MiniCellSim a Tool for Modeling Simple Genetic and Metabolic - PowerPoint PPT Presentation

MiniCellSim a Tool for Modeling Simple Genetic and Metabolic Regulation Networks Peter Schuster Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Systems Chemistry, European Center of Living Technology Venice, 03.10.– 04.10.2005

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

What is systems chemistry? autocatalysis, template action, self-assembly, reaction networks, nonlinearity, complexity, .... but also with atoms and molecules that do not occur in living matter systems chemistry = systems biology without genes and the Darwinian mechanism that, in principle, allows for the reconstruction of phylogenetic trees What is systems biology?

In research on the origin of life and cellular organization the scientist has to face the unsolved problem to explain how hierarchical structures, superstructures, and complex dynamics emerge from simple (perhaps yet unknown) elements. Perhaps we should search for simple or minimal reaction and regulator systems that can be modelled, understood, synthesized, studied experimentally, and made predictable. In the domain of molecular genetics and systems biology it is (more or less) well known, how the individual elements (proteins, nucleic acids) work and how the regulatory switches operate, but network dynamics is not at all understood yet.

1. Forward and inverse problems in reaction kinetics 2. Reverse engineering – A simple example 3. Genetic and metabolic networks – MiniCellSim 4. A glimpse of regulation kinetics 5. How do model metabolisms evolve?

1. Forward and inverse problems in reaction kinetics 2. Reverse engineering – A simple example 3. Genetic and metabolic networks – MiniCellSim 4. A glimpse of regulation kinetics 5. How do model metabolisms evolve?

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 = = = ( ; ) ; ( , , ) ; ( , , ) 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 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 x k 1 analysis (Level II) x

1. Forward and inverse problems in reaction kinetics 2. Reverse engineering – A simple example 3. Genetic and metabolic networks – MiniCellSim 4. A glimpse of regulation kinetics 5. How do model metabolisms evolve?

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 k 4 A A � R- A r X 1 Flow rate = A r A A 0 A X A X A X r 0 X 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 0 A 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 0 A 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 = = α = = − + + α − α = 3 2 , 1 : 2 ( 2 ) 0 k k k k x x a x r a 0 A 1 2 3 4 0 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 = = α = = − + + α − α = 3 2 , 1 : 2 ( 2 ) 0 k k k k x x a x r a 0 A 1 2 3 4 0 0 Polynomial discriminant of the cubic equation: r 2 α 4 a a 2 2 = + α − + α − α + α + α + = 3 2 2 3 2 216 D ( 6 0 ) ( 12 5 ) 8 4 0 0 0 r r r a a X 0 0 8 2

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 = = α = = − + + α − α = 3 2 , 1 : 2 ( 2 ) 0 k k k k x x a x r a 0 A 1 2 3 4 0 0 Polynomial discriminant of the cubic equation: r 2 α 4 a a 2 2 = + α − + α − α + α + α + = 3 2 2 3 2 216 D ( 6 0 ) ( 12 5 ) 8 4 0 0 0 r r r a a X 0 0 8 2 � � D < 0 : 3 roots r , r , and r , 2 are positive r = r - r 1 2 3 1 2

0.6 0.00 0.4 � r 0.2 0.01 0.0 � 2.5 0.02 2.0 1.5 a 0 1.0 0.03 0.5 Range of hysteresis as a function of the parameters a 0 and �

1. Forward and inverse problems in reaction kinetics 2. Reverse engineering – A simple example 3. Genetic and metabolic networks – MiniCellSim 4. A glimpse of regulation kinetics 5. How do model metabolisms evolve?