Modeling Genetic and Metabolic CellularNetworks From Molecules to Cells and Organisms Peter Schuster Institut für Theoretische Chemie der Universität Wien, Austria Seminar Lecture Santa Fe Institute, 18.04.2005
Web-Page for further information: http://www.tbi.univie.ac.at/~pks
1. What is computational systems biology? 2. Genabolic networks 3. Genomes and cellular networks 4. Forward and inverse problems 5. Reverse engineering – A simple example 6. Activation and silencing of genes 7. MiniCellSim – A simulation tool 8. Evolution of genabolic networks
1. What is computational systems biology? 2. Genabolic networks 3. Genomes and cellular networks 4. Forward and inverse problems 5. Reverse engineering – A simple example 6. Activation and silencing of genes 7. MiniCellSim – A simulation tool 8. Evolution of genabolic networks
Structural biology Sequence � Structure � Function Systems biology Genome � Proteome � Dynamics of cells and organisms
Structural biology Sequence � Structure � Function Systems biology Genome � Proteome � Dynamics of cells and organisms Goals : 1. Large scale computer simulations of genetic regulatory and metabolic reaction networks.
Structural biology Sequence � Structure � Function Systems biology Genome � Proteome � Dynamics of cells and organisms Goals : 1. Large scale computer simulations of genetic regulatory and metabolic reaction networks. 2. Understanding the dynamics of cells and organisms including regulation through signal transmission in highly heterogeneous spatial structures.
Structural biology Sequence � Structure � Function Systems biology Genome � Proteome � Dynamics of cells and organisms Goals : 1. Large scale computer simulations of genetic regulatory and metabolic reaction networks. 2. Understanding the dynamics of cells and organisms including regulation through signal transmission in highly heterogeneous spatial structures. 3. Design of genetic and metabolic model systems, which allow for optimization through evolution and which provide explanations for the unique properties of living cells and organisms like robustness, homeostasis, and adaptation to environmental changes.
Structural biology Sequence � Structure � Function Systems biology Genome � Proteome � Dynamics of cells and organisms Goals : 1. Large scale computer simulations of genetic regulatory and metabolic reaction networks. 2. Understanding the dynamics of cells and organisms including regulation through signal transmission in highly heterogeneous spatial structures. 3. Design of genetic and metabolic model systems, which allow for optimization through evolution and which provide explanations for the unique properties of living cells and organisms like robustness, homeostasis, and adaptation to environmental changes.
1. What is computational systems biology? 2. Genabolic networks 3. Genomes and cellular networks 4. Forward and inverse problems 5. Reverse engineering – A simple example 6. Activation and silencing of genes 7. MiniCellSim – A simulation tool 8. Evolution of genabolic networks
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 model genome with 12 genes 1 2 3 4 5 6 7 8 9 10 11 12 Genetic regulatory network Metabolic network Regulatory protein or RNA Regulatory gene Enzyme Structural gene Metabolite Proposal of a new name: Gen etic and met abolic 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-Ingelheim.
The citric acid or Krebs cycle (enlarged from previous slide).
Processing of information in cascades and networks Network Linear chain
• • 2 2 2 • 2 • • • 2 3 • 3 • • 3 3 links # nodes • • 2 14 • 2 14 2 • 10 3 6 • • 5 5 2 2 • 2 10 1 • 5 12 1 • 12 • • 14 1 3 • 2 3 • • • • 2 2 2 2 Analysis of nodes and links in a step by step evolved network
1. What is computational systems biology? 2. Genabolic networks 3. Genomes and cellular networks 4. Forward and inverse problems 5. Reverse engineering – A simple example 6. Activation and silencing of genes 7. MiniCellSim – A simulation tool 8. Evolution of genabolic networks
1. What is computational systems biology? 2. Genabolic networks 3. Genomes and cellular networks 4. Forward and inverse problems 5. Reverse engineering – A simple example 6. Activation and silencing of genes 7. MiniCellSim – A simulation tool 8. Evolution of genabolic networks
RNA sequence RNA sequence that forms the structure as minimum free energy structure Iterative determination of a sequence for the given secondary RNA folding : Inverse folding of RNA : structure Structural biology, Biotechnology, design of biomolecules spectroscopy of Inverse Folding biomolecules, with predefined Algorithm understanding structures and functions molecular function RNA structure RNA structure of minimal free energy Sequence, structure, and design through inverse folding
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 ( ; ) Solution curves : D x f x k ( ) x t ∂ t x i (t) Concentration Parameter set = ( T , p , p H , I , K ) ; j 1 , 2 , K , m k j General conditions : T , p , pH , I , ... t ( 0 ) Initial conditions : x 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 1 n m d t Reaction diffusion equations ∂ x = ∇ 2 + Genome: Sequence I G ( ; ) Solution curves : D x f x k ( ) x t ∂ t x i (t) Concentration Parameter set = ( G I ; , , , , K ) ; 1 , 2 , K , k j T p p H I j m General conditions : T , p , pH , I , ... t ( 0 ) Initial conditions : x 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 cellular 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 , ... Initial conditions ( 0 ) : x Genome: Sequence I G Boundary conditions : � boundary ... S , normal unit vector ... u Parameter set x S = = Dirichlet : ( , ) ( G I ; , , , , K ) ; 1 , 2 , K , g r t k j T p p H I j m ∂ S = x = ⋅ ∇ Neumann : ˆ ( , ) u x g r t ∂ u Data from measurements (t ); = 1, 2, ... , x j N j x i (t ) j Concentration The inverse problem of cellular t reaction kinetics (Level I) Time
The forward problem of bifurcation analysis in cellular dynamics (Level II)
The inverse problem of bifurcation analysis in cellular dynamics (Level II)
1. What is computational systems biology? 2. Genabolic networks 3. Genomes and cellular networks 4. Forward and inverse problems 5. Reverse engineering – A simple example 6. Activation and silencing of genes 7. MiniCellSim – A simulation tool 8. Evolution of genabolic networks
Stock Solution [A] = a Reaction Mixture [A],[X] 0 r A * k 1 A X X A A A X A A k 2 A X A X k 3 A A +2 3 X A X X A A k 4 � R- A r 1 X Flow rate = A r A A A 0 X A X A X r X 0 X X X A A
0.5 � r Stationary concentration x Thermodynamic 0.4 branch 0.3 0.2 Bistability r cr,1 r cr,2 0.1 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Flow rate r
r Kinetic differential equations: A * d [ A ] d a = = − − + + + 2 2 ( ) ( ) ( ) r a a k k x a k k x x 0 1 3 2 4 d t d t k 1 d [ X ] d x A X = = − + + − + 2 2 ( ) ( ) r x k k x a k k x x 1 3 2 4 k 2 d t d t k 3 +2 3 A X X k 4 r A 0 r 0 X
r Kinetic differential equations: A * d [ A ] d a = = − − + + + 2 2 ( ) ( ) ( ) r a a k k x a k k x x 0 1 3 2 4 d t d t k 1 d [ X ] d x A X = = − + + − + 2 2 ( ) ( ) r x k k x a k k x x 1 3 2 4 k 2 d t d t k 3 Steady states: +2 3 A X X + − + + + − = 3 2 k 4 ( ) ( ) 0 x k k x k a x k k r k a 3 4 3 0 1 2 1 0 r A 0 r 0 X
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