Sackmann • Keber • Heinrich

Physics of Cellular Movements Erich Sackmann1,2,*, Felix Keber2, and Doris Heinrich2

1Physics Department, Institute for Biophysics E22, Technische Universität München, D-85748 Garching, Germany; email: sackmann@ph.tum.de

2Fakultät für Physik and Center for NanoScience (CeNS), Ludwig-Maximilians-Universität München, D-80539 Munich, Germany; email: Doris.Heinrich@physik.uni-muenchen.de, Felix.Keber@physik.uni-muenchen.de

*Corresponding author.

Supplemental Material Table of contents A. Extended model of travelling force field motors, mediated by gradients of the signalling

lipid PI-3,4,5-P3 1 B. Actin regulating proteins involved in cell motions 4 C. Regulation of actin network structures by molecular switches and actuators 7 D. Regulation of the actin cortex structure by signal molecules and scaffolding proteins 8 E. Adhesion induced membrane domain formation by receptor clustering 11 F. Magnetic bead microrheometry of Dictyostelium cells 12 G. Passive and active membrane bending excitations and biological functions 14 A. Extended model of travelling force field motors, mediated by gradients of the signalling lipid PI-3,4,5-P3 In the following we propose an extended model of the amoeboid cell movement dur-ing locomotion or the engulfment (phagocy-tosis) of large objects by the SAGW. The basic concept is that the nucleation and po-lar growth of actin gel clusters is mediated by the propagating gradient of the phospho-inositides PI-3,4,5-P3 and PI-4,5-P2, with the signalling lipid PI-3,4,5-P3 being en-riched in adhesion domains. The domains serve as docking stations for cooperative binding of the scaffolding protein CARMIL, which triggers the actin growth by uncap-ping actin plus ends, thus enabling the at-tachment of G-actin or pieces of F-actin provided by the actin provider coronin. Branched gels are formed by subsequent activation of Arp2/3 resulting in the growth

of nascent filaments off the side of pro-longed filaments. The gradient is generated by the interplay of two antagonistic enzymes: the PI-3-kinase (PI-3K) acting as PI-3,4,5-P3 generator and the PI3-phosphatase (PI-3PH, such as PTEN) acting as PI-3,4,5-P3-annihilator. Evidence for the initiation of phagocytosis by the local accumulation of the (PI-3,4,5-P3) generator P3-K has been visualized by fluorescence labelled proteins with specific domains preferentially binding to PI-3K (1, 2). This model of polar growth of the actin gel in the direction of propagation and the sub-sequent branching implies several require-ments which will be discussed below, to-

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gether with experiments justifying the as-sumptions made: 1) Once a local excess concentration of PI-3,4,5-P3 is generated, it has to propagate in one direction along the pillar. A possible answer to this question will be given below. 2) To generate a solitary wave the F-actin must be added at the front of the wave and dismantled at the opposite end. This process is attributed to the actin polymerization promoter coronin which plays a two-fold role (cf. Supplemental material B). It re-moves small pieces of F-actin at the trailing end and transfers them to the growing front. Here its unique capacity to bind preferen-tially fragments of F-actin with bound ADP and P (and not to monomeric ADP-actin) comes into play. Evidence for this role of coronin is provided by the observation that it is intimately associated with newly formed F-actin (as shown in Figure 5 of the main text). 3) The rate of actin polymerization at the front has to be triggered. This task is fulfilled by the scaffolding protein CARMIL (3, 4). Similar to the VASP complex in Figure 4b this supramolecular complex recruits the players involved in the polar actin growth (namely: Arp2/3, ATP-actin, the molecular GTPase switch Rac and the motor protein myosin-IB).The accelerated growth of the actin gel may be mediated by two mecha-nisms: ▲ by activated unbinding of the capping

proteins at the plus-end and attach-ment of fragments of F-actin bound to coronin.

▲ by nucleation and growth of branched fragments through Arp 2/3, as shown in Figure 4b).

Following Uruno et al. (3) and Miyoshi et al. (5) we consider the first mechanism more probable for several reasons. First, coronin (in its non-phosphorylated state) prevents the growth of the actin gels by inhibiting the binding of Arp2/3 to F-actin. Second, in the

resting state the capping protein CP binds strongly to F-actin preventing its growth. Third, the capping protein binds very strongly to CARMIL, with Kd ≈ 0.4x10-6M (similar to binding of myosin-IB to CAR-MIL with Kd ≈ 1x10-6M). Thus, after re-cruitment of activated CARMIL to the membrane the capping protein is removed and the actin filaments can elongate rapidly by attachment of fragments of F-actin pro-vided by coronin. By the uncapping process by CARMIL only assemblies of linear actin filaments can be generated. Branched networks can be formed, however, in a second step by activa-tion of Arp2/3. This can only occur after the coronin is phosphorylated which is mediated by a specific kinase (protein Kinase C). Evi-dence for the simultaneous recruitment of CARMIL and myosin IB and the delayed formation of branched networks is provided by the following observation. At the front of the solitary waves the newly synthesized ac-tin (as indicated by LIM) and myosin IB appear simultaneously (e.g. within about 1 sec after a sudden generation of a gradient of chemo-attractants cAMP). In contrast, the recruitment of Arp2/3 to the front is delayed by 1-2 seconds (7). The key questions discussed now are: (i) How is the PI-3,4,5-P3→PI-4,5-P2-gradient maintained that determines the direction of growth? (ii) How is the protru-sion force generated that drives the cell for-ward? (iii) Does the MT-aster play a role? The gradient of the phosphoinositides is generated by competition of the PI-3K and PI-3PH. In the case of lymphocyte locomo-tion, the PI-3K is switched-on by binding of proteins of the tissue to the β−chain of the integrins (the major CAM mediating cell tissue adhesion) which activates the kinase through the GTPase Ras (8). Very impor-tant recent studies showed that Dictyostelium cells exhibit an integral CAM which shares

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some features with the β−chain of integrin (9). We can assume with some confidence that the same mechanism holds in our case. To drive the SAGW the PI-3,4,5-P3→PI-4,5-P2-gradient has to propagate. This could be achieved by the constant generation of active PI-3K at the front of the spreading pseudopod where the adhesion domains grow and new CAMs are recruited and acti-vate the PI-3K. The adhesion domains en-riched in PI-3,4,5-P3 can now serve as dock-ing station for the CARMIL-myosin-IB complex. CARMIL could be recruited to the adhesion domains in two ways: First, by direct bind-ing to PI-3,4,5-P3 and second with the help of myosin-IB. Myosin-IB can couple to the plasma membrane either directly, by electro-static binding with its long basic tail to the negatively charged lipid moiety of the mem-brane, or indirectly by binding with its tail domain to the actin filaments already an-chored to the adhesion domains via talin (cf. Figure 4b). Evidence for the recruitment of CARMIL by myosin-IB is provided by ob-servations that at the front of the actin po-lymerization waves the newly synthesized actin (as indicated by LIM) and myosin-IB appear simultaneously (e.g. within about 1 sec after a sudden generation of a gradient of chemo-attractants cAMP). Since a large number of CARMIL-complexes can simultaneously assemble at the adhesion domains, the recruitment of these proteins at the front of the growing actin gel is a cooperative process. Some evi-dence for such a role of the adhesion do-mains is provided in the work of Weiner et al. (10), which shows that cells that are stimulated with chemo-attractants produce a random distribution of spots (~1μm diame-ter) of membrane bound Hem-1 (reflecting the heterogeneous distribution of the scaf-folding protein). These patches fuse at the leading front forming the solitary wave and disappear at the rear. The same punctuated

formation of scaffolding proteins precedes the re-establishment of actin networks de-composed by latrunculin, a poison strongly binding G-actin (11). In the present model the motion of the actin gel patches along the side of the elongated pillars is a natural consequence of the dis-mantling of F-actin at the trailing end by coronin. As shown previously (12) disrup-tion of the actin fragments from the adhe-sion domains drastically weakens the adhe-sion strength of the receptors resulting in their unbinding (cf. Supplement Appendix E). This would also provide a new reservoir of CAMs for the growing front of the SAGW. The role of the MT network is poorly un-derstood although it is well established that it plays a regulatory role for global cell movements and shape changes. Thus micro-tubules are required for effective phagocyto-sis since the particle uptake is much slower if the MTs are removed. One established role of the MTs is to recruit PI-3,4,5-P3 to membranes since its concentration in the membrane is lowered after decomposing the MTs. This enrichment of the signalling lip-ids is caused by the recruitment of the PI-3 kinase to membranes since concentration of the signalling lipid in the membrane is low-ered after decomposing the MTs (13). The most important role of the MT-aster is to stabilize the global shape of the cell dur-ing locomotion as predicted by the tenseg-rity model. Reconstructions of the MT-aster by confocal microscopy of cells with GFP-labelled MTs show that they are tightly con-nected to the actin cortex over several μm long segments. Moreover, the motion of the actin gel clusters and the MTs are correlated, strongly suggesting that the very large forces (of some 100 pN) on the MTs are generated by the propagation of the actin columns during cell locomotion.

References to Appendix A 1. Dormann D, Weijer G, Dowler S, Weijer J. 2004. J. Cell Sci. 117:6497–509 2. Cai L, Holoweckyj N, Schaller M, Bear J. 2005. J. Biol. Chem. 280, 31913-23 3. Uruno T, Remmert K, Hammer JA. 2006. J. Biol. Chem. 281:10635–50 4. Jung G, Remmert K, Wu X, Volosky JM, Hammer JA III. 2001. J. Cell Biol. 153:1479–97 5. Miyoshi T, Takahiro T, Higashida C, Hertzog M, Fujita A, Narumyia S. 2006. J. Cell Biol. 175:947–55 6. Cai L, Holoweckyj N, Schaller M, Bear J. 2005. J. Biol. Chem. 280, 31913-23 7. Etzrodt M, Ishikawa H, Dalous J, Mueller-Taubenberger A, Bretschneider T, Gerisch G. 2006. FEBS Lett. 580:6707–13 8. Melikova S, Dylla S, Verfaillie C. 2004. Exp. Hematol. 32:1051–56 9. Cornillon S, Gebbie L, Benghezal M, Nair P, Keller S, et al. 2006. EMBO Rep. 7:617–21 10. Weiner O, Marganski W, Wu L, Altschuler S, Koirschnert M, et al. 2007. PLoS Biol. 5: 2053-62 11. Gerisch G, Bretschneider T, Müller-Taubenberger A, Simmeth E, Ecke M, et al. 2004. Biophys. J. 87:3493–509 12. Simson R, Wallraff E, Faix J, Niewoehner J, Gerisch G, Sackmann E. 1998. Biophys. J. 74:514–22 13. Khandani A, Eng E, Jongstra-Bilen J, Schreiber D, Douda D, Samavarchi-Tehrani P, 2007. J. Leukocyte Biol. 82: 417-28

B. Actin regulating proteins involved in cell motions Biochemical properties of G-actin: The biochemical behaviour of actin monomers is determined by the state of the nucleotide bound in the centre of the molecule. The binding constant of the G-actin to the fast growing plus end of filaments is highest when ATP (denoted as ATP-actin) is bound. It decreases after hydrolysis of ATP (denoted ADP-P-actin) and is changed further after P dissociates (yielding ADP-actin). After for-mation of F-actin the nucleotide is hydro-lysed and a gradient of ADP-actin ADP-P-actin to ATP-actin is formed. Thus, one has to consider three species of actin monomers. This is expected to play a key role for the treadmilling process in pseudopods and the generation of solitary gelation waves as shown in Figures 4 and 5. Capping proteins: Proteins that bind to the fast growing plus ends of actin filaments and block their growth. Capping protein for Dictyostelia cells are severin and CP. The dissociation constant of severin is Kd ≈ 10-7 M. The CP-capper binds very strongly to the plus end (with dissociation constants of

Kd ≈ 10-9 M and a life time of 30 min). The CP-content of cells is 0.1-1 x 10-6 M. It is only two to three orders of magnitude smaller than the G-actin concentration and the actin filaments in cells are therefore short (~1μm). Only activated CARMIL can re-move CP from the plus end which is essen-tial for the treadmilling process described in Figure 4 of the main text. Arp 2/3 can bind to the minus ends of actin monomers. Since this actin binding protein can also bind to the side of actin filaments, it can generate branched networks by forming F-actin budding off the side of existing filaments (as shown in Figure 1 of the main text. Thus, Arp2/3 can play a two-fold role as capping and cross-linking pro-tein. Cofilin and Profilin: Cofilin is a F-actin depolymerization factor that destabilizes actin filaments resulting in the dissociation of actin monomers (G-actin). It is most ac-tive for hydrolysed ADP-actin and is thus responsible for the dismantling of mature

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actin monomers in cells. Cofilin can also sequester G-actin in the cell. Profilin provides activated ATP-actin by accelerating the exchange of ADP by ATP. It can take over ADP-actin from cofilin and activate it by ADP ATP exchange. Profilin loaded with ATP-actin can also bind to the scaffolding proteins WASP or CARMIL. Coronin (Coronin 1B): A promotor of F-actin dismantling. In contrast to Cofilin it binds strongly to F-actin rods through elec-trostatic forces but not to monomers. Im-portantly, it binds much stronger to ADP-P-actin (dissociation constants Kd ≈170 x 10-9M) than to ADP-actin (8 x 10-6M). It can there-fore disrupt fragments of F-actin from ma-tured actin filaments and deposit them at the plus-end after removal of the capping pro-tein from this end. The concentration of coronin in cells is about 0.73 x 10-6 M (compared to actin with typical concentra-tions of 100 x 10-3 M). Coronin often works together with cofilin in dismantling actin filaments. It is important to note that in its non-phosphorylated state, coronin inhibits Arp2/3 binding to actin. However, this in-hibition is abolished after phosphorylation of coronin. Formin (mDia-1): A group of proteins in-volved in the promotion of actin polymeriza-tion. It mediates preferentially the growth of actin bundles and is involved in the formation of thin cellular protrusions (named filipodia). The proteins exist in the cytoplasm in an auto-inhibited state. Activa-tion is most efficiently mediated by GTPase switches of the Rho family (see Reference (1)). The proteins are also assumed to play a key role for binding of the microtubules to the actin cortex.

LIM protein domains, are cystein- and histamin-rich protein motifs. Dimers of LIM can act as non-specific linkers between proteins. Each LIM domain coordinates two Zn(II) ions (forming a so called zinc-finger). LIM binds to actin with dissociation con-stants of Kd ≈10-7M and stabilizes actin bun-dles at low Ca2+-concentration, while it un-binds at high Ca2+-content (>10-6M). It also protects actin filaments against depolymeri-zation by cofilin. Most importantly, the LIM-proteins bind only transiently to newly polymerized actin. This can be used to visu-alize freshly polymerized actin by labelling LIM protein domains with GFP. Myosin IB: This motor exhibits only one motor head. It has a large positively charged tail which can mediate the direct binding to the inner leaflet of the plasma membrane (which contains about 10% negatively charged lipids). It exhibits a specific domain (SH3) of about 60 amino acids at the end of the tail that can bind the motor to all pro-teins exhibiting SH3 binding domains, such as CARMIL the scaffolding protein of Dic-tyostelium cells. Members of the myosin I family have some distinct features. They exhibit two actin binding sites (one at the motor head group) and the other at the tail and can thus crosslink actin filaments. The motor func-tion is activated by phosphorylation of the motor domain by myosin light chain kinase, similar to muscle myosin. It has been reported that myosin I can ex-hibit some type of gear. Under load it can switch from a non-processive (tension gener-ating) to a processive motor that can move towads the plus end of actin filaments. My-osin IB can thus act as force controlled ac-tuator (see Reference (2)).

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Talin (member of family of FERM pro-teins): Talin is a major constituent of the composite cell envelopes of most mammal-ian cells or amoebae. It mediates the direct coupling of actin to the intracellular do-mains of glycolproteins (such as glycophorin in the case of erythrocytes) and integrins, which is present in all animal cells. The binding is in general mediated by the head group of talin exhibiting a so called FERM domain (150 amino acids in length). The FERM domain is found in many other actin membrane couplers such as band IV.1 pro-tein (the major actin-membrane coupler of erythrocytes), ezrin, radixin and moesin. It can exist in an inactive and an active state. In the dorming state the binding site for the membrane protein is shielded. Similar to the situation for band IV.1 (shown in Figure 1) the FERM domain of talin becomes acti-vated by phosphorylation. Talin plays also a key role for the control of cell adhesion strength mediated by in-tegrins. These CAMs exhibit a weakly bind-ing and a high affinity conformation, whereby binding of talin triggers the transi-tion to the latter state. Talin exhibits two binding sites for actin and can thus crosslink filaments (For a comprehensive review of the role of talin see Reference (3)). Microtubule-actin crosstalk: There are several candidates mediating the coupling of the microtubules to actin cortex. For the present work we consider two mechanisms: 1. Coupling via end binding proteins (EB1) with the help of the actin growth pomotor formin (and mDia-1).

2. Coupling via Dynactin: This rod-like supramolecular complex (of ~1.1MDa) is about 37 nm long and 10 nm thick. Its ma-jor constituents are (i) the actin-like filament Arp1, (ii) capping proteins determining the length of the rod and (iii) a constituent me-diating the binding of the motor protein dynein. The thickness of the complex (to-gether with the dynein motor) is about 50 nm. The dynein motor moves towards the minus end of the MT (that is towards the centrosome) and thus generates tension in the filament and may be responsible for the prestress of the cells mentioned in the main text (cf. also Figure S.M.6) In many quiescent cells the microtubules are highly flexible and are not bound to the actin cortex. They grow and shrink continu-ously on the time scale of minutes. However, cross-linking of MTs to the actin network comes into play during adhesion and cell crawling on surfaces and it is essential for the growth of nerve axons. For this purpose a fraction of the MTs becomes fixed with their plus ends at the actin cortex (as shown in Figure 2 of the main text). The structure of the tubulin monomers of these stable MTs is modified post-translationally (see Reference (4)). Although EP1 is called end-binding-protein, it can mediate the binding of several μm long segments of the MTs to the actin cortex. It can also mediate the formation of MT bundles which can mutually slide over each other (for References see (5)).

References to Appendix B 1. Wallar BJ, Stropich BN, Schoenherr JA, Holman HA, Kitchen SM, Alberts AS. 2006. Biol.Chem. 281:4300-07 2. Laakso JM, Lewis JH. Shuman, Ostap EM. 2008. Science 321:133-36 3. Critchley DR, Gingras A. 2008. J. Cell Sci. 121:1345–47 4. Gundersen G, Bulinski J. 1988. Proc. Natl. Acad. Sci. USA 85:5946–50 5. Reilein A, Nelson WJ. 2005. Nat. Cell Biol. 7:463-73

C. Regulation of actin network structures by molecular switches and actuators The rapid reorganisation of the actin cy-toskeleton structure is often mediated by molecular switches of the GTPase-superfamily (called Ras). They are further divided into the subfamilies consisting of Ras, Rho, Rab, Cdc42. These GTPases are small proteins of 20-30 kDa which bind guanine nucleotides (GTP or GDP). They can thus exist in an inactive state (with GDP bound) and an active state (with GTP bound). They are all actuated by external signals (mechanical forces, hormones, growth factors) through the exchange of GDP by GTP. This process is mediated by GDP→GTP exchange factors (GEF, cf. Figure S.M.1). As shown in Figure S.M.1, the members of the three subgroups evoke distinct responses by activating specific actuator proteins (also called effectors or adaptors in the biological literature) which in turn activate different actin manipulation proteins, such as capping proteins (impeding the actin growth); crosslinkers (such as Arp2/3), actin-to-mem-brane linker, such as band IV.1 (shown in Figure 1b of the main text) and talin. The GTPase switches are regulated in a so-phisticated way to trigger or switch off bursts

of cellular activities. Two pathways of activa-tion are known: 1) The GTPases exhibit lipid anchors medi-ating their membrane coupling. But they reside in the cytoplasm in a sleeping con-formation, often mediated by binding of a specific protein: “guanine nucleotide disso-ciation inhibitors” (GDI). The GTPase is activated by exchange of GTP for GDP: a process mediated by a GDP GTP exchange factor (GEF) shown in Figure S.M.2 (left). The lipid chain of the GTPase is now ex-posed. It can bind to the membrane and interact with actuators of the cytoskeleton. 2) The intrinsic GTPase activity of the switches is rather weak resulting in a long lifetime of the activated switch. In order to accelerate this low rate of hydrolysis (which is about 0.01/min), and switch-off the GTPase fast, another regulatory proteins has to come into play. An example is the “GTPase activating protein”(GAP). It stimu-lates the Rho-GTPases to hydrolyse the GTP resulting in a rapid de-activation of the molecular switches. GEF and GAP together control their net activity. The GAP control factor could introduce a timer into GTPase controlled signalling pathways.

Figure S.M.1 Schematic view of the acti-vation of effector proteins (actuators) involved in the control of the structure of the actin-based cytoskeleton.

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Figure S.M.2 Activation of the effectors (actuators) by molecular switches of the Ras super-family. The super-family comprises over 100 members, including Ras, Rho and Rab. Left: activation and membrane binding of a GTPase by exchange of GTP for GDP. After membrane binding the switch controls the activity of a specific actuator. Right: control of the activity of the molecular switches by the tandem GEF↔GAP (described in the text). Activation of proteins by phosphoryla-tion: a general principle. Numerous signal transmission processes in cells are controlled by signal cascades associated with phos-phorylation-dephosphorylation reactions of proteins and lipids (such as phosphoinositi-des). These are mediated by tandems of an-tagonistic enzyme: the kinases (which add phosphate groups) and the phosphatases (which remove phosphate groups). The pro-teins consist of a universal catalytic domain mediating the reactions and a specific do-main controlling the interaction with other

proteins or with membranes (such as the PI-3-kinase or PI-3-phosphatase). In general, the tandems are part of a whole cascade of phosphorylation-dephosphorylation reac-tions. It is important to note that the activation of the kinases and phosphatases requires the cooperation of the GTPase-switches with the associated helper proteins (GEF, GAP and possibly the inhibitor GDI). Therefore, the activation of a certain enzyme is controlled by a set of at least four proteins working together.

D. Regulation of the actin cortex structure by signal molecules and scaffolding proteins Second messenger phosphatidylinositol-3,4,5-triphosphate (PI-3,4,5-P3). This phosphoinositide exposing three phosphate groups is generated by phosphorylation of PI-4,5-P2 by phosphoinositol-3-kinase (PI-3K). PI-3,4,5-P3 has a twofold function. It can first act as second messengers and sec-ond, serve the recruitment of proteins

(which regulate the structure of the actin cortex) to the membrane. PI-3,4,5-P3 and PI-4,5-P2 are connected by the antagonistic pair of enzymes PI-3K and the PI-3-phosphatase (an example is PTEN) remov-ing the phosphate group at the 3-position of the inositol head group.

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Figure S.M.3 Illustration of states of phos-phorylation of head groups of the phospholipid pho-phatidytidylinoisitol.

It is important to note that both enzymes bind to PI-4,5-P2 and PI-3,4,5-P3 through the interaction with a specific protein do-main (named C2 homology domain). The binding involves two to three Ca2+-ions. Note first: PI-4,5-P2 is much more abun-dant (about 1% of the total lipid content) than PI-3,4,5-P3 (~ 0.1%). Note second: the membrane binding of the proteins is en-forced by electrostatic forces due to the binding of basic sequences of the proteins to other negatively charged lipids (mainly phosphatidylserine) as shown in Figure 1c. Scaffolding proteins: (CARMIL, VASP, WASP). The scaffolding proteins serve the recruit-ment of proteins and molecular switches required for the polar growth of actin gels at the front of pseudopods. They are all com-posed of five constituents with defined func-tions. At the N-terminal they exhibit a spe-cific domain (WH1) which binds the mole-cule to proteins associated with focal adhe-sion domains, such as vinculin. In the mid-dle they expose a prolin rich domain (PPP). It acts as docking pocket for proteins exhib-iting so called SH3-domains. Important examples of such proteins are PI-3-kinase and myosin 1B. It exhibits also four binding sited for profilin (which recruits activated ATP-actin to the complex). Finally, the

VCA-domains bind both G-actin and Arp2/3. The scaffolding protein CARMIL (shown schematically in Figure S.M.4) mediates the SAGW generation in Dictyostelium cells. The supramolecular complex (molecular weight of 116 kDa) consists of a 66 nm long tail and a 19 nm large head. In the resting state of cells CARMIL is in a sleeping state with the tail assumed to be wrapped around the head. The CARMIL complexes consist also of five parts binding the different pro-teins required for the directed actin polym-erization. A very important difference to the other scaffolding proteins is the strong bind-ing of myosin IB (dissociation constant Kd = 100 x 10-9 M). Another essential feature is the very strong binding of the capping pro-tein CP of Kd = 0.4 x 10-6 M. Finally CAR-MIL can also form dimers with Kd = 1 x 10-6 M. The concentration of CARMIL and my-osin IB in cells are about 1 x 10-6 M and 2 x 10-6 M, respectively. The concentrations are thus adjusted in such a way that the associa-tion-dissociation equilibrium of the CAR-MIL-myosin IB and CARMIL-CP com-plexes can play a key role under physiologi-cal conditions. In particular CARMIL can remove the capping protein CP from the plus end of actin. This process is assumed to play a key role for the rapid prolongation of actin filaments.

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Figure S.M.4 Schematic structure of the scaffolding proteins mediating the solitary actin gelation waves. Example of CARMIL. Integrins can serve as docking stations for scaffolding proteins which recruits kinases and activation of PI-3-kinase (on the lo-cal generation of PI-3,4,5-P3). Recently it was shown that clusters of in-tegrin can play a key role as docking station for the recruitment of cytoplasmic proteins involved in cell signalling (1). The β-tail of integrin exhibits a specific binding motif (domains) which binds proteins exposing phosphorylated tyrosine side chains. An im-portant example mentioned above is phos-phorylated talin which switches the transi-tion of the integrin from a weakly binding to a high affinity state and simultaneously me-diates the coupling of actin gel patches to the adhesion domains as mentioned above (Supplement Appendix B). Another impor-

tant role of the specific binding domain is the recruitment of scaffolding proteins to the integrin β−chains which serve as docking stations for actuators triggering the activity of other proteins of the signalling pathways. By this mechanism the PI-3-kinase could be recruited to the adhesion domains (see Fig-ure 5 of original manuscript), resulting in the local generation of the signalling mole-cule PI-3,4,5-P3 as postulated in our model of SAGW generation. This mechanism of PI-3,4,5-P3 generation has indeed been veri-fied for leucocytes (see Reference (2)). In the case of Dictyostelium cells, the role of the integrins could be played by the CAM named SibA which was discovered recently by Cornillon et al. (see Reference (3) and Supplement Appendix F).

References to Appendix D 1. Calderwood DA, Fujioka Y, Pereda JM, Garcia-Alvarez B, Nakamoto T, Margolis B, et al. 2003. Proc. Natl. Acad. Sci USA. 100: 2272-77 2. Melikova S, Dylla S, Verfaillie C. 2004. Exp. Hematol. 32:1051–56 3. Cornillon S, Gebbie L, Benghezal M, Nair P, Keller S, et al. 2006. EMBO Rep. 7:617–21

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E. Adhesion induced membrane domain formation by receptor clus-tering The adhesion behaviour of the amoeba-like Dictyostelium cells depends on the state of the live cycle. In the presence of enough food (e.g. bacteria) the cells are in the vege-tative state. They can survive as isolated quasi-spherical cells, search food by random walk and divide. After starving for about 6h the cells become elongated (worm-like). They associate and eventually generate slime molds. In this so-called adhesion-competent state the cells express a specific cell adhesion molecule (CAM) called contact site A. The outside domain is composed of three IgG-like domains to which N-linked oligosaccha-rides are coupled while the CAM are linked to the plasma membrane by lipid anchors. In the vegetative state the situation is less clear. First, the adhesion could occur by non-specific forces. Second, it has been postu-lated that a modification of the contact side A protein (denoted as contact side B pro-tein) acts as CAM. Third, an integral protein SibA (synonym for Similar to Integrin Beta) has recently been discovered as potential CAM of vegetative cells (see Reference (1)). This protein is supposed to penetrate the membrane with nine hydrophobic chains. The most interesting point is that this CAM shares some similarities with the β-chain of integrins. In particular it mediates the direct binding of talin which then recruits F-actin to the membrane. This is important for the following rea-son. As noted above the activation of the PI-3-kinase is triggered by binding to the β-chain of integrins. The same may hold for the SibA and therefore the adhesion of Dic-tyostelium cells could stimulate the activation of the PI-3,4,5-P3 generator similar to the situation in mammalian cells. The adhesion of Dictyostelium on glass sub-strates leads to the formation of adhesion domains (of about 1 μm diameter) which are stabilized by coupling of talin to the inner

domains of the CAM (see Reference (2)). The primary event of adhesion is the forma-tion of adhesion domains which can occur within seconds after contact formation be-tween cells and surfaces. They form by lat-eral segregation of the receptor-ligand pairs interacting via lock-and-key forces (see Ref-erence (3) for a summary of the physical basis of this process). In a second step the adhesion domains are stabilized by coupling of actin assemblies to the intracellular do-mains of the CAM. Model membrane studies strongly sug-gest that the adhesion induced formation of micro-domains is an inevitable consequence of the interplay between the strong short range specific interaction between the CAM and ligands of the tissue and long range re-pulsive forces induced by molecules of the glycocalix or by membrane bending excita-tions described below (in Supplement Ap-pendix F). The distribution and size of the adhesion domains depends on the mechani-cal forces exerted on the cells. The adhesion strength of cells (measured in terms of the work of unbinding) depends sensitively on the membrane bending elastic-ity. Therefore, the coupling of F-actin to the membrane (e.g. via talin) increases the adhe-sion strength drastically. For instance, knock out of talin by mutations reduces both the bending modulus and the work of adhesion of Dictiostelium cells by a factor of five.

The adhesion domains could play a key role for adhesion-induced cell signalling. They can form scaffolding entities for the local assembly of specific proteins involved in signalling. In particular, in the case of SAGW generation the adhesion domains could account for the cooperative binding of the scaffolding protein CARMIL to PI-3,4,5-P3.

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References to Appendix E 1. Cornillon S, Gebbie L, Benghezal M, Nair P, Keller S, et al. 2006. EMBO Rep. 7:617–21 2. Tsujioka M, Joshida K, Inouye K. 2004. EMBO J. 23:2216–25 3. Sackmann E. 2006. J. Phys. Condens. Matter 18:R785–95

F. Magnetic bead microrheometry of Dictyostelium cells In the following some pertinent results of our previous microrheometry studies of the cytoplasmic space of Dictyostelium cells are summarized. Superparamagnetic beads were taken up by the cells through phagocytosis. They are therefore wrapped by the plasma membrane as other phagosomes (such as bacteria) and moved around in the cell for some time, before they are expelled again. Frequently the beads are bound to micro-tubules and transported along the filaments in both directions. Figure S.M.5 shows a micrograph of the cell with fluorescence labelled microtubules. Intracellular motions of 1.4 μm diameter magnetosomes reflect movements of microtubules. To study the viscoelastic behaviour of the cytoplasm of Dictyostelium cells a large num-ber (about 1400) of viscoelastic response curves (evoked by force pulses with force

amplitudes ranging from 100 to 700 nN) were recorded. In Figure S.M.6 we show a frequently encountered scenario. The beads do not follow the applied force but move predominantly perpendicular to the applied external force Fex which is directed towards the left. The force amplitudes for pulses P1 to P4 are f1=450 pN (yellow line), f2=500 pN (orange line), f3=110 pN (red line), and f4=290 pN (purple line), respectively. The most remarkable finding is that the beads return close to the initial position after the pulses P1 to P3. After pulse P4 the bead does not return any more and is most likely detached from the MT. In summary, the repeated return of the bead close to the ini-tial position strongly suggests that the cell exhibits some mechanical shape memory; which is most likely determined by the me-chanical equilibrium of the MT-aster.

Figure S.M.5 Fluorescence micrograph of cell with two centrosomes showing the magnetic bead coupled to a microtubule (Adapted from Reference (1) with permission of the pub-lisher)

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Figure S.M.6 Section of the bead trajectory shown in Fig 3a of the main text, The bead motion was ob-served for about 10 min while viscoelastic re-sponse curves were recorded at different times. The section shows a frequently occurring sce-nario where the bead moves predominantly perpendicular to the applied external force direction. Due to the (diffusive) reversibility of the microtubule deflection, the bead can revisit the same region within the cell several times. (Adapted from Reference (1) with permission of the publisher).

To relate the motion of the bead and the microtubules, cells with GFP-labelled tubu-lin were studied. The trajectory of the bead motion and the conformational change of the MT before, during and after application of a force pulses could be observed, since the

bead remained attached to the MT for the time of observation. A typical scenario is shown in Figure S.M.7b and the major find-ings are discussed in the Figure Caption. A detailed report and analysis of these experi-ments is given in Reference (1).

Figure S. M.7 (a) Motion of microtubule and attached bead in cell, induced by a force pulse of Fext= 40 pN. The thick green dashed line (#1) marks the contour of the MT immediately (56 ms) before application of the force and the thin black lines (numbered 2 to 5) during application of the force. Contour #6 indicates the MT position after switching off the force pulse. The thick red curve with the arrow indicates the motion of the MT. It is drawn to guide the eye. The time interval between contours is 0.5 s.

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(b) The left side shows the trajectory of the bead centre (maximum initial velocity ~1μm/sec). Note that the bead follows the force direction after an initial short deflection in the opposite direction (see small arrow). The right side shows the trajectory of the left centrosome #1 (closest to the bead) with the dots indicating the switching on and off of the external force. The maximum initial velocity of the centro-some is v~3 μms-1. It is seen that also the centrosome moves first fast in a direction perpendicular to the applied force before it returns close to the initial position again (Adapted Reference (1) with permission by the publisher). References to Appendix F 1, Heinrich D. and Sackmann E. (2006). Acta Biomaterialia 2:619-625 G. Passive and active membrane bending excitations and biological functions A striking manifestation of motions in cells is the pronounced random bending excita-tion of cell envelopes exhibiting amplitudes of up to 30 nm (which is also called flicker-ing). This dynamic membrane roughness has stimulated many physicists to enter the field of cell physics. Measurements of the bending excitation spectra (amplitude versus wave vector curves) provide insights into the mo-lecular architecture of the composite cell envelopes and enables measurements of the bending moduli of membranes. Theoretical basis of membrane excitations (the Helfrich model) The mechanical properties of vesicles and erythrocytes are dominated by the bending elastic energy of the fluid membranes. The shape of free and adhering soft shells can therefore be described in terms of the simple model of flexible shells proposed first by Helfrich (and well documented in Chapters 8 and 9 of Reference (1)). The total elastic energy of the fluid plasma membrane is de-termined by the energy functional

where u is the deformation amplitude in the direction normal to the membrane. The first term accounts for the bending deformation (κ is the bending modulus) the second for the lateral tension and the third for the in-teraction between both membranes or be-tween a membrane and a wall (assuming that it can be described in terms of a harmonic potential) is a consequence of the closure of the shell. The state of adhesion and the adhesion en-ergy of tension free shells are determined by the adhesion energy and the pronounced thermally excited bending undulations re-sulting in a dynamic roughness of the mem-brane of the order

κ/22 TLku B≈ .

As shown by Peliti and Nelson (2), the en-ergy functional (Equation S.M.1) can also be applied to tethered membranes exhibiting shear elasticity (such as the composite cell envelopes of erythrocytes) if the bending

∫∫⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−′′+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

+⎥⎦

⎤⎢⎣

⎡∂∂

+∂∂

=Δ 20

222

2

2

2

2

)(22

hhvyu

xu

yu

xudAGi

elaσκ (S.M.1);

14

modulus is replaced by a renormalized modulus κc(q):

20

0 169)(

qTkq

c

BcC πκ

μκκ +=

The second term accounts for the coupling between the bending and the extensional deformations of the shell resulting in the apparent increase of the bending modulus at short wavelengths of excitation. Following Auth et al. (3), the dynamic roughness of the composite shells can be understood on the basis of a two shell model by considering the coupling between the sub-shells. Thus one has to distinguish be-tween two situations: For large wave vectors q>>q* the amplitudes are small and the two sub-shells fluctuate independently. The mean square amplitudes of each shell (i) can be obtained from Equa-tion (S.M.1) by application of the equiparti-tion theorem and can be expressed in terms of the normalized bending modulus )(qiκ as follows:

422

)(2)(

qqTk

Lqu

i

Bi κ

π= .

For fluid plasma membranes (such as vesi-cles) it is

42)( qvqq Bi ′′++= σκκ , (where κB is the bending modulus) and for cells envelopes with tethered cy-toskeleton

42)()( qvqqq Ci ′′++= σκκ . For small wave vectors the fluctuation of the two shells are synchronized and the ampli-tudes are

4422 2

qqTk

Lu

CB

B

κκπ

+=><

The two-shell-model can well explain the experimental data at long wavelengths, with Λ= 2π/q large compared to the mesh size ξ of the cytoskeleton (ξ ~0.1 μm). The bending excitation is dominated by the plasma membrane and exhibits a bending modulus of about 50 kBT (κB = 4 x 10 -19J) in agreement with measurements (4). However, the experiments show an anoma-lously large amplitude for Λ= 2π/q ≤ ξ corresponding to an apparent bending modulus of 5 kBT (over an order of magni-tude larger than the value of 50 kBT ex-pected for a PM containing 50mole % cho-lesterol). This points to non-thermal random driving forces that could be explained in terms of a higher effective temperature Teff. One possible source of these “chemical forces” could be the random phosphoryla-tion and dephosphorylation of the spectrin-membrane coupling protein band IV.1. (cf. Figure 1). This is expected to result in the dynamic binding and unbinding of the spectrin-membrane linker which is associ-ated with the generation of defects in the hexagonal spectrin network (such as local pairs of +60° and -60° disclinations, corre-sponding to dissociated edge dislocations). As illustrated in the inset of Figure S.M.8 (at the upper left), this results in the formation of pairs of saddle like and conical caps and gives rise to an additional roughness of the tethered membranes.

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Figure S.M.8 Mean square amplitude of erythrocyte flicker spectra as function of the excitation wave vector (bottom abscissa) and wavelength (top abscissa)): the dots indicate experimental data for disco-cytes shapes and the stars for echinocytes (see urchin like shapes). The dashed curve is calculated by the two shell model (3). Note that the bilayer exhibits an excess area of about 10% with respect to the av-erage area of the cytoskeleton Inset at top left: Illustration of the Nelson mechanism of buckling of two-dimensional hexagonal teth-ered network by generation of +60° and -60° disclinations at a distance large compared to the mesh size of the tethered network (after Reference (5)) Flickering is a universal phenomenon. Membrane undulations are not unique for erythrocytes but have been observed also for numerous other cells, in particular white blood cells (6). This is remarkable, consider-ing the fact that the bending and shear moduli of these composite shells are κ≈1000kBT and μ~4 10-4 Jm-2 are thus much larger than the values for erythrocytes (10 kBT and 10-6Jm-2). This can be explained in

two ways. First, the thermally excited plasma membrane and the actin cortex are locally decoupled (e.g. between two talin mediated anchoring sites in Figure S.M.8) and the lipid-protein bilayer exhibits some excess area (with respect to the actin cortex). Sec-ond, the bending excitations are driven by non-thermal noise generated by the intracel-lular motions (6).

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The biological functions of flickering: Considering the ubiquitous presence of pas-sive and actively driven membrane bending excitations the question concerning its pos-sible biological function arises. One impor-tant consequence of membrane bending excitations is the generation of entropic dis-joining pressures (7). It is a consequence of the freezing-in of long wavelength modes if the membrane approaches a solid surface (or the cytoskeleton) to a distance which is smaller than the root mean square amplitude <u> of the bending excitations. It is of the order

3

2)(dTkp B

disj κ≈ (corresponding to pdisj.~

0.1N/m2 at d~100 nm, for κ ~ 25 kBT).

Three possible biological functions of the dynamic surface roughness of cell envelopes are summarized below.

1) It generates a disjoining pressure be-tween the two sub-shells of the erythrocyte cell envelope. Thus, their average distance (of d ≈ 30 nm) is controlled by the balance between pdisj and the attractive forces gener-ated by the coupling of the spring like linkers band IV.1 and ankyrin to the membrane proteins

2) The thermal excitations generate at-tractive isotropic forces between two membrane-cytoskeleton linkers (typically 1mN/m). One conse-quence is the generation of excess area of the PM with respect to the cytoskeleton (about 5% in erythro-cytes). The attractive forces between linkers are however balanced, result-ing in an isotropic distribution of the anchoring sites.

3) The undulation forces play impor-tant roles for the control of cell adhe-sion. It controls the swelling of lipids in water and prevents the sticking of cells to solid surfaces through non-specific forces. However, the en-tropic pressure also facilitates the formation of specific bonds between cell adhesion molecules (CAM) that are hidden within the glycocalix of the cells (8).

References to Supplemental Material G

1. Lipowsky R, Sackmann E. 1995. Handbook of Biological Physics, Vol. I. Elsevier: Amsterdam 2. Nelson DR, Peliti L. 1987. J. Phys. France 48:1085 3. Auth T, Safran SA, Gov N. 2007. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76:051910–9 4. Strey H, Peterson M, Sackmann E.1995. Biophys. J. 69:478-88 5. Gov N, Safran S. 2005. Biophys. J. 88:1859–74 6. Zidovska A, Sackmann E. 2006. Phys. Rev. Lett. 96:048103-7 7. Helfrich W. 1978. Z. Naturforschung. 33 a:305–15 8. Pierres A, Benoliel AM, Touchard D, Bongrand P. 2008. Biophys. J. 94:4114-22

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