Analyzing robustness of biological reaction systems
Analyzing robustness of biological
reaction systems
19. 3. 2013
Sven Dražan
Analyzing robustness of biological reaction systems
Contents
• What is Robustness?
• Dynamic reaction systems
• Behavior and properties
• Computing robustness
Analyzing robustness of biological reaction systems
Motivation / Bioreactors
Analyzing robustness of biological reaction systems
Motivation / Photosynthesis
photosystem I - PSI
Analyzing robustness of biological reaction systems
What is robustness
Is stability robustness?
Analyzing robustness of biological reaction systems
What is robustness
Is homeostasis robustness?
Analyzing robustness of biological reaction systems
What is robustness
Analyzing robustness of biological reaction systems
What is robustness
Is
multistability or instability
robustness?
Analyzing robustness of biological reaction systems
What is robustness?
Robustness is a property that allows a system to maintain
its function against internal and external perturbations.
Kitano, 2004a
Analyzing robustness of biological reaction systems
What is robustness…
Robustness is a property that allows a system to maintain
its function against internal and external perturbations.
Kitano, 2004a
function ~ behavior ~ property
Analyzing robustness of biological reaction systems
What is robustness… Robustness is a meta-property!
Robustness is a property that allows a system to maintain
its property against internal and external perturbations.
Kitano, 2004a
Analyzing robustness of biological reaction systems
What is robustness
Analyzing robustness of biological reaction systems
Robustness and tradeoffs
Analyzing robustness of biological reaction systems
What is a dynamic reaction system
Demo
Analyzing robustness of biological reaction systems
Dynamic reaction systems – Example
S → 2 S
W + S → 2 W
W →
k1
k2
k3
Analyzing robustness of biological reaction systems
Dynamic reaction systems – Bigger example
Analyzing robustness of biological reaction systems
What is a behavior?
98.8% common DNA
Any difference in behavior?
Analyzing robustness of biological reaction systems
What is a behavior ~ property
Reachability - F(x>3)
Response - G((x<1)  F(x>3))
Oscillation - G((x<1)  F(x>2)  (x>2)  F(x<1))
t
x
0
3
2
1
t
x
0
3
2
1
t
x
0
3
2
1
Analyzing robustness of biological reaction systems
Computing robustness
t
S
0
3
2
1
Wolfinitialcount
Sheep birth rate
G((S<1)  F(S>2)  (S>2)  F(S<1))
0
Analyzing robustness of biological reaction systems
Computing robustness
t
S
0
3
2
1
Wolfinitialcount
Sheep birth rate
G((S<1)  F(S>2)  (S>2)  F(S<1))
0
k1_min k1_max
w(t0)minw(t0)max
Analyzing robustness of biological reaction systems
Computing robustness
t
S
0
3
2
1
Wolfinitialcount
Sheep birth rate
G((S<1)  F(S>2)  (S>2)  F(S<1))
0
Analyzing robustness of biological reaction systems
Computing robustness
t
S
0
3
2
1
Wolfinitialcount
Sheep birth rate
G((S<1)  F(S>2)  (S>2)  F(S<1))
0
Analyzing robustness of biological reaction systems
Computing robustness
t
S
0
3
2
1
Wolfinitialcount
Sheep birth rate
G((S<1)  F(S>2)  (S>2)  F(S<1))
0
Analyzing robustness of biological reaction systems
Computing robustness
t
S
0
3
2
1
Wolfinitialcount
Sheep birth rate
G((S<1)  F(S>2)  (S>2)  F(S<1))
0
Analyzing robustness of biological reaction systems
Computing robustness
t
S
0
3
2
1
Wolfinitialcount
Sheep birth rate
G((S<1)  F(S>2)  (S>2)  F(S<1))
0
Analyzing robustness of biological reaction systems
Computing robustness
t
S
0
3
2
1
Wolfinitialcount
Sheep birth rate
G((S<1)  F(S>2)  (S>2)  F(S<1))
0
Analyzing robustness of biological reaction systems
Computing robustness – continuity problem
Analyzing robustness of biological reaction systems
Computing robustness – continuity problem
Analyzing robustness of biological reaction systems
Computing robustness – continuity problem
Analyzing robustness of biological reaction systems
Computing robustness – continuity problem
Analyzing robustness of biological reaction systems
Current approaches
BioCham
Breach (Donzé A. and Maler O. 2010)
Analyzing robustness of biological reaction systems
Breach – Key concepts
How does a neighborhood behave?
Analyzing robustness of biological reaction systems
Breach – Key concepts
How does a neighborhood behave?
Analyzing robustness of biological reaction systems
Breach – Key concepts
How does a neighborhood behave?
Sensitivity analysis
Analyzing robustness of biological reaction systems
Breach – Key concepts
Local property robustness
G((S<1)  F(S>2)  (S>2)  F(S<1))
Analyzing robustness of biological reaction systems
Breach – Key concepts
G((S<1)  F(S>2)  (S>2)  F(S<1))
2
1
Local property robustness
Analyzing robustness of biological reaction systems
Breach – Key concepts
G((S<1)  F(S>2)  (S>2)  F(S<1))
2
1
Local property robustness
Analyzing robustness of biological reaction systems
Breach – Key concepts
Hierarchical refinement
Analyzing robustness of biological reaction systems
Breach – Key concepts
Hierarchical refinement
Analyzing robustness of biological reaction systems
Breach – Key concepts
Hierarchical refinement
Analyzing robustness of biological reaction systems
Breach – Key concepts
Hierarchical refinement
Analyzing robustness of biological reaction systems
Breach – Key concepts
Hierarchical refinement
Analyzing robustness of biological reaction systems
Breach – Key concepts
Hierarchical refinement
Analyzing robustness of biological reaction systems
Breach – Key concepts
Hierarchical refinement
Analyzing robustness of biological reaction systems
Breach – Key concepts
Hierarchical refinement
Analyzing robustness of biological reaction systems
Robustness of Stochastic systems
Analyzing robustness of biological reaction systems
Robustness of Stochastic systems
Analyzing robustness of biological reaction systems
Summary and Conclusion
What have you seen
• What is robustness
• Models of biological systems
• Expressing properties
• Current approaches to robustness of continuous systems
• Robustness of Stochastic systems
Analyzing robustness of biological reaction systems
Questions and comments are welcome
Analyzing robustness of biological reaction systems
Thank you for your attention.
Analyzing robustness of biological reaction systems
Sources
• LTL – Linear Temporal Logic
• Amir Pnueli. The temporal logic of programs. In Proc. 18th Annual Symposium on
Foundations of Computer Science (FOCS), pages 46–57, 1977.
• STL – Signal Temporal Logic
• O. Maler and D. Nickovic. Monitoring temporal properties of continuous signals. In
FOR- MATS/FTRTFT, pages 152–166, 2004.
• Donzé, A., & Maler, O. (2010). Robust satisfaction of temporal logic over real-valued
signals. Formal Modeling and Analysis of Timed Systems, 92–106. Springer.
doi:10.1007/978-3-642-15297-9_9
Analyzing robustness of biological reaction systems
Sources
• Google Images
• http://www.nature.com/msb/journal/v4/n1/images/msb200812-f2.jpg
• http://wolf-happy-blog.blog.cz/profil
• http://www.publicdomainpictures.net/view-image.php?picture=ovce-a-jeji-dite&image=124
• Photosynthesis model
• Lazár Dušan (2009) Modelling of light-induced chlorophyll a fluorescence rise (O-J-I-P transient)
and changes in 820 nm-transmittance signal of photosynthesis. Photosynthetica 47(4):483-498,
DOI:10.1007/s11099-009-0074-8
• http://www.e-photosynthesis.org/projects/
• Software
• NetLogo – http://ccl.northwestern.edu/netlogo
• Copasi - http://www.copasi.org
• Biocham - http://contraintes.inria.fr/BIOCHAM
• Breach - http://www-verimag.imag.fr/~donze/breach_page.html
• Wikipedia
• http://en.wikipedia.org/wiki/Lotka_Volterra_equation
• http://en.wikipedia.org/wiki/Snowshoe_Hare
• http://en.wikipedia.org/wiki/Lynx
• Other
• Jan Papoušek’s Bacelor thesis: https://is.muni.cz/auth/th/325494/fi_b/thesis.pdf
• Human vs. Chimp: http://www.sciencedirect.com/science/article/pii/S0002929707640968