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 ThatWould Enable Controlling ImportantCellular Pathways
THE GOAL
To Establish Cellular Automata MethodAs a Basic Method for Modeling Dynamicsof 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 CASCADEA 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
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Iterations
Effe
ctiv
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A aveB aveC aveD aveE aveF aveG aveH ave
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-3 -2,5 -2 -1,5 -1 -0,5 0
MAPKK Protease Propensity, log P(E3)
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ntra
tions
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Example of MAPK-Cascade Spatial Models
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log [MAPKKKo]
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log [MAPKKKo]
MA
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-PP
/MA
PK
-PP
(max
)
MAPK – The Sigmoidal Pattern of Enzymes Cooperative Action
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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 E1 to E4 as a tool for controlling the MAPK pathway
Objectives To Accomplish Do This Validity Range
Decrease [MAPK] Inhibit E2, E3, E4 P = 0.9 P = 0.02
Increase [MAPK] Inhibit E1 P = 0.9 P = 0
Decrease [MAPK-PP] Inhibit E1 P = 0.9 P = 0
Increase [MAPK-PP] Inhibit E3, E4 P = 0.9 P = 0.02
Decrease [MAPKK] Inhibit E3 P = 0.9 P = 0.02
Increase [MAPKK] Inhibit E1 P = 0.9 P = 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 Deathactivator
DISC
Death-Inducing Signaling Complex
Heterodimer DFF
InitiatorCaspases 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 + DFF40CASP-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.infapopt5_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 noThe 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 ASB Blue BSC Green CSD Cyan DSD* Red D*SE Magenta ESE* Yellow E*SF White FSF* DarkBlue F*SG DarkGreen GSG* DarkCyan G*SH DarkRed HSJ Dark Magenta J
The Input Files - 3apopt5_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 0.021 A 0 0 B 0 0
A 0 0 D 0 0 0.021 C 0 0 D 0 0
C 0 0 D* 0 0 0.11 C 0 0 E 0 0
C 0 0 E* 0 0 0.11 C 0 0 F 0 0
C 0 0 F* 0 0 0.11 C 0 0 G 0 0
C 0 0 G* 0 0 0.11 D* 0 0 D 0 0
D* 0 0 D* 0 0 0.51 D* 0 0 E 0 0
D* 0 0 E* 0 0 0.11 D* 0 0 F 0 0
D* 0 0 F* 0 0 0.11 D* 0 0 G 0 0
D* 0 0 G* 0 0 0.11 E* 0 0 E 0 0
E* 0 0 E* 0 0 0.51 E* 0 0 F 0 0
E* 0 0 F* 0 0 0.11 E* 0 0 G 0 0
E* 0 0 G* 0 0 0.11 E* 0 0 H 0 0
E* 0 0 J 0 0 0.051 G* 0 0 F 0 0
G* 0 0 F* 0 0 0.11 G* 0 0 G 0 0
G* 0 0 G* 0 0 0.51 G* 0 0 H 0 0
G* 0 0 J 0 0 0.05
50% Apoptosis Outcome vs Probability of the Caspase-8 Activation
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probability
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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
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Caspase-10 Activation Probability
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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
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Probability of Caspase-7Activation
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Apoptosis Rate Dependence on the Activity of the Two Executor Caspases
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DCBA
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