Some mechanisms governing shape changes
in biological membranes
P. B. Sunil Kumar
Department of Physics
Indian Institute of Technology Madras
Chennai 600036
www.physics.iitm.ac.in/sunil
Collaborators:
N. Ramakrishnan, U.Penn., Philadelphia, USA
John H Ipsen, U. Southern Denmark
Madan Rao, RRI/NCBS, Bengaluru
Mohamed Laradji, Memphis, USA
Sreeja K K , Department of Physics, IIT Madras
Biological Membranes are dynamic multi-component
structures
as a barrier
as a target
as a carrier
Yeast Pichia Pastoris
A characteristic feature of eukaryotic cells
is the variety of identifiable membrane
bound organelles, distinguished by their
unique morphology and chemical
composition
Shape of most cellular organelles are
highly conserved across species
M
G
V
G
N
ER
ER
M
Mammalian
Normal Rat
Kidney
G
L
NE
N
A confocal
fluorescence
image of a COS
cell expressing
an ER-localized
protein
Three-dimensional tomogram of a
chick dendrite mitochondrion
S~20 nm and D~30-nm.
Scale bar - 0.1 μm.
ER
EM image of an NRK cell
intercisternal spacing ~20 nm
irregular intracisternal lumenal spacing.
Scale bar - 0.2 μm.
ER
D
cis fingers
Golgi
stack
S
M
ER
trans ER
trans cisternae
General factors that might be used throughout the cell for organelle shaping.
(1)intrinsic curvature of proteins.
(2)proteins tether membranes, to the cytoskeleton or to other membranes.
(3)regulated fission and fusion of membranes.
(4)protein assembly
Gia K. Voeltz and William A. Prinz Nat. Rev. Mol. cell. Biol vol 8 , 258 2007
Generating such high curvatures by lipid based mechanisms alone will require lipids with very
high spontaneous curvature: Zimmerberg and Kolslov - Nat. Rev. Mol. Bio. 7 , 9, 2006
While there is a rather detailed knowledge of the molecular
processes involved in membrane remodelling, our
understanding of the underlying physical principles is still
quite rudimentary.
To address the broader issue of morphology and composition
changes in cellular organelles we must identify those
minimalistic features of the dynamics that are generic and
incontrovertible.
One important point is that membranes are subject to
the action of curvature sensing and curvature generating
proteins, which modulate membrane shape – A variety of bardomain proteins, coat-proteins and GTPases:- Passive component
Another feature of cellular organelles appears to be that they
are dynamic membranous structures, subject to and driven by
a continuous flux of membrane bound material. Active component
Protein induced conformations of organelles:
a
200 nm
300 nm
Fenestrations in Golgi
100 nm
tubules on endosomes
b
HIV-I viral budding
McMahon et al, Nature, 438, 2005.
c
Caveola
C
d
Palmitoylation
Cholesterol
Caveolae
+
+
+
Scaffolding
domain
N
Parton et al, Mol. Cell. Biol., 8, 2007.
Caveolin
250 nm
Clathrin coated vesicle budding
Curvature generating mechanisms in proteins
Helix insertion
Protein oligomerization
Eg: Epsin, alpha-synuclein, Arf
caveolin, reticulons
Scaffolding
Eg: BAR domain proteins
Protein shape
Eg: transport and receptor
proteins
g
Indirect scaffolding
Eg: Coat proteins like
clathrin, COP I, COP II
Direct scaffolding
(negative curvature)
Eg: Exo70
Direct scaffolding
(positive curvature)
Eg: dynamin proteins
McMahon et al, Nature, 438, 2005
Membrane-protein interactions can be hydrophobic, steric and/or electrostatic
interactions. BAR domains, synucleins, epsin and exo 70 exhibit electrostatic interactions
with membrane
Peptides also exhibit membrane curvature-sensing and curvature-inducing activity
Eg: Islet Amyloid Polypeptide
Natalie C. Kegulian et al. JBC- 290, 25782 2015
Shape of membranes with curvature inducing proteins
κ
Hc =
Av (Hv − C0 ψv )2 .
2 v
Hpφ = −Jpφ
Hψ = −Jψ
ψv ψv Protein concentration
<vv >
ψv φv . Hφ = −Jφ
<vv >
v,v ψv = 1, 0
Curvature
φv φv Lipid φcomposition
v = ±1
Proteins can interact directly or through membrane curvature
Proteins can induce lipid composition inhomogeneities
Midsurface element
Jpφ = 2
R2
R1
Jpφ = 1
c1 = R–1
c2 = R–2
p% = 10
p% = 20
p% = 30
Typically the shapes are buds or tubes
Mean curvature
1 ij
1 1
1
H = g Kij ≡
+
2
2 R1 R 2
ANISOTROPIC INCLUSIONS ON MEMBRANES ---> BEYOND THE HELFRICH MODEL
Free energy functional describing a random surface with in plane
vector fields interacting with itself and the membrane is,
κ
0
H0 , H⊥
sp
spontaneous
curvature induced in
parallel and perpendicular directions to
n̂
bending rigidity of the random surface
splay and bend Frank constants
K1 , K 2
C
κ , κ⊥
anisotropic rigidity parallel and
perpendicular to the nematic vector n̂
κ
2
curvature tensor
H = T r(C)/2
H = HC + HN N + HN C
2
(H − C0 ) dS dS
K1
2
2
+
(∇.n̂)
K2
2
× n̂))
(n̂ × (∇
κ
2
κ⊥
2
mean curvature
dS(n̂C n̂ − H0 )2 +
0 2
)
dS(n̂⊥ C n̂⊥ − H⊥
J. R. Frank and M. Kardar, Phys. Rev. E 77, 041705 2008
N. Ramakrishnan, P. B. Sunil Kumar and John H. Ipsen
Monte Carlo simulations of fluid vesicles with in-plane orientational ordering
Phys. Rev. E. 81, 041922 (2010)
9
CONFORMATIONS OF FULLY DECORATED MEMBRANES
κ = c0 = 0
κ = 10
κ =0
c0
{
>0
κ = 50
κ = 2.5
κ = 20
κ & κ
κ = 10
κ = 30
c0 = −0.5
N. Ramakrishnan, P. B. Sunil Kumar and John H. Ipsen
Monte Carlo simulations of fluid vesicles with in-plane orientational ordering
Phy. Rev. E. 81, 041922 (2010)
c0 = 0.5
c0
<0
κ & κ
10
N. Ramakrishnan, P. B. Sunil Kumar and Ravi Radhakrishnan
Physics Reports 543 , 1-60, 2014
Phase separation can be induced by curvature mediated interaction when
proteins are anisotropic,
HLL
=
−LL
P2 (n̂i .n̂j )
<i,j>
and interact to orient them parallel to each other
−
LL 2
(3 cos2 θij − 1)
<i,j>
Hψ = −Jψ
In addition there could be a line tension for protein domains
ψv ψv <vv >
N. Ramakrishnan, PBSU and J. H. Ipsen PRE 81 041922 ( 2010)
Phase separation induced by
Jψ
Phase separation induced only by curvature
Rigidity : κ = 10
Phase A : Concentration φA =0.7N ; κ = 5 ; κ⊥ = 0 ; C0 = −0.5 ; C0⊥ = 0
Phase B :Concentration φA =0.3N ; κ = 0 ; κ⊥ = 5 ; C0 = 0 ; C0⊥ = 0.5
I
I
J
Membrane-Mediated Aggregation of Curvature-Inducing
Nematogens and Membrane Tubulation
N. Ramakrishnan, P. B. Sunil Kumar, and John H. Ipsen
Biophysical Journal, 104 , 1018 ( 2013)
11
Dynamics of curvature mediated interaction between anisotropic particles
Longitudinal section.
Purple beads attract lipid head beads
Green beads repel lipid head beads.
Both repel lipid tail beads.
Curvature through preferred inter-particle separations.
Transverse slice of the nanoparticle
Alexander D. Olinger, Eric J. Spangler, P.B.S.K and Mohamed Laradji - Faraday discussions - 2016
Coarse-graining of a lipid molecules
Choline
Hydrophilic Head Group
Phosphate
Glycerol
Hydrophobic Tail Group
12
Revalee, Laradji and P. B. S. K., J. Chem. Phys (2008)
(b)
(a)
0.20
P(φ)
0.15
0.10
0.05
0.00
0
50
100
φ(degrees)
150
50
100
φ(degrees)
150
(b)
(c)
0.20
P(φ)
0.15
0.10
0.05
0.00
0
Equilibrium snapshots of lipid vesicles with two
anisotropic particles having an intrinsic radius of
curvature Rc=11 at various adhesion strengths.
Equilibrium splay angle distribution
between two anisotropic particles
13
Alexander D. Olinger, Eric J. Spangler, P.B. Sunil Kumar and Mohamed Laradji - Faraday discussions - 2016
“Particle” complexes made of connected particles with an intrinsic
curvature Rc.
Strength of the attractive interaction between the particles making
up the “protein” and the head group of lipids is characterized by
the parameter ξ
Rc=7.0, ξ = 2.5
14
Rc=11.5, ξ = 3.0
Rc=11.5, ξ = 1.0
15
Despite the differences in
membrane composition, ramified,
tubular or sheet-like shapes are
generic large scale morphologies
observed in internal membranes: —
suggests the involvement of
common features shared by these
organelles.
The most striking common aspect of organelles in the trafficking
pathways is that they are dynamic membranous structures, subject to
and driven by a continuous flux of a membrane bound material.
B. Alberts et l. Molecular Biology of the Cell, Garland Publishing,
16
Active components
bound state
unbound state
ION
CHANNEL
closed state
open state
Various mechanism of curvature induction in biological membranes.
(a) fusion and fission of transport vesicles
(b) Stochastic binding and unbinding of proteins
(c) conformational changes of integral membrane proteins
17
Kolmogorov Loop Condition for Non-Equilibrium Cycle
P21
P23 = +
2
P32 = −
P14 = +
active
1
P41 = −
equilibrium
φ = −1, H = 0
active
φ = −1, H = 0
P12
P43
4
φ = 1, H = 0
equilibrium
P34
3
φ = 1, H = 0
18
DRIVEN CURVATURE REMODELING (DCR)
κ = 20
Active field Concentration φA =0.1N=203 vertices
Spontaneous curvature : C0A = 0.7
κ = 20
Active field Concentration φA =0.1N=203 vertices
Spontaneous curvature : C0A = 0.9
N. Ramakrishnan, John Ipsen, Madan Rao, and PBSK
Soft Matter - 2015
http://arxiv.org/abs/1403.0796
19
20
0.6
equilibrium( = 0)
0.5
0.3
V
V0
= 0.1
= 0.15
= 0.25
= 0.5
= 1.0
0.2
0.1
0
0
0.2
Volume (V) enclosed by a membrane
of spherical topology as a function of
the spontaneous curvature
0.4
C0
0.6
0.8
1
Active curvature
fluctuations lead to an
effective deflating
pressure
V ( C0 )/V0
1
0.5
= 0.0
= 0.1
= 0.25
= 0.5
= 0.75
= 1.0
= 2.0
= 5.0
= 10.0
0
-0.5
Δpa
0.4
-1
-1.5
0
< 10, C0 = 0.5
= 0.5, 0.0 < C0 < 1.0
0
0
< 10, C0 = 0.8
= 1.0, 0.0 < C0 < 1.0
-2
0
-1
0
1
0.5
2
Δp = Δp0 + Δpa
2κC02
R(1+ )
1
1.5
21
3
4
CONCLUSION
We
have shown that vesicle shapes, akin to complex
membrane morphologies associated with cell organelles,
could be generated by a verity of mechanisms involving
proteins and lipids.
This observation is highly relevant for understanding
complex shapes associated with cell organelles, especially
in view of the hypothesis that the shapes of these
organelles may be a result of the complex membrane
remodelling events.
Our simple models shows that the naturally emerging
vesicle shapes, in response to non equilibrium curvature
remodelling events, are discs and tubes which are indeed
the most prevalent conformations in cell organelles
This work was carried out using computational resources at HPCE,
22
IIT Madras.