From Biochemical Kinetics to Systems Biology Peter Schuster - PowerPoint PPT Presentation

From Biochemical Kinetics to Systems Biology Peter Schuster Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA RICAM Special Semester on Quantitative Biology Linz, 05.11.2007

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

1. Biochemical kinetics and systems biology 2. Forward and inverse problems 3. Regulation kinetics and bifurcation analysis 4. Reverse engineering of dynamical systems 5. Future problems of quantitative biology

1. Biochemical kinetics and systems biology 2. Forward and inverse problems 3. Regulation kinetics and bifurcation analysis 4. Reverse engineering of dynamical systems 5. Future problems of quantitative biology

Biochemical kinetics 1910 – 1960 Conventional enzyme kinetics 1950 – 1975 Theory of biopolymers, macroscopic properties 1958 Gene regulation through repressor binding 1965 – 1975 Allosteric effects, cooperative transitions 1965 – 1975 Theory of cooperative binding to nucleic acids 1990 - Revival of biochemical kinetics in systems biology

Biochemical kinetics 1910 – 1960 Conventional enzyme kinetics 1950 – 1975 Theory of biopolymers, macroscopic properties 1958 Gene regulation through repressor binding 1965 – 1975 Allosteric effects, cooperative transitions 1965 – 1975 Theory of cooperative binding to nucleic acids 1990 - Revival of biochemical kinetics in systems biology

Biochemical kinetics 1910 – 1960 Conventional enzyme kinetics 1950 – 1975 Theory of biopolymers, macroscopic properties 1958 Gene regulation through repressor binding 1965 – 1975 Allosteric effects, cooperative transitions 1965 – 1975 Theory of cooperative binding to nucleic acids 1990 - Revival of biochemical kinetics in systems biology

Biochemical kinetics 1910 – 1960 Conventional enzyme kinetics 1950 – 1975 Theory of biopolymers, macroscopic properties 1958 Gene regulation through repressor binding 1965 – 1975 Allosteric effects, cooperative transitions 1965 – 1975 Theory of cooperative binding to nucleic acids 1990 - Revival of biochemical kinetics in systems biology

Biochemical kinetics 1910 – 1960 Conventional enzyme kinetics 1950 – 1975 Theory of biopolymers, macroscopic properties 1958 Gene regulation through repressor binding 1965 – 1975 Allosteric effects, cooperative transitions 1965 – 1975 Theory of cooperative binding to nucleic acids 1990 - Revival of biochemical kinetics in systems biology

Biochemical kinetics 1910 – 1960 Conventional enzyme kinetics 1950 – 1975 Theory of biopolymers, macroscopic properties 1958 Gene regulation through repressor binding 1965 – 1975 Allosteric effects, cooperative transitions 1965 – 1975 Theory of cooperative binding to nucleic acids 1990 - Revival of biochemical kinetics in systems 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-Ingelheim.

The citric acid or Krebs cycle (enlarged from previous slide).

1. Biochemical kinetics and systems biology 2. Forward and inverse problems 3. Regulation kinetics and bifurcation analysis 4. Reverse engineering of dynamical systems 5. Future problems of quantitative 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 ( ; ) Solution curves : ( ) D x f x k x t ∂ t x i (t) Concentration Parameter set = ( T , p , p H , I , ) ; j 1 , 2 , , m K K 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 ; , , , , ) ; 1 , 2 , , K 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 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 , ... ( 0 ) Initial conditions : x Genome: Sequence I G Boundary conditions : boundary ... S , normal unit vector � ... u Parameter set x S = = Dirichlet : ( , ) ( G I ; , , , , ) ; 1 , 2 , , g r t K K 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 biochemical t Time reaction kinetics (Level I)

Kinetic differential equations d x = = = f ( ; ) ; ( , , ) ; ( , , ) K K x k x x x k k k 1 1 n m d t Bifurcation analysis Reaction diffusion equations � ( , ; ) ∂ k k j k i x = ∇ 2 + f ( ; ) Genome: Sequence I G D x x k ∂ t k i P x n P Parameter set x n P x m = ( G I ; , , , , ) ; 1 , 2 , , K K k j T p p H I j m x m ( ) x t General conditions : T , p , pH , I , ... P time ( 0 ) Initial conditions : x x n 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 1 n m d t Reaction diffusion equations ∂ x = ∇ + 2 ( ; ) D x f x k ∂ t General conditions : T , p , pH , I , ... ( 0 ) Initial conditions : x Genome: Sequence I G Boundary conditions : � boundary ... S , normal unit vector ... u Parameter set x S = = Dirichlet : ( , ) ( G I ; , , , , ) ; 1 , 2 , , g r t K K k j T p p H I j m ∂ S = x Neumann : = ⋅ ∇ ˆ ( , ) u x g r t ∂ u Bifurcation pattern � ( , ; ) k k j k i k 2 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. Biochemical kinetics and systems biology 2. Forward and inverse problems 3. Regulation kinetics and bifurcation analysis 4. Reverse engineering of dynamical systems 5. Future problems of quantitative biology

Active states of gene regulation

Promotor III State : inactive state Repressor Activator binding site RNA polymerase Promotor III State : inactive state Activator Repressor RNA polymerase Inactive states of gene regulation

synthesis degradation Cross-regulation of two genes

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

= = = dq [ G ] [ G ] const . g = Q − Q 1 ( ) 1 2 0 k F p d q 1 1 2 1 1 = = [ Q ] , [ Q ] , dt q q 1 1 2 2 = = [ P ] , [ P ] p p dq = − 1 1 2 2 Q Q 2 ( ) k F p d q 2 2 1 2 2 dt n p = Activation : ( ) j F p dp + i j n = − P P K p 1 k q d p j 1 1 2 1 dt K = Repression : ( ) F p + n i j dp K p = − P P 2 j k q d p 2 2 2 2 = , 1 , 2 dt i j − ϑ ϑ = = ϑ Stationary points : ( ( )) 0 , ( ) p F F p p F p 1 1 1 2 2 1 2 2 2 1 Q P Q P k k k k ϑ = ϑ = 1 1 , 2 2 1 2 Q P Q P d d d d 1 1 2 2 Qualitative analysis of cross-regulation of two genes: Stationary points

∂ ∂ ⎛ ⎞ F F ⎜ 1 1 ⎟ Q Q k k − 1 1 ∂ ∂ 0 Q d ⎜ ⎟ p p 1 1 2 ⎧ ⎫ ∂ ∂ ⎜ ⎟ ∂ ⎪ ⎪ − & 0 F F Q x d 2 2 Q Q = = = A ⎨ ⎬ 2 k k i ⎜ ⎟ a 2 2 ∂ ∂ ∂ ⎪ ij ⎪ p p x ⎩ ⎭ ⎜ ⎟ 1 2 j − 0 0 P P ⎜ ⎟ k d 1 1 ⎜ ⎟ − 0 0 P P ⎝ ⎠ k d 2 2 ∂ ∂ F F = = Cross regulation : 1 2 0 ∂ ∂ p p 1 2 ∂ F − − ε 0 0 1 Q Q d k 1 1 ∂ p 2 ∂ F Q Q − − ε 2 0 Q Q 0 ε = = A - I D K d k 2 2 ∂ p P P 1 D K − − ε 0 0 P P k d 1 1 − − ε 0 0 P P k d 2 2 Qualitative analysis of cross-regulation of two genes: Jacobian matrix