Intervention de Manouk Abkarian

Malaria parasites egress from the
red blood cell:
the physics of the gift ribbon
Manouk Abkarian
Gladys Massiera
A Callan Jones, V Lorman
Laboratoire Charles Coulomb
Catherine Braun-Breton ; Laurence Berry (postdoc)
DIMNP, UMR 5235, University of Montpellier 2, France
students: N. Casanova, O. Albarran,
• PhD
• Master Students: M. Roques, J. Lee, L. Vigan
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Malaria in history
• Oldest clinical case of death due to Malaria:
Toutânkhamon
Hawass et al. JAMA 2010
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Malaria in numbers
• Health and Economical Burden :
- 40% world's population exposed
- 1M deaths/year, mostly children
- Definitive cause of poverty in many afflicted
regions
Endemic regions
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Life Cycle
Cowman et al. Cell 124, 755–766, 2006
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RBC life cycle
48 H
Ring stage
Real time
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RBC
life
cycle
Merozoite
1 μm
1.5 μm
Cowman et al. Cell 124, 755–766, 2006
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RBC life cycle
Invasion
Miller et al. 264:1878-1883, Science 1994
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Real time
Moonwalking
Motility without ameoboid deformation or flagella
On Glass
Thesis of Nathalie Casanova
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RBC life cycle
48 H
Ring stage
Real time
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Take home message
• Egress is a fast process at the cellular scale: with a
characteristic mode
10
Abkarian et al. Blood 2011
N=33 events
Infected RBC
Count
8
6
4
2
0
Real time Healthy RBC
Several merozoites body size displacement
0
600
1200 1800
Time (ms)
2400
3000
•
• Four distinct stages resulting from an elastic instability
of the membrane
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Stage I: iRBC Inflation
2 steps :
•A change in shape of iRBC
•A release from the vacuole inside
Top view
DIC
Microsocpy
@ 37°C and
5% of CO2
Build up of osmotic pressure
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Side view
Stage II: Osmotic release
• Fast Osmotic release of the first meros: ~100 ms
Slowed down x10
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Stage II: Osmotic release
A
0 ms
Merozoite 20 ms B
40 ms
Laplace law:
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60 ms
P = 2 ⇥ 1/R
Stage III-IV: Curling & Buckling
60 ms
104 ms
148 ms
Buckling
192 ms
• Release of following meros by membrane curling
236 ms
50
B
Curling
280 ms
T
324 ms
368 ms
3 µm
T
T
H
B
40
M
H
Vy (µm/s)
B
Slowed
down x20
M
30
T
Buckling
Buckling
20
B
H
10
0
0
C
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Curling
M
100
200
300
400
time (ms)
Curling
500
600
700
Why buckling ?
Non linear orthogonal displacement of the membrane due
to curling compression.
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Origin of curling ?
LC copolymer polymersomes
Asymmetric Bilayer
iRBC
Abkarian et al, Blood in press 2011
For Polymersomes: Mabrouk et al. PNAS 2009
Importance of the spontaneous curvature
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What we see for RBC
Healthy RBC under hypo-osmotic conditions in glycerol
Thesis of Octavio Albarran
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Pore thermodynamics
2
F = 2 r⇤
F
r ⇥
Liposome
•
Healing !
⇥ /r
Ub
r =
⇥
r
• Bubble
Sandre et al., PNAS 1999
= const
⇥ /r <<
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Bursting
Debregeas et al., Science 1999
Idea:
Gift
ribbon
physics
Importance of the spontaneous curvature
Eribbon
1
S=
= (c
Area
2
c0 )
2
c
Analogy with the energy of a spring
x
Espring
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1
= K(x
2
x0
x0 )
2
1
Model with curvature
energy of the rim
F = 2 r⇤
r (S + ⇥)
2
Mabrouk et al. PNAS 2009
c
1
S= bending energy per unit area of a cylindrical membrane
1 2
S = dFb /dA =
c
2
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Mabrouk et al.’s Dynamics
Energy dissipated by viscous friction: Re << 1
•
Compact curling
r(t)
2 r
C ṙ
2L
ṙ
2⇥rS ṙ = 2⇥rC ṙ
r + 2rc r = Dt
2
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4
C=
ln(2 rL) +
1
2
4
=
ln
2
2
⇥ln
rc = 2 D =
ec0
2e
Some fits possible
1.2
rc= 0.1 µm D = 7 µm2/s
2
r
=
0.4
µm
D=
40
µm
/s
1 c
rc = 1 µm D= 50 µm2/s
time (s)
0.8
r2 + 2rc r = Dt
0.6
0.4
0.2
0
0
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0.5
1
1.5
2
r (µm)
2.5
3
3.5
Other fits inacceptable
Why ?
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In fact we have 2 regimes
A
100 ms
283 ms
150 ms
iRBC labelled with red PKH 26 lipids
0 ms
B
Circular Opening
Curling
t0
r0
r
R
r0
D(t
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t0 ) = (r
r0 )(r + r0 + 2rc )
2
2r0 ln(
r
)
r0
2L
Discussion for c0
2
rc = 2
ec0
For a red blood cell membrane :
⇥ln
D=
2e
{
e = 50 nm
κ = 50 kBT
η = 0.001 Pa.s
rc = 0.5 - 1.5 μm
c0-1 = 63 - 83 nm
c0 1
Curling radius of the order of the membrane thickness
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Discussion for D
2
rc = 2
ec0
⇥ln
D=
2e
For a red blood cell membrane :
D = 11 - 43
{
e = 50 nm
κ = 50 kBT
η = 0.001 Pa.s
2
μm /s
Dmodel = 8000
2
μm /s
!
Two orders of magnitude of difference !!!!! Why ???
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Two candidates !
⇥ln
D=
2e
Compact curling ?
eequi > e ?
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Dissipation ?
Is curling compact ?
Again our toy model in viscous oil
No ! but not enough
Only a factor 2-4 for D
Thesis of O. Albarran
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Gift Ribbon in a liquid
A
B
iRBC
curling
scale
e0c0
c0-1
e1c0
e
e2c0
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ṙ
e2
e1
e0
Inside-out RBCs
hypotonic lysis on ice cold solutions fixed with OsO4
Lew et al., J Cell Biol (1988) vol. 106 (6) pp. 1893
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Two candidates !
⇥ln
D=
2e
Compact curling ?
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Dissipation ?
rling
Other viscous dissipation ?
Membrane flow ?
Membrane elements
r0
r
R
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2L
case of a circular pore:
ṙ
2
2
⇡r ⌘s ( )
r
Other viscous dissipation ?
Regime analogous and renormalization of D:
⌘s ⇠ 10
D
1+
N.s/m
Dimova et al. Eur. Phys. J. B. (1999)
ln ⌘s
8⇡ ⌘r0
⌘s ⇠ 10
7
N.s/m
Brochard et al. Physica A. (2000)
DN ew /D ⇠ 1
Not clear what to choose
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9
10
2
Buckling:
Biologically relevant ?
Aborted buckling
Less efficient release and dispersion !
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Biologically relevant ?
Sequestration in deep vessels
Adhesion effect
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Biologically relevant ?
A
time
Vmax
#1
#2
#4
#3
#5
...
H
B
#1
#2
#5
#3
Membrane
#4
#6
T
#7
#2
#3
#5
#4
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No Adhesion
M
H
Adhesion
B
#8
#9
H
Perspectives
For the iRBCs
• We need to change the outer fluid viscosity
• We want to modify the membrane leaflets
composition to check the role of the lipid
asymmetry.
• Role of the underlying spectrin cytoskeleton
and the vacuole membrane
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Perspectives
For the model
• Complete the ribbon model with decreasing Re
• Effect of the Gaussian curvature and shear modulus
Problem of the pop ball
r0
r
R
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Curling Buckling elsewhere ?
Green Algea:Volvox
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Funny analogy with plants
Plants scale: High Re seeds spreading
Jet Propulsion
or
The Private Life of Plants, D. Attenborough
Cellular scale: Low Re “seeds” spreading
Both processes
needed !
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Eversion