By Alain Trubuil (INRA)

1. Early embryo development
for Arabidopsis thaliana
Quantitative description of some
events sequence
related to geometry and mechanics
Jean-Christophe Palauqui
Aurélie Urbain
Alain Trubuil
http://www.jouy.inra.fr/mia
31/05/2012 1

2. 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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3. 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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4. Q1: what is the sequence of events?
timelapse
8c 32c 104c 296c
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
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5. Q1: 3D segmentation
• 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)
8 cells 29 cells 103 cells
12 cells
25 cells 32 cells
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278 cells
294 cells

6. xz yz
xy
Steger C., An unbiased detector of curvilinear structure, IEEE Trans
Pattern Anal Mach, 20, 113-125 (1998)
6
31/05/2012

7. Q1: reconstruction of the dynamics (1)
E1, t1 E2, t2 MOVED FIXED
Step 1 :
E2, t1 Affine
Registration
32 cells 24 cells
Step 2 :
Difficulties: symetries
Bspline
 new walls
Registration
Limitation : not well defined correspondance
Step 3 :
Identify the
labels which
are matched
together
Another point of vue
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8. Q1: reconstruction of the dynamics (2)
1. Traces of history in a sample at a given stage
2. Use a representation based on appropriate features (walls)
1 2 8 12 14 7 3 4 9 13 5 6 10 11
2 3
1
8 9 4
13
14 10
12 11
7 5
6
First division plan indetermination: darker l older or signal homogeneity
Main idea : angles
3D implementation
If a1<a2 C1 and C2 sisters else c1 and c3 sisters
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9. Q1: reconstruction of the dynamics (3)
1. Interface decomposition
2. Determination of neigbors patchs
3. Évaluation of coplanarity
• Determistic algo.
• Sochastic algo.
Which plan?
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10. Q1: reconstruction of the dynamics (4)
Lineage of a 23 cells embryo (half)
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11. Q1: reconstruction of the dynamics(4)
p1 2
1
8
p
2
Tapez une équation ici.
| V ( p1 )  V ( p2 ) |
 
* *
min J ( A)  Q1( p )  Q 2( p, q ) 
AC
pP (1) ( p , q )( P (1), P ( P (1))) V ( p1 )  V ( p2 )
* *
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12. Difficulties : use curvature?
93 cells
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13. Q1: reconstruction of the dynamics (4)
Lineage of a 23 cell embryo (half)
Deformation: growth rate
31/05/2012 timing 13

14. Q1: reconstruction of the dynamics: growth (5)
Idea: use the trees for embryos
a1 a2 a1 b1 b1 b2
ou
a1  b2
No combinatorial explosion
Trigger localized alarms during tree ‘climbing’
 
  
  

s1  sgn( G1G2 , i ), s2  sgn( G1G2 , j ), s3  sgn( G1G2 , k )
sgn , ,
  s1a s1b  s2 s2  s3 s3
a b a b
a1 b1, a2b2
  0?
a1 b2, a2b1
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15. Q1: reconstruction of the dynamics: growth (6)
Plug of a 16-cell embryo inside a 23 cell embryo (half)
V161
V162
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16. Q1: reconstruction of the dynamics: growth (7)
V231
V232
Possibility for local referential construction during tree ‘climbing’
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17. Q1: reconstruction of the dynamics: timing
Preliminary idea : link frequency of cell counts inside a population to timing
80
70
60
50
Effectif
40
nbr embryons
30
20
10
0
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 32
Nbr de cellules
The lowest the class the most transitory the configuration
Tree+speed  lifetime of a configuration  chance to observe the configuration
a rg m in V D ( F o b s , F m o d )
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18. Conclusions / Perspectives
1. 3DSegmentation 3D (number of cells, volumes,…)
Make it more robust, publish
2. Reconstruction of the dynamics
Mechanical args
• Q2: Why these events sequence? Molecular flux analyse
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19. Q2: why these sequence of events?
Understanding some aspects of shape
Understanding growth
curvatures
waves
distorsions
shifts
31/05/2012 19

20. Chgt de courbure
bourrelet
3c
5c 8c5
Plan incliné vers le bas
redressement
9c5 9c5
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10c 10c

21. 12
10
9 11
12c2
12c2
13
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13c1 13c1

22. Embryo
==
complex shell’
Identifiy few rules from 3D reconstructions
Simulate geometries related to first stages
Utse directly 3D reconstructions
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