Jean-Christophe PalauquiAurélie Urbain

Alain Trubuilhttp://www.jouy.inra.fr/mia

31/05/2012 1

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]

31/05/2012 2

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]

31/05/2012 3

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?

31/05/2012 4

• 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

31/05/2012 5

Steger C., An unbiased detector of curvilinear structure, IEEE TransPattern Anal Mach, 20, 113-125 (1998)

xy

xz yz

31/05/20126

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

31/05/2012 7

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

31/05/2012 8

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)

31/05/2012 10

Q1: reconstruction of the dynamics(4)

31/05/2012 11

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

31/05/2012 12

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

31/05/2012 15

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

31/05/2012 17

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

31/05/2012 18

31/05/2012 19

Understanding some aspects of shapeUnderstanding growth

curvatures

waves

distorsions

shifts

Q2: why these sequence of events?

31/05/2012 20

3c 5c 8c5

9c5 9c5

10c 10c

bourreletChgt de courbure

Plan incliné vers le bas redressement

31/05/2012 21

12c2

12c2

13c1 13c1

9

10

11

13

12

31/05/2012 22

Embryo

==

complex shell’

Simulate geometries related to first stagesIdentifiy few rules from 3D reconstructions

Utse directly 3D reconstructions