico

networks are limited as
predictors of physiological behavior

What happens?

Probably a very sick mutant?

How to predict behavior from
network?


Build mathematical models!!!!

Organization of the talk


From networks to physiological behavior


Network representations


Mathematical formalisms


Studying a mathematical model

Network representation is
fundamental for clarity of analysis

A

B

What does this mean?

Possibilities:

A

B

Function

B

A

Function

A

B

Function

A

B

Function

B

A

Function

Defining network conventions

A



B

C

Full arrow represents a flux between A and B

Dashed arrow represents modulation of a flux

+

Dashed arrow with a plus sign represents positive
modulation of a flux

-

Dashed arrow with a minus sign represents negative
modulation of a flux

Organization of the talk


From networks to physiological behavior


Network representations


Mathematical formalism


Studying a mathematical model

Representing the time behavior of
your system

A



B

C

+

What is the form of the function?

A



B

C

+

A or C

Flux

Linear

Saturating

Sigmoid

What if the form of the function is
unknown?

A



B

C

+

Taylor Theorem:

f(A,C) can be written as a polynomial function
of A and C using the function’s
mathematical derivatives with respect to the
variables (A,C)




Are all terms needed?

A



B

C

+

f(A,C) can be approximated by considering
only a few of its mathematical derivatives
with respect to the variables (A,C)




Linear approximation

A



B

C

+

Taylor Theorem:

f(A,C) is approximated with a linear function
by its first order derivatives with respect to
the variables (A,C)




What if system is non
-
linear?


Use a first order approximation in a
non
-
linear space.

Logarithmic space is non
-
linear

A



B

C

+

g<0 inhibits flux

g=0 no influence on flux

g>0 activates flux

Use Taylor theorem in Log space

Why log space?


Intuitive parameters


Simple, yet non
-
linear


Linearizes exponential space


Many biological processes are
close to exponential
→ Linearizes
mathematics


Why is formalism important?


Reproduction of observed behavior



Tayloring of numerical methods to specific
forms of mathematical equations

Organization of the talk


From networks to physiological behavior


Network representations


Mathematical formalism


Studying a mathematical model

A model of a biosynthetic pathway

X
0

X
1

_

+

X
2

X
3

X
4

Constant

Protein
using X
3

What can you learn?


Steady state response


Long term or homeostatic systemic
behavior of the network


Transient response


Transient of adaptive systemic
behavior of the network


What else can you learn?


Sensitivity of the system to
perturbations in parameters or
conditions in the medium


Stability of the homeostatic behavior
of the system


Understand design principles in the
network as a consequence of
evolution

Steady state response analysis

How is homeostasis of the flux
affected by changes in X
0
?

Log[X
0
]

Log[V]

Low g
10

Medium g
10

Large g
10

Increases in X0 always increase the
homeostatic values of the flux through the
pathway

How is flux affected by changes in
demand for X
3
?

Log[X
4
]

Log[V]

Large g
13

Medium g
13

Low g
13

How is homeostasis affected by
changes in demand for X
3
?

Log[X
4
]

Log[X
3
]

Low g
13

Medium g
13

Large g
13

What to look for in the analysis?


Steady state response


Long term or homeostatic systemic
behavior of the network


Transient response


Transient of adaptive systemic
behavior of the network


Transient response analysis

Solve numerically

Specific adaptive response

Get parameter values

Get concentration
values

Substitution

Solve
numerically

Time

[X
3
]

Change in X
4

General adaptive response

Normalize

Solve numerically
with
comprehensive
scan of parameter
values

Time

[X
3
]

Increase in X
4

Low g
13

Increasing g
13

Threshold g
13

High g
13

Unstable system, uncapable of
homeostasis if feedback is strong!!

Sensitivity analysis


Sensitivity of the system to changes in
environment


Increase in demand for product causes increase
in flux through pathway


Increase in strength of feedback increases
response of flux to demand


Increase in strength of feedback decreases
homeostasis margin of the system

Stability analysis


Stability of the homeostatic behavior


Increase in strength of feedback
decreases homeostasis margin of the
system

How to do it


Download programs/algorithms and do it


PLAS, GEPASI, COPASI SBML suites,
MatLab, Mathematica, etc.



Use an on
-
line server to build the model
and do the simulation


V
-
Cell, Basis

Design principles


Why is a given pathway design
prefered over another?


Overall feedback in biosynthetic
pathways


Why are there alternative designs of
the same pathway?


Dual modes of gene control

Why regulation by overall feedback?

X
0

X
1

_

+

X
2

X
3

X
4

X
0

X
1

_

+

X
2

X
3

X
4

_

_

Overall
feedback

Cascade
feedback

Overall feedback improves
functionality of the system

Time

Spurious
stimulation

[C]

Overall

Cascade

Proper
stimulus

Overall

Cascade

[C]

Stimulus

Overall

Cascade

Dual Modes of gene control

Demand theory of gene control

Wall
et al
, 2004, Nature Genetics Reviews


High demand

for gene expression

Positive

Regulation


Low demand

for gene expression

Negative

mode of regulation

How to do it


Download programs/algorithms and do it


BST Lab, Mathematica, Maple

Summary


From networks to physiological behavior


Network representations


Mathematical formalism


Studying a mathematical model

Papers to present


Vasquez et al, Nature


Alves et al. Proteins


Computational tools in Molecular
Biology


Predictions & Analysis


Identification of components


Organization of components


Conectivity of components


Behavior of systems


Evolution & Design


Prioritizing wet lab experiments


Most likely elements to test


Most likely processes to test

The Taylor theorem

C

f(C)

0 order

f(C)

1
st

order

2
nd

order

i
th

order

i
th

+ j
th

order

Are all terms needed?

A



B

C

+

f(A,C) can be approximated by considering
only a few of its mathematical derivatives
with respect to the variables (A,C)




Linear approximation

A



B

C

+

Taylor Theorem:

f(A,C) is approximated with a linear function
by its first order derivatives with respect to
the variables (A,C)




What if flux is non linear?

A



B

C

+

Use Taylor theorem in Non
-
Linear space!

Use Taylor theorem with large number of terms





or

How does the transformation
between spaces work?

X

Y

X

Y

How does the Taylor approximation
work in another space?

Variables:

A, B, C, …

f(A,B,…)

Variables:

A, B, C, …

f(A,B,…)

~
f(A,B,…)

Taylor
theorem

Transform to new space

Return to original space

~
f(A,B,…)