Pierre Sens

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SOME EXAMPLES OF MEMBRANE STRUCTURE FORMATION OF
BIOLOGICAL RELEVANCE
Pierre Sens Institut Charles Sadron - C.N.R.S -
Strasbourg - France sens_at_ics.u-strasbg.fr
http//www-ics.u-strasbg.fr/sens/
January 2003
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hydrophilic
hydrophobic
Cell membrane are composed of amphiphilic
molecules which self-assemble into fluid bilayers
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Membrane needs to deform for many fundamental
functions Endocytosis - Cell fusion - Membrane
recycling
Endocytosis intake of large molecules
Role of membrane during endo/exocytosis
Coated vesicles Membrane deformation because of
curvature active proteins
bilayer
5 nm
http//cellbio.utmb.edu/cellbio/recend.htm
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Lipid Membranes - Statics -
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Physical model for fluid membranes
Balance between hydrophobic attraction steric,
electrostatic repulsion
Equilibrium properties
Stretching the membrane
Stretching modulus
Optimal density
Quite large !!
C curvature
Bending the membrane
Non-relaxed state
Relaxed state
Bending modulus
Quite small !!
Quite large !!
Constant lipid density Stretching - extension
Constant area per head No stretching
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Formalism for small membrane deformation
Monge representation
Curvature
With surface tension
Deformation energy
In Fourier space
Equipartition theorem rms of the fluctuations
Small rigidity - large fluctuations
Curvature dominates the small lengthscales
From R. Dimova mpikg-golm
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One refinement for biological membranes
Near the inclusion
membrane inclusions induce a spontaneous
curvature
Curvature instability - S. Leibler (86)
Inclusion density
Landau expansion
Equilibrium distribution of inclusions follows
the curvature
Effective bending rigidity
If the rigidity is lt0 the membrane spontaneously
curves
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Physical model for Caveolar membranes
Location Plasma membrane of many cells
Endothelial cells, adypocytes, cardiac
muscles Fonctions Many Endocytosis - ligand
binding - signaling - cholesterol transport
Cell Membrane
plasma
Clathrin coated pits
caveolae
Quasi-spherical soft shells thermal assembly of
proteins
Internal structure - striated coat Interactions
between proteins ?
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Main constituent of Caveolae Protein Caveolin
from Schlegel - Lisanti Cell Signal 10, 457
(1998)
10 nm
100 nm
5 nm
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Physical effect of the protein modeled as a
force distribution on the membrane
Total force 50 pN
b5nm
Membrane-mediated Interactions
Repulsive interaction
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Bud formation - In-plane phase separation
Driven by preferred curvature
R
?
?cac
Bud energy per brushlet
Equilibrium radius
concentrations
There is an optimal bud size (? curvature
instability)
variation with surface tension
Size insensitive to membrane tension
E010kBT
Protein concentration for budding (very)
sensitive to surface tension Role in cell
mechanosensitivity
equilibrium bud radius
Physiological g
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Origin for striated coat ? Interactions between
oligomers
Striped distribution of protein oligomers
Long range physical repulsion between
inclusions and
Full potential
b few nm k-130 nm Erep10-2 kBT Eattp3-4 kBT
r
b
Short Range specific attraction mediated by
distal third region of C-terminal (10 aa)
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Lipid Membranes - Dynamics -
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Dynamics of membrane deformation
stratified 2 -D fluid in a 3 -D fluid
Dissipated powers
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Dynamics of small fluctuations
Hydrodynamic damping of bending mode
Bending energy
Viscous dissipation
q-1
Membrane motion induce solvent flow
Balance of viscous and elastic forces
Application frequency spectrum of red Blood
Cells (Brochard Lennon 75)
dh0.3 µm
h2 µm
8 µm
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Coupling between membrane composition and shape
fluctuations (Seifert Langer 93)
Membrane asymmetry
The curvature is coupled to membrane asymmetry
The composition relaxes by diffusion
After relaxation
Diffusion coefficient
100 kBT
cross-over length
The bending mode show scale-dependent rigidity
10 kBT
small lengthscales membrane dynamics large
lengthscales solvent dynamics
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Response to a local perturbation
Flippase (Aminophospholipid translocase)
DNA lipides cationiques
Angelova. 99
Bar 30µm
Contraction
extention
100 µm
1 µm
Both diffusion along the membrane and curvature
of the membrane reduce the elastic stress
DNA injection - M. Angelova
Which one is the fastest? It depends on the size
of the perturbation
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Relaxation of local membrane torque
(A)
(A) Energy minimum local contraction extension
uniformly spread over the vesicle Energy zero
(B)
(B) If the membrane deformation is fast the
membrane may be (kinetically)trapped by membrane
fusion buds (endosomes) are formed
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Formalism to study the membrane response
conservation
Parameters
Extension of the perturbation
Number of flips
variables
Model
Density and Curvature are uniform Over the
deformed membrane
Budding parameter
Lowest enery flat membrane with smeared out
perturbation
But !
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Dissipations
Diffusion of the asymmetry
Deformation of the membrane
Solvent mostly volume variation
Membrane mostly volume variation
Membrane flow
Solvent flow
dissipated power - elastic energy
Equation of motion Balance of elastic and
dissipative forces
Characteristic time
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For small deformation
The bulk dominates
Diffusion of the asymmetry
Elastic driving force Stretching bending
Maximum of Bd ? the evolution qualitatively ? for
different sizes
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Maximum of Bd (small deformation)
Conclusion (small deformation)
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Evolution (large deformation)
Assume a critical value of Bd for fusion
like linear
Membrane viscosity prevents the small scale
deformations
membrane
dynamical selection of the size of the endosomes
solvent
initial perturbation to reach critical closure
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Dynamical perturbation (continuous translocation)
Characteristic time to be compared to
t
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- Conclusion -
The concepts of membrane physics are relevant to
some biological phenomena
Equilibrium properties of membrane with inclusion
to understand the action of some membrane
proteins Physical theory can provide explanation
for the function of some membrane proteins and
give guidelines to experiments to better
understand these function (ex. role of surface
tension in Caveolae - Mechanosensitivity of the
cell membrane)
Dynamical properties of lipid membranes are
complex and crucial (membrane walls of a cell
form a dynamical system) Physical theory can
provide framework for the measure of dynamical
parameter (viscosity) And explain the role of
dynamics for some membrane function (ex.
dynamical formation of endosome)
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- Perspective -
Understanding the physical properties of this
complex system will help understand the
regulation pathways
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Evolution (all range of deformation)
Dissipation
outside the bud
inside the bud
Closure is asymptotically slow for
Diffusion promotes closure to minimize solvent
flow