Hierarchical self-assembly of actin bundle networks: Gels...

THE JOURNAL OF CHEMICAL PHYSICS 123, 104902 �2005�

Hierarchical self-assembly of actin bundle networks: Gels with surfaceprotein skin layers

Linda S. HirstMaterials Department, Physics Department, and Molecular, Cellular, and Developmental BiologyDepartment, University of California, Santa Barbara, California 93106

Roger PynnLos Alamos National Laboratory, New Mexico 87545

Robijn F. BruinsmaDepartment of Physics and Astronomy, University of California, Los Angeles, California 90095

Cyrus R. Safinyaa�

Materials Department, Physics Department, and Molecular, Cellular, and Developmental BiologyDepartment, University of California, Santa Barbara, California 93106

�Received 14 February 2005; accepted 26 May 2005; published online 9 September 2005�

The networklike structure of actin bundles formed with the cross-linking protein �-actinin has beeninvestigated via x-ray scattering and confocal fluorescence microscopy over a wide range of�-actinin/F-actin ratios. We describe the hierarchical structure of bundle gels formed at high ratios.Isotropic actin bundle gels form via cluster-cluster aggregation in the diffusion-limited aggregationregime at high �-actinin/actin ratios. This process is clearly observed by confocal fluorescencemicroscopy. Polylysine is investigated as an alternative bundling agent in the high-ratio regime andthe effects of F-actin length are also discussed. One particularly fascinating aspect of this system isthe presence of a structured skin layer at the gel/water interface. Confocal microscopy haselucidated the full three-dimensional structure of this layer and revealed several interestingmorphologies. The protein skin layer is a micron-scale structure composed of a directed network ofbundles and exhibits flat, crumpled, and tubelike shapes. We show that crumpling of the skin layerresults from stresses due to the underlying gel. These biologically based geometric structures maydetach from the gel, demonstrating potential for the generation of biological scaffolds with definedshapes for applications in cell encapsulation and tissue engineering. We demonstrate manipulationof the skin layer, producing hemispherical structures in solution. © 2005 American Institute ofPhysics. �DOI: 10.1063/1.1961229�

INTRODUCTION

The actin cytoskeleton provides a structural frameworkfor the mechanical stability of eukaryotic cells and a broadrange of cellular functions, including adhesion, motility, andcell division.1 In cells, actin is found both in a monomericglobular actin �G-actin, molecular weight �MW�=42 kDa�form or as actin filaments �F-actin�, comprising the polymer-ized G-actin subunits. Interactions between F-actin and actincross-linking proteins �ACPs� may lead to three-dimensional�3D� networks of F-actin imparting gel-like properties to thecytosol. Two-dimensional �2D� networks and bundles ofF-actin also interact with the plasma membrane to determinethe cell shape. Bundles, comprised of a closely packed par-allel arrangement of actin filaments, and networks, contain-ing actin filaments crisscrossed at some large angle, form themost common assembled structures of F-actin.1–3

F-actin is a semiflexible polyelectrolyte with a negativelinear charge density �−0.4 e /Å and a persistence length�10 �m.3 Actin filaments are bundled by the ACP,

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�-actinin, which has a width of �3.5 nm and a length of�33 nm.4,5 This “linker” molecule forms antiparallel dimerswith cationic actin-binding regions at each end6 and a totalMW of 204 kDa. �-actinin dimers behave like sticker mol-ecules and have been shown to bundle F-actin at �-actinin�dimer�/G-actin molar ratios �� of as little as 1 /90 at roomtemperature in vitro.7 Figure 1 shows a model of the struc-ture of an �-actinin/F-actin bundle. It has been shown bysmall-angle x-ray scattering �SAXS�7 that the internal struc-ture of these bundles exhibits a quasisquare packing arrange-ment.

In this paper we have studied F-actin mixed with�-actinin from low ratios �� of 1/100 up to the previouslyunexplored and opposite limit where F-actin is saturatedwith �-actinin at molar ratios of 1��20. In this very high�-actinin regime, the actin filaments and subsequently thebundles are effectively covered with 30 nm long linkers, or“stickers.” At a separation of �30 nm, the electrostatic re-pulsive force between the negatively charged actin rods isnegligible, and therefore the attractive �-actinin/actin inter-action dominates and bundling occurs. The rate of aggrega-tion for actin bundles is determined by the average time be-
tween collisions as observed in the case of diffusion-limited
© 2005 American Institute of Physics02-1

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http://dx.doi.org/10.1063/1.1961229

http://dx.doi.org/10.1063/1.1961229

http://dx.doi.org/10.1063/1.1961229

104902-2 Hirst et al. J. Chem. Phys. 123, 104902 �2005�

aggregation �DLA�. We define a new regime, where ��1. Inthis case, if a bundle in solution covered with stickers en-counters another, they will stick because the attractive energybetween bundles is much larger than the thermal energy re-quired to separate them.

We have found that for dilute actin concentrations��0.01 mg/ml� as � is increased to ��1, the �-actinin/actinsystem undergoes a transition from a fluid “sol” phase �on amacroscopic scale� to an isotropic gel phase of networkedactin bundles �i.e., a fully interconnected cluster extendingthroughout the sample�. The observed gel phase which wedescribe is distinct from the “microgels” observed in actinnetworks at low � ratios2 and also from the �-actinin/actingels studied extensively in the past at low values of � and viadifferent cross-linkers.8–13 This work is carried out mostly atvery high ratios of �-actinin/actin ��, where we observefascinating results.

One very interesting feature of this system is the pres-ence of dense skinlike structures formed on the surface of theisotropic bundle gel. This skin layer forms at the interfacebetween the bundle gel and the surrounding buffer solution.Laser scanning confocal microscopy �LSCM� has revealedthat on the submillimeter scale this skin layer, which may bedescribed as a quenched protein membrane, exhibits a rangeof morphologies including both flat and highly crumpledmembranes and tubelike structures. When the skin layer isexamined on a micron scale, confocal microscopy reveals adirected network of bundles, often highly oriented withbranching side arms. The idea that membrane wrinkling isdue to stresses resulting from the slow shrinkage of the un-derlying actin gel was introduced in a recent publication bythe authors.14 In this paper we now present a more in-depthanalysis of this process. The skin layers present a new classof quenched, yet flexible, protein membranes, irreversiblyproduced and thus far from equilibrium. This is in contrast toself-assembling equilibrium lipid membranes found in theform of spherical and cylindrical micelles, flat bilayers,15 andlipid tubules.16,17 The protein membranes are experimentalrealizations of quenched anisotropic tethered membranes

FIG. 1. Schematic of the internal structure of an �-actinin/actin bundleshowing a closeup of the molecular packing structure. The �-actinin mol-ecules �red� cross-link the long F-actin filaments �green� in a quasisquarearrangement.

with disorder due to random stress rather than thermal fluc-


tuations. Isotropic tethered membranes with random sponta-neous curvature and strain have received much theoreticalattention in recent years.18–20

We have found that the protein skin layers reported maydetach from the gel, an important feature for applications andstudy of their mechanical properties. As we now understandthe mechanism for the formation of the actin skin layer itshould be possible to replace F-actin with synthetic polyelec-trolytes or extracellular matrix fibers for applications requir-ing artificial skin or scaffolds with defined shapes and spe-cific receptors for cell attachment, migration, and growth intissue engineering.21 We present preliminary experimentswhich show the production of skin layers with synthetic ver-sions of the linker biomolecules, such as flexible lysinechains. This result demonstrates that the formation of thebundle gel and skin layers presented in this paper are notspecific to the protein �-actinin but will form at high con-centrations of nonspecific linker molecules where branchingoccurs. The skin layers are also capable of being molded forapplications and we show some first results in this direction,creating hemispherical shapes using colloidal particles.

The bundled actin gels we describe in this paper consti-tute a fascinating system, self-assembling with order onmany length scales. It is possible to form isotropic gels atvery dilute concentrations by allowing the system to aggre-gate in the diffusion-limited aggregation �DLA� regime, us-ing both the linker protein �-actinin and also the nonspecificlinker polylysine. The gel system generates a dense surfaceskin layer of actin bundles and this layer shows potential forbiomedical applications.

MATERIALS AND METHODS

Laser scanning confocal microscopy „LSCM…

G-actin fluorescently labeled with 488 nm Alexa fromMolecular Probes, Inc. �5 mM Tris-HCl pH 8.1,0.2 mM CaCl2 0.2 mM ATP, 0.2 mM DTT, and 10% w/vsucrose� was polymerized at 2 mg/ml, 100 mM KCl to alength of �10 �m for microscopy. The resultant F-actinmolecules were treated with phalloidin in a 1:1 molar ratio toG-actin to prevent depolymerization, then ultracentrifuged at100 000 g to pellet the filaments and remove the supernatantbuffer solution. The F-actin was then resuspended in Milli-pore water at 100 mM KCl. �-actinin and �-actinin labeledwith 568 nm rhodamine, �both supplied by Cytoskeleton,Inc.� were suspended in a 20 mM NaCl, 1 mM�-mercaptoethanol, 20 mM Tris-HCl pH 7.2, 5% sucrose,and 1% dextran buffer.

Small-angle x-ray scattering „SAXS…

Unlabeled G-actin �Cytoskeleton, Inc.� was polymerizedat 2 mg/ml, 100 mM KCl to a length of �3000 Å. TheF-actin filament length was controlled by adding the appro-priate amount of a 1 mg/ml solution of human plasma gelso-lin in a 150 mM NaCl, 2.7 mM KCl, 8 mM Na2HPO4,1.5-mM KH2PO4, 1 mM EGTA, pH 7.2 buffer �Cytoskel-eton, Inc�. The F-actin was stabilized with phalloidin in a 1:1molar ratio to G-actin. Varying molar ratios of unlabeled
�-actinin and actin were incubated at 100 mM KCl at room

104902-3 Hierarchical self-assembly of actin bundle networks J. Chem. Phys. 123, 104902 �2005�

temperature for 30 min before centrifugation for 15 min at11 000 rpm on an Eppendorf table-top centrifuge. The result-ant pellets were inserted into 1 mm quartz capillaries�Charles Supper, Co.� with the supernatant and were sealed.SAXS experiments were performed at beamline 4-2 of theStanford Synchrotron Radiation Laboratory at 11 KeV usinga FUJI-BAS image plate.

RESULTS

The �-actinin/F-actin bundle system has been studied onseveral length scales using different techniques. SAXS al-lows us to probe length scales below �100 nm �i.e., theinternal structure of a bundle�. For length scales between �1and 200 �m we have used laser scanning confocal micros-copy �LSCM�, and for length scales up to 1 mm we haveemployed fluorescence microscopy. These different tech-niques combine to produce a complete picture of the hierar-chical structure of this system.

FIG. 2. Small-angle x-ray scattering data for pelleted �-actinin/actin com-plexes at varying molar ratios of �-actinin to G-actin. Also shown are sche-matics of the molecular arrangement at low and high ratios.


Figure 2 shows the SAXS data for �-actinin/F-actinbundles ranging from the very low �-actinin/�-actin molarratio of �=1/100 to �=5. The data is presented as a functionof q and arbitrary intensity. At �=1/100 little scattering isobserved as this ratio is too low for bundle formation tooccur. Above �=1/50 macromolecular assemblies start toform, as shown by the increase in small-angle scattering, andby �=1/10 two distinct peaks are observed at q=0.19 and0.29 nm−1. These peak positions correspond to a distortedsquare packing arrangement inside the bundle �Pelletier etal.�. As the � ratio is increased still further up to �=5 we seethat the peak at q=0.19 nm−1 becomes more pronounced.This shows a slight increase in the packing order within thebundle, although the peaks remain relatively broad, indicat-ing a disordered filament arrangement inside the bundle.

In order to study the properties of the �-actinin/actinbundle system fluorescent samples were prepared for laserscanning confocal microscopy �LSCM�. Figure 3�c� shows abasic diagram of the sample preparation. In order to preservethe three-dimensional structure of samples as they aggregatea spacer is used between the glass slides. Samples were pre-pared by placing a 2 �l droplet of �-actinin in buffer solu-tion on the slide. This first droplet also contained the KClconcentration required for bundling to occur.A 2 �l droplet of F-actin solution was then added slowly tothe first droplet taking care not to mix the components and tominimize shear to the liquid. Samples were sealed and ob-served using fluorescence microscopy as the bundle struc-tures formed and aggregated. Different samples were pre-pared at varying � ratios and KCl concentrations.

At high � ratios one of the most striking macroscopicfeatures of the bundle assembly is the formation of a gel-likephase in solution, in contrast to the more sol-like behaviorobserved at low �. At low � actin bundles form and aggre-gate into a loosely connected three-dimensional networkwhich fills the sample droplet. This loose, branching networkcan be observed via fluorescence microscopy to flow like aliquid. At high �, however, the actin filaments in solutionform bundles which appear notably thicker �due to their in-creased brightness under the fluorescence microscope�,which then aggregate into a polymer gel suspended in the

FIG. 3. �a� Fluorescence microscopyimages of �-actinin/F-actin complexesat low magnification at varying � ra-tios demonstrating the transition fromsol to gel. All images shown are com-plexes formed at 100 mM KCl. Alsoshown is �b� a phase diagram for thistransition as a function of monovalentsalt concentration and �c� a schematicof the sample geometry formicroscopy.



center of the droplet. This gel is composed of a loose inter-connected branching network of thick bundles, which main-tains a fairly rigid shape inside the droplet. The gel does notflow and exhibits solid properties, retaining distinct macro-scopic structures. All fluorescent actin in the initial sampledroplet appears to fully separate from the buffer solution toform the gel.

Figure 3�a� shows low-magnification fluorescence im-ages of �-actinin/F-actin bundle complexes formed using themethod described above at different � ratios and clearlydemonstrates the macroscopic features. At the low ratio �=1/4 on a macroscopic scale we see a sol-like behavior. Thebundle solution fills the droplet and no permanent structuralfeatures are observed. This complex represents a loose net-work of bundles. It is clear, however, that bundles arepresent, from both x-ray studies �see Fig. 2� and higher-resolution microscopy. As the proportion of �-actinin in thecomplex is increased, gel-like structures form and separateout from the buffer solution. At �=1 some structural featuresare observed; however, the network is still observed to flowso this ratio is defined as intermediate between the gel andsol states. If the amount of �-actinin is increased further to�=2 and above, the complex no longer flows and exhibitspermanent structures; we define this as the gel state. Alsoshown in Fig. 3�b� is a simple phase diagram for complexesformed at different � ratios as a function of monovalent saltconcentration. It is clear that the transition from sol to gel isnot a sharp one, but occurs gradually with a large range inwhich the complexes exhibit both sol and gel-like properties.The x axis on this graph indicates the KCl concentration inthe complex and does not include any other salts in thebuffer solutions used. In fact, 20 mM NaCl is present at allKCl concentrations shown. It is interesting to note that atKCl concentrations less than �100 mM no intermediate gel/sol state is observed.

In order to understand the formation of these gel-likestructures and their interesting morphologies the 3D internalstructure of the aggregates was probed via the confocal mi-croscope. In using this technique we are able to examinethree-dimensional �3D� bundle arrangements without apply-ing any external force to the sample and risking stress-induced shrinkage.

Figure 4 shows two projections of 3D confocal datataken from the gel bundle arrangement at �=10 showingtypical structures observed in the sample. At this high�-actinin/G-actin ratio, thick bundles are observed and alocked-in branching structure is observed, forming a fullyinterconnected 3D network. This figure demonstrates the twotypical bundle arrangements observed in the gel: �Fig. 4�a��an isotropic network of bundles and �Fig. 4�b�� a network inwhich many long bundles are aligned and cross-linked in aladderlike fashion by their branching side arms. The isotro-pic structure is typically observed in the bulk of the gel, withaligned structures often occurring on the surface, i.e., at thegel/water interface. These aligned structures most likelynucleate due to the localized alignment of single filaments inthe initial stages of aggregation.

Polymer gelation as an aggregation process has been22–25
treated theoretically by many authors. Gelation can oc-

cur in two extreme limits: weak �reversible� gels may havetheir cross-links broken by thermal motion, whereas strong�irreversible� gels form permanent bonds. Reversible gela-tion has been theoretically explored via percolation theory;24

however, this treatment does not consider the growth or mo-bility of clusters in solution.

In order to study the aggregation process involved in theformation of this isotropic bundle gel, the 3D LSCM datawas taken for a region of the isotropic gel and the structurefactor �S�q�� was determined using a 3D fast Fourier trans-form �FFT� on the LSCM data for a highly aligned regionand a region displaying isotropic ordering. A slice from the3D FFT was extracted from the center of the volume in thex-y plane and radial line profiles were taken. These wereaveraged radially about the origin or in the x and y directionsas a function of spatial frequency. By plotting the powerspectrum obtained on a log/log plot, a regime with slope 1.72was observed for the isotropic sample �Fig. 5�.

Although classical percolation models do predict a simi-lar exponent of �1.7, it is clear experimentally that an irre-versible cluster-cluster model26 is more appropriate here. Theaggregation process observed involves F-actin filaments andbundles covered with an excess of �-actinin. In this case

FIG. 4. Fluorescence confocal microscopy images of an �-actinin/actinbundle network at �=10 with isotropic ordering �a� and anisotropic ordering�b�.

whenever bundles or clusters of bundles encounter each



other in solution they will stick. The gel is irreversible and,in fact, gentle shaking will cause the gel to shrink as fluctua-tions in the network increase. Optical microscopy shows thatthe homogeneous irreversible aggregation of bundles in thisregime leads initially to many small clusters, and furthercluster growth occurs due to the aggregation of clusters ofbundles of comparable size.

This result is consistent with the slope predicted forcluster-cluster aggregation in an irreversible gel,27,28 wherethe isotropic network of bundles forms as a result of theaggregation of smaller bundle clusters, which diffuse freelyin solution, meet other clusters, and stick.

An analysis was also carried out on an aligned volume,with additional curves plotted for intensity profiles in the xand y directions. A similar S�q� linear regime was observedin this anisotropic sample, with slightly smaller exponents.

It should be commented upon that the binding of thecross-linker �-actinin is commonly accepted to be weak29

and therefore a reversible bond; however, at high �-actininconcentrations the macroscopic structures formed are ob-served to be irreversible. This phenomenon can be explainedby considering cross-linker density inside the bundle. At lowcross-linker concentrations, the local �-actinin density insidethe bundle will be low and the dissociation of a few adjacentcross-linkers may be enough to allow a rearrangement of thestructure. However, if a high density of cross-linkers are in-volved in the structure of a bundle, i.e., at high �-actininconcentrations, the less likely they are to all dissociate simul-taneously and allow a rearrangement of the structure.

The formation of a branching network of bundles is notspecific to the �-actinin-bundled system but also occurs forother nonspecific linker molecules. Polylysine is a polymerformed from the positively charged lysine subunit. This poly-mer will bundle F-actin molecules by nonspecific electro-static interactions and produces similar 3D network struc-tures at comparable ratios to the �-actinin work describedabove. Different polylysine lengths were investigated and itwas found that network structures formed for polylysines
ranging from MW=260 kDa down to a chain of just four

lysine subunits. Bundle systems produced with mono anddivalent salts, however, do not form gels, and a connectednetwork does not form.7 These systems have a much lowerincidence of branching and always display a sol-like behav-ior.

An important parameter in the formation of the actinbundle gel is the length of the F-actin molecules used. Bypolymerizing G-actin in the presence of human plasmagelsolin, an actin-severing and capping protein, one is able tocontrol the average filament length by adjusting the gelsolinconcentration. As shorter F-actin is used to form the bundlenetwork the average mesh size of the network is also re-

FIG. 6. 2D projections of �4 �m-thick LSCM images of actin bundlesformed with �a� 300 nm F-actin and �-actinin at �=5, �b� 300 nmF-actin and polylysine �MW=30–70 kDa� at �=5, �c� 100 nm F-actin andpolyLysine �MW=30–70 kDa� at �=1, and �d� 30 nm F-actin and �-actinin

FIG. 5. Power spectrum analysis of anexample isotropic �a� and an aligned�b� volume in an actin bundle gel. Ineach case the radially averaged inten-sity of the 3D FFT is plotted as a func-tion of spatial frequency and shownwith a 2D projection of the 3D volumeused and a slice of the 3D FFT. Alsoshown for �b� are intensity profiles inthe x and y directions.

at �=5.



duced. Figure 6 shows LSCM images of both �-actinin andpolylysine bundled systems using different F-actin lengths. Itcan clearly be seen that the mesh size in the isotropic gelnetwork decreases significantly as actin length decreases. ForF-actin 10 �m in length the mesh size is large at 10–20 �m,as seen in Fig. 4, but for 0.3 �m actin filaments this meshsize is clearly reduced �Figs. 6�a� and 6�b��. In Fig. 6�c�,100 nm F-actin produces a network with a very small meshsize. When filaments as short as 0.03 �m are used to prepare

FIG. 7. Two examples of the skin layers which form on the surface of theactin bundle gel. These images were taken using fluorescence confocal mi-croscopy and then reconstructed three-dimensionally.

FIG. 8. LSCM cross sections of 3D data for two different actin bundle gel
bundles at �=10 and �b� shows data for �=1 bundles formed using polylysine �

a gel, a different structure is observed to form, bundles showan extremely high rate of branching, and the network clumpstogether into large aggregates which themselves form a loosenetwork. The networks formed from polylysines show asimilar behavior to those formed using �-actinin as the linkermolecule.

As the actin gels presented in this paper form, one of themost striking features of their structure is the presence of thedenser skin layer which forms on the gel surface at the in-terface between the 3D network of actin bundles and theremaining buffer solution. This skin layer can vary in thick-ness from around 10 �m to the thickness of one bundle andis composed of a denser network of actin bundles to theunderlying gel. Figure 7 shows 3D renderings �carried outusing Voxblast by Vaytech� of a small area of the surface oftwo typical gel samples. The denser skin layer is obvious atthe gel/water interface. Beneath the skin layer the isotropicnetwork of bundles can be seen. Skin layers are observed inboth the �-actinin and polylysine systems studied in this pa-per, and the presence of this feature is dependent on thelength of the actin filament.

Figure 8 shows data taken with the confocal microscopeof actin bundle gels formed from different filament lengths.For filament solutions with an average length of 10 and0.3 �m the dense skin layer previously reported clearlyforms on the surface of the gel as can be seen from thecross-sectional views �Fig. 8�a��. Interestingly, samples pre-pared from filaments �0.1 �m and below did not exhibit theskin layer at the gel/water interface �Fig. 8�b��. In this imagethe actin bundle network has clearly formed; however, noextra material is present on the surfaces of the gel.

A key feature of these actin bundle gels leading to thewrinkled skin layer on the surfaces is the fact that the gelsundergo a short shrinking phase after formation. The rate anddegree of this shrinkage appear to depend on the nature ofthe linker protein, as depicted in Fig. 9, although this rela-tionship requires further investigation. Gels were prepared

shows a typical skin layer on the surface of a gel formed using �-actinin
s. �a� 30–70 kDa� with 100 nm F-actin where no skin layer is observed.


using both �-actinin and a polylysine �MW of 70–150 kDa�.It is immediately obvious from these images that in bothcases the gel shrank noticeably after formation. It is striking,however, that the sample formed with polylysine showedmuch more rapid and pronounced shrinkage than the�-actinin sample. In the polylysine sample the wrinkled skinlayer can clearly be seen around the outer edge of the gelcrumpling inwards over time.

In addition to this initial period of shrinkage, gels can beinduced to shrink further by gentle shaking or by physically“prodding” the surface �gel/water interface�. Each bundle iseffectively coated in �-actinin molecules as there is an ex-cess of sticker molecules in solution, so when two bundlesare pushed together they have a high probability of sticking.By applying stresses to the gel or by gently shaking, thenetwork can be forced to shrink and bundles will stick toeach other if they come into contact. Thus the gel shrinksirreversibly due to the action of the sticker molecules.

DISCUSSION

Model for the formation of crumpled skin layers

We propose a brief model to represent the crumpling ofthe skin layer, which occurs as the underlying gel shrinks.The schematic in Fig. 9 demonstrates the basic steps in theformation of the gel over time. Initially, bundles form freelyin solution and, by branching sidearm interactions, will ag-gregate into small clusters. These clusters then continue toaggregate until almost all free actin material is incorporatedinto the 3D network of bundles. As the basic unit of aggre-gation here is a long macromolecule, after gelation manyloose ends will protrude from gel into the buffer solution,fluctuating due to thermal motion. These free ends are stickyand, eventually through fluctuations, will contact the gel sur-face and attach, forming a denser layer on the surface. Thismechanism of formation is supported by the observation thatthe skin layer is absent if very short filaments are used. Inaddition, any actin filaments and bundles still free in solutionwill end up on the gel surface, as it is unlikely that they will
penetrate into the interior of the gel before making contact

FIG. 10. A 3D reconstruction and cross-sectional view of LSCM fluores-cence data for a membrane which has become detached from the bulk

FIG. 9. Two different time series dem-onstrating the shrinkage of actinbundle gels. The upper series shows agel formed using �-actinin at �=5.The lower series shows a gel formedusing polylysine �70–150 kDa� at �=5. The cartoon below breaks the ag-gregation process into stages.

sample. The locked-in wrinkled structure is seen clearly in both views.



with the denser network on the surface. Once the dense skinlayer has formed on the surface of the gel, it is relativelyincompressible compared with the gel interior. The shrinkageof the gel interior then results in buckling of the surface layerdue to the resultant lateral forces on the anchored membraneas the isotopic interior reduces in volume. The wrinkled skinwhich forms on the gel surface is reminiscent of the work byTanaka et al.,30 in which they observed a wrinkled surfacelayer forming on the surface of a swelling polymer gel at theair interface. The phenomenon which we observe, however,is quite different in origin; it is formed by a different mecha-nism at the gel/water interface due to gel shrinkage, and noregular pattern is observed.

The volume of classical polymer gels can be modified bysubtle changes in pH,31 temperature,32 or solvent composi-tion; however, such phase transitions are reversible. In thecase of the actin bundle gel described here, the shrinkage isobserved to be irreversible. A mechanism for this shrinkagecan be understood by considering thermal fluctuations ofbundles in the gel.33 The bundles will fluctuate strongly be-tween link points and as these bundles are covered in stickermolecules, if they come close enough to other bundles theywill stick. This process occurs throughout the entire gel re-sulting in a gradual reduction in volume and continuing untilthe gel reaches a quasi-equilibrium state, where the magni-tude of bundle fluctuations is not great enough to result inadditional “sticking” events. We do not believe that osmoticeffects play a strong role in gel shrinkage. The skin layer,
while dense compared with the interior of the gel, has a mesh

size on the order of 1 �m and allows both excess �-actininand buffer solution to pass freely into the gel.

We can describe the wrinkling of a section of membranewith length L and wave vector k by balancing the free ener-gies of the bulk and surface regions. By minimizing this freeenergy we can then obtain the expression k��E /��1/3, whereE is the bulk elastic modulus and � is the bending modulusof the skin layer. This result suggests that as the gel networkincreases in density, the bulk elastic modulus E also in-creases, and therefore the wavelength of buckling decreases.This result is evident from the wrinkled skin layer on thepolylysine gel shown in Fig. 8. As the volume of the geldecreases the skin layer clearly becomes more wrinkled.

Applications

The crumpling skin layer which forms on the gel surfaceis an example of a quenched protein membrane. The struc-ture of the membrane, once formed, is irreversible, and oneparticularly interesting feature of this system is the ability ofthe membrane to detach from the bulk gel. Figure 10 showsan example of a section of a membrane which has detachedfrom the bulk material. In this figure a 3D rendering isshown together with the LSCM cross-sectional data. Themembrane has a permanent wrinkled shape as the structure is“locked in” due to the networking of the bundles. No mac-roscopic fluctuations are observed over time, although indi-vidual bundles do continue to fluctuate in between linkpoints.

FIG. 11. Two examples of tubelikestructures formed on the surface of anactin bundle gel imaged via a fluores-cent LSCM. �a� 3D reconstructions ofa sample edge with a prominentwrinkled skin layer forming minitubes on the surface and �b� two dif-ferent cross-sectional views of thisstructure. �c� shows an example of avery large tube structure forming as asection of protein membrane tears offfrom the bulk sample and curls up.

Another interesting morphology which the membranes



may adopt is a tubular structure. As a gel shrinks and the skinlayer wrinkles on the surface, highly aligned areas will be-have differently to isotropic areas. The aligned areas on thesurface of the gel essentially consist of two different bendingmoduli being stiffer in the direction normal to the directionof alignment. Long bundles are often seen cross-linked into aladderlike structure, and these weaker cross-links allowbending to occur in a preferential direction. Examples of theresult of this process are shown in Figs. 11�a� and 11�b� inthe form of tubes. The wrinkled surface in an aligned regionhas buckled in one direction to form several minitubularstructures on the surface of the gel. Figure 11�c� shows howcurling can occur on a much larger scale. This partial tube,around 200 �m wide, is starting to form as a large section ofmembrane tears off from the bulk and curls in on itself. Asthe material in these situations is saturated with sticker mol-ecules, a skin layer curling in on itself may stick in thatposition to form a permanent tube structure.

The different structures which can form from these pro-tein skin layers could possibly be manipulated for applica-tions in the field of biotechnology and tissue engineering.The networked membrane has a mesh size on the order of thesize of a cell and is biocompatible, depending on the linkermolecule. For such applications it would be necessary tocontrol the shape of the membrane. This is possible as dem-onstrated in Fig. 12. A fully enclosed tube structure is shown,which was observed to from spontaneously; we hope to pro-duce such structures by manipulation. By forming the skinlayer over a surface with the required morphology and sur-face properties, in this case negatively charged colloidalbeads �Fig. 12�, the membrane will take on the shape of thatsurface to retain the shape. Such a membrane can then be

FIG. 12. Laser scanning confocal microscopy data of �a� a fully detachedtube, with three cross sections shown and �b� a skin layer on the actin gelsurface, formed around two 21 �m colloidal particles. �b� and �c� show twodifferent cross sections in the x-y plane; �d� and �e� are perpendicular cutsthrough the volume as marked on �c� �the upper line on �e� corresponds tothe z position of image �c� in the volume and the lower line to image �b�.

removed after stabilization. It will be possible to form these


molded networks using either actin or a synthetic polymerand suitable linker molecules as a specialized framework forcell growth.

CONCLUSION

Novel protein membrane structures resulting from theaggregation of F-actin with a high concentration of the cross-linking protein �-actinin have been observed and investi-gated. These skin layers form on the surface of the actin gelcomprised of an isotropic network of actin bundles. The skinlayers themselves consist of a network of aligned actinbundles. They exhibit many interesting morphologies, in-cluding pleated or flat sheets and tubules resulting from theshrinkage of the underlying bundle network. The skinlikelayers are also observed to form using different polylysinemolecules, although this behavior is not observed for diva-lent bundling alone.

For aggregation to occur, as described in this paper, twoimportant processes must be considered. Firstly, the stickermolecules chosen ��-actinin and polylysine� should not sim-ply allow the actin filaments to aggregate in any direction butmust firstly induce bundling. Secondly, that bundles grow toa finite size and then aggregate with each other via stickermolecules and branching sidearm interactions. A cluster-cluster aggregation process in the DLA regime seems themost accurate for this system.

Two common mechanisms leading to large-scale hierar-chical structures in biological systems include self-assemblyat thermal equilibrium �case 1�, such as lipid self-assemblyand out-of-equilibrium energy dissipative biomolecular as-sembly and disassembly involving hydrolysis of high-bond-energy molecules ATP or GTP �case 2�. In the latter systems,the structures may reach a steady-state structure, which areinfluenced by kinetic parameters, concentrations of relevantmolecules, and solution conditions. The protein membranesthat we have described present a third paradigm for self-assembly. The protein membranes are assembled through ir-reversible aggregation at an interface. The hierarchical struc-ture is now out of equilibrium �like case 2�, even thoughdissipation is absent �unlike case 2�.

The semiflexible protein-membrane skin layers mayhave applications in cell manipulation, either on the gel sur-face or detached in solution as these delicate protein mem-branes are highly compatible with living systems. The skinlayers will adopt different shapes, both spontaneously and bycontrolled manipulation, and such structures, including syn-thetic analogs, could be formed as biological scaffolds toencapsulate or compartmentalize cells or to provide a back-bone for 3D tissue growth in tissue engineering applications.

ACKNOWLEDGMENTS

This work was supported by the NIH, Grant No. GM-59288 and the NSF Grants No. DMR-0203755, No. DMR-0503347, No. CTS-0404444, and No. CTS-0103516. Sup-port was also provided by Los Alamos National Laboratory,
University of California Grant No. 45909-0012-2P. SAXS


was conducted at the Stanford Synchrotron Radiation Labo-ratory �supported by the Department of Energy�. The Mate-rials Research Laboratory at the UCSB is supported by NSFGrant No. DMR-0080034.

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