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Fig. 2. a) Cartoon of three-layered composite cell membrane. The central leaflet is composed of a multicomponent lipid/protein bilayer. It is coupled at the cytoplasmic side to the actin-based cytoskeleton (the actin cortex); a several hundred nm thick meshwork of actin filaments which are partially interconnected by crosslinkers (including myosin) and which is locally connected to the bilayer membrane. Note that the actin filaments are in fact about twice as thick (8 nm) as the bilayer (4 nm). The outside is covered by the (several ten nm thick) glycocalix which is made up of the head groups of cell receptors (carrying mostly several oligosaccharide chains) of glycolipids but also of huge macromolecules of the extracellular matrix (such as hyaluronic acid and fibronectin) which are transiently coupled to their respective receptors. b) Coarse grained models of local coupling of actin filaments to bilayers resulting in the formation of a thin shell of partially crosslinked actin (left) or of bundles (right) that can act as stress fibers and may serve the enforcement of local cell adhesion.

to 40 nm into the extracellular space (cf. Fig. 3). Many of these molecules may act as receptors or repellers depending on the surface of the target cell or tissue. In addition the e ect of the glycocalix may be enhanced by huge macromolecules of the extracellular matrix such as fibronectins ( 70 nm long) or hyaluronic acid (= hyaluran, a linear polysaccharide of up to 25 000 monomers) attached to their respective receptors. The formation

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Fig. 3. Text see on page 291.

of tight cell-cell contacts thus requires the expulsion of these repellers from the adhesion zone.

Secondly, the cell adhesion molecules are randomly distributed within the plasma membrane and the formation of tight adhesion zones by receptor segregation is a di usion controlled process [3].

Thirdly, long term modulations of adhesion associated with adhesion induced cell signaling have to be considered. Examples are the transfer of receptors from cytoplasmic storage compartments to the plasma membrane

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Caption to Figure 3: Summary of families of cell adhesion molecules (involved in the process of migration of white blood cells through endothelial cell layers lining the inner wall of blood vessels [2]) stressing structure of extracellular domains only. The lengths of the head groups are approximately drawn to scale. The head groups of the family of selectin receptors are composed of chains of identical polypeptides and exhibit a lectin-like outer domain which recognizes glycolipids and oligosaccharide side chains of glycoproteins (Gly-CAMs) with acidic sialic acid residues (such as so-called sialylated Lewis X factors). The different members of the family are distinguished by the number of repeat units. The longest representative with eight repeat units (P-selectin) may extend up to 30 nm into the extracellular space. The superfamily of so-called cell adhesion molecules (CAM) comprises two families: X-CAMs and Gly-CAMs. The extracellular domains of the family of X-CAMs are composed of chains of immunoglobulin(IgG)-like polypeptides (composed of about 100 amino acids) which are separated from the α-helical membrane anchor by a domain (also called III-domain) which is also found in fibronectins. The second superfamily of CAM-receptors (also called Gly-CAMs or “muccin”-like receptors) are composed of long polypeptide chains, rich in serin and threonin, to which sialylated oligosaccharide chains are coupled. Gly-CAMs are found on white blood cells (leucocytes). The head group may exhibit up to 80 oligosugar chains and may extend up to 40 nm into the extracellular space. These molecules act both as repeller and receptor [2,3] depending on whether the target cell exhibits a receptor or not. The superfamily of cadherins belongs to the group of homophilic (or self-recognizing) receptors which can mediate the tight mutual coupling of cells within cell monolayers (such as the epithelial cell layers of skin or the endothelial cell layers lining the inner wall of blood vessel). The cadherin family also plays a central role for the control of the formation of specific tissue during embryonal development where epithelial cell layers enclosing specific developing organs (e.g. the neural tube or the precursor of muscle cells) are interconnected by a specific class of cadherins which are genetically expressed at the cell surface. Integrin is the most versatile type of receptor found hitherto. It is a heterodimer composed of an α- and a β-chain with 15 nm long headgroups. Since there exist a number of di erent types of α- and β-chains a matrix of integrin receptors αiβj can be formed. Many integrins bind giant macromolecules of the extracellular matrix such as fibronectin (which are about 50 nm long) and these may act as repulsive spacers between cells which compete transiently with receptor-ligand pair formation. A cell receptor which is only involved in cell-matrix interaction is the CD44. It recognizes hyaluronic acid a giant polysaccharide which may exhibit Flory radii of up to 500 nm and which can thus also contribute to long range cell-cell repulsions.

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or the de novo synthesis of these receptors. A prominent and fascinating example of the regulation of adhesion by cell signaling is the activation of strong adhesion of leucocytes on endothelial cells by chemoattractants which triggers the emigration of the cells through the endothelial cell layer of blood vessels [2, 3]. This process is assumed to be initiated by activation of the G-proteins through the receptor for the chemoattractants which span the membrane with seven helices (thus resembling hormone receptors) and results eventually in the opening of gaps in the monolayer by centrifugal contraction of the endothelial cells [4].

The enormous interest in cell adhesion is exemplified by the more than 20 000 publications on this topic in 6 years. One group of studies concentrate on the molecular basis of specific cell-cell and cell-tissue-interaction and resulted in the discovery of an appallingly large number of receptors and conjugate ligands. Fortunately, these can be classified in terms of a relatively small number of sub groups which share the same structural motifs (cf. Ref. [2] and Fig. 3 for a summary). Moreover, concerning the interaction mechanisms the receptors may be divided into two distinct groups: (1) homophilic receptors which interact by non-covalent association with an anti-parallel oriented receptor of the same type in the opposing membrane mostly of the same type of cell and (2) heterophilic receptors which recognize distinct ligands (called adhesion epitopes) of opposing cell membranes or tissue (called “lock-and-key bonds” or “links”, below).

A second major group of studies deals with the cell biological basis of cell-cell interaction processes associated with immune responses, such as the above mentioned inflammation-induced selective interaction of white blood cells (leucocytes) with the endothelial cell layers of blood vessels [2]. These studies showed impressively that cell adhesion is a multistep process (as pointed out above) which involves the whole composite cell plasma membrane and that adhesion processes are intimately linked (i) to di u- sive lateral reorganizations within the lipid/protein membrane, (ii) to reorganizations of the actin cortex, (iii) to the exchange of material between cytoplasm and plasma membrane through endocytosis and exocytosis and (iv) to genetic expression of new receptors.

2 Mimicking cell adhesion

To study the physical basis of cell adhesion model systems were designed which exhibit key elements of the cell surface involved in adhesion and which enable the simultaneous measurement of free energies of adhesion and adhesion forces with high precision (for literature cf. Refs. [5, 6]). Test cells are mimicked by giant vesicles with reconstituted homophilic receptors (such as natural lipid coupled homophilic cell surface receptors [5]) or lipid-coupled

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Fig. 4. a) Design of mimetics of tissue surfaces. Fractions of giant extracellular matrix proteins or synthetic peptides (called “adhesion epitopes”) which are specifically recognized by receptors (e.g. of the integrin family) are coupled to lipids (via spacers) which are reconstituted into supported lipid monolayers or bilayers. To avoid denaturing of the proteins, the lipid layers must be separated from solid supports (e.g. semiconductors) by ultrathin polymer cushions. In the example shown, these films are made by deposition of multilayers of cellulose filaments exposing alkylchains (called hairy) [5]. On the left side the cartoon shows adhesion epitopes of fibronectin composed of cyclic hexapeptide with arginin-glycin-aspartate (RGD-) tripeptide sequence which are specifically recognized by integrin αvβ3 and the right side shows collagen epitopes composed of a recombinant triple helix of collagen [L. Moroder, private communication]. b) Typical model system mimicking cell adhesion. Giant vesicle with reconstituted lipid-coupled RGD-ligands shown in a) serves as test cell and supported membrane with reconstituted integrin receptors of blood platelets (α2bβ3) acts as target cell or target tissue. To mimick the repulsion by the glycocalix, lipids with macromolecular head groups (polyethyleneglycol) are reconstituted in one or both membranes [6, 7].

ligands (such as cyclic peptides with arginin-glycin-aspartate tripeptide motifs (so-called RGD-ligands) which are recognized by receptors of the integrin family; cf. Fig. 4). The generic long range repulsion is modeled by embedding lipopolymers such as phospholipids with polyethyleneglycol (= PEG) head groups (abbreviated as PEG-lipids or “repellers” in the following). Target cells are modelled by supported membranes with reconstituted receptors (such as integrins recognizing RGD-ligands) or lipid-coupled

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adhesion epitopes while target tissue is mimicked by coupling of adhesion epitopes to ultrathin hydrophilic polymer cushions anchored on solids [5].

3Microinterferometry: A versatile tool to evaluate adhesion strength and forces

Microinterferometry is a most versatile technique (1) to visualize cell adhesion and (2) to determine local free energies of adhesion or to measure unbinding forces between membrane-bound receptor-ligand pairs [6]. The technique (called reflection interference contrast microscopy RICM) is summarized in Figure 5. The image is formed by interference of light reflected from the surface of the adhering shells and from the biofunctionalized substrate, respectively. It is essentially a Fourier transformation of the height distribution h (x, y) of the adhering shell hovering over the substrate. The surface profile of the shell can be reconstructed by inverse cosine transform of the intensity distribution I (x, y) with a relative height resolution of about 1 nm and a lateral resolution of about 0.3 µm [5]. The maximum height accessible is 5 µm, the time resolution is 10 ms. Several procedures for the improvement of RICM image analysis have been developed [6].

4 Soft shell adhesion is controlled by a double well interfacial potential

The non-specific potential of interaction V (h) between an adherent soft shell and the target cell or tissue is composed of several contributions (cf. Appendix A). These include the (attractive) van der Waals potential Vvdw, electrostatic interactions Vel, repulsive undulation forces Vund and the short range repulsions exerted firstly by the supported membrane and secondly by the repeller molecules of the glycocalix. For practical purposes it is useful to fill the model cell with a higher density fluid which attributes a gravitational potential Vg (h) and which corresponds to real biological situations.

The undulation force (discovered by W. Helfrich [8]) is a unique feature of soft membranes. It is a consequence of thermal excitations of bending undulation of the highly flexible bilayers (bending modulus κ ≈ 25 kBT ). As illustrated in Figure 6, it results in a pronounced dynamic surface roughness of the soft shell membrane. It counteracts adhesion since in order to approach the membrane to the solid surface the Brownian motion has to be frozen in and this corresponds to a decrease in entropy. The resulting disjoining pressure is analogous to the pressure generated by a compressed ideal gas. In biology, undulation forces may play a key role for the control of adhesion of erythrocytes since these cells exhibit very strong undulatory excitations. The undulations are suppressed in normal cell membranes. At small membrane tensions (σ < 10−6 mN/m) the repulsion decays with

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Fig. 5. a) Schematic view of image formation by interference of light reflected from the surface of the soft shell and from the substrate surface, respectively.

b)Interferogram of adhering vesicle on solid support with adhesion zone defined by dark disc. The Newtonian fringes define the contour of the vesicle close to the substrate. The horizontal line defines the direction of contour reconstruction b).

c)Schematic view of typical surface profile of soft shell vesicle adhering moderate strength. Note that the profile exhibits a straight regime with the slope θ defining a contact angle (very similar to a partially wetting fluid droplet on a solid). However, the finite bending sti ness of the membrane leads to a smooth transition from the free to the adherent membrane at the rim of the adhesion disc defining a contour curvature Rc. The distance between the rim of the adhesion disc (defined by the contact line L) and the intersection of the tangent to the straight profile with the abscissa defines the capillary length λ = κ/σ (κ is the membrane bending modulus and σ is the membrane tension). λ is a measure for the range of the membrane deformation dominated by bending elasticity that is at x > λ the deformation is dominated by lateral membrane tension and at x < λ by bending elasticity.

distance d, as Vund = (kBT )2/κd2 while it is reduced with increasing tension [8].

Even more important is the repulsion potential due to the repeller molecules which plays the key role for the control of adhesion. It is not only determined by the interaction potential due to the steric repulsion between the head groups but also by the chemical potential of the repellers in the non-adherent part of the shell [6] and determines the depth of the strong attraction potential [5, 6].

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Fig. 6. a) Demonstration of dynamic surface roughness of vesicles caused by thermally excited bending undulations of lipid bilayer as visualized by temporal change of local contrast of leopard-like pattern of adhesion disc (cf. left and right image). The distance between dark and bright areas is about 250 nm. b) Time fluctuation of membrane-substrate distance (at encircled area of a)) demonstrating the oscillatory transition of membrane between state of strong and weak adhesion (courtesy of Stefanie Marx and J¨org Schilling).

Some of the interactions decrease hyperbolically with distance (such as Vvdw and Vund which decay with the square of the inter-membrane distance) while some decay exponentially (such as the electrostatic and steric forces). It is obvious that the superposition yields a general potential V (h) consisting of an attractive and a repulsive branch but that the di erent interaction potentials cannot be determined separately. For moderate interaction potentials, V (h) may be approximated by a harmonic potential [10, 11]

2V (h) = ∂2V /∂h2(h − h0)2 = V0 (h − h0)2.

(4.1)

Under this condition one always finds two limiting situations: at small generic attractions the soft shells hover over the surface at a distance of about 30 nm exhibiting strong flickering (since the adhesion induced tension is small). At increasing attraction the shells start to adhere to the surface forming a circular adhesion disc (as shown in Fig. 5b). The reason for this transition to the adherent state is that the undulations are suppressed by the adhesion-induced tension (which is in fact the case in Fig. 5b). In fact, the “tension-induced” transition from the free to the bound state has typical features of a first order phase transition. As demonstrated by the time

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series of distance fluctuations in Figure 6, one finds an intermediate situation where the membrane switches between a state of weak and strong adhesion, suggesting that the adhesion is determined by a double well potential with minima at a short (ho 10 nm) and a long distance (h1 40 nm) [5, 6].

The reason for the appearance of a double well potential is the chemical potential (µR = kBT · ln cR) of the repeller molecules (of concentration cR) in the non-adherent part of the membrane which controls the relative height of the two minima. At high repeller content the van der Waals minimum Vvdw (ho) is higher than the shallow minimum and the vesicle hovers 30– 40 nm over the surface. With decreasing cR the Van der Waals minimum is lowered and eventually becomes the absolute minimum resulting in the transition from the weakly to the strongly bound state. The analysis of the local interaction potential by the above flicker spectroscopy suggests the following adhesion laws:

•Since the two minima are separated by an activation barrier this adhesion transition is of first order and is a typical nucleation and growth process. Therefore the initial phase of the adhesion process consists in the formation of adhesion domains which can slowly merge into a single adhesion disc;

•The repeller chemical potential µR corresponds to the osmotic pressure πR exerted by the reservoir of repellers in the bulk (non-adhering part) of the membrane. There exists a state of coexistence of weak and strong adhesion when the two minima exhibit the same depth. This

occurs when the osmotic pressure becomes equal to the Van der Waals adhesion energy πR = Wvdw [5, 12];

•The osmotic pressures of the repellers but also of the receptors in the non-adherent part of the membrane [12] relax the strong attraction forces by orders of magnitude as demonstrated in a model membrane study by Nardi et al. [14] where oppositely charged lipids were used as toy receptor-ligand pairs. This is absolutely necessary to maintain the mechanical equilibrium between the intrinsic membrane tension and the adhesion-induced tensions (which is determined by the Young equation) at the contact line.

5 How is adhesion controlled by membrane elasticity?

The physical laws controlling the state of adhesion and the shape of soft shells and of fluid droplets (e.g. of water on glass), respectively, share some common features but di er in one aspect: the surface elasticity. The free energy ∆Gad of a partially wetting fluid droplet (that is the work gained by the partial spreading of a droplet) is equal to the gain in adhesion energy

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∆Gad = w · Ac (where w is the specific adhesion energy and Ac the contact area; cf. Fig. 5) minus the energy cost, σ∆O, associated with the increase, ∆O, of the surface area caused by the deformation of the initially spherical droplet (σ is the surface tension):

∆G = −wAc + σ · ∆O.

(5.1)

The work of adhesion of soft shells is also determined by these contributions but, in addition, one has to consider the elastic energy ∆Gb associated with the bending of the fluid shell. The bending deformation of a thin (nonspherical) shell is determined by the mean curvature H = 1/R1 + 1/R2 (where R1 and R2 are the principal radii of curvature of the surface). If the thickness of the shell (∆s 4 nm for bilayers) is small compared to its radius (R 103 µm) the bending elastic energy associated with the deformation of the initially flat plate into the adhering shell is, according to

Hook’s law, ∆Gbend = 1/2κ H2dO. κ is the two-dimensional bending elastic modulus of the membrane which is measured in units of energy. It

is typically of the order of 25 kBT for lipid layers at 37 ◦C. The total free energy (work) of adhesion is thus

∆Gadh = −wAc + σ∆O + 1/2κ H2dO. (5.2)

The state of adhesion and the shape of the adhering shell can in principle be calculated by application of the variation calculus methods [13]. This is a very complex problem which can only be solved analytically for the very simple situation of a single-component bilayer vesicle adhering weakly on a homogeneous smooth surface. The adhesion energy can then be accounted for by a harmonic interfacial interaction potential (introduced above). The problem has been solved by Lipowsky & Seifert [10] who showed that the state of adhesion and the vesicle shape depends in a subtle way on two parameters: the normalized adhesion energy w = wR2/κ and the reduced volume v = V /(4πR3/3) (where v is the ratio of the actual volume to the volume of a sphere with the same membrane area A = 4πR2).

The balance between the gain in adhesion energy and the cost in bending energy has surprising consequences. For instance by monotonous deflation (decrease of v) a vesicle may undergo a transition from the free to the bound state which can, however, be followed by an unbinding transition due to local membrane budding. A second result is that the suppression of the membrane bending excitation (and thus of the undulation force) by adhesion induced membrane tension can induce a binding transition (tension-induced switching).

In the case of mixed membranes (such as the system of Fig. 4) the variational problem can only be solved numerically. Fortunately, the adhesion