Relating cell and tissue mechanics: Implications and applications



The Differential Adhesion Hypothesis (DAH) posits that differences in adhesion provide the driving force for morphogenetic processes. A manifestation of differential adhesion is tissue liquidity and a measure for it is tissue surface tension. In terms of this property, DAH correctly predicts global developmental tissue patterns. However, it provides little information on how these patterns arise from the movement and shape changes of cells. We provide strong qualitative and quantitative support for tissue liquidity both in true developmental context and in vitro assays. We follow the movement and characteristic shape changes of individual 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 under realistic three-dimensional culture conditions is not possible. Our findings confirm the usefulness of tissue liquidity and provide the scientific underpinning for a novel tissue engineering technology. Developmental Dynamics 237:2438–2449, 2008. © 2008 Wiley-Liss, Inc.


Embryonic development represents a complex schedule of events through which a living organism acquires its final shape. All these events are under genetic control. However, genes by themselves do not create forms and shapes: physical mechanisms do. Genes set up the inherent physical and chemical properties of cells, extracellular matrix and tissues. These in turn generate forces, which drive structure formation and cause subsequent alterations in gene activity. It is this delicate interplay of genetic, molecular and physical factors that constitutes the evolving modern understanding of early morphogenesis (Hove et al.,2003; Farge,2003; Forgacs and Newman,2005; Lecuit and Lenne,2007; Ninomiya and Winklbauer,2008). A specific pattern forming mechanism where this interplay has extensively been studied is differential cell affinity. This mechanism underlies segregation of cell populations and the formation of compartment boundaries (Irvine and Rauskolb,2001). The Differential Adhesion Hypothesis (DAH; Steinberg,1963) explains such morphogenetic processes in terms of cell motility combined with differences in tissue affinities. The validity of DAH has been demonstrated both in vitro (Foty et al.,1996; Forgacs et al.,1998; Duguay et al.,2003; Foty and Steinberg,2005; Schötz et al.,2008; Ninomiya and Winklbauer,2008) and in vivo (Godt and Tepass,1998; González-Reyes and St Johnston,1998; Hayashi and Carthew,2004). Numerous molecular signals have been identified that control differential cell affinities (Tepass et al.,2002). On the other hand, differences in tissue affinities can be quantified in terms of differences in tissue surface tension, a physical material constant characteristic of liquids. Indeed, it has been demonstrated that embryonic tissues in many respects behave analogously to liquids (Steinberg and Poole,1982). In nonadhesive environments irregular tissue fragments round up to form a spheroid (Foty et al.,1996), just as liquid drops do in the absence of external forces. The final equilibrium configuration of a random mixture of two distinct cell types is akin to that of phase separated immiscible liquids (e.g., oil and water): the two cell types sort, and a spheroid of the more cohesive cells forms within a spheroid of the less cohesive cells (Steinberg and Takeichi,1994; Foty et al.,1996; Beysens et al.,2000). If the two cell types form tissues that are contiguous in normal development, the sorted pattern corresponds to the arrangement that these tissues assume under physiological conditions (Steinberg,1970; Technau and Holstein,1992). Apparent surface tensions have been measured for several embryonic tissues with results in complete agreement with observed sorting patterns (Foty et al.,1996; Davis et al.,1997; Duguay et al.,2003; Foty and Steinberg,2005; Schötz et al.,2008). Computer simulations based on tissue liquidity have reproduced predictions by DAH (Glazier and Graner,1993).

According to the liquid analogy then, compartments and boundaries form as the more cohesive cell populations (of higher surface tension) sort out or separate from the less cohesive ones (of lower surface tension). Such configurations are maintained as long as the genetically controlled difference in surface tensions exists. As development proceeds, molecular signals (i.e., changes in gene expression controlling cell adhesion) lead to changes in surface tension (Foty et al.,1996; Ninomiya and Winklbauer,2008), which in turn result in altered tissue pattern. The arising mechanical signals elicit new molecular signals (Farge,2003; Lecuit and Lenne,2007).

We asked the question whether tissue liquidity represents solely a convenient heuristic mechanical description of equilibrium tissue patterns or a tissue-level manifestation of the complex mechanical behavior of cells impacting morphogenetic processes (such as convergent extension [Keller,2002], establishment of planar polarity [Mlodzik,2002], or cellular rosette formation [Blankenship et al.,2006]). Specifically, we addressed the following questions. (1) Can the analogy between tissues (composed of motile and adhesive cells) and liquids, observed in equilibrium tissue configurations, be extended to the time dependent process of approaching equilibrium? (2) How can the formation of the observed liquid-like tissue configurations be reconciled with the motion and shape changes of individual cells that lead to these configurations? (3) Can the tissue-liquid analogy provide information that cannot be obtained by other means? To answer the first question, we studied tissue fusion (Perez-Pomares and Foty,2006) in true developmental context. We considered the fusion of embryonic chicken cardiac cushions, the morphogenetic process that underlies the formation of septa and valves in early heart development (Wessels and Sedmera,2003; de la Cruz and Markwald,1998). To answer the second question, we followed fusion in time in a controlled in vitro assay using well-characterized cell lines (genetically transformed Chinese Hamster Ovary [CHO] cells). Individual cellular movement and shape changes were also studied and quantified in the course of equilibration of deformed (i.e., compressed) cell aggregates (i.e., model tissues). These studies revealed that the final fused or postcompressed states indeed are liquid-like. Of interest, even the approach to the final states resembles equilibration in liquids. Upon more detailed analysis, however, we found that in tissues the relaxation to equilibrium is driven predominantly by cell shape changes, a unique property of living systems with no analogy in liquids. To answer the third question, we measured biophysical properties that quantify the relaxation process at the tissue level and related them to molecular entities that control the relaxation process at the cellular level.


Manifestation of Tissue Liquidity in Early Development: The Fusion of Cardiac Cushions

In the chicken, the heart begins to form during the second day of development from a crescent-shaped region of tissue derived from the splanchnic (i.e., inner body tube) mesoderm at the head or cranial end of the embryo. The primitive heart tube that subsequently forms contains two epithelial layers: the inner endocardium and the outer myocardium (Manasek,1968). The two layers are separated by an extracellular matrix known as the cardiac jelly. Formation of the septa and valves that separate the four chambers of the heart is initiated at specific sites of the endocardium by swellings known as the cardiac cushions and proceeds by their fusion and an associated epithelial–mesenchymal transition (Wessels and Sedmera,2003; de la Cruz and Markwald,1998).

We followed this morphogenetic process both in vitro and in vivo. Our findings are summarized in Figure 1. We extracted cardiac cushion tissue from 5-day chick embryos (Hamburger-Hamilton [HH] stage 27). When the irregular-shaped tissue explants were incubated in tissue culture medium in hanging drop configuration they rounded up into almost perfect spherical shape (Fig. 1A). This observation suggests that these tissues have properties in common with liquids in that they minimize their interfacial area with the surrounding. Next, we followed the fusion of two contiguously placed similar sized round-up explants in time (selected images in Fig. 1B). We found that the in vitro process strongly resembles the in vivo process, the latter being observed by recording the instantaneous configuration of the fusing cushions after extraction, at regular time intervals (Fig. 1C). It needs to be emphasized that the in vitro and in vivo processes initially involve the same tissues. The quantitative analysis of the in vitro fusion (Fig. 1B), presented in Figure 2, revealed that both the final fused pattern and the approach to it are liquid-like. (For details of the quantitative analysis see the Discussion section.)

Figure 1.

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

Figure 2.

Quantitative characterization of the fusion process. Points represent the measured values of the (square of the) quantity shown in the inset, obtained form the series of snapshots (partially) shown in Figure 1. The line over the data is the result of a fluid-dynamical analysis (for details, see the Discussion section).

Direct Observation of Cellular Movement

The two cardiac cushion spheroids eventually fuse into a single spheroid. This is consistent with the property of liquids, which under no external forces evolve into a state with minimal interfacial area (i.e., a sphere). To analyze more directly the movement of individual cells in the course of tissue rearrangements we first studied the fusion of spherical cell aggregates composed of genetically transformed CHO cells with fixed average number of N cadherins (see the Experimental Procedures section). (We used CHO cell aggregates, instead of the cushion tissue spheroids because the latter contain several cell types, such as cardiomyocytes, endothelial cells and fibroblasts, as well as extracellular matrix. The heterogeneity of these spheroids makes the observation of individual cells difficult, a problem we could avoid by using a cell line.) Using differential staining of the cells in the two aggregates we followed the time evolution of the cellular pattern. Results in Figure 3 show that even though the final equilibrium state of the system is liquid-like (i.e., rounded), the distribution of cells in it is not. Cells move minimally across and along the interface between the fusing aggregates, just enough to facilitate the formation of a final state with minimal surface area. The fully coalesced state of two true liquid drops is characterized by the complete mixing of molecules.

Figure 3.

Fusion of two 300-μm Chinese Hamster Ovary (CHO) cell aggregates. Comparison with Figure 1 shows that fusion of cardiac cushions (a true tissue) 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.

Next, we compressed the same spherical aggregates between parallel plates and studied the movement of individual cells in the postcompressive relaxation process. Compressions were performed with control aggregates and aggregates pretreated with latrunculin A, an F-actin destabilizing agent (Coué et al.,1987; Fig. 4). (Because the actin cytoskeleton participates in numerous cell functions, its disruption by latrunculin may have effects beyond cell adhesion. We chose latrunculin A because it is specific for actin and it is a widely used tool in cell biology when the consequences of cytoskeletal disruption on adhesion or cell movement are to be evaluated.) Such compressive deformation, to which embryonic tissues are often exposed, causes increase in area. The area of a true liquid drop increases (or decreases) by the migration of the loosely bound mobile molecules from the bulk to the periphery (or vice versa). In contrast, the surface area of an elastic solid increases (or decreases) mostly by the stretching (or contraction) of bonds between the immobile molecules or atoms.

Figure 4.

Scanning electron microscopy of cell morphology. Images in the lower row are enlargements of the indicated areas in the upper row. Left column: control aggregate (no latrunculin). Most of the surface cells are flat, indicating that they strongly adhere to the cells around and beneath them. Right column: aggregate incubated in 0.5 μM = 0.2 μg/ml latrunculin. Cells are predominantly spherical in shape, thus form minimal adhesive contacts with their neighbors. Aggregate diameter is ∼500 μm, the side of the squares is 135 μm.

To determine which of these mechanisms is responsible for the increase in surface area, aggregates were optically sectioned perpendicular to the direction of compression (taken as the z axis) and the x–y displacements of fluorescently labeled cells (constituting 10% of all cells) followed by confocal microscopy. Images, acquired in different sections at regular time intervals (every 2 min), were stacked to form layers (with thickness of approximately one cell diameter) within the aggregate at different depths. Figure 5 shows the mean radial displacement (within the x–y plane), as function of time, of cells moving outward (toward the periphery of the aggregate) and inward (toward the interior of the aggregate) within different layers. The mean was calculated over all fluorescent cells within the layer. In the absence of latrunculin the mean resultant postcompressive displacements were more or less uniform across the shown layers and in each layer cells moved preferentially toward the periphery (Fig. 5, left column). This observation suggests that the aggregate relaxed to its new equilibrium state (with increased area) similarly to a liquid drop. Upon latrunculin treatment, the extent of outward radial displacement was larger than in control aggregates close to the periphery and the resultant displacement diminished rapidly with increasing depth into the aggregate (Fig. 5, right column). Because these experiments were performed at room temperature postcompressive relaxation is slower than at 37°C (compare with the relaxation of aggregates in Fig. 7). (Note that these experiments were performed with no latrunculin in the culture medium, see the Experimental Procedures section.)

Figure 5.

Individual cell movement during postcompressive equilibration. The graphs show the mean outward and inward (respectively above and below the horizontal axis) displacement of cells in a particular compressed aggregate as function of time. The means were calculated every 2 min over cells within the indicated depth interval (top left of each panel) inside the aggregate (measured from 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 a Chinese Hamster Ovary (CHO) cell. The fluctuations in the graphs are partially due to the fact that data was collected only from the 10% fluorescently labeled portion of cells composing an aggregate. Similar trends were observed on four different aggregates.

Because only the nuclei of cells were fluorescently labeled, compression experiments by themselves did not provide information on the evolution of cell shape during the postcompressive relaxation process. To gain such information field emission scanning electron microscopy (FESEM) was used. In Figure 6, we present FESEM images and schematic drawings of individual cells in a precompressed, compressed, and postcompressed equilibrated aggregate. The schematic representation (Fig. 6C) illustrates that immediately after compression a pressure gradient (similar to that in a compressed elastic sphere; Egholm et al.,2006) is set up, because cells in the vicinity of the compressive plates and toward the vertical axis of symmetry of the compressed aggregate are deformed respectively more strongly than those near the equator and side boundary (Fig. 6D). The pressure difference, which itself favors the outward migration of cells is eliminated by the end of the relaxation process, as can be deduced from the recovery of precompressed cell shape (Fig. 6E,F). Phillips and coworkers arrived at similar conclusions by analyzing cellular patterns in aggregates compressed by centrifugation (Phillips et al.,1977). (Note that in an elastic sphere the postcompressive pressure gradient would not change in time.) As the schematic panels in Figure 6 suggest, overall aggregate shape (and thus volume) did not change during the relaxation process (the shapes in Fig. 6C,E are identical). Indeed, as the accurate measurement of geometric parameters revealed, during the 50- to 60-min relaxation process, the change in aggregate volume is negligible (consistent with the cell division time of CHO cells being ∼20 hr). Note that the increase in the number of surface cells in the schematic figure can be achieved by the movement of the internal cells by a meager ∼1 cell diameter, despite the fact that (in terms of aggregate height) panels 6C and 6D correspond to a near 30% compression. These observations indicate, that the postcompressive relaxation of a cell aggregate to the new equilibrium state proceeds through the migration of cells predominantly toward the surface (consistent with Fig. 5), in the course of which cells eventually regain their precompressed shape. This finding suggests that the equilibrium state is indeed liquid-like, with the pressure being everywhere the same in the aggregate (fulfilling Pascal's law for liquids) and the increase in surface area supplied by cells originating from the interior of the aggregate.

Figure 6.

Variation in pressure and individual cell shape during compression experiments, shown schematically (left) and by field emission scanning electron microscopy (FESEM; right). Only half of the aggregate is shown in the two-dimensional schematic panels, its top being in contact with the compressive plate. The FESEM panels correspond to sections approximately 50 μm 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 immediately after compression. Cell shape at this point varies across the aggregate. Thus, the schematic figure (C) shows the expected relative pressure distribution within the aggregate, pressure increasing toward lighter colors, being maximal at the middle of the aggregate's contact area with the plate. Shapes of cells at selected locations of the aggregate are shown in blowup. E,F: Equilibrated aggregate, with recovered cell shape. FESEM images correspond to aggregates with no latrunculin treatment. The shades of cells in A and E correspond respectively to the uniform minimal pressure in the precompressed aggregate and increased pressure in the postcompressed equilibrated aggregate, being compatible with the situation shown in C. In E, there are more cells along the periphery than in A. Scale bar = 10 μm (applies to B,D and F).

Relating Tissue-Liquid Properties to Molecular and Cellular Characteristics

Surface tension is the amount of work needed to increase the surface area of a liquid by one unit. It reflects the cohesive properties of the liquid (Israelachvili,1991). For liquid-like tissues, the surface tension, σ ∝ JN, where J and N are, respectively the strength (i.e., bond energy) and the average cell surface density of cell adhesion molecules (CAMs; Forgacs et al.,1998). Measuring σ thus provides information on tissue cohesivity or alternatively, varying the density of CAMs results in changes in σ. The linear dependence of σ on N has been experimentally confirmed by using cells with varying expression level of cadherins (Foty and Steinberg,2005). Furthermore, η ∝ JNτB/a, where η, τB, and a are, respectively, the apparent viscosity of the tissue, average lifetime of a bond between CAMs and average linear size of cells composing the tissue (Forgacs et al.,1998; Howard,2001). Measuring η thus provides information on the off rate, koff (=1/τB) of CAM bonds, or alternatively, variation in the off rate of adhesive bonds results in predictable changes in tissue viscosity.

Most cadherins are transmembrane proteins with attachment to the actin cytoskeleton, and their adhesive capacity is impaired if this connection is damaged (Ozawa et al.,1990; Gumbiner,1996,2000). Therefore, it is expected that loss of cytoskeletal integrity decreases J and with it σ. For quantitative analysis, we performed surface tension measurements using N-cadherin transfected CHO cell aggregates with differential disruption of the actin cytoskeleton. We compressed the aggregates and followed the relaxation of the compressive force, as shown in Figure 7. (For the quantitative analysis of these curves, see the Discussion section.) As Figure 7 indicates, postcompressive relaxation is more rapid with increasing latrunculin concentration. In all compression experiments used for quantitative analysis, decompressed aggregates regained their spherical shape and they did so in approximately the same time that was needed to reach postcompressive equilibrium (results not shown). (Note that these experiments were performed at 37°C, with no latrunculin in the culture medium, see the Experimental Procedures section.)

Figure 7.

Typical force relaxation upon compression of spherical aggregates of N-cadherin expressing Chinese Hamster Ovary (CHO) cells. The difference in the initial compressive force (to reach the same, near 30% compression) between control and 1 μM latrunculin treatment was nearly sevenfold (larger for the control and progressively decreasing with latrunculin concentration), what made it cumbersome to place the relaxation curves on the same graph. Thus, values along the vertical axis show forces normalized by the magnitude of the initial compressive force. All aggregates used in the compression experiments had similar size and were compressed to the same extent, approximately 30% of their original diameter.

The equilibrium flat portions of the curves in Figure 7 and the geometric properties of the relaxed aggregates determine the tissue–liquid's surface tension σ (see Experimental Procedures). The dependence of σ on latrunculin concentration is plotted in Figure 8. The figure shows that to high accuracy σ decreases linearly with latrunculin concentration. The approach-to-equilibrium part of the curves in Figure 7 contains information on η, which also decreases with latrunculin concentration (see the Discussion section). These results suggest that measuring tissue level biomechanical properties may provide molecular level information. Alternatively, they provide a recipe for how to modify tissue level physical parameters by molecular manipulations in a predictive manner.

Figure 8.

Dependence of tissue surface tension on latrunculin concentration. Error bars indicate standard errors calculated on the basis of 8–12 compressions for each latrunculin concentration. The correlation coefficient (R2 value) for the linear fit is 0.97.


Morphogenesis evolves under the control of myriad molecular signals that give rise to the coordinated motion of cells. Nevertheless, a few generic properties are often sufficient to interpret the resulting characteristic tissue patterns (Forgacs and Newman,2005; Ninomiya and Winklbauer,2008). The connection between these generic properties and specific cellular behavior is not known in general. The main objective of this work was to dissect this connection when the generic properties are associated with the apparent liquid nature of the tissue.

To accomplish this objective, we first provided suggestive evidence that apparent tissue liquidity is manifest in true developmental context, by considering the fusion of cardiac cushions (Fig. 1). The quantitative analysis of the data presented in Figure 1 revealed that the function r2=A(1−e−t/τ (with A=3.7×104 μm2 and τ=300 min in Fig. 2) fit well the time (t) variation of the circular interfacial area (of instantaneous radius, r, see inset in Fig. 2) between the two spherical fragments. In the limit t/τ<<1 this function is well approximated by r2=At/τ. This result is consistent with the expression r2=σRt/η (R, initial radius of the fusing drops, equal to 180 μm in Figure 1; η, viscosity of the tissue; σ, interfacial tension between the tissue and the embedding medium) obtained by Frenkel for the initial coalescence of two identical, strongly viscous liquid drops (Frenkel,1945). Comparison with Frenkel's result relates the relaxation time τ to the properties of the tissue: τ≈Rη/σ. (For the application of Frenkel's result see also Gordon et al.,1972; Grima and Schnell,2007; Schötz et al.,2008.) Measurement of cushion tissue-culture medium interfacial tension resulted in σ≈16.0 dyne/cm. This value, when combined with the expression and experimentally obtained information for τ, leads to η≈107 Poise for chicken embryonic cushion tissue, a value consistent with earlier estimates obtained with an independent method for various embryonic chicken tissues (Forgacs et al.,1998). These results suggest that tissue liquidity is a useful framework for the analysis of both equilibrium and time dependent phenomena underlying tissue patterning.

Next, by combining special in vitro kinetic assays (i.e., fusion; Fig. 3) and compression (Fig. 5) with electron microscopy (Figs. 4, 6) we elucidated how metabolically controlled individual cell properties (i.e., cell shape and motility) can give rise to liquid-like (model) tissue configurations. The results of these studies are consistent with the notion of tissue liquidity, in the sense that the equilibrium configurations of tissues and cell aggregates correspond to the minimum in surface area (under given external conditions), increase in area takes place by the movement of individual cells from the interior toward the periphery of the tissue, and the pressure in these configurations is uniform (in the absence of spatially varying external forces). However, importantly, our findings also demonstrate that the approach toward equilibrium itself is not purely liquid-like. Cells of fusing tissues, contrary to liquid molecules, do not appreciably mix (at least on the time scale of fusion; Fig. 3). This suggests that tissue fusion is energy-dominated with entropy playing negligible role. As soon as the interfacial energy of the fusing construct reaches its minimum value, cellular motion halts. The minimum in energy is not accompanied by the maximum in entropy that would correspond to complete cell mixing. Furthermore, the pressure distribution within the tissue immediately after compressive deformation is similar to that in dominantly elastic materials. Uniform pressure across the tissue (and thus a state with minimal internal stresses) is re-established primarily through characteristic shape changes of individual cells, as observed in numerous morphogenetic processes (Lecuit and Lenne,2007). These findings support the view that the mechanical response of tissues (composed of motile and adhesive cells) to deformations is time dependent. On short and longer time scale tissues manifest respectively mostly elastic and viscous liquid properties.

Latrunculin treatment of precompressed aggregates resulted in greater and faster postcompressive cellular displacement near the aggregate's surface, smaller and slower mean displacement toward the aggregate's interior (Fig. 5), gradual decrease of apparent aggregate surface tension and faster postcompressive equilibration with increasing concentration of the drug (Fig. 7). These observations provide further insight in how cellular level non-liquid processes can give rise to liquid-like properties at the tissue level.

As Figure 4 suggests, latrunculin renders cells less adhesive (presumably by both destabilizing the cytoskeletal attachment of CAMs and the cytoskeleton itself) and less stiff (cells round up). Thus in a compressed aggregate cells are displaced easier and faster (Fig. 5) by the arising spatially dependent pressure gradient (Fig. 6C). (Note that due to the rounding of cells, consistent with Fig. 5, in the presence of latrunculin eventually more cells need to be displaced from the interior of a compressed aggregate to its periphery to supply the additional aggregate surface area.)

Changes at the cellular level due to latrunculin are manifest in the multi-cellular aggregate's postcompressive relaxation, as shown in Figure 7. The relaxation curves indicate that latruculin-treated aggregates relax faster, thus their apparent viscosity (η) diminishes. These curves show bimodal character typical for classic viscoelastic materials and can accurately be approximated with a combination of two exponential functions, Feq + Aemath image+Bemath image (A and B are constants). Here, the equlibrium force, Feq (together with the geometric properties of the aggregate) is used to calculate the tissue/aggregate surface tension (Forgacs et al.,1998; Norotte et al.,2008; see the Experimental Procedures section). The two relaxation times τ1 and τ2 (their values listed in Table 1) can also be interpreted in terms of cell and tissue/aggregate level properties. The smaller of the two (τ1) accounts for the more rapid cellular level processes (Forgacs et al.,1998). The longer relaxation time reflects the more global cellular rearrangement (i.e., displacement of cells as seen in Fig. 5) needed to reach the postcompressive equilibrium state. As a consequence, it is related to aggregate level quantities (τ2 =η/G, where G is the tissue/aggregate shear modulus; Fung,1993; Forgacs et al.,1998; Shaw et al.,2004). With increasing latrunculin concentration the same deformation can be achieved with progressively smaller initial compression force, (Fig. 7). This suggests that the aggregate becomes more compliant, thus G diminishes (Landau and Lifshitz,1970). We thus deduce that upon latrunculin treatment of CHO cells, both measurable aggregate-level viscoelastic coefficients, η and G decrease. These results suggest, that molecular changes at the cell level (here brought about by latrunculin), on occasion, can result in quantitatively predictable changes at the multicellular level.

Table 1. Relaxation Times Obtained From the Double Exponential Fit to Curves Shown in Figure 7
Latrunculin concentration (μM)τ1 (sec)aτ2 (sec)a
  • a

    Note the order of magnitude difference between τ1 and τ2, characterizing the rapid initial, more elastic and the later, more viscous relaxation, respectively. Errors are standard errors.

08.6 + 0.42117.58 + 2.75
0.17.18 + 0.14106.39 + 1.99
0.25.35 + 0.16101.65 + 1.71
0.53.86 + 0.0985.53 + 1.13
1.03.78 + 0.1871.27 + 1.59

Our biomechanical measurements on multicellular aggregates establish quantitative constraints between molecular and tissue-level generic parameters. The expression η ∝ JN/(koff a) (discussed earlier) relates the strength (J), surface density (N) and off rate (koff) of the CAM bonds to the apparent viscosity of the tissue-aggregate, η. The conclusion that η diminishes with latrunculin concentration is thus consistent with the expectation that J and/or koff respectively decreases and increases as the cytoskeleton becomes progressively more disorganized. Through the dependence of apparent tissue-aggregate surface tension on latrunculin concentration (Fig. 8), we can quantitatively relate the adhesive bond energy, J (established by means of CAMs) between the composing cells, to cytoskeletal integrity. The simultaneous validity of the two relationships σ ∝ JN (Forgacs et al.,1998; Foty and Steinberg,2005) and σ=a−bC (Fig. 8; a, b- constants; C, latrunculin concentration) suggests that for given cadherin surface density (i.e., fixed N) J decreases linearly with C. This conclusion suggests that, as far as tissue cohesivity (i.e., σ) is concerned, diminishing cytoskeletal integrity (here quantified in terms of C) can be compensated by the up-regulation of the number of active adhesive bonds. Alternatively, the loss of adhesive bonds (decrease in N) can be compensated by the re-establishment of cytoskeletal integrity (in the present case by decrease in C and increase in J). Such compensatory mechanisms may prove valuable in controlling epithelial–mesenchymal transitions and tumor metastasis.

What biologically useful information can be deduced from this study? Most importantly we related non-liquid cellular behavior to liquid-like tissue behavior. We presented examples of how the multitude of genetically controlled cellular processes can be summarized in a few measurable generic parameters (such as tissue surface tension, viscosity and shear modulus) that characterize processes and phenomena at the tissue level (Ninomiya and Winklbauer,2008). Even when the connection of these generic parameters to molecular mechanisms is not known, they can provide practical information on morphogenetic processes. Thus, the value of the time constant τ characterizing cushion tissue fusion (Figs. 1, 2) may correlate with normal or abnormal cardiogenesis. We also provided examples when explicit relationship between molecular and generic tissue parameters could be established. In such cases predictions can be made on how molecular manipulations may influence a morphogenetic process. Specifically, we related tissue surface tension σ and viscosity η to cytoskeletal integrity, the density of CAMs and the strength and lifetime of CAM bonds. As the combination σ/η (with dimension of velocity) often controls the time evolution of morphogenetic processes (Newman et al.,1997; Forgacs et al.,1998; Grima and Schnell,2007; Schötz et al.,2008), our results offer a recipe to molecularly influence tissue rearrangements. The finding on the fusion time τ∼η/σ−1, has important practical applications; it provides the scientific underpinning for a novel technology (“bioprinting”) to engineer three-dimensional tissue constructs of definite shape, as recently reported (Jakab et al.,2004,2008; Neagu et al.,2005).


Cushion Tissue Preparation

Cell culture medium, salt solutions, antibiotics and enzymes were obtained from Gibco BRL (Grand Island, NY), fetal bovine serum (FBS) was purchased from US Biotechnologies (Parkerford, PA). Leghorn chicken eggs (Ozark Hatcheries, Neosho, MO) were incubated at 40°C in 80% humidity for 4–6 days. Excised cushion tissue explants were washed in Earle's Balanced Salt Solution and cut into similar size fragments. Fragments were incubated in a gyratory shaker (at 120 RPM with 5% CO2 at 37°C) in Dulbecco's Modified Eagle Medium (DMEM) supplemented with FBS and 1% penicillin-streptomycin. In 24–36 hr (depending on size), this procedure reproducibly yielded round aggregates. In vitro fusion experiments were performed in hanging drop configuration, each drop containing two round aggregates. For in vivo fusion studies eggs were cut open, the embryos placed in Earle's Balanced Salt Solution, and the heart dissected. Fusing atrioventricular cushion tissue buds of approximately 400 micron were pinched from the opened myocardial tube at regular time intervals between HH stages 26 and 28 and placed in a Petri dish with fresh medium. The evolution of both in vitro and ex vitro fusion was recorded with a Spot-Insight CCD camera (Diagnostic Instruments, Sterling Heights, MI) attached to a dissecting microscope (Olympus SZ60, St. Louis, MO).

Cell Aggregate Preparation

CHO cells, transfected with N-cadherin (courtesy of A. Bershadsky, Weizmann Institute, Rehovot, Israel), were grown in DMEM supplemented with 10% FBS, 10 μg/ml of penicillin-streptomycin, gentamicin, kanamycin sulphate, and 400μg/ml geneticin. The confluent cultures containing approximately 3–4×106 cells per 75 cm2 TC dish were washed twice with Hanks' Balanced Salt Solution containing 2mM CaCl2, then treated for 10 min with trypsin 0.1%. Cell solutions were subsequently centrifuged at 2,500 RPM for 4 min. The resulting pellet was transferred into capillary micropipettes of 500 μm diameter and incubated at 37°C with 5% CO2 for 10 min. The firm cylinders of cells removed from the pipettes were cut into 500-μm-long fragments (aspect ratio 1), then incubated in 10-ml tissue culture flasks (Bellco Glass, Vineland, NJ) with 3 ml of DMEM on a gyratory shaker at 120 RPM with 5% CO2 at 37°C for 24–36 hr. This protocol reproducibly produced spherical model tissue aggregates of similar size. For kinetic assays (i.e., fusion of two aggregates and compression) aggregates (approximately 300 μm diameter) were prepared with fluorescently labeled cells to follow cellular movement. To visualize cellular mixing during fusion, one of the aggregates was prepared from cells stained with fluorescent membrane dye using DiIC18(5)-DS lipophilic carbocyanine tracer per manufacturer's instruction (Molecular Probes, Carlsbad, CA). To follow the movement of individual cells during compression, aggregates were prepared with 10% of the N-cadherin transfected CHO cells infected with histone binding H2B-YFP retrovirus (kindly provided by R.D. Lansford, Beckman Institute at California Institute of Technology) to express yellow fluorescent protein in their nuclei.

Surface Tension Measurements

The parallel plate compression tensiometer used in this work to measure liquid tissue properties is shown in Figure 9. Modified from previously used similar devices (Foty et al.,1996; Forgacs et al.,1998), it is controlled by Labview software (National Instruments, Austin, TX) to record the entire force relaxation following the uniaxial compression of an aggregate between parallel plates. Geometric parameters listed in the inset in Figure 9 were measured through a dissecting microscope positioned horizontally in front of the compression chamber. To minimize the adhesion of the aggregate to the plates, these were coated with poly(DTE co 7% PEG1000 oxalate). The poly(DTE co 7% PEG1000 oxalate) was synthesized as described by Yu and Kohn (1999), substituting the phosgene catalyzer with the less hazardous oxalyl-chloride. Structure and composition was confirmed with 13C and 1H NMR analysis and infrared spectroscopy. Aggregates were compressed in CO2 independent medium. A typical measurement was performed as explained in the caption to Figure 9. To assess the role of the actin cytoskeleton in tissue liquid properties, surface tension measurements were performed with aggregates incubated in varying concentration of latrunculin A (Molecular Probes, Eugene, OR; Coué et al.,1987) for 40 min, before compression. The overall shape of the postcompression force relaxation curves was similar when measurements were performed in medium with or without latrunculin present. However, quantitative analysis was performed only on data collected with aggregates compressed in latrunculin-free medium for reasons explained below.

Figure 9.

Tensiometer for surface tension measurements. A: The initially spherical aggregate was placed 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 a definite magnitude (the same when comparative studies with varying latrunculin concentration were carried out). To avoid irreversible damage to the cells, aggregates were compressed maximum 30% of their original diameter. B: The relaxation of the compressive force was followed (by measuring 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 equilibrium value, at which point the compression plates were separated, and the aggregate let to regain its original shape. Measurements in which the aggregate did not regain its precompressed shape where discarded. The inset shows the geometric parameters of a compressed aggregate used for the evaluation of the surface tension (see Data Analysis).

Figure 10.

A,B: Compression apparatus for kinetic assay. A: Aggregates were compressed between two 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 and lowered by a z-directional micromanipulator (MM) of 10 μm resolution. The LC is positioned on the metallic disk (MD) that also holds the micromanipulator. The apparatus is mounted on the stage of an Olympus IX-70 microscope with confocal imaging attachment (CM), used to record individual cell trajectories during the force relaxation process. A 60- to 80-μm section of the aggregate's lower part was scanned in 2-μm steps. Complete confocal scans were taken in 2-min time intervals up 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, were stored and later used for the reconstruction of cell trajectories. While x–y positions were determined accurately based on the fluorescent contour of the labeled nuclei, the accuracy of the z coordinate was limited by the 2 μm resolution preset on the confocal microscope when acquiring the images. Average total displacements were calculated using 15–40 cells per depth range.

Data Analysis

The shape of an aggregate compressed in the tensiometer shown in Figure 9 was recorded before, during, and after compression using a Spot Insight CCD camera fitted to the horizontally positioned dissecting microscope (described above). The surface tension was evaluated with the help of the Laplace equation, Feq/(πR32)=σ(1/R1+1/R2). Here σ is the tissue's surface tension (i.e., interfacial tension with the surrounding tissue culture medium), Feq is the equilibrium value of the compressive force (given by the flat portion of the curves in Fig. 7) and R3 is the radius of the circular contact area of the compressed aggregate with the plates. The quantities R1 and R2 are the radii of curvature of the aggregate's surface, respectively along its circular equatorial plane, and its profile, near this plane (see inset in Fig. 9). The geometric parameters were determined from the recorded profile by an in-house built tracking program, with a precision of 3 μm. The program evaluated the aggregate's profile on the basis of variation in gray scale values in its vicinity.

The accurate determination of σ requires the accurate measurement of the geometric parameters. This was not possible when latrunculin was present in the medium during compression because aggregate contour was often fuzzy. It is for this reason that compressions were performed in latrunculin-free medium. This modification does not affect our conclusions for the following reasons. When a cell is incubated in latrunculin-containing medium, at chemical equilibrium:

equation image(1)

Here Kd is the equilibrium dissociation constant of the latrunculin-G actin binding reaction and [G]0, [L]eq, [LG]eq are respectively the equilibrium concentrations of G actin (i.e., critical concentration), free latrunculin, and latrunculin-G actin complex. In vitro, [G]0 = 0.2 μM and Kd≈0.2 μM, as measured respectively in pure actin solutions (Pollard and Earnshaw,2002) and solutions containing actin and latrunculin (Coué et al.,1987). The in vitro results for Kd and [G]0 provide values for [LG]eq which are inconsistent with experimental findings in real cells stimulated with any reasonable latrunculin concentration. Pring and co-workers (Pring et al.,2002) measured [L]eq and [LG]eq, in real cells. Their values drastically differed from those that could be expected on the basis of in vitro results. In particular, these authors showed that cells retain latrunculin. After a mere 90-sec stimulation of cells with the drug, they found [L]≅0 in the medium indicating that almost all the latrunculin in the cells was sequestered. This means that under cellular conditions, [L]eq and [LG]eq in Eq. (1) are respectively very small and large. Thus, if after the establishment of equilibrium, as described by Eq. (1), cells (or aggregates of cells) are transferred into latrunculin-free fresh medium, very little cellular latrunculin will be released into the medium. This suggests that tensiometry data collected with latrunculin-free or latrunculin-containing medium do not significantly differ.

Kinetic Assay

A special compression apparatus, shown in Figure 10, was designed to investigate the movement of individual cells inside aggregates after compression. Because the apparatus was kept on the stage of a confocal microscope (Bio-Rad Radiance 200, Carl Zeiss Microimaging, Thornwood, NY), for technical reasons, compressions were performed at room temperature. A typical experiment was performed as explained in the caption to Figure 10. Experiments with latrunculin-treated aggregates were performed as described above.

Cell Viability Assay

After compression measurements were performed, the trypan blue exclusion test was used to determine whether the cells near the surface of the tissue explants/aggregates were viable. Additionally, explants/aggregates were cut in half to determine whether necrotic cells were present in the interior. Explants/aggregates were allowed to soak in a droplet of DMEM containing 20% trypan blue stain for 10 min. Trypan blue was then diluted, explants/aggregates placed into a Petri dish containing fresh DMEM and observed under the microscope. A small number (∼5%) of dead cells were typically found. Cell viability was also checked by the de-compression of aggregates after they reached postcompressive equilibrium. In all experiments that were used for data analysis de-compression resulted in the rounding of the aggregates to their precompressed state in approximately the same time as was needed to reach equilibrium.

Electron Microscopy of Aggregate Surface

The morphology of cells on the surface and in the interior of aggregates was analyzed by FESEM. Spherical aggregates were fixed in 4% paraformaldehyde (Electron Microscopy Sciences, Hatfield, PA) in phosphate-buffered saline (PBS) for 90 min, on a low speed shaker. Subsequently, samples were rinsed 3 times for 10 min in PBS. Dehydration was performed by an increasing concentration series of ethanol as follows: 10%, 25%, 50%, 75%, 95%, for 30 min each and finally in 100% ethanol overnight. After critical point drying (Samdri-PVT-3B, Tousimis, Rockville, MD), aggregates were spread on carbon adhesive tabs mounted on stub and sputter coated with platinum to a nominal thickness of 2 nm. Aggregate surface was examined using a Hitachi S4700 cold-cathode field-emission scanning electron microscope at an accelerating voltage of 5 kV.

Electron Microscopy of Cut-open Aggregates

FESEM was performed on uncompressed, compressed and compressed-equilibrated aggregates. Aggregates were fixed and kept for 4 hr in 2% glutaraldehyde, 2% (v/v) paraformaldehyde in 0.1 M cacodylate buffer. For the second group compression took place in the fixative itself, whereas for the third group fixation was carried out after postcompressive equilibrium has been reached in CO2 independent medium. After fixation, aggregates were washed 3 times for 10 min in 0.1 M cacodylate buffer. All aggregates were cryo-protected by incubating first for 3 hr in 25% (v/v) DMSO and subsequently in 50% DMSO overnight. The next day, after freezing in liquid nitrogen, aggregates were sectioned on a cryo-ultramicrotome (Ultracut UCT, Leica, Northvale, NJ) at −113°C. After removal of approximately fifty 1-μm-thick sections from compressed and compressed-equilibrated aggregates (parallel to the compression plates), cut-open aggregates were thawed in PBS. Aggregates were dehydrated and critical point dried (as above) and carefully placed on carbon adhesive tabs with the open face on top. Sputter-coating and FESEM settings were as above.


We thank Endre Szuromi for help in preparing the nonadhesive coverage of the compression plates. We also thank Cyrille Norotte for useful discussions. This work was supported by NSF-052684 (G.F., V.M., I.K., R.M.) and NIH (stipend for B.D.).