Systems biology and complexity research Peter Schuster Institut fr - - PowerPoint PPT Presentation

Systems biology and complexity research

Peter Schuster

Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA

Interdisciplinary Challenges for Complexity Sciences Brussels, 27.– 28.05.2009

Web-Page for further information: http://www.tbi.univie.ac.at/~pks

1. Complex networks in cellular regulation 2. Experimental data and modeling in biology 3. Parameter determination and reverse engineering 4. Gene regulation dynamics 5. Inverse bifurcation analysis 6. Current challenges in biology

1. Complex networks in cellular regulation 2. Experimental data and modeling in biology 3. Parameter determination and reverse engineering 4. Gene regulation dynamics 5. Inverse bifurcation analysis 6. Current challenges in biology

1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Enzyme Metabolite Regulatory gene Structural gene

A model genome with 12 genes

Sketch of a genetic and metabolic network

A B C D E F G H I J K L 1

Biochemical Pathways

2 3 4 5 6 7 8 9 10

The reaction network of cellular metabolism published by Boehringer-Mannheim.

The citric acid

• r Krebs cycle

(enlarged from previous slide). The reaction network of cellular metabolism published by Boehringer-Mannheim.

• E. coli:

Genome length 4×106 nucleotides Number of cell types 1 Number of genes 4 460 Four books, 300 pages each Man: Genome length 3×109 nucleotides Number of cell types 200 Number of genes 30 000 A library of 3000 volumes, 300 pages each Complexity in biology

1. Complex networks in cellular regulation 2. Experimental data and modeling in biology 3. Parameter determination and reverse engineering 4. Gene regulation dynamics 5. Inverse bifurcation analysis 6. Current challenges in biology

From qualitative data to quantitative modeling Genomics, transcriptomics, proteomics Metabolomics, functional genomics Computational systems biology

time

Analysis by gel electrophoresis

Jeff Rogers, Gerald F. Joyce. RNA 7:395-404, 2001

The same section of the microarray is shown in three independent hybridizations. Marked spots refer to: (1) protein disulfide isomerase related protein P5, (2) IL-8 precursor, (3) EST AA057170, and (4) vascular endothelial growth factor.

Gene expression DNA microarray representing 8613 human genes used to study transcription in the response of human fibroblasts to serum. V.R.Iyer et al., Science 283: 83-87, 1999

Embryonic stem cell

SOM-based “GEDI maps” (Eichler, G.S. et al., Bioinformatics 2003)

Brain Liver Muscle Kidney Prostate

Log2(ratio) HIGH

LOW

Hsiao, L.L. et al., Physiol.Genomics 2001 Affymetrix, ~ 7000 genes

Drawings by Stuart A. Kauffman, 2009

A pH-modulated, self-replicating peptide

Shao Yao, Indraneel Ghosh, Reena Zutshi, Jean Chmielewski. J.Am Chem.Soc. 119:10559-10560, 1997

Time t Concentration xi (t) Stoichiometric equations

SBML – systems biology markup language

Kinetic differential equations

ODE Integration

Solution curves

A + B X 2 X Y Y + X D y x k d y x k x k y y x k x k b a k x b a k b a

3 3 2 2 3 2 2 1 1

t d d t d d t d d t d d t d d = − = − − = − = = The elements of the simulation tool MiniCellSim

SBML: Bioinformatics 19:524-531, 2003; CVODE: Computers in Physics 10:138-143, 1996

Stefan Bornholdt. Less is more in modeling large genetic networks. Science 310, 449-450 (2005)

1. Complex networks in cellular regulation 2. Experimental data and modeling in biology 3. Parameter determination and reverse engineering 4. Gene regulation dynamics 5. Inverse bifurcation analysis 6. Current challenges in biology

General conditions Initial conditions : T , p , pH , I , ... :

...

... S ,

u

Boundary conditions

boundary normal unit vector Dirichlet Neumann :

:

:

) ( x

) , ( t r g x S =

• Time

t Concentration ( ) x t Solution curves: xi(t) Kinetic differential equations ) ; (

2

k x f x D t x + ∇ = ∂ ∂

) , , ( ; ) , , ( ; ) ; (

1 1 m n

k k k x x x k x f t d x d

K K

= = = Reaction diffusion equations

) , ( ˆ t r g x u u x

S =

∇ ⋅ = ∂ ∂

Parameter set

m , , 2 , 1 j ; ) , I , H p , p , T (

j

K K = k

The forward problem of chemical reaction kinetics (Level I)

General conditions Initial conditions : T , p , pH , I , ... :

...

... S ,

u

Boundary conditions

boundary normal unit vector Dirichlet Neumann :

:

:

) ( x

) , ( t r g x S =

• Time

t Concentration ( ) x t Solution curves: xi(t) Kinetic differential equations ) ; (

2

k x f x D t x + ∇ = ∂ ∂ ) , , ( ; ) , , ( ; ) ; (

1 1 m n

k k k x x x k x f t d x d K K = = = Reaction diffusion equations

) , ( ˆ t r g x u u x

S =

∇ ⋅ = ∂ ∂

Parameter set

m j I H p p T kj , , 2 , 1 ; ) , , , , ; I ( G K K =

Genome: Sequence IG

The forward problem of biochemical reaction kinetics (Level I)

The inverse problem of biochemical reaction kinetics (Level I)

Time t Concentration Data from measurements (t ); = 1, 2, ... , x j N

j

xi (t )

j

Kinetic differential equations

) ; (

2

k x f x D t x + ∇ = ∂ ∂ ) , , ( ; ) , , ( ; ) ; (

1 1 m n

k k k x x x k x f t d x d

K K

= = = Reaction diffusion equations General conditions Initial conditions : T , p , pH , I , ... :

...

... S ,

u

Boundary conditions

boundary normal unit vector Dirichlet Neumann :

:

:

) ( x

) , ( t r g x S =

• )

, ( ˆ t r g x u u x

S =

∇ ⋅ = ∂ ∂

Parameter set

m j I H p p T k j , , 2 , 1 ; ) , , , , ; I ( G K K

=

Genome: Sequence IG

General conditions Initial conditions : T , p , pH , I , ... :

...

... S ,

u

Boundary conditions

boundary normal unit vector Dirichlet Neumann :

:

:

) (

x

) , ( t r g x S =

• Kinetic differential equations

) ; ( f

2

k x x D t x + ∇ = ∂ ∂

) , , ( ; ) , , ( ; ) ; ( f

1 1

m n

k k k x x x k x t d x d

K K

= = = Reaction diffusion equations

) , ( ˆ t r g x u u x

S =

∇ ⋅ = ∂ ∂

Parameter set

m j I H p p T k j , , 2 , 1 ; ) , , , , ; I ( G K K =

Genome: Sequence IG

Bifurcation analysis

( , ; ) k k

i j k

kj ki

x t

( )

time

xn

xm

P

xn

xm

P P

xn xm

P

The forward problem of bifurcation analysis (Level II)

The inverse problem of bifurcation analysis (Level II)

Kinetic differential equations

) ; (

2

k x f x D t x + ∇ = ∂ ∂

) , , ( ; ) , , ( ; ) ; (

1 1 m n

k k k x x x k x f t d x d

K K

= = = Reaction diffusion equations General conditions Initial conditions : T , p , pH , I , ... :

...

... S ,

u

Boundary conditions

boundary normal unit vector Dirichlet Neumann :

:

:

) (

x

) , ( t r g x S =

• )

, ( ˆ t r g x u u x

S =

∇ ⋅ = ∂ ∂

Parameter set

m j I H p p T kj

, , 2 , 1 ; ) , , , , ; I ( G K K

=

Genome: Sequence IG

Bifurcation pattern

( , ; ) k k

i j k

k1 k2

P2

xn xm

P1

x

x

P

x

x

P

1. Complex networks in cellular regulation 2. Experimental data and modeling in biology 3. Parameter determination and reverse engineering 4. Gene regulation dynamics 5. Inverse bifurcation analysis 6. Current challenges in biology

Three states of a gene regulated by activator and repressor

synthesis degradation Cross-regulation of two genes

2 , 1 , ) ( : Repression ) ( : Activation

n n n

= + = + = j i p K K p F p K p p F

j j i j j j i

Gene regulatory binding functions

Hill coefficient: n Act.-Act. Act.-Rep. Rep.-Rep. 1 S , E S S 2 E , B(E,P) S S , B(P1,P2) 3 E , B(E,P) S , O S , B(P1,P2) 4 E , B(E,P) S , O S , B(P1,P2)

S ...... stable point attractor E ...... extinction O ...... oscillations B ...... bistability

An example analyzed and simulated by MiniCellSim

The repressilator: M.B. Ellowitz, S. Leibler. A synthetic oscillatory network of transcriptional

• regulators. Nature 403:335-338, 2002

Stable stationary state Limit cycle oscillations Fading oscillations caused by a stable heteroclinic orbit Hopf bifurcation Bifurcation to May-Leonhard system Increasing inhibitor strength

1e+07 2e+07 3e+07 4e+07 5e+07 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Proteins

1e+07 2e+07 3e+07 4e+07 5e+07 0.02 0.04 0.06 0.08 1e+07 2e+07 3e+07 4e+07 5e+07 0.1 0.2 0.3 0.4 0.5 0.6 0.7

mRNAs

1e+07 2e+07 3e+07 4e+07 5e+07 0.05 0.1 0.15 0.2 0.25 0.3

The repressilator limit cycle

2e+08 4e+08 6e+08 8e+08 0.2 0.4 0.6 0.8 1

Proteins

2e+08 4e+08 6e+08 8e+08 0.05 0.1 0.15 0.2 0.25 0.3 2e+08 4e+08 6e+08 8e+08 0.2 0.4 0.6 0.8 1

mRNAs

2e+08 4e+08 6e+08 8e+08 0.05 0.1 0.15 0.2 0.25 0.3

The repressilator heteroclinic orbit

1 100 10000 1e+06 1e+08 0.2 0.4 0.6 0.8 1

Proteins

1 100 10000 1e+06 1e+08 0.05 0.1 0.15 0.2 0.25 0.3 1 100 10000 1e+06 1e+08 0.2 0.4 0.6 0.8 1

mRNAs

1 100 10000 1e+06 1e+08 0.05 0.1 0.15 0.2 0.25 0.3

The repressilator heteroclinic orbit (logarithmic time scale)

P1 P2 P3

start start

The repressilator limit cycle

1. Complex networks in cellular regulation 2. Experimental data and modeling in biology 3. Parameter determination and reverse engineering 4. Gene regulation dynamics 5. Inverse bifurcation analysis 6. Current challenges in biology

The bifurcation manifold

Defininition of the forward operator F(p)

Iterative solution for min J(p)

δ δ β β α α = = = =

i i i i

h h , , ,

Inverse bifurcation analysis of the repressilator model

• S. Müller, J. Hofbauer, L. Endler, C. Flamm, S. Widder, P. Schuster. A generalized

model of the repressilator. J. Math. Biol. 53:905-937, 2006.

Inverse bifurcation analysis of the repressilator model

• J. Lu, H.W. Engl, P. Schuster. Inverse bifurcation analysis: Application to simple

gene systems. AMB Algorithms for Molecular Biology 1:11, 2006.

[ ] [ ] [ ] [ ]

pRB pRB ] E2F1 [ E2F1 pRB

pRB 11 11 1 1

φ − + + = J J K k dt d

m

[ ] [ ] [ ] [ ]

E2F1 pRB ] E2F1 [ E2F1 E2F1

E2F1 12 12 2 2 2 2 2 1

φ − + + + + = J J K a k k dt d

m P

[ ] [ ] [ ] [ ]

AP1 pRB' ] p [ E2F1 AP1

AP1 11 65 15 15 25

φ − + + + = J J RB J J k F dt d

m

A simple dynamical cell cycle model J.J. Tyson, A. Csikasz-Nagy, B. Novak. The dynamics of cell cycle regulation. Bioessays 24:1095-1109, 2002

A simple dynamical cell cycle model J.J. Tyson, A. Csikasz-Nagy, B. Novak. The dynamics of cell cycle regulation. Bioessays 24:1095-1109, 2002

Inverse bifurcation analysis of a dynamical cell cycle model

• J. Lu, H.W. Engl, P. Schuster. Inverse bifurcation analysis: Application to simple

gene systems. AMB Algorithms for Molecular Biology 1:11, 2006.

1. Complex networks in cellular regulation 2. Experimental data and modeling in biology 3. Parameter determination and reverse engineering 4. Gene regulation dynamics 5. Inverse bifurcation analysis 6. Current challenges in biology

Explanation of important global properties homeostasis robustness stability against mutation self-repair or regeneration ..........

The bacterial cell as an example for a simple form of autonomous life Escherichia coli genome: 4 million nucleotides 4460 genes The structure of the bacterium Escherichia coli

Evolution does not design with the eyes of an engineer, evolution works like a tinkerer.

François Jacob. The Possible and the Actual. Pantheon Books, New York, 1982, and Evolutionary tinkering. Science 196 (1977), 1161-1166.

The difficulty to define the notion of „gene”. Helen Pearson, Nature 441: 399-401, 2006

ENCODE Project Consortium. Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project. Nature 447:799-816, 2007

ENCODE stands for ENCyclopedia Of DNA Elements.

Web-Page for further information: http://www.tbi.univie.ac.at/~pks