A compositional approach to the stochastic dynamics of gene networks
A compositional approach to the stochastic dynamics of gene networks
Ralf Blossey (IRI, Lille)
Luca Cardelli, Andrew Phillips (Microsoft Research, Cambridge UK) 0-0
The menu:
• Motivation • Gene networks as gene circuits in stochastic π -calculus • Examples, from simple to less simple
• Outlook
0-1
...finding structures in complexity...
0-2
...modules and motifs...
0-3
...but watch out for anthropomorphisms...
0-4
...with better resolution...
...what you see might not be there!
0-5
... engineered modules: a useful paradigm?
0-6
...let’s try to build gene networks as gene circuits... a) A gene gate which transcribes constitutively:
null(b) = τε .(tr(b)|null(b)) tr(b) =!b.tr(b) + τδ .0
0-7
b) an inhibitory gate:
neg(a, b) =?a.τη .neg(a, b) + τε .(tr(b)|neg(a, b))
0-8
c) an excitatory gate:
pos(a, b) =?a.τη .(tr(b)|pos(a, b)) + τε .(tr(b)|pos(a, b))
0-9
Examples: very simple 1
0-10
Examples: very simple 2
0-11
Examples: very simple 3
0-12
Examples: simple
0-13
Examples: less simple 1
0-14
Examples: less simple 2
0-15
Example: The Repressilator
neg(c, a)|neg(a, b)|neg(b, c)
0-16
...the real system: three bacterial genes (+ GFP)
M. B. Elowitz, S. Leibler, Nature (2000) 0-17
...ODE modeling...
dmi α = −mi + + α0 n dt 1 + pj dpi = −β(pi − mi ) dt
i = (lacI, tetR, cI) , j = (cI, lacI, tetR)
... compare with
neg(c, a)|neg(a, b)|neg(b, c) 0-18
...the ODE results...and Gillespie...
0-19
...to be compared with...
0-20
... and more parameter play...
0-21
More complex example: combinatorial gene circuits
C. C. Guet, M. B. Elowitz, W. Hsing, S. Leibler, Science (2002)
0-22
A specific case study: D038
0-23
D038 in π -gate modelling
0-24
D038: Experimental results
0-25
A second example: D052
0-26
A second example
0-27
D038 in π -gate modelling: ...more complex gates needed...
negp(a, (ε, η), p) =?a.τη .negp(a, (ε, η), p)+τε .(p()|negp(a, (ε, η), p))
0-28
...repressible transcription factors...
rtr(b, r) =!b.rtr(b, r)+!r.0 + τδ .0 rep(r) =?r.rep(r) 0-29
D038: Boolean analysis
no repressors: GFP = 0 → lcI = 1 → LacI = 0 → TetR = 1; self-loop: TetR = 1 → TetR = 0 → GFP = 0.5.
0-30
D038
0-31
A final example: D016
0-32
A final example: D016
0-33
A final example: D016
0-34
Outlook: chromatin, the nucleosome
0-35
Outlook: chromatin, histone tail modifications
0-36
Outlook: chromatin, stochastic π -network
0-37
Organisational outlook: next meeting Aci VicAnne
´ Modelisation et Cancer Institut de Biologie de Lille
17/18 mai 2006
0-38
Ralf Blossey (IRI, Lille)
Luca Cardelli, Andrew Phillips (Microsoft Research, Cambridge UK) 0-0
The menu:
• Motivation • Gene networks as gene circuits in stochastic π -calculus • Examples, from simple to less simple
• Outlook
0-1
...finding structures in complexity...
0-2
...modules and motifs...
0-3
...but watch out for anthropomorphisms...
0-4
...with better resolution...
...what you see might not be there!
0-5
... engineered modules: a useful paradigm?
0-6
...let’s try to build gene networks as gene circuits... a) A gene gate which transcribes constitutively:
null(b) = τε .(tr(b)|null(b)) tr(b) =!b.tr(b) + τδ .0
0-7
b) an inhibitory gate:
neg(a, b) =?a.τη .neg(a, b) + τε .(tr(b)|neg(a, b))
0-8
c) an excitatory gate:
pos(a, b) =?a.τη .(tr(b)|pos(a, b)) + τε .(tr(b)|pos(a, b))
0-9
Examples: very simple 1
0-10
Examples: very simple 2
0-11
Examples: very simple 3
0-12
Examples: simple
0-13
Examples: less simple 1
0-14
Examples: less simple 2
0-15
Example: The Repressilator
neg(c, a)|neg(a, b)|neg(b, c)
0-16
...the real system: three bacterial genes (+ GFP)
M. B. Elowitz, S. Leibler, Nature (2000) 0-17
...ODE modeling...
dmi α = −mi + + α0 n dt 1 + pj dpi = −β(pi − mi ) dt
i = (lacI, tetR, cI) , j = (cI, lacI, tetR)
... compare with
neg(c, a)|neg(a, b)|neg(b, c) 0-18
...the ODE results...and Gillespie...
0-19
...to be compared with...
0-20
... and more parameter play...
0-21
More complex example: combinatorial gene circuits
C. C. Guet, M. B. Elowitz, W. Hsing, S. Leibler, Science (2002)
0-22
A specific case study: D038
0-23
D038 in π -gate modelling
0-24
D038: Experimental results
0-25
A second example: D052
0-26
A second example
0-27
D038 in π -gate modelling: ...more complex gates needed...
negp(a, (ε, η), p) =?a.τη .negp(a, (ε, η), p)+τε .(p()|negp(a, (ε, η), p))
0-28
...repressible transcription factors...
rtr(b, r) =!b.rtr(b, r)+!r.0 + τδ .0 rep(r) =?r.rep(r) 0-29
D038: Boolean analysis
no repressors: GFP = 0 → lcI = 1 → LacI = 0 → TetR = 1; self-loop: TetR = 1 → TetR = 0 → GFP = 0.5.
0-30
D038
0-31
A final example: D016
0-32
A final example: D016
0-33
A final example: D016
0-34
Outlook: chromatin, the nucleosome
0-35
Outlook: chromatin, histone tail modifications
0-36
Outlook: chromatin, stochastic π -network
0-37
Organisational outlook: next meeting Aci VicAnne
´ Modelisation et Cancer Institut de Biologie de Lille
17/18 mai 2006
0-38
