Study of Study of T ricyclic ricyclic Cascade Netw Cascade - PowerPoint PPT Presentation

Study of Study of T ricyclic ricyclic Cascade Netw Cascade Networks using orks using Dynamic Optimization Dynamic Optimization

• Systems Biology – interdisciplinary field that focuses on the systematic study of complex interactions in biological systems • Signal transduction pathways o enable cells to integrate external and internal signals and to respond to them, o are present in major developmental changes in organism (embryo development, but also in cancer, asthma, diabetes…) H. Kestler, C. Wawra, B. Kracher and M. Kuhl: “Network modeling of signal transduction: establishing the global view”. Bioessays. 30:1110-1125. 2008

• Basic module • Protein • Inactive - X • Active – X* • Enzymes – S* and P X • phosphorylation/dephosphorylation in MAPK cascades • methylation/demethylation in bacterial chemotaxis

Direct Approach : Inverse Approach : Both direct and inverse approaches work synergistically! • Dynamic optimization • very well suited for studying biochemical networks • it allows dealing with large-scale, nonlinear dynamic models • can handle a great variety of objective functions and constraints.

• balance equations, conservation equations • kinetic expressions

• balance equations, conservation equations • kinetic expressions * , ˜ * , ˜ X , ˜ • Kinetic parameters: ˜ X , , ˜ a a d d k X X X

 Concentration ratios  Saturation parameters  Activity coefficient

Inverse Approach :

max. activity kinase activity Concentration Input stimulus 0 Time max. activity max. activity 90% Concentration kinase upstream Concentration activity kinase kinase activity upstream kinase 10% Time Time

1 Steady-state kinase activity 90% Typical graded response Ultrasensitive response 10% 0 Input stimulus α X 0.1 α X 0.9 • Go from a typical graded response to a switch-like response

• Optimal ultrasensitivity for fixed values of ratios between total concentrations of enzymes and substrate: Ultrasensitivity [S]/[X] = 0.01

• Optimal ultrasensitivity for fixed values of ratios between total concentrations of enzymes and substrate: Ultrasensitivity Ultrasensitivity Ultrasensitivity [S]/[X] = 0.01 [S]/[X] = 0.1 [S]/[X] = 1

Ultrasensitivity Saturation parameter K X Saturation parameter K* X Concentration ratio [P X ]/[X] Concentration ratio [P X ]/[X] Concentration ratio [P X ]/[X] Concentration ratio [S]/[X] Concentration ratio [S]/[X] Concentration ratio [S]/[X] 1 Steady-state kinase activity  Ultrasensitivity can be achieved for small values of concentration ratios  The closer to saturation, the more ultrasensitive the monocyclic cascade. 0 Input stimulus

* , ˜ * , ˜ X , ˜ * , ˜ Y , ˜ * , ˜ Y , ˜ • Kinetic parameters: * ˜ X , , ˜ X , ˜ Y , ˜ a a d d k a a d d k k X X Y Y Y

 Concentration ratios ρ S / X , ρ P X / X , ρ X / Y , ρ P Y / Y  Saturation parameters * + 1 ˜ X + ˜ ˜ d k d * = ˜ ˜ X X K K X = X * ˜ a ˜ a X X * + ˜ ˜ Y + ˜ ˜ * d k d k * = ˜ ˜ Y Y Y K K Y = Y * a ˜ ˜ a Y Y  Activity coefficients ˜ ρ S / X ρ X / Y k α X = ˜ Y k α Y = ˜ X ρ P X / X * ρ P Y / Y k Y

Maximal values of ultrasensitivity objective measure, with corresponding values of saturation parameters for activation reaction of each level in a signaling cascade model: Ultrasensitivity Saturation parameter K X Saturation parameter K Y Concentration ratio [S]/[X] Concentration ratio [S]/[X] Concentration ratio [S]/[X] Concentration ratio [X]/[Y] Concentration ratio [X]/[Y] Concentration ratio [X]/[Y]

saturated unsaturated  Maximum ultrasensitivity when the first kinase is saturated, but not the second kinase  An An optimal optimal multicycle multicycle cascade cascade does does not not corr correspond espond to a series of optimal monocyclic cascades to a series of optimal monocyclic cascades

* , ˜ * , ˜ * , ˜ X , ˜ * , ˜ Y , ˜ * , ˜ Y , ˜ Z , ˜ * , ˜ Z , ˜ * , ˜ * • Kinetic parameters: ˜ X , , ˜ X , ˜ Y , ˜ Z , ˜ a a d d k a a d d k k a a d d k k X X Y Y Y Z Z Z

 Concentration ratios ρ S / X , ρ P X / X , ρ X / Y , ρ P Y / Y , ρ Y / Z , ρ P Z / Z  Saturation parameters * + 1 ˜ X + ˜ ˜ d k d * = ˜ ˜ X X K K X = X * ˜ a ˜ a X X * + ˜ ˜ Y + ˜ ˜ * d k d k * = ˜ ˜ Y Y Y K K Y = Y * a ˜ ˜ a Y Y * + ˜ ˜ Z + ˜ ˜ * d k d k * = ˜ ˜ Z Z Z K K Z = Z * a ˜ ˜ a  Activity coefficients Z Z ˜ ˜ ρ S / X ρ X / Y ρ Y / Z k k α X = ˜ Y Z k α Y = α Z = ˜ ˜ X ρ P X / X * ρ P Y / Y * ρ P Y / Z k k Y Z

Optimal ultrasensitivity for various combinations of saturation parameters : ˜ ˜ ˜ K X = 0.1 K Y = 1 K Z = 10 ˜ ˜ ˜ ˜ ˜ ˜ K X = 0.1 K Y = 10 K Z = 10 K X = 0.1 K Y = 10 K Z = 1 ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ K X = 1 K Y = 10 K Z = 10 K X = 1 K Y = 10 K Z = 1 K X = 1 K Y = 1 K Z = 10

Ultrasensitivity • Optimal ultrasensitivity Concentration ratio [X]/[Y] for fixed values of ratios between total concentrations of enzymes and substrate Concentration ratio [Y]/[Z]

Ultrasensitivity • Optimal ultrasensitivity Concentration ratio [X]/[Y] for fixed values of ratios between total concentrations of enzymes and substrate Concentration ratio [Y]/[Z] Saturation parameter K Y Saturation parameter K X Saturation parameter K Z Concentration ratio [X]/[Y] Concentration ratio [Y]/[Z] Concentration ratio [Y]/[Z] Concentration ratio [Y]/[Z]

saturated unsaturated unsaturated  Optimal ultrasensitivity is achieved if the first kinase is saturated by its target kinase, but not the subsequent two kinases.

K X K Y K Z Ultrasensitivity Monocyclic ~ 3 ~ 0.1 Bicyclic ~ 5.5 ~ 0.1 ~ 200 Tricyclic ~9.8 ~ 0.1 ~ 350 ~ 150

max. activity max. activity max. activity 90% kinase kinase Concentration Concentration upstream activity Concentration activity kinase kinase activity Input stimulus upstream kinase 10% 0 Time Time Time • Amplification in signaling cycles - a measure of response strength - measure of how fast a signal is transduced through a cycle and time needed to reach 90% of the maximum substrate activation – time needed for the substrate activity to decrease to within 10% of the ground state

 d X ˜ k X Γ Γ ˜ a X Γ ˜ * d X * ˜ a X Γ Γ

 Optimal multicycle cascades may not correspond to multiple levels of an optimal single level cascade  The larger the number of levels in the cascade, the more robust that cascade - variation in concentration regimes  Fast signal propagation can be achieved with different sets of kinetic parameters