Growth stops rapidly after the applied deformation Fast and far from the stimulated area : remote response Transmission of a signal throughout the plant 3
Hypothesis about the origin of the long distance signal
Signal propagation speed ≈ cm/s
1- Chemical signals carried by the sap Too slow (cm/h) 2- Propagation of electrical signals No clear evidence 3- Overpressure generated by an hydro/mechanical coupling Julien 1993, Malone 1994 4
Hypothesis about the origin of the long distance signal
Signal propagation speed ≈ cm/s
1- Chemical signals carried by the sap Too slow (cm/h) 2- Propagation of electrical signals No clear evidence 3- Overpressure generated by an hydro/mechanical coupling Julien 1993, Malone 1994 5
Overpressure pulse when bending
INRA-PIAF
An hydro/mechanical coupling
1) Origins and amplitude of the overpressure ?
Lopez et al. J.Exp.Bot 2014
2) Dynamic (speed, damping...) ? 6
Overpressure pulse when bending
INRA-PIAF
An hydro/mechanical coupling
1) Origins and amplitude of the overpressure ?
Lopez et al. J.Exp.Bot 2014
2) Dynamic (speed, damping...) ? 7
Non trivial origin of the overpressure
Compression
Tension
No changement of volume
No changement in pressure
??? 8
From the natural branch to the biomimetic artificial branch
L=0.1−1 m d =10−50μ m
E≈1GPa
Simplified geometry : Longitudinal flux PDMS : elastic and isotrope media Silicon Oil : Newtonian fluid
9
From the natural branch to the biomimetic artificial branch Poutre en élastomère de silicone remplie d’un fl uide visqueux
L≈10 cm D=1 cm d =0.5 mm E ≈1 MPa ν=0.5 η≈1 Pa.s
10
Experimental device and bending procedure
Fixed
Control parameter : imposed bending deformation
ε=
DC 2
with
Pressure measurements of the fluid inside the beam for a closed geometry 11
Typical response of the system while bending
Flexion Return
ε=8 %
Generation of a steady overpressure !!!
12
Pressure/Deformation relation
ΔP proportionnal to ε 13
2
Interpretation ???
Compression
Tension
No changement of volume
No pressure variation 14
A non linear coupling ?
Idea : During bending, it's energetically favorable for a porous media to minimize its section
Similar to the phenomenon of tube ovalization (Brazier) 15
Simple energetic model
Elastic energy of a beam under bending U bend (δ)=
EV 2 2 D C 32
U bend (δ)=
EV 2 2 (D−2δ) C 32
Landau Lifchitz
Elastic energy of a beam under compression EV 2δ 2 U squeeze (δ )≈ ( ) 32 D
Minimization of the total elastic energy
d (U bend +U squeeze )=0 dδ
2
2d 1 DC ≈ ( ) D 4 2 16
2 ε ε⊥ ≈ 4
Link to the volume and pressure change
B : Module of compressibility of the beam
5
Poutres : B≈2.10 Pa
ε≈10 %
Δ P≈ kPa
Validation of this mecanism for real branches ? 17
OK
Mesurements made on tree branches
INRA
Overpressure (kPa)
With E. Badel
Experimental device
Deformation Same relation for Pressure = f(strain) ! 18
Experiments made on living things : characterization of tree branches
Bulk modulus measurements
Cytologic cuts : Size of the channels, porosity, permeability Young modulus measurements : 1.5-4 GPa 19
Comparison between artificial and real branches
Beams : E=2 MPa
Artificial branches Poplar Green Oak
am e B
s
Branches : E=1.5-4 GPa
a Re
ee r t l
s he c n bra
ε Same physical mecanism 20
Perspectives
Physics
Biology
Let's play with the parameters : Porosity, channels' distribution, bulk modulus….
Effect of the overpressure on growth Confirm the effect on different species
Study of the signal dynamic relaxation in an open system, its speed of propagation…
Expression of the TCH2 gene when the conduction system is put under overpressure
E. Badel, PIAF-INRA 21
Thank you for your attention
22
Link between the volume change and the measured overpressure
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