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 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

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MAPKK Protease Propensity, log P(E3)

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Example of MAPK-Cascade Spatial Models

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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 - 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 0.021 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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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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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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Apoptosis Rate Dependence on the Activity of the Two Executor Caspases

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Other ProjectsCorrelated Topology/Dynamics Patterns