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A PHYSICAL MODEL FOR
CAVEOLAR MEMBRANES
Matthew Turner & Alun Evans (Univ. Warwick - U.K)
Pierre Sens (CNRS: Inst. Charles Sadron - Strasbourg & Inst. Curie - Paris )
http://perso.curie.fr/Pierre.Sens/[email protected]
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hydrophobic
hydrophilic
Membranes Proteins :
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“Curvature active” Proteins :
Drive Membrane DeformationDrive Membrane DeformationEndocytosis - Cell fusionEndocytosis - Cell fusionMembrane recycling …Membrane recycling …
Concentrate binding sitesConcentrate binding sites Cell signalling …Cell signalling …
Ex: endocytosis by formation of Clathrin coated pits
Ex. Caveolae
receptors
Target molecules
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Physical model for fluid membranes
Equilibrium propertiesEquilibrium properties Balance between hydrophobic attractionsteric, electrostatic repulsion
Equilibrium area per lipid headEquilibrium area per lipid head
Bilayer thicknessBilayer thickness
Bending the membrane cost energy
fairly smallfairly small
CC = curvature = curvature
Bending modulusBending modulus
The membrane in under tension
EnergyEnergy
EnergyEnergy
= area increase= area increase
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Example - Thermal fluctuations of membranes
Monge representationMonge representation Curvature
Deformation energy
With surface tension
Curvature dominatesthe small lengthscales
From R. Dimovampikg-golm
Excess area
50nm < < Large
biological ”free membranes”
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Curvature instability - S. Leibler (‘86)- S. Leibler (‘86)
membrane inclusions inducemembrane inclusions inducea “spontaneous curvature”a “spontaneous curvature”
Near the inclusion
One refinement for “biological” membranes
Equilibrium distribution of inclusionsEquilibrium distribution of inclusionsfollows the curvaturefollows the curvature
Effective bending rigidityEffective bending rigidityIf the rigidity is <0
the membrane spontaneously curves
- Pure membrane - Curvature cost energy
Bending rigidity Membrane ~flatMembrane ~flat
- decorated membrane - The inclusions follow the curvature
Reduces Bending rigidity
Unstable for any inclusion density
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Curvature instability- formalism -- formalism -
membrane inclusions inducemembrane inclusions inducea “spontaneous curvature”a “spontaneous curvature”
Near the inclusion
Inclusion density
Equilibrium distribution of inclusionsEquilibrium distribution of inclusionsfollows the curvaturefollows the curvature
Effective bending rigidityEffective bending rigidity
If the rigidity is <0the membrane spontaneously curves
~ Landau expansion~ Landau expansion
Effective attractionEffective attraction
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Physical interactions between membrane inclusions
Attraction between junctionmediated by the membrane deformation
Bruinsma etal. ‘94
Attraction / Repulsion - Goulian etal. ‘93
Effect on Thermal Fluctuations (Casimir force)
Attraction - Goulian etal. ‘93 - Kardar etal. ‘98
Asymmetric inclusions
Cell Junction
Many-body interactions Oster etal. ‘99
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Quasi-spherical “Soft” Shells Thermal Self-Assembly of Caveolin aggregates
Internal Structure - Striated CoatAsymmetrical Interaction between Aggregates
Physical Origin ?
Structures of Caveolae
cell membrane
cell interior
clathrin-coated vesicle
caveolae
Location Plasma membrane of many cells: Endothelial cells, adypocytes, cardiac muscles…
Function Many: Endocytosis - ligand binding Interaction with signaling proteins - cholesterol transport…
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Caveolae pictures
100 nm.
Epon section of a portion of a rat adipocyte. (BL): basal lamina, (SER): smooth ER (FD): fat droplet
M. Stahlhut etal.Experimental Cell Research 261, 111–118 (2000)
T. Fujimoto etal.J. Electron Microscopy 47, 452 (1998)
Electron micrograph of caveolae in the rat smooth muscle cell Barr=100nm
As
C
M . Gumbleton Adv. Drug Delivery Rev. 49 (2001) 281
TEM of the alveolar-pulmonary capillary barrier in rat lung (As: Alveolar space; C: capillary lumen)
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Hypothetical model of the principal actions of caveolae and caveolins in signaling. Left of dashed line: The major part of caveolins (brown) is present as oligomers in structurally defined caveolae. Filamin (turquoise)– caveolin interactions link some caveolae to actin filaments (tan). Caveolin molecules with a ligand-binding site (scaffolding domain) not involved in oligomer formation can instead sequester and inhibit signaling proteins such as H-Ras (yellow). Activated growth factor receptors (blue-gray) in caveolae recruit adaptor proteins (red-white) like Grb2 and mSOS and can activate caveola-resident H-Ras. Outside of caveolae a fraction of caveolin-1 associates with integrins (gold) and keeps Src-family kinases like Fyn (orange) in an inactive conformation. Upon cell–matrix adhesion (integrin ligation) caveolin-1 and Fyn are coclustered with the integrins, and in the presence of GPI-linked uPAR (red) glycolipid rafts are recruited to the adhesion site. Fyn is activated and the inhibitory action of caveolin-1 is relieved. Fyn signals, via adapter molecules (Shc, Grb2/mSOS), to H-Ras. The activation of H-Ras (in rafts or caveolae) eventually leads to the activation of MAP kinases and signaling to the cell nucleus. K-Ras (light yellow) is present in a different membrane compartment from caveolins due to a polybasic region (pink) and takes part in different signaling events. Raft and caveola membranes are indicated in green. Small vertical lines within the noncaveolar membranes indicate cholesterol concentration. Fyn, mSOS, and Ras associate with the plasma membrane via lipid modifications (black dots). Right of dashed line: Cholesterol depletion of the membrane leads to the loss of the caveolin coat from the membrane. Concomitantly caveolae and functional rafts disappear. This prohibits the local enrichment of H-Ras, Src kinases, adapters, and uPAR. Thus, signaling via caveolin is abolished.
Experimental Cell Research 261, 111–118 (2000)Martin Stahlhut, Kirsten Sandvig and Bo van Deurs
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CAVEOLAE - Membrane invagination // Main constituant: protein Caveolin
Protein StructurePeripheral membrane protein
C-terminal135-178 a.a
N-terminal1-101 a.a
transmembrane domain102-134
attractive part61-101 a.a
membrane
Homo-oligomer ≈ 14-16 caveolinCaveolin protein
Caveolin - 178 aaCaveolin aggregates14-16 molecules : 4-6 nm
Caveolae Bud50-80 nm
from Schlegel - Lisanti Cell Signal 10, 457 (1998)
Specific attractionsN-terminals: aggregationC-terminals: organization
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STRATEGY
• Model for Caveolin - force distribution
• Membrane deformation - Interactions between proteins
• Protein organization I : Oligomer formation• Protein organization II : Bud formation• Protein organization III : Stripes of proteins
• Comparison with experimental observations
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MODEL FOR CAVEOLIN OLIGOMERSForce on the membrane
Polymer chain grafted on a wall
r
monomer concentration
(Thermal) Fluctuations force (pressure) on the wall
Force distribution for the polymer entropic effect (thermal fluctuations of the chain)
Caveolin protein on membrane
r
pressure distribution
Applied force for the protein complex ???
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and we know the lengthscales
Not possible to calculate the force distribution
rb~4nm
a~2nm
No net force / no net torque
Origin for pressure in caveolin brushlets: Thermal fluctuation (small if rigid)
Steric constraint - Bad solvent effect
Most of the force is in the center
fa.a2 ~10pN
Strength of the force
we know the symmetries of the force
ab
We can estimate the strength of the force
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PROTEIN-INDUCED MEMBRANE DEFORMATION-
MEMBRANE-MEDIATED PROTEIN INTERACTIONS
Important physical parameters
Surface tension
Bending Rigidity } k−1 = κ / γ ~30nmκ =20kBT
€
γ=0.1−1mN /m
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Decay length
f1 f2
Overlapp between deformations
Membrane-mediated Interactions (exact)
Small repulsive interaction
Input :membrane deformation energy
Surface tension
Bending energy
force
membrane displacement
Output :membrane deformation
Interactions between inclusions
Deformation
u
f
ζ = d2r∫ I0(kr) f(r)
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PROTEIN ORGANIZATION
Oligomer formation - Bud formation - Stripes of proteins
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Thermal aggregation - cf. Micelle formation in surfactant solution
Protein oligomer formation
Aggregates of 15 molecules
Membrane buds formation
Aggregates of 103 oligomers
5 10 15 20 25 30
10
20
30
40
5 10 15 20 25 30
0.2
0.4
0.6
0.8
1
Input: energy in aggregate fp Output : Aggregate size p* and critical aggregation concentration (c-a-c)
Densities Cp ∝ e−p( fp −μ)
aggregates (size p)
∂p f p =0Optimal size p* f p* =μChemical potential at c-a-c
μ ∝ logC μ ∝1p*
logC ~constbelow c-a-c: ideal gas above c-a-c:
C1 ∝ e−( f1−μ )
isolated particles
C <<Ccac
C =Ccac
p
p
p fp −μ( )
Cp
5nm100nm
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Oligomerisation ~ 2-D micellisation process
But, theory is questionable for small aggregatesdetails of the protein attraction may matter
Sticking energy
polymer brushentropic repulsion - =3/2
Energy gain per protein
Proteins on the outskirtsdon’t get full contact
α >1
Oligomer formation
Driven by:sticking energy
Hindered by:Crowding ?
N-terminal attractions
Q proteinsper oligomer
Energy per proteinhas a minimum
crowding
To obtain experimental values
we need
ΔQ=2Q =15
α =2kBT β =10kBT
Reasonable numbersRepulsion: entropic energy scale
Attraction: Hydrogen bond energy scale
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below c-a-c
above c-a-c
Bud energy per brushlet
Bud formation - In-plane phase separation
Driving force: preferred curvature
Energy difference
cac
R
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Protein concentration for budding(very) sensitive to surface tension
Role in cell mechanosensitivity
Equilibrium radius
variation with surface tension
equilibrium bud radius
E0=10kBT
cac
E0=15kBT
concentrations
There is an optimal bud size(≠ curvature instability)
Size ~ insensitive to membrane tension
Physiological γ
Results
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Striped distribution of protein oligomers
Origin for striated coat ?Interactions between oligomers
Short Range specific attractionmediated by distal third region of C-terminal (10 aa)
b~ few nmk-1~30 nm
Erep~10-2 kBTEattp~3-4 kBT
(r)
r
b k 1
Full potential
Long range physical repulsion between inclusionsand
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Small density (islands) large density (stripes)
r
r <λ
r
Monte Carlo Simul Sear & Gelbart., Phys Rev E (1999)
width ~range ofattraction
Perturbation in Fourier space
Optimal size q− 1
~kb( )
1 / 5
b
A few brushlet dimension
Liquid-gas transition
Strength of the attraction - few kBTentropy interaction
Ea >kBT
4φ0 1−φ0( )
Microphase separation
Strength of the repulsion - 10-2 kBT enough !
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CONCLUSIONThree levels of organisation :
Caveolin aggregation into brushlets
Concentration of brushlets in membrane pits
Striations at the surface of the pits
can be explained by simple physical arguments
Comparison with mutational analysisof caveolin-induced vesicle formation
Shengwen Li1 etal.FEBS Letters 434 (1998) 127
Deletion of sticky part on N-terminalNo oligomer (brushlets)
strong reduction of typical energy scale E0
Deletion of main part of C-terminal No (weak) short range attraction between oligomerincrease of interaction parameter (virial coef)
Both mutans are able to drive vesicle formation, but much larger vesicles ~ 1µm
Qualitatively consistent with our results
Testable predictions Effect of membrane tension... cf. Role in cell mechanosensitivity