Thermal membrane fluctuations: the impact on
lateral protein diffusion and specific adhesion
Ellen Reister
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II. Institut für Theoretische Physik
Universität Stuttgart
Germany
11th May 2009
motivation lateral diffusion specific adhesion conclusions
outline
1
motivation
system: cell membrane
2
lateral protein diffusion
free diffusion
curvature coupled diffusion
3
specific adhesion of a fluctuating membrane
model
simulations
results
4
conclusions
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
system
cell membrane
membrane
outside
carbohydrate chains
O
X
O
−
P
hydrophilic
head
O
O
glycerin
HC
H
H
C
H
CH
O
O
O
O
C
C
plasma
membrane
phospho−
lipid
membrane
glycoprotein glyco−
sphingo−
inside
sugar sidechain
lipid
hydrophilic
regions
hydrophobic
tails
hydrophobic
region
glycoprotein
flexible “plane”: shape fluctuations
lipid bilayer: two-dimensional fluid
several lipid species: possible domain formation
proteins: lateral diffusion along membrane
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
lateral protein diffusion
in a fluctuating membrane
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
usually neglected in analysis of lateral diffusion
measurement uses projected path
fluctuating membrane
projected path 6= actual path
measured diffusion coeff. function of membrane fluctuations
fluctuations depend on temperature, osmotic pressure, . . .
What’s difference between intramembrane and projected diff.?
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
freely diffusing particle
membrane shape: Monge gauge: r = (x, y , h(x, y ))
z
R
h(x,y)
y
x
fluctuations: h(x, y , t) is time dependent
diffusion on a flat surface
Smolouchovski equation = eq. of motion for particle
probability distribution P(x, y , t)
∂t P(x, y , t) = D ∆P(x, y , t)
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
freely diffusing particle
membrane shape: Monge gauge: r = (x, y , h(x, y ))
z
R
h(x,y)
y
x
fluctuations: h(x, y , t) is time dependent
diffusion on a curved surface
Smolouchovski equation = eq. of motion for particle
probability distribution P(x, y , t)
∂t P(x, y , t) = D P(x, y , t)
curved surface: replace Laplace op. ∆ with Laplace-Beltrami
op. = [hx , hy , hxx , hxy , hyy ]
with hx ≡ ∂h/∂x, etc.
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
preaveraging approximation
Both P(x, y , t) and hx , hy , etc. time dependent!
estimate time scales of membrane fluctuations and diffusion
membrane fluctuations “faster” than diffusion
protein “feels” average membrane shape
preaveraging approximation
replace prefactors containing hx , hy , etc. with thermal averages
[hx , hy , hxx , hxy , hyy ] −→ h[hx , hy , hxx , hxy , hyy ]i
result: Smolouchovski equation for planar diffusion
∂t P(x, y , t) = Dproj ∆P(x, y , t)
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
effective diffusion constant Dproj
projection causes rescaling of diffusion coefficient
1
1
Dproj /D =
1+
2
g
with metric g ≡ 1 + hx2 + hy2
calculate h1/g i using Helfrich Hamiltonian:
Z
H[h(r, t)] =
A
κ
σ
d2 r
hκ
2
(∇2 h)2 +
i
σ
(∇h)2
2
bending rigidity
surface tension
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
1
1
0,98
0,98
0,96
0,96
0,94
0,94
0,92
0,92
Dproj/D
Dproj/D
Dproj /D for σ = 0
0,9
0,88
0,86
0,84
0,82
0,8
6
10
βκ=5
βκ=6
βκ=8
βκ=10
βκ=14
βκ=20
βκ=30
βκ=50
7
10
0,9
2log(qmL)=6
2log(qmL)=7
2log(qmL)=8
2log(qmL)=9
2log(qmL)=10
2log(qmL)=11
0,88
0,86
0,84
0,82
8
10 (Lq )
m
2 109
10
10
11
10
0,8
10,00
20,00
30,00
βκ
40,00
50,00
strongest effect for low rigidity κ, large systems L, and low
tension σ
free diffusion
Dproj up to 15% smaller than free D
The stronger the fluctuations the stronger the reduction!
Fluctuations increase path of protein.
E.R. and U. Seifert, EPL 71:859 (2005)
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
stochastic simulations
free diffusion
membrane dynamics
Z
∂h(r, t)/∂t = −
d2 r0 Λ(r0 , r) δH/δh(r0 ) + ξ(r)
A
Λ(r0 , r). . . . . .
ξ(r, t) . . . . . .
Onsager coefficient:expresses membrane dynamics
caused by surrounding fluid
obeys fluctuation-dissipation theorem
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
stochastic simulations
free diffusion
membrane dynamics
Z
∂h(r, t)/∂t = −
d2 r0 Λ(r0 , r) δH/δh(r0 ) + ξ(r)
A
Λ(r0 , r). . . . . .
ξ(r, t) . . . . . .
Onsager coefficient:expresses membrane dynamics
caused by surrounding fluid
obeys fluctuation-dissipation theorem
free protein diffusion on curved surface
∂Ri (t)
D ∂ √ ij
=√
( g g ) + ζi
∂t
g ∂Rj
FDT: hζi (t)i = 0
metric: g ≡ 1 + hx2 + hy2
hζi (t)ζj (t 0 )i = 2Dg ij δ(t − t 0 )
inv. metric tensor: g ij ≡
Ellen Reister
1
g
1 + hy2
−hx hy
−hx hy
1 + hx2
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
stochastic simulations
free diffusion
membrane dynamics
Z
∂h(r, t)/∂t = −
d2 r0 Λ(r0 , r) δH/δh(r0 ) + ξ(r)
A
Λ(r0 , r). . . . . .
ξ(r, t) . . . . . .
Onsager coefficient:expresses membrane dynamics
caused by surrounding fluid
obeys fluctuation-dissipation theorem
free protein diffusion on curved surface
∂Ri (t)
D ∂ √ ij
=√
( g g ) + ζi
∂t
g ∂Rj
FDT: hζi (t)i = 0
metric: g ≡ 1 + hx2 + hy2
hζi (t)ζj (t 0 )i = 2Dg ij δ(t − t 0 )
inv. metric tensor: g ij ≡
1
g
1 + hy2
−hx hy
−hx hy
1 + hx2
apparent force on particle caused by curvature
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
simulation scheme
simulation: integration of coupled stochastic equations
1
evolve membrane shape (q-space on lattice):
p
h(q; t) = h(q; t − ∆t) − Λ(q) κq 4 + σq 2 ∆t + 2Λ(q)∆t r
2
Fourier-transform: h(q; t) → h(r; t)
3
calculate hx , hy , g , etc. at particle position R = (X , Y )
4
move particle in real space (off-lattice):
√
D
∂ √ ij Ri (t + ∆t) = Ri (t) + ∆t √
gg
+ 2D∆t G ij rj
g ∂Rj
G ik G kj = g ij
r , rj . . . Gaussian random numbers: hr i = 0, hr 2 i = 1
5
continue with 1.
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
visualisation of free membrane bound diffusion
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
projected/measured diffusion constant Dproj
preaveraging regime
simulation: Dproj /D = hR2 (t)i/4Dt
hR2 i – t
250
βκ=1
βκ=3
βκ=8
200
Flat: ⟨R ⟩=4Dt
2
2
⟨R ⟩
300
150
100
σ=0
50
0
0
0.0002
0.0004
t [s]
0.0006
0.0008
average over 600 runs; 50×50 lattice; 106 timesteps; ∼ 12 min. per run
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
projected/measured diffusion constant Dproj
preaveraging regime
simulation: Dproj /D = hR2 (t)i/4Dt
analytical (τM τD ): Dproj /D = (1 + h1/g i)/2
hR2 i – t
1
250
βκ=1
βκ=3
βκ=8
200
Flat: ⟨R ⟩=4Dt
0.95
Dproj/D
2
2
⟨R ⟩
300
Dproj /D – βκ
150
100
0
0.0002
0.0004
t [s]
0.0006
2
analytical: βσL =500
2
simulation: βσL =0
σ=0
2
0.85
50
0
2
analytical: βσL =0
0.9
0.0008
0.8
0
simulation: βσL =500
2
4
βκ
6
8
average over 600 runs; 50×50 lattice; 106 timesteps; ∼ 12 min. per run
good agreement
Ellen Reister
The impact of thermal membrane fluctuations
10
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
simulations beyond the preaveraging approximation
simulations for various intramembrane diffusion coefficients D
for largest regarded D: τM ' 2τD
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
simulations beyond the preaveraging approximation
simulations for various intramembrane diffusion coefficients D
for largest regarded D: τM ' 2τD
Dproj /D – βκ
1
σ=0
Dproj/D
0.95
preaveraging
0.9
4
D=10
5
D=10
6
D=10
6
D=5x10
7
D=10
0.85
0.8
0
1
2
3
4
5
βκ
6
7
8
9
10
preaveraging is applicable for all physical membranes!
E.R., S.M. Leitenberger, and U. Seifert PRE 75:011908 (2007)
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
simulations beyond the preaveraging approximation
simulations for various intramembrane diffusion coefficients D
for largest regarded D: τM ' 2τD
Dproj,drift /D – βκ
Dproj /D – βκ
1
0.02
βκ=1
βκ=2
σ=0
0.015
preaveraging
0.9
4
D=10
5
D=10
6
D=10
6
D=5x10
7
D=10
0.85
0.8
0
Dproj,drift/D
Dproj/D
0.95
1
2
3
4
5
βκ
6
7
8
0.01
0.005
9
10
0
0
2
4
6
6 2
D [units of 10 a /s]
8
preaveraging is applicable for all physical membranes!
E.R., S.M. Leitenberger, and U. Seifert PRE 75:011908 (2007)
Ellen Reister
The impact of thermal membrane fluctuations
10
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
curvature coupled diffusion
protein interacts with membrane
here: coupling to local membrane curvature
protein is attracted to position with certain curvature
protein energy
Z
hm
2 κ
2 i
Hprot [h, R] = d2 r g (r − R)
∇2r h(r) − Cp −
∇2r h(r)
2
2
A
Cp
m
g (r) = exp(−r2 /ap2 )
spontaneous curvature
bending rigidity of the protein
weighting function for protein extension
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
equations of motion
(total energy Htot = H + Hprotein )
membrane dynamics
Z
∂h(r, t)/∂t = −
d2 r0 Λ(r0 , r) δHtot /δh(r0 ) + ξ(r)
A
protein diffusion (preaveraging)
∂R/∂t = −µ ∇R Hprotein [h] + ζ
with hζ(t)i = 0
and hζi (t)ζj (t 0 )i = 2Dproj δij δ(t − t 0 )
µ. . . mobility
Einstein relation: µ = Dproj /kB T
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
curvature-coupled diffusion coefficient Dcc
free membrane fluctuations
assumption: membrane fluctuations not influenced by protein
2
Dcc /D – βσ/qm
Dcc /D – βκ
1.8
2
1.7
1.6
1.6
1.5
1.5
Dcc/D
Dcc/D
1.8
-4
βσ/qm =5x10
1.7
1.4
1.3
analytical
simulation
1.2
βκ=10
1.4
1.3
1.2
analytical
simulation
1.1
1.1
1
0
5
10
βκ
15
20
25
1
1e-06
0.0001
0.01
βσ/qm
2
curvature coupling enhances diffusion
qualitative difference compared to free diffusion
diffusion in simulations is less enhanced
particle will try to follow an energy minimum
S.M. Leitenberger, E.R.-G., U. Seifert, Langmuir 24:1259 (2008)
Ellen Reister
The impact of thermal membrane fluctuations
1
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
curvature-coupled diffusion coefficient Dcc
diffusion in a periodic potential
simulations: membrane feels protein influence
1
D0=50000
D0=100000
D0=1000000
Dcc/D0
0.8
0.6
0.4
0.2
0
0
10
20
βm
30
40
50
diffusion is reduced!
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
free diffusion curvature coupled
curvature-coupled diffusion coefficient Dcc
diffusion in a periodic potential
simulations: membrane feels protein influence
1
D0=50000
D0=100000
D0=1000000
Dcc/D0
0.8
0.6
0.4
0.2
0
0
10
20
βm
30
40
50
diffusion is reduced!
protein feels (time-dependent) periodic potential
diffusion is always reduced (in equilibrium)
Dcc 6 D0
previous approximation effectively drives the system
possible relevance for active processes in membrane
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
specific adhesion of a
fluctuating membrane
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
specific membrane adhesion
biological membranes are typically not free
confined by surrounding membranes
adhere to other membranes
model systems that mimic biological membranes
lipid bilayers deposited on solid or polymer substrates
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
specific membrane adhesion
biological membranes are typically not free
confined by surrounding membranes
adhere to other membranes
model systems that mimic biological membranes
lipid bilayers deposited on solid or polymer substrates
membrane adhesion via specific receptor-ligand pairs
membrane subject to thermal fluctuations
reaction rate is height dependent
Goal: understanding of influence of shape fluctuations
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
motivation
recent experiments with weak binding
black regions = bound
weak binding → unbinding becomes important
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
energy
H = H0 + Hns + Hs
h0
l0
h
Helfrich energy H0 (bending rigidity κ)
Z
κ
d2 r (∇2 h)2
2
A
H0 [h(r, t)] =
non-specific potential Hns (strength γ)
Z
Hns [h(r, t)] =
γ
d2 r (h − h0 )2
2
A
energy of springs Hs (binding energy b ; tether stiffness K )
Hs [h(r, t)] =
N
X
i=1
bi
(
1
K
(h(ri ) − l0 )2 − b with bi =
2
0
Ellen Reister
i-th bound
i-th not bound
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
energy
H = H0 + Hns + Hs
h0
l0
h
Helfrich energy H0 (bending rigidity κ)
Z
κ
d2 r (∇2 h)2
2
A
H0 [h(r, t)] =
non-specific potential Hns (strength γ)
Z
Hns [h(r, t)] =
γ
d2 r (h − h0 )2
2
A
energy of springs Hs (binding energy b ; tether stiffness K )
Hs [h(r, t)] =
N
X
i=1
bi
(
1
K
(h(ri ) − l0 )2 − b with bi =
2
0
Ellen Reister
i-th bound
i-th not bound
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
energy
H = H0 + Hns + Hs
h0
l0
h
Helfrich energy H0 (bending rigidity κ)
Z
κ
d2 r (∇2 h)2
2
A
H0 [h(r, t)] =
non-specific potential Hns (strength γ)
Z
Hns [h(r, t)] =
γ
d2 r (h − h0 )2
2
A
energy of springs Hs (binding energy b ; tether stiffness K )
Hs [h(r, t)] =
N
X
i=1
bi
(
1
K
(h(ri ) − l0 )2 − b with bi =
2
0
Ellen Reister
i-th bound
i-th not bound
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
energy
H = H0 + Hns + Hs
h0
l0
h
Helfrich energy H0 (bending rigidity κ)
Z
κ
d2 r (∇2 h)2
2
A
H0 [h(r, t)] =
non-specific potential Hns (strength γ)
Z
Hns [h(r, t)] =
γ
d2 r (h − h0 )2
2
A
energy of springs Hs (binding energy b ; tether stiffness K )
Hs [h(r, t)] =
N
X
i=1
bi
(
1
K
(h(ri ) − l0 )2 − b with bi =
2
0
Ellen Reister
i-th bound
i-th not bound
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
dynamics
membrane fluctuations
fluctuating membrane: h(x, y , t) is time dependent
equation of motion (Fourier space)
n
∂h(k, t)
= −Λ(k) κk 4 + γ h(k, t)
∂t
Nt
h
io
X
+
bi K (h(ri , t) − l0 )e −ik·ri
+ ξ(k, t)
i=1
Λ(k). . . . . .
ξ(k, t) . . .
Onsager coefficient
obeys fluctuation-dissipation theorem
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
dynamics
receptor-ligand reaction
receptors and ligands at fixed sites
intuition
unbinding less likely
unbinding more likely
height-dependent reaction rates
unbinding rate: Kramers’ rate theory
koff = k0 exp [βK α (h(ri , t) − l0 )]
binding rate: detailed balance
1
βb
2
kon /koff = e exp − βK (h(ri , t) − l0 )
2
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
simulations
simulation: integration of coupled stochastic equations
membrane: 64 × 64 lattice with lattice spacing a ' 10nm
N = 64 binding sites on 8 × 8 lattice with spacing 8a
initial distance membrane–substrate: h0 = 12a
rest length of springs: l0 = 8a
starting configuration: equilibrated membrane without bonds
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
visualization of adhesion process
βK = 1.25; βκ = 10; b = 3.91
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
visualization of adhesion process
βK = 1.25; βκ = 10; b = 3.91
unbinding also observed
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
visualization of adhesion process
βK = 1.25; βκ = 10; b = 3.91
unbinding also observed
questions
equilibrium for stiff and fluctuating membrane
role of membrane fluctuations on adhesion dynamics
connection to experimental results
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
Phase diagram for stiff membrane (κ → ∞)
infinite system
stiff membrane — effective free energy per bond site
βε
1
e b=2.0
βε
e b=2.7
βε
e b=4.0
βε
e b=8.0
K=2
βf(h)
0.5
0
K=1.25
-0.5
-1
l0=8
9
10
11
h0=12
13
h in units of a
two minima
competition of bonds and non-specific potential
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
Phase diagram for stiff membrane (κ → ∞)
infinite system
stiff membrane — phase diagram
4.5
βε
e b=2.0
βε
e b=2.7
βε
e b=4.0
βε
e b=8.0
K=2
βf(h)
0.5
4
3.5
exp(βεb)
1
0
2.5
unbound
2
K=1.25
-0.5
bound
3
K-> inf
1.5
-1
l0=8
9
10
11
h0=12
13
h in units of a
1
0.1
1
10
2
a βK
first order transition from bound to free membrane
for very stiff tethers saturation of coexistence line
Ellen Reister
The impact of thermal membrane fluctuations
100
motivation lateral diffusion specific adhesion conclusions
model simulations results
influence of fluctuations and binding energy b
height hhi — b
bond density hφi — b
1
13
(b)
flat
βκ=10
12
(a)
0.8
0.6
φ
<h>
11
10
0.4
9
0.2
8
2
4
6
exp[βεb]
8
10
0
2
4
6
exp[βεb]
8
10
fluctuations make transition more “continuous”
higher binding energy necessary for comparable adhesion with
fluctuations
fluctuations cause additional entropy contribution in free energy
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
coordination number of bonds
compare coordination number of bonds for fluctuating membrane
with random binding of same bond density φ
0.8
exp(βεb)=2.7
rand.: <φ>=0.06
probability
0.6
0.4
0.2
0
0
1
Ellen Reister
2
coord. no.
3
4
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
coordination number of bonds
compare coordination number of bonds for fluctuating membrane
with random binding of same bond density φ
0.8
exp(βεb)=2.7
rand.: <φ>=0.06
exp(βεb)=3.25
rand.: <φ>=0.33
probability
0.6
0.4
0.2
0
0
1
Ellen Reister
2
coord. no.
3
4
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
coordination number of bonds
compare coordination number of bonds for fluctuating membrane
with random binding of same bond density φ
0.8
exp(βεb)=2.7
rand.: <φ>=0.06
exp(βεb)=3.25
rand.: <φ>=0.33
exp(βεb)=10.0
rand.: <φ>=0.85
probability
0.6
0.4
0.2
0
0
1
Ellen Reister
2
coord. no.
3
4
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
coordination number of bonds
compare coordination number of bonds for fluctuating membrane
with random binding of same bond density φ
0.8
exp(βεb)=2.7
rand.: <φ>=0.06
exp(βεb)=3.25
rand.: <φ>=0.33
exp(βεb)=10.0
rand.: <φ>=0.85
probability
0.6
0.4
0.2
0
0
1
2
coord. no.
3
4
membrane mediates interaction between bonds
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
global adhesion dynamics
average height hh(t)i
stiff membrane
fluctuating membrane
exp(βεb)=10
exp(βεb)=20
11
10
9
8
0
0.001
0.002 0.003
t [s]
0.004
0.005
exp(βε)=2.7
exp(βε)=3.25
exp(βε)=4.0
exp(βε)=8.0
12
<h> in units of a
<h> in units of a
12
11
10
9
8
0
0.001
0.002 0.003
t [s]
0.004
0.005
adhesion takes place much faster with fluctuations
bond formation encouraged through chance encounters of
membrane with substrate
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
model simulations results
adhesion dynamics
single systems
1
0.8
0.8
0.6
0.6
φ
φ
1
0.4
0.4
0.2
0.2
0
0
0.001
0.002
t [s]
0.003
0.004
weak binding: e βb = 3
0
0
0.0005
0.001
t [s]
0.0015
“strong” binding: e βb = 10
much noise for weak binding
competition between membrane dynamics and binding
E.R.-G., K. Sengupta, B. Lorz, E. Sackmann, U. Seifert, and A.-S. Smith, PRL 101, 208103 (2008)
Ellen Reister
0.002
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
conclusions
free lateral protein diffusion
projection causes apparent reduction of diffusion coefficient
curvature-coupled protein diffusion
interaction of protein with membrane reduces effective
diffusion coefficient
specific membrane adhesion
fluctuations make higher binding energy necessary for adhesion
fluctuations speed up adhesion
membrane fluctuations induce effective interaction between
bonds
outlook
combination of both thechniques: include lateral diffusion of
ligands to specific adhesion simulations
Ellen Reister
The impact of thermal membrane fluctuations
motivation lateral diffusion specific adhesion conclusions
acknowledgements
Stefan M. Leitenberger
Ana-Sunčana Smith
Kheya Sengupta (CINaM/CNRS, Marseille)
Udo Seifert
Ellen Reister
The impact of thermal membrane fluctuations