Systems biology and complexity research

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2 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,

3 Web-Page for further information:

4 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

5 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

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7 A model genome with 12 genes Regulatory gene Structural gene Regulatory protein or RNA Enzyme Metabolite Sketch of a genetic and metabolic network

8 A B C D E F G H I J K L 1 Biochemical Pathways The reaction network of cellular metabolism published by Boehringer-Mannheim.

9 The citric acid or Krebs cycle (enlarged from previous slide). The reaction network of cellular metabolism published by Boehringer-Mannheim.

10 E. coli: Genome length nucleotides Number of cell types 1 Number of genes Four books, 300 pages each Man: Genome length nucleotides Number of cell types 200 Number of genes A library of 3000 volumes, 300 pages each Complexity in biology

11 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

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

13 time Analysis by gel electrophoresis Jeff Rogers, Gerald F. Joyce. RNA 7: , 2001

14 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

15 Embryonic stem cell Brain Liver Muscle Kidney Prostate Log 2 (ratio) HIGH -0 LOW SOM-based GEDI maps (Eichler, G.S. et al., Bioinformatics 2003) Hsiao, L.L. et al., Physiol.Genomics 2001 Affymetrix, ~ 7000 genes Drawings by Stuart A. Kauffman, 2009

16 A ph-modulated, self-replicating peptide Shao Yao, Indraneel Ghosh, Reena Zutshi, Jean Chmielewski. J.Am Chem.Soc. 119: , 1997

17 A + B X 2 X Y Y + X D Stoichiometric equations SBML systems biology markup language da dt = db dt = k 1 ab Kinetic differential equations dx dt d y dt = k 1 = k 2 ab x 2 k k 2 3 x 2 x y k 3 x y ODE Integration dd dt = k 3 x y x i (t) Solution curves The elements of the simulation tool MiniCellSim SBML: Bioinformatics 19: , 2003; CVODE: Computers in Physics 10: , 1996 Concentration Time t

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

19 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

20 dx dt = Kinetic differential equations f x; k); x= ( x, K, x ); k = ( k, K, k ( 1 n 1 m ) Reaction diffusion equations x 2 = D x + f ( x; k) t () Solution curves: x t x i (t) Parameter set k ( T, p, ph, I, K ) ; j= 1, 2, K,m j General conditions: T, p, ph, I,... Initial conditions : x(0) Concentration Time t Boundary conditions: boundary... S, normal unit vector... u Dirichlet : Neumann : x S = g( r, t) x = uˆ x S g( r, t) u = The forward problem of chemical reaction kinetics (Level I)

21 dx dt Kinetic differential equations = f ( x; k); x= ( x1, K, xn ); k= ( k1, K, km ) Genome: Sequence I G Reaction diffusion equations x t = D General conditions : T, p, ph, I,... Initial conditions : 2 Parameter set x + f ( x; k) k j ( I G ; T, p, ph, I, K ) ; j = 1, 2, K, m x(0) Concentration Solution curves: x() t x i (t) Time t Boundary conditions : boundary... S, normal unit vector... u Dirichlet : Neumann : x S = g( r, t) x = uˆ x S g( r, t) u = The forward problem of biochemical reaction kinetics (Level I)

22 Genome: Sequence I G Parameter set k j ( I G ; T, p, ph, I, K ) ; j = 1, 2, K, m d x dt = Kinetic differential equations f ( x; k); x = ( x1, K, xn ); k = ( k1, K, km Reaction diffusion equations x t Data from measurements x i (t ) j = D 2 x + f ( x; k) General conditions : T, p, ph, I,... Initial conditions : Boundary conditions : boundary Dirichlet : Neumann : x(0)... S, normal unit vector... u x S = g ( r, t) x = uˆ x S g( r, t) u = x (t j); j= 1, 2,..., N ) The inverse problem of biochemical reaction kinetics (Level I) Concentration Time t

23 Genome: Sequence I G d x dt Kinetic differential equations = ( x; k); x= ( x, K, x ); k = ( k, K, k f 1 n 1 m Reaction diffusion equations x 2 = D x + f ( x; k) t Parameter set k j ( I G ; T, p, ph, I, K ) ; j = 1, 2, K, m General conditions : T, p, ph, I,... Initial conditions : x(0) ) k i Bifurcation analysis x n x m P ( k, k; ) i xt () j k time x n x n P P xm P Boundary conditions : boundary... S, normal unit vector u... x m k j Dirichlet : Neumann : x S = g( r, t) x = uˆ x S g( r, t) u = The forward problem of bifurcation analysis (Level II)

24 Genome: Sequence I G Parameter set k j ( I G ; T, p, ph, I, K ) ; j= 1, 2, K, m d x dt = Kinetic differential equations f x; k); x= ( x, K, x ) ; k = ( k, K, k ( 1 n 1 m Reaction diffusion equations x t = D 2 x + f ( x; k) General conditions: T, p, ph, I,... Initial conditions : Boundary conditions: boundary Dirichlet : Neumann : k 2 x(0)... S, normal unit vector... u x S = g ( r, t) x = uˆ x S g( r, t) u = Bifurcation pattern ( k, k; ) i j k ) P 1 x n P 2 x P xm The inverse problem of bifurcation analysis (Level II) x x P x k 1

25 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

26 Three states of a gene regulated by activator and repressor

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28 Cross-regulation of two genes synthesis degradation

29 Activation : Repression : i, F F i i ( p ( p j j j = 1,2 ) ) = = K K p + n j p K + p n j n j Gene regulatory binding functions

30 Hill coefficient: n Act.-Act. Act.-Rep. Rep.-Rep. 1 S, E S S 2 E, B(E,P) S S, B(P 1,P 2 ) 3 E, B(E,P) S, O S, B(P 1,P 2 ) 4 E, B(E,P) S, O S, B(P 1,P 2 ) S... stable point attractor E... extinction O... oscillations B... bistability

31 An example analyzed and simulated by MiniCellSim The repressilator: M.B. Ellowitz, S. Leibler. A synthetic oscillatory network of transcriptional regulators. Nature 403: , 2002

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

33 Proteins mrnas e+07 2e+07 3e+07 4e+07 5e e+07 2e+07 3e+07 4e+07 5e e+07 2e+07 3e+07 4e+07 5e e+07 2e+07 3e+07 4e+07 5e+07 The repressilator limit cycle

34 Proteins mrnas e+08 4e+08 6e+08 8e e+08 4e+08 6e+08 8e e+08 4e+08 6e+08 8e e+08 4e+08 6e+08 8e+08 The repressilator heteroclinic orbit

35 Proteins mrnas e+06 1e e+06 1e e+06 1e e+06 1e+08 The repressilator heteroclinic orbit (logarithmic time scale)

36 P 1 start start P 2 P 3 The repressilator limit cycle

37 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

38 The bifurcation manifold

39 Defininition of the forward operator F(p)

40 Iterative solution for min J(p)

41 α α, β = β, h = h, δ = δ i = i i i 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: , 2006.

42 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.

43 d dt [ prb] = k [ E2F1] 11 1 prb K 1 + [E2F1] J11 + [ prb] φ m J [ prb] d dt [ E2F1] = k P + k [ E2F1] 2 2 a + J12 1 φ 2 2 E2F1 Km2 + [E2F1] J12 + [ prb] [ E2F1] d dt [ AP1] = F + k [ E2F1] m J15 + [prb] φap1 J15 J11 + [ prb' ] J [ AP1] A simple dynamical cell cycle model J.J. Tyson, A. Csikasz-Nagy, B. Novak. The dynamics of cell cycle regulation. Bioessays 24: , 2002

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

45 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.

46 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

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

48 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

49 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),

50 The difficulty to define the notion of gene. Helen Pearson, Nature 441: , 2006

51 ENCODE stands for ENCyclopedia Of DNA Elements. ENCODE Project Consortium. Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project. Nature 447: , 2007

52 Web-Page for further information:

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