RESEARCH ARTICLE

Relating Cell and Tissue Mechanics:Implications and ApplicationsKaroly Jakab,1† Brook Damon,1,2 Francoise Marga,1 Octavian Doaga,2 Vladimir Mironov,3

Ioan Kosztin,1 Roger Markwald,3 and Gabor Forgacs1,4*

The Differential Adhesion Hypothesis (DAH) posits that differences in adhesion provide the driving forcefor morphogenetic processes. A manifestation of differential adhesion is tissue liquidity and a measure forit is tissue surface tension. In terms of this property, DAH correctly predicts global developmental tissuepatterns. However, it provides little information on how these patterns arise from the movement and shapechanges of cells. We provide strong qualitative and quantitative support for tissue liquidity both in truedevelopmental context and in vitro assays. We follow the movement and characteristic shape changes ofindividual cells in the course of specific tissue rearrangements leading to liquid-like configurations. Finally,we relate the measurable tissue-liquid properties to molecular entities, whose direct determination underrealistic three-dimensional culture conditions is not possible. Our findings confirm the usefulness of tissueliquidity and provide the scientific underpinning for a novel tissue engineering technology. DevelopmentalDynamics 237:2438–2449, 2008. © 2008 Wiley-Liss, Inc.

Key words: Differential Adhesion Hypothesis; tissue liquidity; tissue surface tension; multicellular aggregate; spheroid;cell adhesion; cytoskeleton

Accepted 25 June 2008

INTRODUCTION

Embryonic development represents acomplex schedule of events throughwhich a living organism acquires itsfinal shape. All these events are undergenetic control. However, genes bythemselves do not create forms andshapes: physical mechanisms do.Genes set up the inherent physicaland chemical properties of cells, extra-cellular matrix and tissues. These inturn generate forces, which drivestructure formation and cause subse-quent alterations in gene activity. It isthis delicate interplay of genetic, mo-lecular and physical factors that con-stitutes the evolving modern under-

standing of early morphogenesis(Hove et al., 2003; Farge, 2003; For-gacs and Newman, 2005; Lecuit andLenne, 2007; Ninomiya and Win-klbauer, 2008). A specific patternforming mechanism where this inter-play has extensively been studied isdifferential cell affinity. This mecha-nism underlies segregation of cell pop-ulations and the formation of com-partment boundaries (Irvine andRauskolb, 2001). The Differential Ad-hesion Hypothesis (DAH; Steinberg,1963) explains such morphogeneticprocesses in terms of cell motility com-bined with differences in tissue affin-ities. The validity of DAH has been

demonstrated both in vitro (Foty etal., 1996; Forgacs et al., 1998; Duguayet al., 2003; Foty and Steinberg, 2005;Schotz et al., 2008; Ninomiya andWinklbauer, 2008) and in vivo (Godtand Tepass, 1998; Gonzalez-Reyesand St Johnston, 1998; Hayashi andCarthew, 2004). Numerous molecularsignals have been identified that con-trol differential cell affinities (Tepasset al., 2002). On the other hand, dif-ferences in tissue affinities can bequantified in terms of differences intissue surface tension, a physical ma-terial constant characteristic of liq-uids. Indeed, it has been demon-strated that embryonic tissues in

1Department of Physics and Astronomy, University of Missouri, Columbia, Missouri2Department of Biophysics, “Carol Davila” Medical University, Bucharest, Romania3Department of Anatomy and Cell Biology, Medical University of South Carolina, Charleston, South Carolina4Department of Biology, University of Missouri, Columbia, Missouri†Dr. Jakab’s present address is Department of Cell Biology, University of Virginia, Charlottesville, Virginia.*Correspondence to: Gabor Forgacs, Department of Physics and Astronomy, University of Missouri, Columbia, MO, 65211.E-mail: forgacsg@missouri.edu

DOI 10.1002/dvdy.21684Published online 26 August 2008 in Wiley InterScience (www.interscience.wiley.com).

DEVELOPMENTAL DYNAMICS 237:2438–2449, 2008

© 2008 Wiley-Liss, Inc.

many respects behave analogously toliquids (Steinberg and Poole, 1982). Innonadhesive environments irregulartissue fragments round up to form aspheroid (Foty et al., 1996), just asliquid drops do in the absence of ex-ternal forces. The final equilibriumconfiguration of a random mixture oftwo distinct cell types is akin to that ofphase separated immiscible liquids(e.g., oil and water): the two cell typessort, and a spheroid of the more cohe-sive cells forms within a spheroid ofthe less cohesive cells (Steinberg andTakeichi, 1994; Foty et al., 1996; Bey-sens et al., 2000). If the two cell typesform tissues that are contiguous innormal development, the sorted pat-tern corresponds to the arrangementthat these tissues assume under phys-iological conditions (Steinberg, 1970;Technau and Holstein, 1992). Appar-ent surface tensions have been mea-sured for several embryonic tissueswith results in complete agreementwith observed sorting patterns (Fotyet al., 1996; Davis et al., 1997; Duguayet al., 2003; Foty and Steinberg, 2005;Schotz et al., 2008). Computer simula-tions based on tissue liquidity havereproduced predictions by DAH (Gla-zier and Graner, 1993).

According to the liquid analogy then,compartments and boundaries form asthe more cohesive cell populations (ofhigher surface tension) sort out or sep-arate from the less cohesive ones (oflower surface tension). Such configura-tions are maintained as long as the ge-netically controlled difference in surfacetensions exists. As development pro-ceeds, molecular signals (i.e., changes ingene expression controlling cell adhe-sion) lead to changes in surface tension(Foty et al., 1996; Ninomiya and Win-klbauer, 2008), which in turn result inaltered tissue pattern. The arising me-chanical signals elicit new molecularsignals (Farge, 2003; Lecuit and Lenne,2007).

We asked the question whether tis-sue liquidity represents solely a con-venient heuristic mechanical descrip-tion of equilibrium tissue patterns ora tissue-level manifestation of thecomplex mechanical behavior of cellsimpacting morphogenetic processes(such as convergent extension [Keller,2002], establishment of planar polar-ity [Mlodzik, 2002], or cellular rosetteformation [Blankenship et al., 2006]).

Specifically, we addressed the follow-ing questions. (1) Can the analogy be-tween tissues (composed of motile andadhesive cells) and liquids, observedin equilibrium tissue configurations,be extended to the time dependentprocess of approaching equilibrium?(2) How can the formation of the ob-served liquid-like tissue configura-tions be reconciled with the motionand shape changes of individual cellsthat lead to these configurations? (3)Can the tissue-liquid analogy provideinformation that cannot be obtainedby other means? To answer the firstquestion, we studied tissue fusion(Perez-Pomares and Foty, 2006) intrue developmental context. We con-sidered the fusion of embryonicchicken cardiac cushions, the morpho-genetic process that underlies the for-mation of septa and valves in earlyheart development (Wessels and Sed-mera, 2003; de la Cruz and Markwald,1998). To answer the second question,we followed fusion in time in a con-trolled in vitro assay using well-char-acterized cell lines (genetically trans-formed Chinese Hamster Ovary[CHO] cells). Individual cellularmovement and shape changes werealso studied and quantified in thecourse of equilibration of deformed(i.e., compressed) cell aggregates (i.e.,model tissues). These studies revealedthat the final fused or postcompressedstates indeed are liquid-like. Of inter-est, even the approach to the finalstates resembles equilibration in liq-uids. Upon more detailed analysis,however, we found that in tissues therelaxation to equilibrium is drivenpredominantly by cell shape changes,a unique property of living systemswith no analogy in liquids. To answerthe third question, we measured bio-physical properties that quantify therelaxation process at the tissue leveland related them to molecular entitiesthat control the relaxation process atthe cellular level.

RESULTS

Manifestation of TissueLiquidity in EarlyDevelopment: The Fusion ofCardiac Cushions

In the chicken, the heart begins toform during the second day of devel-

opment from a crescent-shaped regionof tissue derived from the splanchnic(i.e., inner body tube) mesoderm at thehead or cranial end of the embryo. Theprimitive heart tube that subse-quently forms contains two epitheliallayers: the inner endocardium and theouter myocardium (Manasek, 1968).The two layers are separated by anextracellular matrix known as the car-diac jelly. Formation of the septa andvalves that separate the four cham-bers of the heart is initiated at specificsites of the endocardium by swellingsknown as the cardiac cushions andproceeds by their fusion and an asso-ciated epithelial–mesenchymal tran-sition (Wessels and Sedmera, 2003; dela Cruz and Markwald, 1998).

We followed this morphogeneticprocess both in vitro and in vivo. Ourfindings are summarized in Figure 1.We extracted cardiac cushion tissuefrom 5-day chick embryos (Hamburg-er-Hamilton [HH] stage 27). When theirregular-shaped tissue explants wereincubated in tissue culture mediumin hanging drop configuration theyrounded up into almost perfect spher-ical shape (Fig. 1A). This observationsuggests that these tissues have prop-erties in common with liquids in thatthey minimize their interfacial areawith the surrounding. Next, we fol-lowed the fusion of two contiguouslyplaced similar sized round-up ex-plants in time (selected images in Fig.1B). We found that the in vitro processstrongly resembles the in vivo process,the latter being observed by recordingthe instantaneous configuration of thefusing cushions after extraction, atregular time intervals (Fig. 1C). Itneeds to be emphasized that the invitro and in vivo processes initiallyinvolve the same tissues. The quanti-tative analysis of the in vitro fusion(Fig. 1B), presented in Figure 2, re-vealed that both the final fused pat-tern and the approach to it are liquid-like. (For details of the quantitativeanalysis see the Discussion section.)

Direct Observation ofCellular Movement

The two cardiac cushion spheroidseventually fuse into a single spheroid.This is consistent with the property ofliquids, which under no external

RELATING CELL AND TISSUE MECHANICS 2439

forces evolve into a state with minimalinterfacial area (i.e., a sphere). To an-alyze more directly the movement ofindividual cells in the course of tissuerearrangements we first studied thefusion of spherical cell aggregatescomposed of genetically transformedCHO cells with fixed average numberof N cadherins (see the ExperimentalProcedures section). (We used CHOcell aggregates, instead of the cushiontissue spheroids because the lattercontain several cell types, such as car-diomyocytes, endothelial cells and fi-broblasts, as well as extracellular ma-trix. The heterogeneity of thesespheroids makes the observation of in-dividual cells difficult, a problem wecould avoid by using a cell line.) Usingdifferential staining of the cells in thetwo aggregates we followed the timeevolution of the cellular pattern. Re-sults in Figure 3 show that eventhough the final equilibrium state ofthe system is liquid-like (i.e.,rounded), the distribution of cells in itis not. Cells move minimally acrossand along the interface between thefusing aggregates, just enough to fa-cilitate the formation of a final statewith minimal surface area. The fully

coalesced state of two true liquiddrops is characterized by the completemixing of molecules.

Next, we compressed the samespherical aggregates between parallelplates and studied the movement ofindividual cells in the postcompres-sive relaxation process. Compressionswere performed with control aggre-gates and aggregates pretreated withlatrunculin A, an F-actin destabilizingagent (Coue et al., 1987; Fig. 4). (Be-cause the actin cytoskeleton partici-pates in numerous cell functions, itsdisruption by latrunculin may have ef-fects beyond cell adhesion. We choselatrunculin A because it is specific foractin and it is a widely used tool in cellbiology when the consequences of cy-toskeletal disruption on adhesion orcell movement are to be evaluated.)Such compressive deformation, towhich embryonic tissues are often ex-posed, causes increase in area. Thearea of a true liquid drop increases (ordecreases) by the migration of theloosely bound mobile molecules fromthe bulk to the periphery (or viceversa). In contrast, the surface area ofan elastic solid increases (or de-creases) mostly by the stretching (or

contraction) of bonds between the im-mobile molecules or atoms.

To determine which of these mech-anisms is responsible for the increasein surface area, aggregates were opti-cally sectioned perpendicular to thedirection of compression (taken as thez axis) and the x–y displacements offluorescently labeled cells (constitut-ing 10% of all cells) followed by confo-cal microscopy. Images, acquired indifferent sections at regular time in-tervals (every 2 min), were stacked toform layers (with thickness of approx-imately one cell diameter) within theaggregate at different depths. Figure5 shows the mean radial displacement(within the x–y plane), as function oftime, of cells moving outward (towardthe periphery of the aggregate) andinward (toward the interior of the ag-gregate) within different layers. Themean was calculated over all fluores-cent cells within the layer. In the ab-sence of latrunculin the mean result-ant postcompressive displacementswere more or less uniform across theshown layers and in each layer cellsmoved preferentially toward the pe-riphery (Fig. 5, left column). This ob-servation suggests that the aggregaterelaxed to its new equilibrium state(with increased area) similarly to aliquid drop. Upon latrunculin treat-ment, the extent of outward radial dis-placement was larger than in controlaggregates close to the periphery andthe resultant displacement dimin-ished rapidly with increasing depthinto the aggregate (Fig. 5, right col-umn). Because these experiments

Fig. 1. Apparent liquid-like properties of embryonic cushion tissue. A: An irregular cushion tissuefragment, excised from 5-day (Hamburger and Hamilton [HH] stage 27) chick embryo rounds upinto a spheroid in approximately 24 hr. B: Two contiguous spheroids in culture medium, in hangingdrop configuration, fuse in time (indicated in minutes). Note that the interface between the twofusing drops has circular geometry. C: In vivo cushion tissue fusion during chicken heart devel-opment. Panels from the left image (4.5 day, HH stage 26 embryo), show the gradual blending ofthe two atrioventricular cushion tissues. Fusion is complete by day 5.5 (HH stage 28). Scale bars �100 �m.

Fig. 2. Quantitative characterization of the fu-sion process. Points represent the measuredvalues of the (square of the) quantity shown inthe inset, obtained form the series of snapshots(partially) shown in Figure 1. The line over thedata is the result of a fluid-dynamical analysis(for details, see the Discussion section).

2440 JAKAB ET AL.

were performed at room temperaturepostcompressive relaxation is slowerthan at 37°C (compare with the relax-ation of aggregates in Fig. 7). (Notethat these experiments were per-formed with no latrunculin in the cul-ture medium, see the ExperimentalProcedures section.)

Because only the nuclei of cells werefluorescently labeled, compression ex-periments by themselves did not pro-vide information on the evolution of cellshape during the postcompressive re-laxation process. To gain such informa-tion field emission scanning electronmicroscopy (FESEM) was used. In Fig-ure 6, we present FESEM images andschematic drawings of individual cellsin a precompressed, compressed, andpostcompressed equilibrated aggregate.The schematic representation (Fig.6C) illustrates that immediately aftercompression a pressure gradient (sim-ilar to that in a compressed elasticsphere; Egholm et al., 2006) is set up,because cells in the vicinity of thecompressive plates and toward thevertical axis of symmetry of the com-pressed aggregate are deformed re-spectively more strongly than thosenear the equator and side boundary(Fig. 6D). The pressure difference,which itself favors the outward migra-tion of cells is eliminated by the end ofthe relaxation process, as can be de-duced from the recovery of precom-pressed cell shape (Fig. 6E,F). Phillipsand coworkers arrived at similar con-clusions by analyzing cellular pat-

terns in aggregates compressed bycentrifugation (Phillips et al., 1977).(Note that in an elastic sphere thepostcompressive pressure gradientwould not change in time.) As theschematic panels in Figure 6 suggest,overall aggregate shape (and thus vol-ume) did not change during the relax-ation process (the shapes in Fig. 6C,Eare identical). Indeed, as the accuratemeasurement of geometric parame-ters revealed, during the 50- to 60-minrelaxation process, the change in ag-gregate volume is negligible (consis-tent with the cell division time of CHOcells being �20 hr). Note that theincrease in the number of surfacecells in the schematic figure can beachieved by the movement of the in-ternal cells by a meager �1 cell diam-eter, despite the fact that (in terms ofaggregate height) panels 6C and 6Dcorrespond to a near 30% compres-sion. These observations indicate, thatthe postcompressive relaxation of acell aggregate to the new equilib-rium state proceeds through the mi-gration of cells predominantly towardthe surface (consistent with Fig. 5), inthe course of which cells eventuallyregain their precompressed shape.This finding suggests that the equilib-rium state is indeed liquid-like, withthe pressure being everywhere thesame in the aggregate (fulfilling Pas-cal’s law for liquids) and the increasein surface area supplied by cells orig-inating from the interior of the aggre-gate.

Relating Tissue-LiquidProperties to Molecular andCellular Characteristics

Surface tension is the amount of workneeded to increase the surface area ofa liquid by one unit. It reflects thecohesive properties of the liquid (Is-raelachvili, 1991). For liquid-like tis-sues, the surface tension, � � JN,where J and N are, respectively thestrength (i.e., bond energy) and theaverage cell surface density of cell ad-hesion molecules (CAMs; Forgacs etal., 1998). Measuring � thus providesinformation on tissue cohesivity or al-ternatively, varying the density ofCAMs results in changes in �. Thelinear dependence of � on N has beenexperimentally confirmed by usingcells with varying expression level ofcadherins (Foty and Steinberg, 2005).Furthermore, � � JN�B/a, where �, �B,and a are, respectively, the apparentviscosity of the tissue, average life-time of a bond between CAMs and av-erage linear size of cells composing thetissue (Forgacs et al., 1998; Howard,2001). Measuring � thus provides in-formation on the off rate, koff ( � 1/�B)of CAM bonds, or alternatively, varia-tion in the off rate of adhesive bondsresults in predictable changes in tis-sue viscosity.

Most cadherins are transmembraneproteins with attachment to the actincytoskeleton, and their adhesive ca-pacity is impaired if this connection isdamaged (Ozawa et al., 1990; Gum-biner, 1996, 2000). Therefore, it is ex-

Fig. 3. Fusion of two 300-�m Chinese Hamster Ovary (CHO) cell aggregates. Comparison with Figure 1 shows that fusion of cardiac cushions (a truetissue) is considerably faster (completed in 30 hr). Because CHO cells divide in approximately 20 hr, the volume of the aggregates increases noticeably.Note the sharp boundary between the fusing aggregates, indicating minimal mixing of cells across the interface.

RELATING CELL AND TISSUE MECHANICS 2441

pected that loss of cytoskeletal integ-rity decreases J and with it �. Forquantitative analysis, we performedsurface tension measurements usingN-cadherin transfected CHO cell ag-gregates with differential disruptionof the actin cytoskeleton. We com-pressed the aggregates and followedthe relaxation of the compressiveforce, as shown in Figure 7. (For thequantitative analysis of these curves,see the Discussion section.) As Figure7 indicates, postcompressive relax-ation is more rapid with increasinglatrunculin concentration. In all com-pression experiments used for quanti-tative analysis, decompressed aggre-gates regained their spherical shapeand they did so in approximately thesame time that was needed to reachpostcompressive equilibrium (resultsnot shown). (Note that these experi-ments were performed at 37°C, withno latrunculin in the culture medium,see the Experimental Procedures sec-tion.)

The equilibrium flat portions of thecurves in Figure 7 and the geometricproperties of the relaxed aggregatesdetermine the tissue–liquid’s surfacetension � (see Experimental Proce-dures). The dependence of � on latrun-culin concentration is plotted in Fig-ure 8. The figure shows that to highaccuracy � decreases linearly with la-trunculin concentration. The ap-proach-to-equilibrium part of thecurves in Figure 7 contains informa-tion on �, which also decreases withlatrunculin concentration (see theDiscussion section). These results sug-gest that measuring tissue level bio-mechanical properties may providemolecular level information. Alterna-tively, they provide a recipe for how tomodify tissue level physical parame-ters by molecular manipulations in apredictive manner.

DISCUSSION

Morphogenesis evolves under the con-trol of myriad molecular signals thatgive rise to the coordinated motion ofcells. Nevertheless, a few genericproperties are often sufficient to inter-pret the resulting characteristic tissuepatterns (Forgacs and Newman, 2005;Ninomiya and Winklbauer, 2008). Theconnection between these genericproperties and specific cellular behav-

Fig. 4. Scanning electron microscopy of cell morphology. Images in the lower row are enlarge-ments of the indicated areas in the upper row. Left column: control aggregate (no latrunculin). Mostof the surface cells are flat, indicating that they strongly adhere to the cells around and beneaththem. Right column: aggregate incubated in 0.5 �M � 0.2 �g/ml latrunculin. Cells are predomi-nantly spherical in shape, thus form minimal adhesive contacts with their neighbors. Aggregatediameter is �500 �m, the side of the squares is 135 �m.

Fig. 5. Individual cell movement during postcompressive equilibration. The graphs show themean outward and inward (respectively above and below the horizontal axis) displacement of cellsin a particular compressed aggregate as function of time. The means were calculated every 2 minover cells within the indicated depth interval (top left of each panel) inside the aggregate (measuredfrom the compressive plates), thus they correspond to the x–y projections of the full three-dimensional cellular displacements. The width of these intervals is similar to the linear size of aChinese Hamster Ovary (CHO) cell. The fluctuations in the graphs are partially due to the fact thatdata was collected only from the 10% fluorescently labeled portion of cells composing anaggregate. Similar trends were observed on four different aggregates.

2442 JAKAB ET AL.

ior is not known in general. The mainobjective of this work was to dissectthis connection when the genericproperties are associated with the ap-parent liquid nature of the tissue.

To accomplish this objective, wefirst provided suggestive evidencethat apparent tissue liquidity is man-ifest in true developmental context, byconsidering the fusion of cardiac cush-ions (Fig. 1). The quantitative analy-sis of the data presented in Figure 1revealed that the function r2 � A�1� et/� (with A � 3.7104 �m2 and� � 300 min in Fig. 2) fit well the time

(t) variation of the circular interfacialarea (of instantaneous radius, r, seeinset in Fig. 2) between the two spher-ical fragments. In the limit t/� �� 1 this function is well approxi-mated by r2 � At/�. This result isconsistent with the expression r2

� �Rt/� (R, initial radius of the fus-ing drops, equal to 180 �m in Figure 1;�, viscosity of the tissue; �, interfacialtension between the tissue and theembedding medium) obtained byFrenkel for the initial coalescence oftwo identical, strongly viscous liquiddrops (Frenkel, 1945). Comparison

with Frenkel’s result relates the relax-ation time � to the properties of thetissue: � � R�/�. (For the applicationof Frenkel’s result see also Gordon etal., 1972; Grima and Schnell, 2007;Schotz et al., 2008.) Measurement ofcushion tissue-culture medium inter-facial tension resulted in � � 16.0dyne/cm. This value, when combinedwith the expression and experimen-tally obtained information for �, leadsto � � 107 Poise for chicken embry-onic cushion tissue, a value consistentwith earlier estimates obtained withan independent method for various

Fig. 6. Variation in pressure and individual cell shape during compression experiments, shown schematically (left) and by field emission scanningelectron microscopy (FESEM; right). Only half of the aggregate is shown in the two-dimensional schematic panels, its top being in contact with thecompressive plate. The FESEM panels correspond to sections approximately 50 �m into the aggregate along the axis of compression (i.e., z-axis). A,B:Uncompressed aggregate with cells denoted by squares in A and having near circular z-directional cross-section in B. C,D: Aggregate immediatelyafter compression. Cell shape at this point varies across the aggregate. Thus, the schematic figure (C) shows the expected relative pressure distributionwithin the aggregate, pressure increasing toward lighter colors, being maximal at the middle of the aggregate’s contact area with the plate. Shapesof cells at selected locations of the aggregate are shown in blowup. E,F: Equilibrated aggregate, with recovered cell shape. FESEM images correspondto aggregates with no latrunculin treatment. The shades of cells in A and E correspond respectively to the uniform minimal pressure in theprecompressed aggregate and increased pressure in the postcompressed equilibrated aggregate, being compatible with the situation shown in C. InE, there are more cells along the periphery than in A. Scale bar � 10 �m (applies to B,D and F).

RELATING CELL AND TISSUE MECHANICS 2443

embryonic chicken tissues (Forgacs etal., 1998). These results suggest thattissue liquidity is a useful frameworkfor the analysis of both equilibriumand time dependent phenomena un-derlying tissue patterning.

Next, by combining special in vitrokinetic assays (i.e., fusion; Fig. 3) andcompression (Fig. 5) with electron mi-croscopy (Figs. 4, 6) we elucidated howmetabolically controlled individualcell properties (i.e., cell shape and mo-tility) can give rise to liquid-like(model) tissue configurations. The re-sults of these studies are consistentwith the notion of tissue liquidity, inthe sense that the equilibrium config-urations of tissues and cell aggregatescorrespond to the minimum in surfacearea (under given external condi-tions), increase in area takes place bythe movement of individual cells fromthe interior toward the periphery ofthe tissue, and the pressure in theseconfigurations is uniform (in the ab-sence of spatially varying externalforces). However, importantly, ourfindings also demonstrate that the ap-proach toward equilibrium itself is notpurely liquid-like. Cells of fusing tis-sues, contrary to liquid molecules, donot appreciably mix (at least on thetime scale of fusion; Fig. 3). This sug-gests that tissue fusion is energy-dom-inated with entropy playing negligiblerole. As soon as the interfacial energy

of the fusing construct reaches itsminimum value, cellular motion halts.The minimum in energy is not accom-panied by the maximum in entropythat would correspond to complete cellmixing. Furthermore, the pressuredistribution within the tissue immedi-ately after compressive deformation issimilar to that in dominantly elasticmaterials. Uniform pressure acrossthe tissue (and thus a state with min-imal internal stresses) is re-estab-lished primarily through characteris-tic shape changes of individual cells,as observed in numerous morphoge-netic processes (Lecuit and Lenne,2007). These findings support theview that the mechanical response oftissues (composed of motile and adhe-sive cells) to deformations is time de-pendent. On short and longer timescale tissues manifest respectivelymostly elastic and viscous liquid prop-erties.

Latrunculin treatment of precom-pressed aggregates resulted in greaterand faster postcompressive cellulardisplacement near the aggregate’ssurface, smaller and slower mean dis-placement toward the aggregate’s in-terior (Fig. 5), gradual decrease of ap-parent aggregate surface tension andfaster postcompressive equilibrationwith increasing concentration of thedrug (Fig. 7). These observations pro-vide further insight in how cellular

level non-liquid processes can giverise to liquid-like properties at the tis-sue level.

As Figure 4 suggests, latrunculinrenders cells less adhesive (presum-ably by both destabilizing the cy-toskeletal attachment of CAMs andthe cytoskeleton itself) and less stiff(cells round up). Thus in a compressedaggregate cells are displaced easierand faster (Fig. 5) by the arising spa-tially dependent pressure gradient(Fig. 6C). (Note that due to the round-ing of cells, consistent with Fig. 5, inthe presence of latrunculin eventuallymore cells need to be displaced fromthe interior of a compressed aggregateto its periphery to supply the addi-tional aggregate surface area.)

Changes at the cellular level due tolatrunculin are manifest in the multi-cellular aggregate’s postcompressiverelaxation, as shown in Figure 7. Therelaxation curves indicate that latru-culin-treated aggregates relax faster,thus their apparent viscosity (�) di-minishes. These curves show bimodalcharacter typical for classic viscoelas-tic materials and can accurately beapproximated with a combinationof two exponential functions, Feq �Aet/�1�Bet/�2 (A and B are con-stants). Here, the equlibrium force,Feq (together with the geometric prop-erties of the aggregate) is used to cal-culate the tissue/aggregate surfacetension (Forgacs et al., 1998; Norotteet al., 2008; see the Experimental Pro-cedures section). The two relaxationtimes �1 and �2 (their values listed inTable 1) can also be interpreted interms of cell and tissue/aggregate

Fig. 7. Typical force relaxation upon compression of spherical aggregates of N-cadherin express-ing Chinese Hamster Ovary (CHO) cells. The difference in the initial compressive force (to reach thesame, near 30% compression) between control and 1 �M latrunculin treatment was nearlysevenfold (larger for the control and progressively decreasing with latrunculin concentration), whatmade it cumbersome to place the relaxation curves on the same graph. Thus, values along thevertical axis show forces normalized by the magnitude of the initial compressive force. All aggre-gates used in the compression experiments had similar size and were compressed to the sameextent, approximately 30% of their original diameter.

Fig. 8. Dependence of tissue surface tensionon latrunculin concentration. Error bars indicatestandard errors calculated on the basis of 8–12compressions for each latrunculin concentra-tion. The correlation coefficient (R2 value) forthe linear fit is 0.97.

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level properties. The smaller of thetwo (�1) accounts for the more rapidcellular level processes (Forgacs et al.,1998). The longer relaxation time re-flects the more global cellular rear-rangement (i.e., displacement of cellsas seen in Fig. 5) needed to reach thepostcompressive equilibrium state. Asa consequence, it is related to aggre-gate level quantities (�2 � �/G, whereG is the tissue/aggregate shear modu-lus; Fung, 1993; Forgacs et al., 1998;Shaw et al., 2004). With increasinglatrunculin concentration the samedeformation can be achieved with pro-gressively smaller initial compressionforce, (Fig. 7). This suggests that theaggregate becomes more compliant,thus G diminishes (Landau and Lif-shitz, 1970). We thus deduce thatupon latrunculin treatment of CHOcells, both measurable aggregate-levelviscoelastic coefficients, � and G de-crease. These results suggest, thatmolecular changes at the cell level(here brought about by latrunculin),on occasion, can result in quantita-tively predictable changes at the mul-ticellular level.

Our biomechanical measurementson multicellular aggregates establishquantitative constraints between mo-lecular and tissue-level generic param-eters. The expression � � JN/�koff a�(discussed earlier) relates the strength�J�, surface density (N) and off rate (koff)of the CAM bonds to the apparent vis-cosity of the tissue-aggregate, �. Theconclusion that � diminishes with la-trunculin concentration is thus consis-tent with the expectation that J and/orkoff respectively decreases and increasesas the cytoskeleton becomes progres-sively more disorganized. Through the

dependence of apparent tissue-aggre-gate surface tension on latrunculin con-centration (Fig. 8), we can quantita-tively relate the adhesive bond energy,J (established by means of CAMs) be-tween the composing cells, to cytoskel-etal integrity. The simultaneous va-lidity of the two relationships � � JN(Forgacs et al., 1998; Foty and Stein-berg, 2005) and � � a � bC (Fig. 8;a, b- constants; C, latrunculin concen-tration) suggests that for given cad-herin surface density (i.e., fixed N) Jdecreases linearly with C. This conclu-sion suggests that, as far as tissuecohesivity (i.e., �) is concerned, dimin-ishing cytoskeletal integrity (herequantified in terms of C) can be com-pensated by the up-regulation of thenumber of active adhesive bonds. Al-ternatively, the loss of adhesive bonds(decrease in N) can be compensated bythe re-establishment of cytoskeletalintegrity (in the present case by de-crease in C and increase in J). Suchcompensatory mechanisms may provevaluable in controlling epithelial–mesenchymal transitions and tumormetastasis.

What biologically useful informa-tion can be deduced from this study?Most importantly we related non-liq-uid cellular behavior to liquid-like tis-sue behavior. We presented examplesof how the multitude of geneticallycontrolled cellular processes can besummarized in a few measurable ge-neric parameters (such as tissue sur-face tension, viscosity and shear mod-ulus) that characterize processes andphenomena at the tissue level (Ni-nomiya and Winklbauer, 2008). Evenwhen the connection of these genericparameters to molecular mechanisms

is not known, they can provide practi-cal information on morphogenetic pro-cesses. Thus, the value of the timeconstant � characterizing cushion tis-sue fusion (Figs. 1, 2) may correlatewith normal or abnormal cardiogen-esis. We also provided examples whenexplicit relationship between molecu-lar and generic tissue parameterscould be established. In such casespredictions can be made on how mo-lecular manipulations may influence amorphogenetic process. Specifically,we related tissue surface tension �and viscosity � to cytoskeletal integ-rity, the density of CAMs and thestrength and lifetime of CAM bonds.As the combination �/� (with dimen-sion of velocity) often controls the timeevolution of morphogenetic processes(Newman et al., 1997; Forgacs et al.,1998; Grima and Schnell, 2007;Schotz et al., 2008), our results offer arecipe to molecularly influence tissuerearrangements. The finding on thefusion time ���/�1, has importantpractical applications; it provides thescientific underpinning for a noveltechnology (“bioprinting”) to engineerthree-dimensional tissue constructs ofdefinite shape, as recently reported(Jakab et al., 2004, 2008; Neagu et al.,2005).

EXPERIMENTALPROCEDURES

Cushion Tissue Preparation

Cell culture medium, salt solutions,antibiotics and enzymes were ob-tained from Gibco BRL (Grand Island,NY), fetal bovine serum (FBS) waspurchased from US Biotechnologies(Parkerford, PA). Leghorn chickeneggs (Ozark Hatcheries, Neosho, MO)were incubated at 40°C in 80% humid-ity for 4–6 days. Excised cushion tis-sue explants were washed in Earle’sBalanced Salt Solution and cut intosimilar size fragments. Fragmentswere incubated in a gyratory shaker(at 120 RPM with 5% CO2 at 37°C) inDulbecco’s Modified Eagle Medium(DMEM) supplemented with FBS and1% penicillin-streptomycin. In 24–36hr (depending on size), this procedurereproducibly yielded round aggre-gates. In vitro fusion experimentswere performed in hanging drop con-figuration, each drop containing two

TABLE 1. Relaxation Times Obtained From the Double Exponential Fitto Curves Shown in Figure 7

Latrunculinconcentration (�M) �1 (sec)a �2 (sec)a

0 8.6 � 0.42 117.58 � 2.750.1 7.18 � 0.14 106.39 � 1.990.2 5.35 � 0.16 101.65 � 1.710.5 3.86 � 0.09 85.53 � 1.131.0 3.78 � 0.18 71.27 � 1.59

aNote the order of magnitude difference between �1 and �2, characterizing the rapidinitial, more elastic and the later, more viscous relaxation, respectively. Errors arestandard errors.

RELATING CELL AND TISSUE MECHANICS 2445

round aggregates. For in vivo fusionstudies eggs were cut open, the em-bryos placed in Earle’s Balanced SaltSolution, and the heart dissected. Fus-ing atrioventricular cushion tissuebuds of approximately 400 micronwere pinched from the opened myo-cardial tube at regular time intervalsbetween HH stages 26 and 28 andplaced in a Petri dish with fresh me-dium. The evolution of both in vitroand ex vitro fusion was recorded witha Spot-Insight CCD camera (Diagnos-tic Instruments, Sterling Heights, MI)attached to a dissecting microscope(Olympus SZ60, St. Louis, MO).

Cell Aggregate Preparation

CHO cells, transfected with N-cad-herin (courtesy of A. Bershadsky,Weizmann Institute, Rehovot, Israel),were grown in DMEM supplementedwith 10% FBS, 10 �g/ml of penicillin-streptomycin, gentamicin, kanamycinsulphate, and 400�g/ml geneticin. Theconfluent cultures containing approx-imately 3–4 � 106 cells per 75 cm2

TC dish were washed twice withHanks’ Balanced Salt Solution con-taining 2mM CaCl2, then treated for10 min with trypsin 0.1%. Cell solu-tions were subsequently centrifugedat 2,500 RPM for 4 min. The resultingpellet was transferred into capillarymicropipettes of 500 �m diameter andincubated at 37°C with 5% CO2 for 10min. The firm cylinders of cells re-moved from the pipettes were cut into500-�m-long fragments (aspect ratio1), then incubated in 10-ml tissue cul-ture flasks (Bellco Glass, Vineland,NJ) with 3 ml of DMEM on a gyratoryshaker at 120 RPM with 5% CO2 at37°C for 24–36 hr. This protocol re-producibly produced spherical modeltissue aggregates of similar size. Forkinetic assays (i.e., fusion of two ag-gregates and compression) aggregates(approximately 300 �m diameter)were prepared with fluorescently la-beled cells to follow cellular move-ment. To visualize cellular mixingduring fusion, one of the aggregateswas prepared from cells stained withfluorescent membrane dye usingDiIC18(5)-DS lipophilic carbocyaninetracer per manufacturer’s instruction(Molecular Probes, Carlsbad, CA). Tofollow the movement of individualcells during compression, aggregates

were prepared with 10% of the N-cad-herin transfected CHO cells infectedwith histone binding H2B-YFP retro-virus (kindly provided by R.D. Lans-ford, Beckman Institute at CaliforniaInstitute of Technology) to expressyellow fluorescent protein in their nu-clei.

Surface TensionMeasurements

The parallel plate compression tensi-ometer used in this work to measureliquid tissue properties is shown inFigure 9. Modified from previouslyused similar devices (Foty et al., 1996;Forgacs et al., 1998), it is controlled byLabview software (National Instru-ments, Austin, TX) to record the en-tire force relaxation following the uni-axial compression of an aggregatebetween parallel plates. Geometricparameters listed in the inset in Fig-ure 9 were measured through a dis-secting microscope positioned horizon-tally in front of the compressionchamber. To minimize the adhesion ofthe aggregate to the plates, these werecoated with poly(DTE co 7% PEG1000

oxalate). The poly(DTE co 7% PEG1000

oxalate) was synthesized as described

by Yu and Kohn (1999), substitutingthe phosgene catalyzer with the lesshazardous oxalyl-chloride. Structureand composition was confirmed with13C and 1H NMR analysis and infra-red spectroscopy. Aggregates werecompressed in CO2 independent me-dium. A typical measurement wasperformed as explained in the captionto Figure 9. To assess the role of theactin cytoskeleton in tissue liquidproperties, surface tension measure-ments were performed with aggre-gates incubated in varying concentra-tion of latrunculin A (MolecularProbes, Eugene, OR; Coue et al., 1987)for 40 min, before compression. Theoverall shape of the postcompressionforce relaxation curves was similarwhen measurements were performedin medium with or without latruncu-lin present. However, quantitativeanalysis was performed only on datacollected with aggregates compressedin latrunculin-free medium for rea-sons explained below.

Data Analysis

The shape of an aggregate compressedin the tensiometer shown in Figure 9was recorded before, during, and after

Fig. 9. Tensiometer for surface tension measurements. A: The initially spherical aggregate wasplaced on the lower compression plate (LCP) in the inner chamber (IC) filled with 11 ml of CO2

independent medium (maintained at 37°C by a circulating water bath through the outer chamber[OC]) and rapidly compressed against the upper compression plate (UCP) by a stepping motor (M)(through the lower assembly [LA]), which was preprogrammed to produce a deformation of adefinite magnitude (the same when comparative studies with varying latrunculin concentrationwere carried out). To avoid irreversible damage to the cells, aggregates were compressed maxi-mum 30% of their original diameter. B: The relaxation of the compressive force was followed (bymeasuring the apparent weight of the UCP with a Cahn-Ventron (Cerritos, CA) electrobalance,connected to the UCP through a nickel-chromium wire [NCW]) until it reached a constant equilib-rium value, at which point the compression plates were separated, and the aggregate let to regainits original shape. Measurements in which the aggregate did not regain its precompressed shapewhere discarded. The inset shows the geometric parameters of a compressed aggregate used forthe evaluation of the surface tension (see Data Analysis).

2446 JAKAB ET AL.

compression using a Spot Insight CCDcamera fitted to the horizontally posi-tioned dissecting microscope (de-scribed above). The surface tensionwas evaluated with the help of theLaplace equation, Feq/� R3

2� � ��1/R1

� 1/R2�. Here � is the tissue’s surfacetension (i.e., interfacial tension withthe surrounding tissue culture me-dium), Feq is the equilibrium value ofthe compressive force (given by theflat portion of the curves in Fig. 7) andR3 is the radius of the circular contactarea of the compressed aggregate withthe plates. The quantities R1 and R2

are the radii of curvature of the aggre-gate’s surface, respectively along itscircular equatorial plane, and its pro-file, near this plane (see inset in Fig.9). The geometric parameters were de-termined from the recorded profile byan in-house built tracking program,with a precision of 3 �m. The programevaluated the aggregate’s profile onthe basis of variation in gray scalevalues in its vicinity.

The accurate determination of � re-quires the accurate measurement ofthe geometric parameters. This wasnot possible when latrunculin waspresent in the medium during com-pression because aggregate contourwas often fuzzy. It is for this reasonthat compressions were performed in

latrunculin-free medium. This modifi-cation does not affect our conclusionsfor the following reasons. When a cellis incubated in latrunculin-containingmedium, at chemical equilibrium:

Kd �[G]0[L]eq

[LG]eq. (1)

Here Kd is the equilibrium dissocia-tion constant of the latrunculin-G ac-tin binding reaction and [G]0, [L]eq,[LG]eq are respectively the equilib-rium concentrations of G actin (i.e.,critical concentration), free latruncu-lin, and latrunculin-G actin complex.In vitro, [G]0 � 0.2 �M and Kd

� 0.2 �M, as measured respectivelyin pure actin solutions (Pollard andEarnshaw, 2002) and solutions con-taining actin and latrunculin (Coue etal., 1987). The in vitro results for Kd

and [G]0 provide values for [LG]eq

which are inconsistent with experi-mental findings in real cells stimu-lated with any reasonable latrunculinconcentration. Pring and co-workers(Pring et al., 2002) measured [L]eq and[LG]eq, in real cells. Their values dras-tically differed from those that couldbe expected on the basis of in vitroresults. In particular, these authorsshowed that cells retain latrunculin.After a mere 90-sec stimulation ofcells with the drug, they found [L] � 0

in the medium indicating that almostall the latrunculin in the cells was se-questered. This means that under cel-lular conditions, [L]eq and [LG]eq inEq. (1) are respectively very small andlarge. Thus, if after the establishmentof equilibrium, as described by Eq. (1),cells (or aggregates of cells) are trans-ferred into latrunculin-free fresh me-dium, very little cellular latrunculinwill be released into the medium. Thissuggests that tensiometry data col-lected with latrunculin-free or latrun-culin-containing medium do not sig-nificantly differ.

Kinetic Assay

A special compression apparatus,shown in Figure 10, was designed toinvestigate the movement of individ-ual cells inside aggregates after com-pression. Because the apparatus waskept on the stage of a confocal micro-scope (Bio-Rad Radiance 200, CarlZeiss Microimaging, Thornwood, NY),for technical reasons, compressionswere performed at room temperature.A typical experiment was performedas explained in the caption to Figure10. Experiments with latrunculin-treated aggregates were performed asdescribed above.

Cell Viability Assay

After compression measurements wereperformed, the trypan blue exclusiontest was used to determine whether thecells near the surface of the tissue ex-plants/aggregates were viable. Addi-tionally, explants/aggregates were cutin half to determine whether necroticcells were present in the interior. Ex-plants/aggregates were allowed to soakin a droplet of DMEM containing 20%trypan blue stain for 10 min. Trypanblue was then diluted, explants/aggre-gates placed into a Petri dish containingfresh DMEM and observed under themicroscope. A small number (�5%) ofdead cells were typically found. Cellviability was also checked by the de-compression of aggregates after theyreached postcompressive equilibrium.In all experiments that were used fordata analysis de-compression resultedin the rounding of the aggregates totheir precompressed state in approxi-mately the same time as was needed toreach equilibrium.

Fig. 10. A,B: Compression apparatus for kinetic assay. A: Aggregates were compressed betweentwo glass compression plates (UC and LC) immersed in a culture medium reservoir (CMR)containing 10 ml of CO2 independent medium. Using a metallic ring (MR), the UC is attached to andlowered by a z-directional micromanipulator (MM) of 10 �m resolution. The LC is positioned on themetallic disk (MD) that also holds the micromanipulator. The apparatus is mounted on the stage ofan Olympus IX-70 microscope with confocal imaging attachment (CM), used to record individualcell trajectories during the force relaxation process. A 60- to 80-�m section of the aggregate’slower part was scanned in 2-�m steps. Complete confocal scans were taken in 2-min time intervalsup to 1 hr. The positions of the fluorescently labeled cells (relative to the centers of the two-dimensional sections), determined by superposition of bright field and confocal images, werestored and later used for the reconstruction of cell trajectories. While x–y positions were deter-mined accurately based on the fluorescent contour of the labeled nuclei, the accuracy of the zcoordinate was limited by the 2 �m resolution preset on the confocal microscope when acquiringthe images. Average total displacements were calculated using 15–40 cells per depth range.

RELATING CELL AND TISSUE MECHANICS 2447

Electron Microscopy ofAggregate Surface

The morphology of cells on the surfaceand in the interior of aggregates wasanalyzed by FESEM. Spherical aggre-gates were fixed in 4% paraformalde-hyde (Electron Microscopy Sciences,Hatfield, PA) in phosphate-bufferedsaline (PBS) for 90 min, on a low speedshaker. Subsequently, samples wererinsed 3 times for 10 min in PBS. De-hydration was performed by an in-creasing concentration series of etha-nol as follows: 10%, 25%, 50%, 75%,95%, for 30 min each and finally in100% ethanol overnight. After criticalpoint drying (Samdri-PVT-3B, Tousi-mis, Rockville, MD), aggregates werespread on carbon adhesive tabsmounted on stub and sputter coatedwith platinum to a nominal thicknessof 2 nm. Aggregate surface was exam-ined using a Hitachi S4700 cold-cath-ode field-emission scanning electronmicroscope at an accelerating voltageof 5 kV.

Electron Microscopy of Cut-open Aggregates

FESEM was performed on uncom-pressed, compressed and compressed-equilibrated aggregates. Aggregateswere fixed and kept for 4 hr in 2%glutaraldehyde, 2% (v/v) paraformal-dehyde in 0.1 M cacodylate buffer. Forthe second group compression tookplace in the fixative itself, whereas forthe third group fixation was carriedout after postcompressive equilibriumhas been reached in CO2 independentmedium. After fixation, aggregateswere washed 3 times for 10 min in 0.1M cacodylate buffer. All aggregateswere cryo-protected by incubatingfirst for 3 hr in 25% (v/v) DMSO andsubsequently in 50% DMSO over-night. The next day, after freezing inliquid nitrogen, aggregates were sec-tioned on a cryo-ultramicrotome (Ul-tracut UCT, Leica, Northvale, NJ) at113°C. After removal of approxi-mately fifty 1-�m-thick sections fromcompressed and compressed-equili-brated aggregates (parallel to thecompression plates), cut-open aggre-gates were thawed in PBS. Aggre-gates were dehydrated and criticalpoint dried (as above) and carefullyplaced on carbon adhesive tabs with

the open face on top. Sputter-coatingand FESEM settings were as above.

ACKNOWLEDGMENTSWe thank Endre Szuromi for help inpreparing the nonadhesive coverageof the compression plates. We alsothank Cyrille Norotte for useful dis-cussions. This work was supported byNSF-052684 (G.F., V.M., I.K., R.M.)and NIH (stipend for B.D.).

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