Reconstructing the Embryo: Replacing Measured Data by Computed Data ~ Bioemergences Meeting, Málaga, Spain, December 2006 ~
René Doursat
Paul Bourgine
Institut des Systèmes Complexes, CREA CNRS & Ecole Polytechnique 1, rue Descartes, 75005 Paris
Applied developmental biology
December 2006
Reconstructing the Embryo
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The big picture MACHINE (MODEL) t → t+1 prediction laws & parameters
INDUCTION II reconstruction
MEASURED embryonic states E(t)
COMPARISON distance → GA fitness
INDUCTION I extraction
MICROLEVEL DEDUCTION simulation
COMPUTED embryonic states E'(t)
MACROLEVEL
RAW embryonic data
December 2006
Reconstructing the Embryo
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Current extraction (Embryomics)
output
input
¾ Image analysis MEASURED embryonic states E(t)
9 input: images and movies 9 methods: segmentation, tracking
INDUCTION I extraction
RAW embryonic data
December 2006
9 output: lineage tree labeled with dynamic variables (positions, velocities, division rates, etc.) → extensive set of measured states that can be replayed “by rote”
Reconstructing the Embryo
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Current extraction (Embryomics)
output
input
¾ Labeled lineage tree 9 complete measured state 4
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x, y, z, t vx, vy, vz θ, φ, ψ ......
December 2006
Reconstructing the Embryo
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Current morphogenetic machine (R. Doursat) MACHINE t → t+1 prediction laws & parameters
DEDUCTION simulation
¾ Morphogenetic machine 9 input: gene network, rate mappings (functions of genetic identity) 9 laws: rates of division, migration & positioning, gradient diffusion, genetic expression
COMPUTED embryonic states E'(t)
r = .05 v = 1.3 Δ = 50
9 output: full shape & labeled lineage → relies on an intensive parameter set December 2006
Reconstructing the Embryo
r = .08 v = 2.7 Δ = 30 6
Predicting is modeling MACHINE 1 prediction MACHINE MACHINElaws 2 &t+1 parameters prediction laws t MACHINE → prediction 3 laws & parameters & parameters t → t+1 prediction laws & parameters MEASURED embryonic states E(t)
COMPUTED embryonic states E'(t)
¾ Different levels of generality vs. specificity for the machine 9 too specific: lookup table or “rote playback”. . . no generalization! 9 too generic: agnostic statistical estimator. . . no convergence! → best: heuristic model, with genetic-biomechanic laws & parameters December 2006
Reconstructing the Embryo
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Predicting is modeling & optimizing MACHINE t → t+1 prediction laws & parameters
¾ The morphogenetic machine is a parametrized function 9 each state is “predicted” or “reconstructed” as a function of the previous state: E(t+1) = Fλ (E(t)) (or more past states) 9 this function relies on built-in mechanisms and parameters λ 9 the parameters are “learned” (by machine learning) or “optimized” (by genetic algorithms), etc. → learning does not occur directly on the extensive state variables, but on the intensive set of parameters December 2006
Reconstructing the Embryo
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Future morphogenetic machine: design methodology INDUCTION II reconstruction
MACHINE t → t+1 prediction laws & parameters
¾ Morphogenetic machine’s design MEASURED embryonic states E(t)
9 start from tree & annotated organs, back in time: get polyclonal ratios
9 from the polyclonal ratios, induce the identity domains, the basic components of the reconstruction 9 from the identity domains, induce the dynamic mappings (field functions): division rates, velocity vectors, deformation tensors, etc. → model dynamic maps by { mechanisms + parameter } computation December 2006
Reconstructing the Embryo
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Future morphogenetic machine: design methodology MACHINE t → t+1 prediction laws & parameters
INDUCTION II reconstruction
¾ Morphogenetic machine’s design MEASURED embryonic states E(t)
9 start from tree & annotated organs, back in time: get polyclonal ratios
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75%
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25%
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9 19
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100%
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coloring the identity domains
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calculating the dynamic maps December 2006
Reconstructing the Embryo
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Future morphogenetic machine: design methodology INDUCTION II reconstruction
MACHINE t → t+1 prediction laws & parameters
¾ Morphogenetic machine’s design MEASURED embryonic states E(t)
9 model dynamic maps by execution of local and global transformations at specific locations and times
involution Figures from Learning Objects Development Team. Wesleyan University 2005.
intercalation December 2006
extension Reconstructing the Embryo
deformation, flows 11
Comparing measured and computed embryos ¾ Morphological distance 9 shape comparison and lineage comparison 0 1 4
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MEASURED embryonic states E(t)
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COMPARISON distance → GA fitness
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COMPUTED embryonic states E'(t)
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9 compare 2 measured embryos → variability, BioEmergences 9 compare a measured embryo with a computed embryo → errorcorrection (in learning), fitness (in evolutionary optimization) December 2006
Reconstructing the Embryo
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