Jean-Christophe PalauquiAurélie Urbain
Alain Trubuilhttp://www.jouy.inra.fr/mia
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Early embryo development for Arabidopsis thalianaQuantitative description of some
events sequencerelated to geometry and mechanics
Sagital plane: from the first cell division Transversal plane: delimitate basal and apical domains inside the embryo [Hudson, Plant Phys., 2000]
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Approach :
• Q1: How the structure is built? What is the sequence of events?
[deform, add elements]
• Q2: Why this sequence of events and not another?[biophysics, mechanics, genetics]
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timelapse
Several embryos at different stages
Characterize events: cells, walls, [stiffness],…
1. 3D segmentation (number of cells, volumes,…)
2. Reconstruction of the dynamics
3. Mechanical properties
8c 32c 104c 296c
Q1: what is the sequence of events?
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• Embryo not alone• Observation of a continuous process (walls under construction)• 3D• Complexity (from 1-300 cells)• Artifact due to experiment• Validation
pipeline (C, Matlab, Avizo)
278 cells 294 cells
8 cells12 cells
25 cells29 cells
32 cells103 cells
Q1: 3D segmentation
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Steger C., An unbiased detector of curvilinear structure, IEEE TransPattern Anal Mach, 20, 113-125 (1998)
xy
xz yz
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Q1: reconstruction of the dynamics (1)
E1, t1 E2, t2
E2, t1
32 cells 24 cells
MOVED FIXED
Step 1 : Affine Registration
Step 2 : Bspline Registration
Step 3 :Identify the labels which are matched together
Difficulties: symetries new walls
Limitation : not well defined correspondance
Another point of vue
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Q1: reconstruction of the dynamics (2)
12
4
3
76 5
8109
11121413
1 32 8 712 14 4 9 13 5 6 10 11
First division plan indetermination: darkerl older or signal homogeneity
1. Traces of history in a sample at a given stage2. Use a representation based on appropriate features (walls)
If a1<a2 C1 and C2 sisters else c1 and c3 sisters
Main idea : angles
3D implementation
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Q1: reconstruction of the dynamics (3)
1. Interface decomposition2. Determination of neigbors patchs 3. Évaluation of coplanarity
• Determistic algo.• Sochastic algo.
Which plan?
931/05/2012
Q1: reconstruction of the dynamics (4)
Lineage of a 23 cells embryo (half)
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Q1: reconstruction of the dynamics(4)
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12
8
Tapezuneéquationici.
1
(1)( ) ( )
p PJ A Q p
Cmin
A
p1
2p
2
( , ) ( (1), ( (1)))( , )
p q P P PQ p q
* *1 2
* *1 2
| ( ) ( ) |( ) ( )
V p V pV p V p
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Difficulties : use curvature?
93 cells
Q1: reconstruction of the dynamics (4)
Lineage of a 23 cell embryo (half)
Deformation: growth rate
timing31/05/2012 13
Q1: reconstruction of the dynamics: growth (5)
Idea: use the trees for embryos
No combinatorial explosion Trigger localized alarms during tree ‘climbing’
a1 a2 b1 b2a1
a1
b1
b2ou
1 1 2 2 1 2 3 1 2sgn( , ), sgn( , ), sgn( , )s G G i s G G j s G G k
sgn , ,
1 1 2 2 3 3a b a b a bs s s s s s
0? a1 b1, a2b2
a1 b2, a2b131/05/2012 14
Q1: reconstruction of the dynamics: growth (6)
Plug of a 16-cell embryo inside a 23 cell embryo (half)
V162
V161
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Q1: reconstruction of the dynamics: growth (7)
V231
V232
Possibility for local referential construction during tree ‘climbing’ 31/05/2012 16
Q1: reconstruction of the dynamics: timing
The lowest the class the most transitory the configuration
Tree+speed lifetime of a configuration chance to observe the configuration
Preliminary idea : link frequency of cell counts inside a population to timing
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 320
10
20
30
40
50
60
70
80
nbr embryons
Nbr de cellules
Effe
ctif
m o da rg m in ( , )V o b sD F F
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Conclusions / Perspectives
1. 3DSegmentation 3D (number of cells, volumes,…)
2. Reconstruction of the dynamicsMake it more robust, publish
• Q2: Why these events sequence?
Mechanical args
Molecular flux analyse
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Understanding some aspects of shapeUnderstanding growth
curvatures
waves
distorsions
shifts
Q2: why these sequence of events?
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3c 5c 8c5
9c5 9c5
10c 10c
bourreletChgt de courbure
Plan incliné vers le bas redressement
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12c2
12c2
13c1 13c1
9
10
11
13
12
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Embryo
==
complex shell’
Simulate geometries related to first stagesIdentifiy few rules from 3D reconstructions
Utse directly 3D reconstructions