Why the mesophyll cell sizes
decrease with tree height?
g
---A
A mechanical view
Ming GUO
01/11/2008
Mesophyll cell sizes versus heights
Red Scale Bar = 20 μm
Mesophyll cell sizes versus heights
Mesophyll cell diameter (μm)
30
Parashorea
a as o ea cchinensis
e ss
Terminalia bellirica
Dysoxylum cupuliforme
Elaeocarpus braceanus
Syzygium
y yg latilimbum
Parthenocissus quinquefolia
25
20
Populus
opu us tomentosa
to e tosa
Populus hopeiensis
Fraxinus chinensis
Ginkgo biloba
Platanus orientalis
Wisteria sinensis
Lonicera maackii
Parthenocissus tricuspidata
Buxus bodinieri
15
10
5
0
20
40
Leaf height (m)
60
80
Summary on observations
•
Our microscopic observations of mesophyll
cells reveal that the cell sizes are
remarkably reduced with increasing heights
of
f th
the lleaves.
s
•
The reduction rates depend strongly upon
the growth regions.
•
My previous explanation was based on a
famous plant growth model.
Why the mesophyll cell sizes
d
decrease
with
h tree height,
h h
from the view of mechanics?
3. Evaporation into
air (transpiration)
22. Transport in
xylem vessels
Plant Physiology, 3rd ed. (2005)
1. Absorb water
from soil by roots
Mesophyll cells – The Engines
Symplasm
water
10~40 nm pores on outer surface
generate large negative pressure
~MPa
How Tall Can
Trees Grow?
Koch, G. W., Sillett, S. C.,
Jennings, G. M. & Davis, S. D.
The limits to tree height.
height
Nature 428, 851-854 (2004)
Relationship Between Xylem
P
Pressure
and
dT
Tree Height
H i h
Predawn
Midday
Hydrostatic gradient
before dawn is equal
to the gradient due to
gravity.
At midday, 2/3 of the
xylem
l
pressure d
due tto
gravity.
Guess negative water
pressure is the reason.
• An important process in tree’s life is the
continuous water transport to tree leaves
leaves,
which is mainly driven by the negative
pressure inside the leaf mesophyll cells
cells,
generated by transpiration.
• However,
H
th effects
the
ff t off these
th
negative
ti
pressures on the mesophyll cells are
mostly
tl unknown.
k
Focus on cells under transpiration!
Negative Pressures
¾ Transpiration on nanoscale
wall-pores generate
negative pressure in
apoplast water
water.
¾ Xylem negative pressures
become more negative with
increasing height.
¾ What’s the effects of
negative pressure to the
evolution and structure of
mesophyll cells？
2R
Negative Pressure
Negative apoplast
water pressure
Straw Collapse Analogy
When drinking
furiously through a
straw, the straw may
suddenly collapse
into flat
flat, due to the
negative pressure
inside.
inside
Straw Collapse Analogy
F cylindrical
For
li d i l thi
thin shell:
h ll
2 Et 3
Pcr = 3
D 1− v2
(
)
2 Et 3
so, Dcr = 3
(1 −ν 2 ) P
Timoshenko, Theory of elastic stability
Elastic Instability Mechanism
f large
for
l
cells
ll
sever transpiration
p
cylindrical shell model:
3
2 Et
D < Dcr = 3
2
(1 −ν ) P
Mesophyll cell sizes versus heights
Red Scale Bar = 20 μm
Strength Failure Mechanism
f smallll cells
for
ll
Assume isotropic elastic material
σr |
D
r = −t
2
=P
σ r |r =D / 2 = 0
P(D − 2t )
PD (D − 2t )
+
σr = − 2
2
2
2
2
D − (D − 2t ) 4 D − (D − 2t ) r
2
2
(
2
)
P(D − 2t )
PD (D − 2t )
−
σφ = − 2
2
2
2
D − (D − 2t ) 4 D − (D − 2t ) r 2
2
2
(
2
)
Strength Failure Mechanism
f smallll cells
for
ll
Max stresses:
σ r |r = a = P
D + (D − 2t )
σ φ |r = a = − 2
P
2
D − (D − 2t )
2
2
Strength criteria:
| σ r (r = a ) |= P < σ s + (= tensile strength )
D 2 + (D − 2t )
| σ φ (r = a ) |= 2
P < σ s − (= compressiv
p
e strength
g )
2
D − (D − 2t )
2
Strength Failure Mechanism
f smallll cells
for
ll
So
2
⎡ σ
⎤
σ
⎛
⎞
D < Dcr ~ ⎢1 + s − + ⎜ s − ⎟ − 1⎥t
P
P ⎠
⎥
⎢
⎝
⎣
⎦
Detailed parameters
parameters…
Plow = P0 + ( n + 1) ρ gH
extra pressure
flow resistance index
E = 130 MPa; υ = 0.3; t = 1.5 μm
σ s − = 2.3 MPa for rainforest trees
σ s − = 3.5 MPa dry-temperate trees
Curve fitting results:
n = 0.5 for rainforest zone trees
n = 4.6
4 6 ffor d
dry-temperate zone trees
Model Estimates
elastic instability
mechanism, BLACK lines
material failure
mechanism , RED lines
In both
h mechanisms,
h
leaf
l
cells
ll should
h l decrease their
h
sizes to
prevent structure and material collapse, with increasing height.