Shapes of Closed Phospholipid Membranes with Compartments

Bojan Božič

Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Slovenia

Shapes of discoid intracellular compartments

Shape transformations of vesicles induced by β2-glycoprotein I

Schematic representation of β2GPI

Hydrophobic loop embedded in the membrane

Theory

The free energy of the system

G = W + Gp

is the sum of the elastic energy of the phospholipid membrane

and the free energy of the membrane bound proteins

Gp = -εNp – kT(N0lnN0 – NplnNp – (N0 – Np)ln(N0 –Np))

20

020

2021 )(

2

1)(

2

1AA

Ah

kdACCCkW r

c

))((2

1120 PPL ANANNA

ΔA0 = (N2 – N1)AL + NPAP PPL

LPPP

ANAN

CCANC

2

0

)(

The equilibrium

S8 hR

A

S

0

8 hR

A

KD = KD,0e(dW/dNp)/kT

cK

cNN

D

0P

the shape equation

)4/(0 ARS

Dependence of the number of buds on the relative volume and the concentration

v V Rs / ( )4

33

Rs = 20 µm

= 15 µm

= 10 µm

Shape deformations of a flaccid vesicle during injection of β2GPI

The time dependence of the number of buds during the injection of β2GPI

β2GPI was injected in three periods of 150 s each.

Dependence of the number of buds on the relative volume and on the radius of a sphere with the same membrane area

Experimentally acquired data from vesicles A to E are positioned on the diagram.

Rs

(22)

(6)(9)

(6)

(19)

[µm]

A larger β2GPI concentration is needed to produce the same degree of budding.

The effect of the gravity

The dependence of the radius of a vesicle at a rim on the number of buds

• The extent of budding is an increasing function of βThe extent of budding is an increasing function of β22GPI concentration. GPI concentration.

• The budding can be rationalized by assuming that part of βThe budding can be rationalized by assuming that part of β22GPI is GPI is

inserted into the outer leaflet of the bilayer.inserted into the outer leaflet of the bilayer.

• The contribution to ΔThe contribution to ΔAA00 of each bound β of each bound β22GPI was estimated to be about GPI was estimated to be about

one tenth of the area of the cross-section of its inserted portion.one tenth of the area of the cross-section of its inserted portion.

• The greater number of buds is characteristic of more flaccid and larger The greater number of buds is characteristic of more flaccid and larger vesicles. vesicles.

• Different vesicles behave differently because the neck between the main Different vesicles behave differently because the neck between the main vesicle body and buds or strings of buds can be either closed or open.vesicle body and buds or strings of buds can be either closed or open.

Conclusions

Shapes of intracellular compartments

The discoid shape can be stabilized by adhesion in the central part,

weak lateral segregation of mobile membrane constituents and

formation of stiffer membrane regions with a defined spontaneous curvature.

)(

4 0 AAkhR

kN

cs

r

Phase diagram describing the values of v and N at which the membrane comes into contact.

Shape features of discoid compartments with homogeneous membrane

v = 0.2

v

Shape changes due to adhesion in the central discoid part

Lateral segregation of membrane constituents

1000 adhesion molecules per µm2

ck

A 0

Shapes with two distinct membrane regions

softc

stiffc

k

k

,

,

The stiffer membrane regions are presented by red lines and the soft membrane regions by black lines.

c0=C0Rs

EM micrographs of fusiform vesicles (FV) in urothelial umbrella cells

The plaque regions of FVs are highlighted by red lines and the hinge regions by blue lines.

Apical region of an umbrella cell with numerous FVs.

100 nm1 µm

Conclusions

•• A noticeable effect on the shape can be realized even when the A noticeable effect on the shape can be realized even when the local membrane composition does not vary considerably across local membrane composition does not vary considerably across the membrane.the membrane.

•• The spontaneous curvature of protein scaffolds supporting the rim The spontaneous curvature of protein scaffolds supporting the rim may be even more important than their relative stiffness.may be even more important than their relative stiffness.

•• The stiffness of plaques is at least an order of magnitude larger The stiffness of plaques is at least an order of magnitude larger than the stiffness of bare membrane.than the stiffness of bare membrane.

• • All three scenarios can lead to qualitatively similar shapes with a All three scenarios can lead to qualitatively similar shapes with a flattened central part and a drop-like cross-section at the rim.flattened central part and a drop-like cross-section at the rim.

•• At certain values of model parameters the three scenarios can At certain values of model parameters the three scenarios can also yield different shapes. also yield different shapes.

Saša SvetinaJure DergancJasna Prebil Janja MajhencGregor GomiščekVeronika Kralj-IgličRok Romih (Institute of Cell Biology, Faculty of Medicine, Ljubljana)Jure Stojan (Institute of Biochemistry, Faculty of Medicine, Ljubljana)Blaž Rozman (Department of Rheumatology, University Medical

Centre, Ljubljana)