Abstract
Intercellular surface tension is a key variable in understanding cellular mechanics. However, conventional methods are not well suited for measuring the absolute magnitude of intercellular 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. This method exploits the cytoplasmic flow that accompanies laser-induced cell fusion when the pressure difference between cells is large. Because the cytoplasmic viscosity can be measured using well-established technology, this method can be used to estimate the absolute magnitudes 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 30-90 µN/m range. Our estimate was in close agreement with cell-medium surface tensions measured at single-cell resolution.
Abstract
3
Abstract
During embryogenesis, cells migrate and undergo morphological changes and rearrangements. These dynamic processes are mediated by the contractility of the cell cortex and adhesion between cells. From the viewpoint of mechanics, the contributions of contractility and adhesion can be combined into a single quantity: cell surface tension [1] [2] [3] [4] . Therefore, the cell surface tension is critical for understanding the mechanical aspects of embryogenesis. 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 for developmental biology. Thus, the cell surface tension at these interfaces is a matter of interest.
Abstract
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 are computed. Because cell movements are in an overdamped regime and forces acting on the cell are proportional to the velocity in this regime, the relative magnitudes of tension can be inferred. An excellent example of this strategy is laser microsurgery [5] [6] [7] [8] [9] [10] . Laser microsurgery, which monitors the recoil of cells or the cell cortex after laser ablation, has 4 provided significant insights into developmental mechanics. Other velocity-based methods observe spontaneous cell movements [11] or responses to externally applied stresses [12] .
Abstract
However, despite its successful applications in developmental biology, the velocitybased strategy has one problem that remains unsolved: it is difficult to measure the absolute magnitudes 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 hard to measure experimentally. This is particularly true for effective viscosity of the whole cell, a quantity 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, the validity 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 extracellular components [18] .
Abstract
The abovementioned drawback of the velocity-based strategy could be solved by focusing on specific cellular components that are more amenable to rheological measurements. The cytoplasm is constitutively much simpler than the whole cell, and its viscoelasticity can be evaluated by microrheological methods [19] [20] [21] [22] [23] . On the basis of this 5 idea, we developed a novel method that analyzed the cytoplasmic velocity for estimating intercellular surface tensions.
Abstract
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 two consequences: first, the cell-cell interface will be curved like an arc ( Fig. 1 A) ; second, the cytoplasm 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.
Abstract
The curvature of a cell-cell interface is related to the intercellular surface tension and the pressure difference by Laplace's law:
Abstract
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.
Abstract
We used laser-induced cell fusion to perforate the cell-cell interface. Two cells in contact can be selectively fused by irradiating their interface with a UV laser [24] [25] [26] . Upon cell fusion, the cytoplasm of the cell with higher hydrostatic pressure will flow into the cell with lower pressure (Fig. 1 B) . The flow velocity is related to the pressure difference ΔP and 6 the cytoplasmic viscoelasticity. To elucidate this relationship, computer simulation of fluid dynamics will be required for the general situation. However, the cytoplasm of some specific cell types can be approximated as simple Newtonian fluids, and we consider these situations hereafter.
Abstract
We modeled the cytoplasmic flow as an incompressible fluid flowing through a circular 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 states that the pressure difference across the wall is
Abstract
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.
Abstract
We applied this theory to the two-cell-stage embryos of C. elegans, which is the simplest system in terms of cell-cell interfaces (Fig. 2 A) . The viscoelasticity of their cytoplasm 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 7 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.
Abstract
The two-cell-stage embryo comprises an anterior AB cell and a posterior P 1 cell, and its shape is nearly symmetric around the anterior-posterior axis. The cell-cell interface is initially flat; however, it gradually forms a bulge extending from AB to P 1 . Application of laser irradiation to this interface causes fusion of the two cells and is accompanied by cytoplasmic flow from AB to P 1 [24] .
Abstract
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 the irradiated sites ( Fig. 2 B and Movie S1 in the Supporting Material). This flow was directed from AB to P 1 , 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-cell interfaces. These interfaces, which were curved at the onset of fusion, became flat after 30 s.
Abstract
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 8 flow velocity v was maximal at the onset of fusion (Fig. 3 A) , with a value of 0.9 ± 0.1 µm/s.
Abstract
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) .
Abstract
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 a nearly 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.
Abstract
We then estimated the pressure difference ΔP from Eq. 2. The estimated ΔP had a maximal value of 3.4 ± 0.4 Pa at the onset of fusion and then gradually decreased (Fig. 3 D) .
Abstract
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 was within the 39-50 µN/m range over the next 40 s (Fig. 3 E) . Correction coefficients were introduced to take into account the possible effects of membrane geometry, and the estimates of γ were widened to the 27-93 µm range (for details, see the Supporting Material).
Abstract
Our estimates were compared with the reported values of cell surface tensions and were found to be similar to those of cell-medium interfaces, but not to those of cell-cell [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.
Abstract
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 intercellular surface tensions: 27-93:330:22900 µN/m. This consideration reconfirms the importance of using 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.
Abstract
elegans embryos, the probe size of Daniels et al. (100 nm) will be larger than the length scale of 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 the meshwork 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.
Abstract
One drawback of our method is the assumption that the cytoplasm is a Newtonian 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, our method might be applicable to early embryogenesis, even in its current state.
Abstract
Another drawback of our method is that it is applicable only to cell-cell interfaces that 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 difference is 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, the estimation of R became highly unstable when the interface was nearly flat (Fig. 3 C) . This suggests that the current limitation of our method primarily arises from the inability to measure 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 for curvature computation.
Abstract
In conclusion, we have presented a novel method for estimating the intercellular surface tension. This method has single-cell resolution and allows estimation of the absolute 11 magnitude of this tension. Because the applicability of our method is currently limited, further study will be required to extend its areas of application.
Text
During embryogenesis, cells migrate and undergo morphological changes and rearrangements. These dynamic processes are mediated by the contractility of the cell cortex and adhesion between cells. From the viewpoint of mechanics, the contributions of contractility and adhesion can be combined into a single quantity: cell surface tension [1] [2] [3] [4] .
Text
Therefore, the cell surface tension is critical for understanding the mechanical aspects of embryogenesis. 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 for developmental biology. Thus, the cell surface tension at these interfaces is a matter of interest.
Text
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 are computed. Because cell movements are in an overdamped regime and forces acting on the cell are proportional to the velocity in this regime, the relative magnitudes of tension can be inferred. An excellent example of this strategy is laser microsurgery [5] [6] [7] [8] [9] [10] . Laser microsurgery, which monitors the recoil of cells or the cell cortex after laser ablation, has 4 provided significant insights into developmental mechanics. Other velocity-based methods observe spontaneous cell movements [11] or responses to externally applied stresses [12] .
Text
However, despite its successful applications in developmental biology, the velocitybased strategy has one problem that remains unsolved: it is difficult to measure the absolute magnitudes 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 hard to measure experimentally. This is particularly true for effective viscosity of the whole cell, a quantity 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, the validity 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 extracellular components [18] .
Text
The abovementioned drawback of the velocity-based strategy could be solved by focusing on specific cellular components that are more amenable to rheological measurements. The cytoplasm is constitutively much simpler than the whole cell, and its viscoelasticity can be evaluated by microrheological methods [19] [20] [21] [22] [23] . On the basis of this 5 idea, we developed a novel method that analyzed the cytoplasmic velocity for estimating intercellular surface tensions.
Text
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 two consequences: first, the cell-cell interface will be curved like an arc ( Fig. 1 A) ; second, the cytoplasm 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.
Text
The curvature of a cell-cell interface is related to the intercellular surface tension and the pressure difference by Laplace's law:
Text
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.
Text
We used laser-induced cell fusion to perforate the cell-cell interface. Two cells in contact can be selectively fused by irradiating their interface with a UV laser [24] [25] [26] . Upon cell fusion, the cytoplasm of the cell with higher hydrostatic pressure will flow into the cell with lower pressure (Fig. 1 B) . The flow velocity is related to the pressure difference ΔP and 6 the cytoplasmic viscoelasticity. To elucidate this relationship, computer simulation of fluid dynamics will be required for the general situation. However, the cytoplasm of some specific cell types can be approximated as simple Newtonian fluids, and we consider these situations hereafter.
Text
We modeled the cytoplasmic flow as an incompressible fluid flowing through a circular 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 states that the pressure difference across the wall is
Text
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.
Text
We applied this theory to the two-cell-stage embryos of C. elegans, which is the simplest system in terms of cell-cell interfaces (Fig. 2 A) . The viscoelasticity of their cytoplasm 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 7 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.
Text
The two-cell-stage embryo comprises an anterior AB cell and a posterior P 1 cell, and its shape is nearly symmetric around the anterior-posterior axis. The cell-cell interface is initially flat; however, it gradually forms a bulge extending from AB to P 1 . Application of laser irradiation to this interface causes fusion of the two cells and is accompanied by cytoplasmic flow from AB to P 1 [24] .
Text
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 the irradiated sites ( Fig. 2 B and Movie S1 in the Supporting Material). This flow was directed from AB to P 1 , 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-cell interfaces. These interfaces, which were curved at the onset of fusion, became flat after 30 s.
Text
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 8 flow velocity v was maximal at the onset of fusion (Fig. 3 A) , with a value of 0.9 ± 0.1 µm/s.
Text
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) .
Text
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 a nearly 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.
Text
We then estimated the pressure difference ΔP from Eq. 2. The estimated ΔP had a maximal value of 3.4 ± 0.4 Pa at the onset of fusion and then gradually decreased (Fig. 3 D) .
Text
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 was within the 39-50 µN/m range over the next 40 s (Fig. 3 E) . Correction coefficients were introduced to take into account the possible effects of membrane geometry, and the estimates of γ were widened to the 27-93 µm range (for details, see the Supporting Material).
Text
Our estimates were compared with the reported values of cell surface tensions and were found to be similar to those of cell-medium interfaces, but not to those of cell-cell [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.
Text
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 intercellular surface tensions: 27-93:330:22900 µN/m. This consideration reconfirms the importance of using 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.
Text
elegans embryos, the probe size of Daniels et al. (100 nm) will be larger than the length scale of 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 the meshwork 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.
Text
One drawback of our method is the assumption that the cytoplasm is a Newtonian 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, our method might be applicable to early embryogenesis, even in its current state.
Text
Another drawback of our method is that it is applicable only to cell-cell interfaces that 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 difference is 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, the estimation of R became highly unstable when the interface was nearly flat (Fig. 3 C) . This suggests that the current limitation of our method primarily arises from the inability to measure 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 for curvature computation.
Text
In conclusion, we have presented a novel method for estimating the intercellular surface tension. This method has single-cell resolution and allows estimation of the absolute 11 magnitude of this tension. Because the applicability of our method is currently limited, further study will be required to extend its areas of application. 
Figure legends


{'paper_id': '7462867', 'title': 'Estimating intercellular surface tension by laser-induced cell fusion.', 's2_url': 'https://api.semanticscholar.org/CorpusID:7462867', 'source': 'S2ORC'}