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 β 2 -glycoprotein I

Schematic representation of β 2 GPI Hydrophobic loop embedded in the membrane

Theory The free energy of the system G = W + G p is the sum of the elastic energy of the phospholipid membrane and the free energy of the membrane bound proteins G p = -εN p – kT(N 0 lnN 0 – N p lnN p – (N 0 – N p )ln(N 0 –N p )) ΔA 0 = (N 2 – N 1 )A L + N P A P

The equilibrium K D = K D,0 e (dW/dN p )/kT the shape equation

Dependence of the number of buds on the relative volume and the concentration R s = 20 µm = 15 µm = 10 µm

Shape deformations of a flaccid vesicle during injection of β 2 GPI

The time dependence of the number of buds during the injection of β 2 GPI β 2 GPI 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. RsRs (22) (6)(6) (9)(9) (6)(6) (19) [µm]

A larger β 2 GPI 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 β 2 GPI concentration. The budding can be rationalized by assuming that part of β 2 GPI is inserted into the outer leaflet of the bilayer. The budding can be rationalized by assuming that part of β 2 GPI is inserted into the outer leaflet of the bilayer. The contribution to ΔA 0 of each bound β 2 GPI was estimated to be about one tenth of the area of the cross-section of its inserted portion. The contribution to ΔA 0 of each bound β 2 GPI was estimated to be about 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 vesicles. The greater number of buds is characteristic of more flaccid and larger vesicles. Different vesicles behave differently because the neck between the main vesicle body and buds or strings of buds can be either closed or open. Different vesicles behave differently because the neck between the main 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.

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 µm 2

Shapes with two distinct membrane regions The stiffer membrane regions are presented by red lines and the soft membrane regions by black lines.

c0=C0Rsc0=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 nm 1 µm

Conclusions A noticeable effect on the shape can be realized even when the local membrane composition does not vary considerably across the membrane. A noticeable effect on the shape can be realized even when the local membrane composition does not vary considerably across the membrane. The spontaneous curvature of protein scaffolds supporting the rim may be even more important than their relative stiffness. The spontaneous curvature of protein scaffolds supporting the rim may be even more important than their relative stiffness. The stiffness of plaques is at least an order of magnitude larger than the stiffness of bare membrane. The stiffness of plaques is at least an order of magnitude larger than the stiffness of bare membrane. All three scenarios can lead to qualitatively similar shapes with a flattened central part and a drop-like cross-section at the rim. All three scenarios can lead to qualitatively similar shapes with a flattened central part and a drop-like cross-section at the rim. At certain values of model parameters the three scenarios can also yield different shapes. At certain values of model parameters the three scenarios can also yield different shapes.

Saša Svetina Jure Derganc Jasna Prebil Janja Majhenc Gregor Gomišček Veronika Kralj-Iglič Rok 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 )