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Life in Soft Elastic Shells

Erich Sackmann (TUM +LMU)

Curvature Elasticity Concept of

Self- Assembly and Biological

Functions of Cell Membranes

Literatur: E. Sackmann + R. Merkel Lehrbuch der Biophysik Wiley 2010

Kapitel 9-13

Farbige Bilder und Lösung der Aufgaben über

http://www.biophy.de frei zugänglich

Ongoing Budding Fission Fusion

The ( coarse grained) dynamic image of cells as assembly of organelles

interconnected by continuous bi-directional material flow .

Dynamic order formation by continuous bi-directional Material Flow

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The Mosaic Model of Biological Membranes : (Summary:

Sackmann J. Phys. Condens. Matter 18 (2006) R785–R825)

Biochemical Reaction Centres

Modules

Cytoskeleton

The most simple Prototyp of a Composite

Shell (The Erythrocyte)

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Erythrocyte membrane coupled to quasi-two dimensional macromolecular network

composed of flexible spectrin filaments forming sides and 35 nm long rods of actin

oligomers forming edges of triangular network.

Quasi-hexagonl network Network coupled to membrane proteins

glycophorin and band III

Coupling is dynamic. Band IV.1 actively

bound and unbound by ATP turnover

Fundamental property I

Membranes are soft (fluid) shells as demonstrated by thermally

excited bending fluctuations of giant vesicle and erythrocyte

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Control of membrane structure and

functions by Thermoelastic forces

Two physical properties do the job

(I): Membrane Elasticity

(II) Lateral phase separation mediated by lipid phase transitions

1. A short Summary on the lipid

structure

2. A first role of membrane elasticity:

Sorting of lipids and proteins by principle

of hydrophobic matching

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Interplay of Genetics and Physics mediates the

self assembly of membranes .

The Genetis determines the order of amino acids in proteins (the primary structure),

The hydrophobic effect provides the driving force for their insertion into the bilayer

Three classes of thermodynamically distinct lipids

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Experimental evidence for lipid and protein

sorting between cell compartments.

Bretcher and Munro Science 1993

Analysis of Hydrophobic Thicknesses (H)

of Proteins in Cell Membranes

Plasma Membrane

Protein Thickness

H=3nm Rich in SPM Cholesterol

Golgi-Membran

Protein Thickness

H=2.5 nm Rich in Glycerol-Lipid

A Local deformation mode determines the energy required to

incorporate proteins into lipid bilayer

K Compression Modulus : K ≈ k/ h2

dO

h

hHKWelast

2

2

1

(H-h0) = 0,5 nm →Welast ≈ 100kBT

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Elastic mechanism of Lipid-Potein Sorting

Sphingomyelins + Cholesterol

Glycerol-

Phospholipids

The shape of cells and cellular

organelles determines their function

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The shape of cells determines the function

Problem: Maximizing area to volume ratio of ER-

membranes in crowded environment of cytoplasmic

space. At constant volume,flattened vesicles (cisternae) and tubular networks

exhibit largest area to volume ratio.

ER tubules of 25 nm diameter

can penetrate neural cells to tip

of the axons and dendrites

Dysfunctions create spastic

laming

Discoid shapes of erythrocytes minimize the elastic deformation

energy cost during transport through narrow blood capillaries

Why would spherical shapes create problems??

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How to control the shape ?

Answer

Principle of Minimum Bending

Elastic Energy

E(w); >1MHz

Membranes are elastic shells :Deformation determined by

three modes of deformation: Bending Shearing Tension

Deformation of Erythrocytes in high

frequencz electric field

Force by Maxwell/Wagner Polarisation

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Fluid membranes form soft elastic shells

K measured in units of energy ( kBT)

Deformation: Krümmung

21

112

RRH

Hooke‘sches Gesetz elastischer Schalen

Deformations-Energie =1/2 const x (Dehnung)2

Asymmetric

Membranes

C0

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Variation principled

Gela =o

Membrane shape is determined by minimum of elastic energy.

Two universal parameters

determine the shape Spontaneous curvature C0

Area to Volume Ratio

Can we also generate more complex shapes (such as

echinocytes) by minimium bending energy concept ?,

Echinocyte formed by aging of

cells due to loss of lipids or

crosslinking of ctoskeleton

The answer is no.

Neads also shear elasticity (Shear Modulus µ)

The diameter of the spicules is of the order

kR

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The concept of induced curvature

determines the intracellular material

transport by vesicle trafficking

Uptake of Iron by Endocytosis

By induced bending followed by budding

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Wie würde ein naiver Physiker das Problem

lösen?

Curvature induced by insertion of lipids of adaptor in inner

lipid monolayer. Stabilisation by clathrin binding to adaptor

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How hydrophobic matching could

mediate sorting of lipids and proteins

Some

experimental

Evidence

Two driving forces mediate tubular

network formation

First mechanism: Maximization of the area to

volume ratio.

Generation of spherical shapes during synthesis

of new membranes (for instance in the

interphase of the cell cycle) would expand the

cytoplasm. The osmotic pressure would kill the

cells by apoptosis

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Second mechanism of tubular network formation

by specific forces: Reticulons as generators of tubular networks of the ER

The hydrophobic sections are

longer than the bilayer thicknes

and form wedge like shapes which

induce spontaneous curvature

Generation of tubular

networks by addition of

Reticulon to Endoplasmatic

Reticulum

Another problem is the stabilisation of the junctions:

Model of stabilisation of junctions by two-arned Reticulon. Each

pair of hydrophobic wedges stabilisaes one of the orthogonal

oriented tubules.

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The self organisation and function of biomembranes is

controlled by elastic and specific protein-mediated forces

Lipids phase separation and concept of hydrophobic

matching plays a key role for the sorting of lipids and

proteins between the compartments.

Example: Concept of hydrophobic thickness matching.

Conclusions

The global shape of cells and intracellular

organelles determines their function.

The shape is controlled by non-specific elastic

forces and specific curvature-inducing proteins