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

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Study of Study of T ricyclic ricyclic Cascade Netw Cascade Networks using

• rks using

Dynamic Optimization Dynamic Optimization

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• H. Kestler, C. Wawra, B. Kracher and M. Kuhl:

“Network modeling of signal transduction: establishing the global view”.

• Bioessays. 30:1110-1125. 2008
• Systems Biology – interdisciplinary

field that focuses on the systematic study of complex interactions in biological systems

• Signal transduction pathways
• enable cells to integrate external

and internal signals and to respond to them,

• are present in major

developmental changes in organism (embryo development, but also in cancer, asthma, diabetes…)

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

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Inverse Approach: Direct 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.

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• balance equations, conservation equations
• kinetic expressions

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• balance equations, conservation equations
• kinetic expressions
• Kinetic parameters:

˜ a

X ,, ˜

a

X * , ˜

d

X, ˜

d

X * , ˜

k

X

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 Concentration ratios  Saturation parameters  Activity coefficient

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Inverse Approach:

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Concentration Time

Input stimulus

kinase activity

• max. activity

Concentration Time upstream kinase

kinase activity

• max. activity

90%

Concentration Time upstream kinase

kinase activity

• max. activity

10%

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• Go from a typical graded response to a switch-like response

Typical graded response

Input stimulus Steady-state kinase activity

1

Ultrasensitive response

90% 10%

αX

0.1 αX 0.9

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• Optimal ultrasensitivity for fixed values of ratios between

total concentrations of enzymes and substrate:

Ultrasensitivity [S]/[X] = 0.01

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• 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

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Ultrasensitivity

Concentration ratio [S]/[X] Concentration ratio [PX]/[X]

Input stimulus Steady-state kinase activity

1

 Ultrasensitivity can be achieved for small values of concentration ratios  The closer to saturation, the more ultrasensitive the monocyclic cascade.

Concentration ratio [PX]/[X] Concentration ratio [S]/[X]

Saturation parameter KX Saturation parameter K*X

Concentration ratio [PX]/[X] Concentration ratio [S]/[X]

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• Kinetic parameters:

˜ a

X ,, ˜

a

X * , ˜

d

X, ˜

d

X * , ˜

k

X, ˜

a

Y, ˜

a

Y *, ˜

d

Y, ˜

d

Y *, ˜

k

Y, ˜

k

Y *

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 Concentration ratios  Saturation parameters  Activity coefficients

ρS / X,ρPX / X,ρX /Y,ρP

Y /Y

˜ K

X =

˜ d

X + ˜

k

X

˜ a

X

˜ K

Y =

˜ d

Y + ˜

k

Y

˜ a

Y

˜ K

Y * =

˜ d

Y * + ˜

k

Y *

˜ a

Y *

˜ K

X * =

˜ d

X * +1

˜ a

X *

αX = ˜ k

X

ρS / X ρPX / X αY = ˜ k

Y

˜ k

Y *

ρX /Y ρP

Y /Y

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Maximal values of ultrasensitivity objective measure, with corresponding values of saturation parameters for activation reaction of each level in a signaling cascade model:

Concentration ratio [X]/[Y] Concentration ratio [S]/[X] Concentration ratio [X]/[Y] Concentration ratio [X]/[Y] Ultrasensitivity Saturation parameter KX Saturation parameter KY Concentration ratio [S]/[X] Concentration ratio [S]/[X]

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 Maximum ultrasensitivity when the first kinase is saturated, but not the second kinase  An An optimal

• ptimal 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

saturated unsaturated

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• Kinetic parameters: ˜

a

X ,, ˜

a

X * , ˜

d

X, ˜

d

X * , ˜

k

X, ˜

a

Y, ˜

a

Y *, ˜

d

Y, ˜

d

Y *, ˜

k

Y, ˜

k

Y *, ˜

a

Z, ˜

a

Z * , ˜

d

Z, ˜

d

Z *, ˜

k

Z, ˜

k

Z *

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 Concentration ratios  Saturation parameters  Activity coefficients

ρS / X,ρPX / X,ρX /Y,ρP

Y /Y,ρY / Z,ρPZ / Z

˜ K

X =

˜ d

X + ˜

k

X

˜ a

X

˜ K

Y =

˜ d

Y + ˜

k

Y

˜ a

Y

˜ K

Y * =

˜ d

Y * + ˜

k

Y *

˜ a

Y *

˜ K

X * =

˜ d

X * +1

˜ a

X *

αX = ˜ k

X

ρS / X ρPX / X αY = ˜ k

Y

˜ k

Y *

ρX /Y ρP

Y /Y

˜ K

Z =

˜ d

Z + ˜

k

Z

˜ a

Z

˜ K

Z * =

˜ d

Z * + ˜

k

Z *

˜ a

Z *

αZ = ˜ k

Z

˜ k

Z *

ρY / Z ρP

Y / Z

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Optimal ultrasensitivity for various combinations of saturation parameters:

˜ K

X = 0.1

˜ K

Y =10

˜ K

Z =10

˜ K

X = 0.1

˜ K

Y =10

˜ K

Z =1

˜ K

X = 0.1

˜ K

Y =1

˜ K

Z =10

˜ 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

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• Optimal ultrasensitivity

for fixed values of ratios between total concentrations of enzymes and substrate

Ultrasensitivity

Concentration ratio [Y]/[Z] Concentration ratio [X]/[Y]

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• Optimal ultrasensitivity

for fixed values of ratios between total concentrations of enzymes and substrate

Ultrasensitivity

Concentration ratio [Y]/[Z] Concentration ratio [X]/[Y] Concentration ratio [X]/[Y] Concentration ratio [Y]/[Z] Concentration ratio [Y]/[Z] Concentration ratio [Y]/[Z]

Saturation parameter KX Saturation parameter KY Saturation parameter KZ

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

unsaturated saturated unsaturated

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Ultrasensitivity

KX KY KZ Monocyclic Bicyclic Tricyclic ~ 0.1 ~ 0.1 ~ 5.5 ~ 200 ~ 3 ~ 0.1 ~9.8 ~ 350 ~ 150

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Time Concentration Concentration Concentration Time Time

Input stimulus

upstream kinase upstream kinase

kinase activity kinase activity kinase activity

• max. activity
• max. activity
• max. activity

90% 10%

• 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

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˜ a

X

˜ k

X

 d

X

˜ a

X *

˜ d

X *

Γ Γ Γ Γ Γ

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 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

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