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
A model genome with 12 genes 1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Regulatory gene Enzyme Structural gene Metabolite Sketch of a genetic and metabolic network
A B C D E F G H I J K L Biochemical Pathways 1 2 3 4 5 6 7 8 9 10 The reaction network of cellular metabolism published by Boehringer-Mannheim.
The citric acid or Krebs cycle (enlarged from previous slide). The reaction network of cellular metabolism published by Boehringer-Mannheim.
4×10 6 nucleotides E. coli : Genome length Number of cell types 1 Number of genes 4 460 Four books, 300 pages each 3×10 9 nucleotides Man : Genome length Number of cell types 200 � 30 000 Number of genes 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 Brain Prostate Liver Muscle Kidney Log 2 (ratio) HIGH -0 LOW Hsiao, L.L. et al., Physiol.Genomics 2001 Affymetrix, ~ 7000 genes SOM-based “GEDI maps” (Eichler, G.S. et al., Bioinformatics 2003) 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
Stoichiometric equations A + B � X 2 X � Y Y + X � D SBML – systems biology markup language d a d b = = − k a b 1 Kinetic differential equations d t d t d x = − − 2 k a b k x k x y 1 2 3 d t ODE Integration d y = − 2 k x k x y 2 3 d t d d Solution curves = k x y x i (t) 3 d t Concentration The elements of the simulation tool MiniCellSim t SBML : Bioinformatics 19 :524-531, 2003; Time 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
Kinetic differential equations d x = = = K K f ( x ; k ) ; x ( x , , x ) ; k ( k , , k ) 1 1 n m d t Reaction diffusion equations ∂ x = ∇ + 2 D x f x k ( ; ) Solution curves : ( ) x t ∂ t x i (t) Concentration Parameter set = K K k ( T , p , p H , I , ) ; j 1 , 2 , , m j General conditions : T , p , pH , I , ... t x ( 0 ) Initial conditions : Time Boundary conditions : � boundary ... S , normal unit vector ... u x S = Dirichlet : g ( r , t ) ∂ S = x = ⋅ ∇ ˆ Neumann : u x g ( r , t ) ∂ u The forward problem of chemical reaction kinetics (Level I)
Kinetic differential equations d x = = = K K ( ; ) ; ( , , ) ; ( , , ) f x k x x x k k k 1 n 1 m d t Reaction diffusion equations ∂ x = ∇ + Genome: Sequence I G 2 D x f ( x ; k ) Solution curves : ( ) x t ∂ t x i (t) Concentration Parameter set = K K ( G I ; , , , , ) ; 1 , 2 , , k j T p p H I j m General conditions : T , p , pH , I , ... t ( 0 ) x Initial conditions : Time Boundary conditions : � boundary ... S , normal unit vector ... u x S = Dirichlet : ( , ) g r t ∂ S = x = ⋅ ∇ ˆ ( , ) Neumann : u x g r t ∂ u The forward problem of biochemical reaction kinetics (Level I)
Kinetic differential equations d x = = = K K f ( x ; k ) ; x ( x , , x ) ; k ( k , , k ) 1 1 n m d t Reaction diffusion equations ∂ x = ∇ + 2 ( ; ) D x f x k ∂ t General conditions : T , p , pH , I , ... x Initial conditions ( 0 ) : Genome: Sequence I G Boundary conditions : � boundary ... S , normal unit vector u ... Parameter set x S = = Dirichlet : g ( r , t ) K K ( G I ; , , , , ) ; 1 , 2 , , k j T p p H I j m ∂ S = x = ⋅ ∇ Neumann : ˆ u x g ( r , t ) ∂ u Data from measurements x (t ); = 1, 2, ... , j N j x i (t ) j Concentration The inverse problem of biochemical t Time reaction kinetics (Level I)
Kinetic differential equations d x = = = K K f ( x ; k ) ; x ( x , , x ) ; k ( k , , k ) 1 n 1 m d t Bifurcation analysis Reaction diffusion equations � ( , ; ) ∂ k k j k x i = ∇ + 2 Genome: Sequence I G D x f ( x ; k ) ∂ t k i P x n P Parameter set x n P x m = K K k j ( G I ; T , p , p H , I , ) ; j 1 , 2 , , m x m x t ( ) General conditions : T , p , pH , I , ... P time x x n ( 0 ) Initial conditions : x m k j Boundary conditions : � boundary ... S , normal unit vector u ... x S = Dirichlet : g ( r , t ) ∂ S = x = ⋅ ∇ ˆ Neumann : u x g ( r , t ) ∂ u The forward problem of bifurcation analysis (Level II)
Kinetic differential equations d x = = = f x k x x K x k k K k ( ; ) ; ( , , ) ; ( , , ) 1 n 1 m d t Reaction diffusion equations ∂ x = ∇ + 2 D x f ( x ; k ) ∂ t General conditions : T , p , pH , I , ... x ( 0 ) Initial conditions : Genome: Sequence I G Boundary conditions : � ... S , boundary normal unit vector u ... Parameter set x S = = Dirichlet : g ( r , t ) K K k j T p p H I j m ( G I ; , , , , ) ; 1 , 2 , , ∂ S = x = ⋅ ∇ Neumann : ˆ ( , ) u x g r t ∂ u Bifurcation pattern � ( , ; ) k k j k k 2 i P 1 x n P 2 x P x m x The inverse problem of bifurcation P analysis (Level II) x k 1 x
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
n p = j Activation : F ( p ) + i j n K p j K = Repression : F ( p ) + i j n K p j = i , j 1 , 2 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(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
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 Hopf bifurcation Increasing Limit cycle oscillations inhibitor strength Bifurcation to May-Leonhard system Fading oscillations caused by a stable heteroclinic orbit
Proteins mRNAs 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 1e+07 2e+07 3e+07 4e+07 5e+07 0 1e+07 2e+07 3e+07 4e+07 5e+07 0.3 0.08 0.25 0.2 0.06 0.15 0.04 0.1 0.02 0.05 0 0 0 1e+07 2e+07 3e+07 4e+07 5e+07 0 1e+07 2e+07 3e+07 4e+07 5e+07 The repressilator limit cycle
Proteins mRNAs 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 2e+08 4e+08 6e+08 8e+08 0 2e+08 4e+08 6e+08 8e+08 0.3 0.3 0.25 0.25 0.2 0.2 0.15 0.15 0.1 0.1 0.05 0.05 0 0 0 2e+08 4e+08 6e+08 8e+08 0 2e+08 4e+08 6e+08 8e+08 The repressilator heteroclinic orbit
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