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/Pierre.Sens@curie.fr

hydrophobic

hydrophilic

Membranes Proteins :

“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

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

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”

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

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

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

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…

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)

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

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

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

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 ???

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

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

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)

PROTEIN ORGANIZATION

Oligomer formation - Bud formation - Stripes of proteins

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

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

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

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

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

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 !

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