Signaling and Metabolic Pathways

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Dec 1, 2013 (3 years and 11 months ago)

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Cellular Automata Modeling of
Signaling and Metabolic Pathways






Danail Bonchev






Lemont B. Kier






Chao
-
Kun Cheng

Some Introductory Remarks



Does a Biologist Need Philosophy of Science?



broader horizons




critical thinking



openness to new ideas



Does a Biologist Need Math?



Hegel



Math is beauty and fun!





Math begins with definitions



If You Don’t Want To Be an Outsider, Be a Forerunner!



The next 10
-
15 Years Will Be the Most Exciting in the History of


Biology and Medicine

Remarks on Cellular Automata Method
for Modeling Dynamics of Systems



A method that mirrors the discreteness of systems in space, time, and state


in contrast to the continuum created by differential equations.



It provides both temporal and spatial models of systems dynamics, and


enables identifying patterns of dynamic behavior.



CA models indicate potential targets for destroying pathogens or protecting


human cells, thus leading to pharmaceutical applications.




The technique is incredibly simple, fast, and entertaining.



CA models provide predictions of dynamic behavior that can be verified


experimentally.

To Identify Dynamic Patterns That

Would Enable Controlling Important

Cellular Pathways

THE GOAL

To Establish Cellular Automata Method

As a Basic Method for Modeling Dynamics

of Biological Pathways and Networks

The Lysine Biosysnthesis Pathway

KEGG release 4.1 (December 1997)

The Yeast Protein
-
Protein


Interaction Network

H. Jeong, S. P. Mason, A.
-
L. Barabasi, Z. N. Oltvai,
Nature

(2001)
411
, 41.

MAPKKK*

E1


E2

E3

MAPKK

MAPKK
-
P


MAPKK
-
PP

E4


MAPK


MAPK
-
P

MAPK
-
PP

MAPKKK

THE MAPK CASCADE

A signaling pathway, relaying signals from the plasma membrane


to targets in the cytoplasm and nucleus


L. B. Kier, D. Bonchev, G. A. Buck, Modeling Biochemical Networks: A Cellular Automata Approach,
Chem. Biodiversity

2, 233
-
243 (2005).


Information the CA Models Can Provide



Temporal Models


Variation of Ingredients Concentration With Time



Spatial Models


Effective Concentrations at Steady
-
State Conditions



Signal Amplification



Specific Dynamics Prediction




Means of Pathway Control

Example of A Temporal Dependence

Temporal Dependence of MAPK
Cascade Ingredients
0
50
100
150
200
250
300
350
400
450
500
0
1000
2000
3000
4000
5000
Iterations
Effective Concentration
A ave
B ave
C ave
D ave
E ave
F ave
G ave
H ave
0
50
100
150
200
250
300
350
400
450
500
-3
-2,5
-2
-1,5
-1
-0,5
0
MAPKK Protease Propensity, log P(E3)
Steady-State Concentrations
H
E
C
F
D
G
A
B
Example of MAPK
-
Cascade Spatial Models

0
50
100
150
200
250
300
350
400
450
500
0
1
2
3
log [MAPKKKo]
Steady-State Concentrations
C
F
H
E
A = B
D
G
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
-1,5
-1,0
-0,5
0,0
0,5
1,0
log [MAPKKKo]
MAPK-PP/MAPK-PP(max)
MAPK


The Sigmoidal Pattern of


Enzymes Cooperative Action

250
250
250
250
250
250
250
250
200
200
200
200
200
200
200
150
150
100
400
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300
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300
300
300
150
150
150
150
150
150
100
100
100
100
100
50
50
50
50
50
log P(E3)
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
MAPKKK Initial Concentration
50
100
150
200
250
MAPK


The Concentration/Enzyme Activity


Contour Plots


Table

1
.

Effects

of

modeling

enzyme

inhibition

in

the

MAPK

cascade


by

decreasing

the

variable

enzyme

propensity


Enzyme


Species


Concentration
Change


Change in %


E1


MAPK
-
PP


330


100


-
70


MAPKK
-
PP


140


25


-
82


MAPKK


220


400


+82


MAPK


60


230


+383


E2


MAPKK


395


210


-
47


MAPK


260


60


-
77


MAPK
-
P


140


340


+243


E3


MAPKK


420


95


-
77


MAPK


300


25


-
92


MAPK
-
PP


80


400


+500


E4


MAPK
-
PP


100


430


+430


MAPK


290


10


-
97

Table

2
.

Inhibiting

enzymes

E
1

to

E
4

as

a

tool

for

controlling

the

MAPK

pathway






Objectives To Accomplish


Do This Validity Range


Decrease [MAPK]

†††
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-
偐P ††††

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P 㴠0

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-
偐P ††††

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P 㴠0

The Apoptosis Pathway



Cellular suicide
, also known as
programmed cell death




A normal method of disposing of damaged, unwanted, or unneeded cells




Eliminate cells that threaten the organism's survival




Some forms of cancer result when this process of cell death


is somehow interrupted, and the cells grow without any control

FAS
-
L

FAS
-
R

FADD

CASP10

CASP8

CASP6

CASP3

CASP7

DFF45

DFF40


Death

activator

DISC

Death
-
Inducing Signaling Complex

Heterodimer DFF


Initiator

Caspases


Executor

Caspases


Start DNA

Fragmentation

Cleavage of Caspase


Substrates

The Apoptosis Pathway

Membrane


protein

FAS
-
L + DISC


DISC’ + CASP
-
8*


FAS
-
L + DISC


DISC’’ + CASP
-
1


CASP
-
8* + CASP
-
10


CASP
-
8* + CASP
-
10*


CASP
-
8* + CASP
-
3


CASP
-
8* + CASP
-
3*


CASP
-
8* + CASP
-
6


CASP
-
8* + CASP
-
6*


CASP
-
8* + CASP
-
7


CASP
-
8* + CASP
-
7*


CASP
-
10* + CASP
-
10


2CASP
-
10*


CASP
-
10* + CASP
-
3


CASP
-
10* + CASP
-
3*


CASP
-
10* + CASP
-
6


CASP
-
10* + CASP
-
6*


CASP
-
10* + CASP
-
7


CASP
-
10* + CASP
-
7*


CASP
-
3* + CASP
-
3


2CASP
-
3*


CASP
-
3* + CASP
-
3


2CASP
-
3*


CASP
-
3* + CASP
-
6


CASP
-
3* + CASP
-
6*


CASP
-
3* + CASP
-
7


CASP
-
3* + CASP
-
7*


CASP
-
3* + DFF


CASP
-
3* + DFF45 + DFF40

CASP
-
7* + CASP
-
7


2CASP
-
7*

CASP
-
7* + CASP
-
6


CASP
-
7* + CASP
-
6*

CASP
-
7* + DFF


CASP
-
7* + DFF45 + DFF40

The Interactions

The file name is:apopt5_7.inf

apopt5_7.str is the Str file on which the prb file is based


100 Num of Columns


100 Num of Rows


1 Torus 1 for yes 0 for no

The number of cells per cell types are below:


cell type number of cells


A 100


B 100


C 0


D 0


D* 0


E 100


E* 0


F 100


F* 0


G 100


G* 0

The Input Files
-

1

The Input Files
-

2

The file name is:apopt5_6.str


13 number of side types 13 number of cell
types


Their names are: Their colors are: Their names are:

SA Black A

SB Blue B

SC Green C

SD Cyan D

SD* Red D*

SE Magenta E

SE* Yellow E*

SF White F

SF* DarkBlue F*

SG DarkGreen G

SG* DarkCyan G*

SH DarkRed H

SJ Dark Magenta J


The Input Files
-

3

apopt5_7.str is the Str file on which the prb file is based


0 Num of SidevsSide (w.r.t symm and anti
-
symm)


1 1 for symmetric


0 1 for anti
-
symm.

The breaking and joining prb. w.r.t. side vs side are below:


side vs side breaking prb. joining prb


SA vs SA 1 0


SA vs SB 1 1


SA vs SC 1 0


SA vs SD 1 0


SA vs SD* 1 0


SA vs SE 1 0


SA vs SE* 1 0


SA vs SF 1 0


SA vs SF* 1 0


SA vs SG 1 0


SA vs SG* 1 0


SA vs SH 1 0


SA vs SJ 1 0


SB vs SB 1 0


SB vs SC 1 0


SB vs SD 1 0


SB vs SD* 1 0


SB vs SE 1 0


SB vs SE* 1 0


SB vs SF 1 0


SB vs SF* 1 0


SB vs SG 1 0


10

rules for *****Paired change after move*****

1

A

0

0

B

0

0



A

0

0

C

0

0

0.02

1

A

0

0

B

0

0



A

0

0

D

0

0

0.02

1

C

0

0

D

0

0



C

0

0

D*

0

0

0.1

1

C

0

0

E

0

0



C

0

0

E*

0

0

0.1

1

C

0

0

F

0

0



C

0

0

F*

0

0

0.1

1

C

0

0

G

0

0


C

0

0

G*

0

0

0.1

1

D*

0

0

D

0

0



D*

0

0

D*

0

0

0.5

1

D*

0

0

E

0

0



D*

0

0

E*

0

0

0.1

1

D*

0

0

F

0

0



D*

0

0

F*

0

0

0.1

1

D*

0

0

G

0

0



D*

0

0

G*

0

0

0.1

1

E*

0

0

E

0

0



E*

0

0

E*

0

0

0.5

1

E*

0

0

F

0

0



E*

0

0

F*

0

0

0.1

1

E*

0

0

G

0

0



E*

0

0

G*

0

0

0.1

1

E*

0

0

H

0

0



E*

0

0

J

0

0

0.05

1

G*

0

0

F

0

0



G*

0

0

F*

0

0

0.1

1

G*

0

0

G

0

0



G*

0

0

G*

0

0

0.5

1

G*

0

0

H

0

0



G*

0

0

J

0

0

0.05

50% Apoptosis Outcome vs Probability of
the Caspase-8 Activation
600
700
800
900
1000
1100
1200
1300
1400
1500
0
0.2
0.4
0.6
0.8
1
probability
Number of Iterations
Apoptosis Rate Dependence on Caspase
-
8 Activation

Series # 3. Variation of Probabilities of
Activation of Caspaces-3, -6, and -7 by
Caspase-8 and Caspase-10
600
700
800
900
1000
1100
1200
1300
1400
0
0.2
0.4
0.6
0.8
1
Caspase-10 Activation Probability
Number of Iterations Needed
for 50% Outcome Signal
0.005
0.02
0.08
0.2
0.8
Apoptosis Rate Dependence on the Activity of


the Two Initiator Caspases

Variations in the Apoptosis Rate As a Function
of the Probabilities of Activation of Caspase-3
and Caspase-7
500
700
900
1100
1300
1500
1700
1900
2100
2300
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Probability of Caspase-7Activation
Iterations for 50% outcome
Series1
Series2
Series3
Series4
Series5
Series6
Apoptosis Rate Dependence on the Activity of


the Two Executor Caspases

B


A

C


C

B

C


B

A

D

C

B

A

B

A

C

D

B

A

C

D

B

A

C

D

B

A

C

D


B

A

C

D

B

A

C

D

A

1300

65

1020

48

1300

65

1060

76

680

63

1040

110

1080

76

700

80

1020

122

1740

102

740

82

640

73

2100

99

860

90

920

78

1520

72

2000

228

620

63

1160

76

1500

73

660

70

1180

48

1280

143

700

122

1000

49

1120

110

1020

166

1

2

3

4

5

6

7

8

9

10


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