Estimating intercellular surface tension by laser-induced cell fusion
Masashi Fujita1,2 and Shuichi Onami1,2*
Affiliations:
1

Laboratory for Developmental Dynamics, RIKEN Quantitative Biology Center

2

Developmental Systems Modeling Team, Advanced Computational Sciences Department,

RIKEN Advanced Science Institute2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan*

Corresponding author: Shuichi Onami

Laboratory for Developmental Dynamics, RIKEN Quantitative Biology Center
2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
Phone: +81-78-306-3440
Fax: +81-78-306-3442
E-mail: sonami@riken.jp

1

Abstract
Intercellular surface tension is a key variable in understanding cellular mechanics. However,conventional methods are not well suited for measuring the absolute magnitude ofintercellular surface tension because these methods require determination of the effective
viscosity of the whole cell, a quantity that is difficult to measure. In this study, we present a
novel method for estimating the intercellular surface tension at single-cell resolution. Thismethod exploits the cytoplasmic flow that accompanies laser-induced cell fusion when thepressure difference between cells is large. Because the cytoplasmic viscosity can be measured
using well-established technology, this method can be used to estimate the absolutemagnitudes of tension. We applied this method to two-cell-stage embryos of the nematode
Caenorhabditis elegans and estimated the intercellular surface tension to be in the 30–90µN/m range. Our estimate was in close agreement with cell–medium surface tensions
measured at single-cell resolution.

2

Text
During embryogenesis, cells migrate and undergo morphological changes andrearrangements. These dynamic processes are mediated by the contractility of the cell cortex
and adhesion between cells. From the viewpoint of mechanics, the contributions ofcontractility and adhesion can be combined into a single quantity: cell surface tension [1-4].
Therefore, the cell surface tension is critical for understanding the mechanical aspects ofembryogenesis. Cell surfaces can be classified on the basis of milieu, such as cell–medium
and cell–cell interfaces. Among these, cell–cell interfaces are the most important fordevelopmental biology. Thus, the cell surface tension at these interfaces is a matter of interest.
However, measurement of the intercellular surface tension is not straightforward
because the cell–cell interfaces are physically inaccessible. To circumvent this difficulty,
current measurement methods employ a velocity-based strategy. In this strategy, tensiondriven movements of cells (or subcellular structures) are observed and their velocities arecomputed. Because cell movements are in an overdamped regime and forces acting on thecell are proportional to the velocity in this regime, the relative magnitudes of tension can beinferred. An excellent example of this strategy is laser microsurgery [5-10]. Laser
microsurgery, which monitors the recoil of cells or the cell cortex after laser ablation, has3

provided significant insights into developmental mechanics. Other velocity-based methods
observe spontaneous cell movements [11] or responses to externally applied stresses [12].
However, despite its successful applications in developmental biology, the velocitybased strategy has one problem that remains unsolved: it is difficult to measure the absolutemagnitudes of intercellular surface tension. Theoretically, because of the overdamped
dynamics, the absolute magnitude can be estimated by multiplying the movement velocity by
the viscosity of relevant materials. However, the problem is that the relevant viscosity is hardto measure experimentally. This is particularly true for effective viscosity of the whole cell, aquantity that rules all aspects of cell movements [13, 14]. Several researchers have assumed
that the effective viscosity is equal to the cytoplasmic viscosity [9, 11, 12]. However, thevalidity of this assumption is uncertain because the effective viscosity could be produced not
only by the cytoplasm but also by the cell cortex [15], nuclei [16, 17], and extracellularcomponents [18].
The abovementioned drawback of the velocity-based strategy could be solved byfocusing on specific cellular components that are more amenable to rheologicalmeasurements. The cytoplasm is constitutively much simpler than the whole cell, and its
viscoelasticity can be evaluated by microrheological methods [19-23]. On the basis of this4

idea, we developed a novel method that analyzed the cytoplasmic velocity for estimatingintercellular surface tensions.
This method focuses on specific situations when two cells in contact have a large
difference in their intracellular hydrostatic pressures. This pressure difference will have twoconsequences: first, the cell–cell interface will be curved like an arc (Fig. 1 A); second, thecytoplasm will flow between the cells when their interface is perforated (Fig. 1 B). By
relating these two phenomena, our method estimates the surface tension at the interface.
The curvature of a cell–cell interface is related to the intercellular surface tension andthe pressure difference by Laplace’s law:
"P =

2#
,
R

(1)

where ΔP is the pressure difference, γ is the intercellular surface tension, and R is the!

interface curvature radius (Fig. 1 A). Therefore, γ can be determined if the values of ΔP and
R are known. The value of R can be obtained by curve fitting using microscopic images.
We used laser-induced cell fusion to perforate the cell–cell interface. Two cells incontact can be selectively fused by irradiating their interface with a UV laser [24-26]. Upon
cell fusion, the cytoplasm of the cell with higher hydrostatic pressure will flow into the cellwith lower pressure (Fig. 1 B). The flow velocity is related to the pressure difference ΔP and5the cytoplasmic viscoelasticity. To elucidate this relationship, computer simulation of fluid
dynamics will be required for the general situation. However, the cytoplasm of some specificcell types can be approximated as simple Newtonian fluids, and we consider these situations
hereafter.
We modeled the cytoplasmic flow as an incompressible fluid flowing through acircular pore in a thin planar wall. Many cell-scale phenomena are found in the low Reynolds
number regime [27], and the flow in this regime follows Sampson’s law [28], which statesthat the pressure difference across the wall is"P = 3#

vµ
,
c

(2)

where v is the mean flow velocity through the pore, µ is the shear viscosity of the fluid, and c!

is the pore radius. The intercellular surface tension γ can be estimated by combining Eqs. 1
and 2.
We applied this theory to the two-cell-stage embryos of C. elegans, which is thesimplest system in terms of cell–cell interfaces (Fig. 2 A). The viscoelasticity of theircytoplasm was previously investigated by Daniels et al. [22]. The cytoplasm had negligible
elasticity, suggesting that it satisfied Newtonian fluidity, a prerequisite for using Eq. 2. The
cytoplasmic viscosity was µ = 10 ± 1 Poise. Although Daniels et al. studied one-cell-stage
6

embryos, they found no significant difference between the anterior and posterior regions,which are the immediate predecessors of two-cell-stage blastomeres. Therefore, we assumed
that µ in the two-cell stage was identical to that in the one-cell stage.
The two-cell-stage embryo comprises an anterior AB cell and a posterior P1 cell, andits shape is nearly symmetric around the anterior–posterior axis. The cell–cell interface isinitially flat; however, it gradually forms a bulge extending from AB to P1. Application oflaser irradiation to this interface causes fusion of the two cells and is accompanied bycytoplasmic flow from AB to P1 [24].
We performed this fusion experiment to estimate the intercellular surface tension (n =9). Immediately after laser irradiation, a flow of cytoplasmic granules was observed near theirradiated sites (Fig. 2 B and Movie S1 in the Supporting Material). This flow was directedfrom AB to P1, consistent with a previous report [24]. The flow gradually attenuated,
although it continued until approximately 50 s. The membrane pore size was initially small,but gradually enlarged, indicating that contractile forces were acting on the cell–cellinterfaces. These interfaces, which were curved at the onset of fusion, became flat after 30 s.
We quantified the flow velocities, pore radii, and curvature radii of these interfaces
from the 9 image sequences and computed the sample means and SEMs (mean ± SEM). The
7

flow velocity v was maximal at the onset of fusion (Fig. 3 A), with a value of 0.9 ± 0.1 µm/s.
The pore radius c had a minimum value of 2.6 ± 0.2 µm at the onset of fusion (Fig. 3 B). The
curvature radius R was initially 32 ± 2 µm and then gradually increased for 25 s (Fig. 3 C).
30 s after the onset of fusion, both the mean and SEM values of R showed a sudden increase,presumably because of the flatness of the interface. Because the curvature estimation for anearly flat surface is technically difficult, we believe that these values of R after 30 s may
contain large computational artifacts. Therefore, the latter half of the time course requires
careful interpretation.
We then estimated the pressure difference ΔP from Eq. 2. The estimated ΔP had amaximal value of 3.4 ± 0.4 Pa at the onset of fusion and then gradually decreased (Fig. 3 D).
The intercellular surface tension γ was then estimated by substituting the values of ΔP and R
into Eq. 1. The intercellular surface tension was estimated to be γ = 51 ± 5 µN/m and waswithin the 39–50 µN/m range over the next 40 s (Fig. 3 E). Correction coefficients wereintroduced to take into account the possible effects of membrane geometry, and the estimatesof γ were widened to the 27–93 µm range (for details, see the Supporting Material).
Our estimates were compared with the reported values of cell surface tensions andwere found to be similar to those of cell–medium interfaces, but not to those of cell-cell
8interfaces. For example, cell–medium surface tensions of fish cells were in the 30–80 µN/m
range (Figure 2d in [29]), whereas those of neutrophils were in the 10–30 µN/m range [30,31]. In contrast, the intercellular surface tension of fly epithelia corresponded to 330 µN/m[9], while that of a cell aggregate was estimated to be 22.9 mN/m [12]. These large

discrepancies between intercellular surface tensions could be attributable to sample
differences or to differences in the assumed viscosity values.
We used a value of 10 Poise for viscosity, whereas previous papers used values of
100 and 9600 Poise. Their ratio matches up well with the ratio of the measured intercellularsurface tensions: 27–93:330:22900 µN/m. This consideration reconfirms the importance ofusing an accurate viscosity value. It might be argued that viscoelasticity might have a lengthscale dependency because the cytoplasm is highly inhomogeneous. However, in the case of C.
elegans embryos, the probe size of Daniels et al. (100 nm) will be larger than the length scaleof non-uniformity in the cytoplasm. This is because actin meshwork, which plays the central
role in cell rheology, apparently absent from the embryo cytoplasm [32]. Even if themeshwork exists, its length scale is ~50 nm [33]. Therefore, the value of viscosity we used
would reflect bulk viscosity of the cytoplasm in the nematode embryos.
One drawback of our method is the assumption that the cytoplasm is a Newtonian9

fluid. Although generalization to non-Newtonian fluids might be possible with the aid ofcomputational fluid dynamics, this Newtonian assumption could be practically limiting.
However, undifferentiated cells have more fluid-like behavior than differentiated cells [22,23]. Furthermore, weak elasticity has little effect on Sampson’s law [34]. Therefore, ourmethod might be applicable to early embryogenesis, even in its current state.
Another drawback of our method is that it is applicable only to cell–cell interfacesthat are curved because of the large pressure differences involved. This raises a question
regarding which part of our estimation procedure will face obstacles if the pressure differenceis small. In our results, the magnitudes of ΔP became significantly small at 30 s or later (Fig.
3 D); however, we could still detect the cytoplasmic flow (Fig. 3 A). In contrast, theestimation of R became highly unstable when the interface was nearly flat (Fig. 3 C). Thissuggests that the current limitation of our method primarily arises from the inability tomeasure R accurately for weakly curved interfaces. The application range of our method may
be extended using improved microscopy for cell-shape imaging or numerical algorithms forcurvature computation.
In conclusion, we have presented a novel method for estimating the intercellularsurface tension. This method has single-cell resolution and allows estimation of the absolute
10magnitude of this tension. Because the applicability of our method is currently limited,further study will be required to extend its areas of application.

Acknowledgments
The N2 strain was provided by the Caenorhabditis Genetics Center, which is funded by the
NIH National Center for Research Resources (NCRR). This study was supported by grants
from KAKENHI (Grant-in-Aid for Scientific Research) on the ‘Systems Genomics’ Priority
Area from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

11References[1]

Lecuit T, Lenne P-F. Cell surface mechanics and the control of cell shape, tissue patterns andmorphogenesis. Nat Rev Mol Cell Biol. 2007 Aug 1;8(8):633-44.
[2]

Mammoto T, Ingber DE. Mechanical control of tissue and organ development. Development.

2010 May 1;137(9):1407-20.
[3]Montell DJ. Morphogenetic cell movements: diversity from modular mechanical properties.

Science. 2008 Dec 5;322(5907):1502-5.
[4]

Manning ML, Foty RA, Steinberg MS, Schoetz E-M. Coaction of intercellular adhesion andcortical tension specifies tissue surface tension. Proc Natl Acad Sci USA. 2010 Jun
28;107(28):12517–22.
[5]

Hutson M, Tokutake Y, Chang M, Bloor J, Venakides S, Kiehart D, et al. Forces formorphogenesis investigated with laser microsurgery and quantitative modeling. Science.
2003;300(5616):145.
[6]

Farhadifar R, Röper J-C, Aigouy B, Eaton S, Jülicher F. The influence of cell mechanics,

cell-cell interactions, and proliferation on epithelial packing. Curr Biol. 2007 Dec 18;17(24):2095-104.
[7]

Rauzi M, Verant P, Lecuit T, Lenne P-F. Nature and anisotropy of cortical forces orienting

Drosophila tissue morphogenesis. Nat Cell Biol. 2008 Nov 2;10(12):1401 - 10.
[8]

Ma X, Lynch HE, Scully PC, Hutson MS. Probing embryonic tissue mechanics with laserhole drilling. Phys Biol. 2009 Jan 1;6(3):036004.
[9]

Hutson MS, Veldhuis J, Ma X, Lynch HE, Cranston PG, Brodland GW. Combining laser

microsurgery and finite element modeling to assess cell-level epithelial mechanics. BiophysicalJournal. 2009 Dec 16;97(12):3075-85.
[10]Mayer M, Depken M, Bois JS, Jülicher F, Grill SW. Anisotropies in cortical tension reveal

the physical basis of polarizing cortical flows. Nature. 2010 Nov 1;467(7315):617-21.
[11]

Brodland GW, Conte V, Cranston PG, Veldhuis J, Narasimhan S, Hutson MS, et al. Video

force microscopy reveals the mechanics of ventral furrow invagination in Drosophila. Proc Natl Acad
Sci USA. 2010 Dec 21;107(51):22111-6.
[12]

Yang J, Brodland GW. Estimating interfacial tension from the shape histories of cells incompressed aggregates: a computational study. Ann Biomed Eng. 2009 Feb 13;37(5):1019-27.
[13]

Chen HH, Brodland GW. Cell-level finite element studies of viscous cells in planar

aggregates. J Biomech Eng. 2000 Aug 1;122(4):394-401.
[14]

Cranston PG, Veldhuis JH, Narasimhan S, Brodland GW. Cinemechanometry (CMM): A
12

Method to Determine the Forces that Drive Morphogenetic Movements from Time-Lapse Images.
Ann Biomed Eng. 2010 Sep 8;38(9):2937-47.
[15]

Zhou J, Kim HY, Davidson LA. Actomyosin stiffens the vertebrate embryo during crucial

stages of elongation and neural tube closure. Development. 2009 Feb 15;136(4):677-88.
[16]

Guilak F, Tedrow JR, Burgkart R. Viscoelastic Properties of the Cell Nucleus. Biochemicaland biophysical research communications. 2000 Mar 1;269(3):781-6.
[17]

Caille N, Thoumine O, Tardy Y, Meister JJ. Contribution of the nucleus to the mechanicalproperties of endothelial cells. J Biomech. 2002;35(2):177-87.
[18]

Ebihara T, Venkatesan N, Tanaka R, Ludwig MS. Changes in extracellular matrix and tissue

viscoelasticity in bleomycin-induced lung fibrosis. Temporal aspects. American journal of respiratory
and critical care medicine. 2000;162(4):1569.
[19]

Bausch AR, Möller W, Sackmann E. Measurement of local viscoelasticity and forces in living

cells by magnetic tweezers. Biophysical Journal. 1999 Jan 1;76(1 Pt 1):573-9.
[20]

Tseng Y, Kole TP, Wirtz D. Micromechanical mapping of live cells by multiple-particle-

tracking microrheology. Biophysical Journal. 2002 Dec 1;83(6):3162-76.
[21]

Tolić-Nørrelykke IM, Munteanu E-L, Thon G, Oddershede L, Berg-Sørensen K. Anomalous

diffusion in living yeast cells. Phys Rev Lett. 2004 Aug 13;93(7):078102.
[22]

Daniels BR, Masi BC, Wirtz D. Probing single-cell micromechanics in vivo: themicrorheology of C. elegans developing embryos. Biophys J. 2006 Jun 15;90(12):4712-9.
[23]

Daniels BR, Hale CM, Khatau SB, Kusuma S, Dobrowsky TM, Gerecht S, et al. Differencesin the Microrheology of Human Embryonic Stem Cells and Human Induced Pluripotent Stem Cells.
Biophysical Journal. 2010 Jan 12;99(11):3563-70.
[24]

Schierenberg E. Altered cell-division rates after laser-induced cell fusion in nematodeembryos. Dev Biol. 1984;101(1):240-5.
[25]

Wiegand R, Weber G, Zimmermann K, Monajembashi S, Wolfrum J, Greulich KO. Laser-induced fusion of mammalian cells and plant protoplasts. J Cell Sci. 1987 Sep 1;88(2):145-9.
[26]

Irle T, Schierenberg E. Developmental potential of fused Caenorhabditis elegans oocytes:

generation of giant and twin embryos. Dev Genes Evol. 2002 Jul 1;212(6):257-66.
[27]

Purcell EM. Life at low Reynolds number. Am J Phys. 1977;45(1):3-11.

[28]

Happel J, Brenner H. Low Reynolds number hydrodynamics: with special applications toparticulate media. The Hague: Martinus Nijhoff Publishers; 1983.
[29]

Krieg M, Arboleda-Estudillo Y, Puech P-H, Käfer J, Graner F, Müller DJ, et al. Tensile

forces govern germ-layer organization in zebrafish. Nat Cell Biol. 2008 Apr 1;10(4):429-36.
13

[30]

Hochmuth RM. Micropipette aspiration of living cells. J Biomech. 2000 Jan 1;33(1):15-22.

[31]

Lomakina EB, Spillmann CM, King MR, Waugh RE. Rheological analysis and measurementof neutrophil indentation. Biophys J. 2004 Oct 28;87(6):4246-58.
[32]

Strome S. Fluorescence visualization of the distribution of microfilaments in gonads and early

embryos of the nematode Caenorhabditis elegans. J Cell Biol. 1986 Dec 1;103(6 Pt 1):2241-52.
[33]

Wirtz D. Particle-tracking microrheology of living cells: principles and applications. Annual

Review of Biophysics. 2009 Jan 1;38:301-26.
[34]

Rothstein JP, McKinley GH. The axisymmetric contraction-expansion: the role of extensionalrheology on vortex growth dynamics and the enhanced pressure drop. Journal of non-newtonian fluid
mechanics. 2001;98(1):33-63.

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Figure legends
Figure 1 Schematic illustration of two cells with a large pressure difference. (A) When two
cells have intracellular hydrostatic pressures of P and P + ΔP, the difference ΔP causes thecell–cell interface to become curved. The curvature radius R is determined from ΔP and theintercellular surface tension γ. (B) When the two cells are fused, the pressure difference ΔP
produces a cytoplasmic flow through the membrane pore. The flow velocity is denoted by v.

Figure 2 (A) Differential interference contrast image of a two-cell-stage embryo of C.
elegans at 8 min after the onset of the two-cell stage. The anterior is oriented to the left. The
larger anterior cell is AB, and the smaller posterior cell is P1. Scale bar = 10 µm. (B)Cytoplasmic flow immediately after cell fusion. Scale arrow = 1 µm/s.

Figure 3 Measured and estimated quantities as a function of time after the onset of cellfusion. (A) Flow velocity. (B) Membrane pore radius. (C) Interface curvature radius (D)Pressure difference between AB and P1. (E) Intercellular surface tension. Error bars indicate
SEMs of 9 samples.

15

A

P + ΔP

B

R

γ

v
P

P + ΔPP

Figure. 1

16

A

B

Figure. 2

17

A

B

0.8

4.0

0.6
0.4

2.0

0.2
0.0

0

10

C 400

20 30
Time (s)

40

50

0

10

20
30
Time (s)

40

50

0

10

20
30
Time (s)

40

50

3.0
ΔP (Pa)R (μm)

0.0

D 4.0

300

2.0

200

1.0

100
0

6.0

c (μm)v (μm/s)

1.0

0

10

20 30
Time (s)

40

50

0

10

20 30
Time (s)

40

50

E 80

0.0

γ (μΝ/m)

60
40
20
0

Figure. 318