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Imaging Biological Cells Using Liquid Crystals Jiyu Fang,* Wu Ma, Jonathan V. Selinger, and R. Shashidhar Center for Bio/Molecular Science and Engineering, Naval Research Laboratory, Code 6900, Washington, D.C. 20375 Received August 14, 2002. In Final Form: October 10, 2002 Biological cells have been imaged using liquid crystals as an optical amplification medium. Preferential orientation of the liquid-crystal molecules at the surfaces of cells immobilized on substrates leads to wellresolved images, with very sharp contrast compared to images observed by standard phase-contrast microscopy. The feasibility of this technique has been demonstrated for muscle cells, fat cells, and neurons. Calculations based on a continuum elastic theory reproduce the observed features of the images of muscle and fat cells and allow us to estimate the optimum resolution that can be achieved by this technique.
Introduction Nematic liquid crystals are anisotropic fluids, which have long-range orientational order of the constituent molecules without long-range positional order. The energy required to perturb the molecular order of liquid crystals is very small, and any defect or nonuniformity of the surface in contact with the liquid crystals leads to changes in the local order.1 This in turn leads to different types of optical patterns or textures when observed in a polarizing microscope. Also, the changes in the molecular order induced by surface defects and the associated optical patterns can extend over several tens of micrometers into the liquid crystal medium, enabling the use of liquid crystals as on optical amplification medium. This property has been used to image in-plane structural defects in selfassembled monolayers (SAMs) formed by thiol-based molecules as well as lipid surfactants.2-4 Recently liquid crystals have been used for optical detection of biological and chemical interactionssparticularly binding of receptor molecules to ligands hosted within a SAM5 and detection of specific chemical analytes.6 In this paper, we show that we can use the same principles to map the external morphological features of different types of biological cells. We immobilize muscle cells, fat cells, and neurons on a substrate, place a liquid crystal above them, and observe the biological structure through crossed polarizers. We find that each type of cell gives characteristic features in the liquid-crystal image. Muscle cells give two parallel bright bands along the cell periphery, while fat cells give four bright lobes around the periphery. In the case of neurons, the processes emanating from the cell body are clearly distinguishable. We propose a continuum elastic theory to explain how the cells realign the liquid-crystal director configuration. The theory explains the characteristic features of the experimental images of muscle and fat cells, and determines the corresponding configurations of the three-dimensional liquid-crystal director field. From this theory, we estimate * To whom correspondence should be addressed: e-mail: JYF@ CBMSE.NRL.Navy.Mil. (1) Jerome, B. Rep. Prog. Phys. 1991, 54, 391-451. (2) Gupta, V. K.; Abbott, N. L. Phys. Rev. E 1996, 54, R4540-R4543. (3) Fang, J. Y.; Gehlert, U.; Shashidhar, R.; Knobler, C. M. Langmuir 1999, 15, 297-299. (4) Cheng, Y. L.; Batchelder, D. N.; Evans, S. D.; Henderson, J. R.; Lydon, J. E.; Ogier, S. D. Liq. Cryst. 2000, 27, 1267-1275. (5) Gupta, V. K.; Skaife, J. J.; Dubrovsky, T. B.; Abbott, N. L. Science 1998, 279, 2077-2080. (6) Shah, R. R.; Abbott, N. L. J. Am. Chem. Soc. 1999, 121, 1130011310.
that the optimum resolution of this technique is the optical wavelength divided by twice the birefringence of the liquid crystal, which is about 1.5 µm for the liquid crystal we have used. Materials and Methods Myoblast cultures were obtained as described in previous papers.7-8 Briefly, muscles were stripped from the hindlimbs of 21 days old fetal rats, trypsinized to dissociate, plated for 1 h to remove fibroblasts, and then replated on 0.5% gelatin-coated dishes in dulbeccos modified Eagle’s medium (DMEM) supplemented with 10% horse serum (Life Technologies, Gaithersburg, MD) and 10% fetal calf serum (Intergen, Purchase, NY) (growth medium). Approximately 48 h later, cells were incubated with 0.05% Dispase II (Roche Molecular Biochemicals, Indianapolis, IN) to selectively detach myoblasts and replated for 30 min to remove more fibroblasts. Finally, 0.5 × 106 cells were plated in 35 mm dishes on either gelatin- and carbon-coated 13 mm-round coverslips (Clay Adams Gold Seal, Becton-Dickinson Labware, Oxnard, CA) (for immunostaining) or on gelatin-coated dishes only (for protein). Forty-eight hours after cell plating, all cultures were re-fed with 90% DMEM, 10% horse serum to discourage fibroblast growth. Twenty-four hours later, the cultures were again re-fed with 95% DMEM, 5% horse serum. All media also contained penicillin/streptomycin (100U/100 mg/mL) and fungizone (2.5 µg/mL). Freshly isolated cells were used for each experiment. Cells were maintained at 37 °C, 100% humidity with 8% CO2. Some cultures were treated with 1.5 µM tetrodotoxin to inhibit myotube contraction, starting 2 days after plating and continuing until the time of harvest, 12-13 days after final myoblast plating. At the time of harvest, very few myoblasts were detected by desmin immunostaining, which indicated a fusion index of >95%. Since fat cells are located throughout the body in loose connective tissue, they appeared in muscle cultures. Hippocampal cells were dissociated from embryonic day 18 or 19 rats by papain digestion according to the method of Huettner and Baughman.9 At these ages, hippocampal cells were less susceptible to damage during dissociation and the number of their progenitors was near its peak, and thus they yielded the highest number of viable cells. The cells were plated onto poly(D-lysine) coated glass coverslips at a density of 2 × 104 cells/cm2. Cultures were maintained in serum-free Neurobasal medium containing B27 and 0.5 mM L-glutamine.10 Phase contrast images of cells on glass slips were taken with a 20× objective in a T041 Olympus microscope. (7) Dutton, E. K.; Uhm, C.-S.; Samuelsson, S. J.; Schaffner, A. E.; Fitzgerald, S. C.; Daniels, M. P. J. Neurosci. 1995, 15, 7401-7416. (8) Daniels, M. P.; Lowe, B. T.; Shah, S.; Ma, J.; Samuelsson, S. J.; Lugo, B.; Parakh, T.; Uhm, C.-S. Microsc. Res. Technol. 2000, 49, 2637. (9) Huettner, J. E.; Baughman, R. W. J. Neurosci. 1986, 6, 3044-3060. (10) Brewer, G. J.; Torricelli, J. R.; Everge, E. K.; Price, P. J. J. Neurosci. Res. 1993, 35, 567-576.
10.1021/la0264062 CCC: $25.00 © 2003 American Chemical Society Published on Web 01/01/2003
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Figure 1. Schematic geometry of a cell adsorbed on a microscope slide, with a nematic liquid crystal above the cell.
Figure 3. (a) Polarized microscope image of fat cells below the nematic liquid crystal 5CB. (b) Phase-contrast image of fat cells. These two images show different fields of view on the same slide.
Figure 2. (a) Polarized microscope image of muscle cells below the nematic liquid crystal 5CB. (b) Phase-contrast image of muscle cells. These two images show different fields of view on the same slide. A drop of nematic liquid crystal 5CB (4′-pentyl-4-cyanobiphenyl) was first placed on a cell-covered glass slide, and then a poly(D-lysine) coated glass slide was placed on the 5CB drop to form a sandwich structure with a space of about 40-50 µm, as shown in Figure 1. To avoid creating any directional orientation during the sample preparation, the 5CB was applied to the cell surfaces in its isotropic phase at 35 °C and then cooled into the nematic phase at room temperature. 5CB textures on cell surfaces were imaged with a 20× objective in a BX 60 Olympus polarized microscope with a hot stage. For the polarized microscope, the optics were adjusted to complete extinction before placing samples on the stage.
Cell Images Figures 2 and 3 show optical microscopic pictures of muscle cells and fat cells under the 5CB liquid crystal
between crossed polarizers. The corresponding phasecontrast microscope pictures of the same type of cells (without liquid crystals) are also shown in each case. Clearly the muscle and fat cells are decorated by the liquid crystals. The optical amplification caused by the differences in the orientation of the liquid-crystal molecules on the cell surfaces compared to the orientation of the molecules far away from the cells leads to high-contrast pictures that show details of the cell morphology. Muscle cells (Figure 2A) are characterized by their elongated shape. The two edges of the long muscle cells are broad bright bands in the liquid-crystal images. The brightness of these bands changes as the plane of optical polarization is rotated. There is a dark region at the center of the cell. Fat cells (Figure 3A) are characterized by a circular shape. The edge of the cells is decorated by four bright lobes with an angular width of 90°. There is some dark fine structure within the lobes. The central portion of the fat cells appears dark. By comparison, images of the liquid crystal without cells appear uniformly dark, which shows that 5CB molecules have a homeotropic alignment on the poly(Dlysine) coated glass slide. The details of liquid crystal orientation around cell surfaces will be discussed in the theoretical section.
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Given the boundary conditions, the director in the interior of the liquid crystal can be derived by minimizing the elastic free energy. We suppose that the elastic constants for splay, twist, and bend distortions of the director are all equal to a single elastic constant K. In that case, the free energy has equal contributions from all spatial derivatives of the director ∂Rnβ. Hence, it can be written as11
1 F) K 2
Figure 4. Polarized microscope image of neurons below the nematic liquid crystal 5CB.
Figure 4 shows a liquid crystal image of neurons that were immobilized 6 days after the culture was prepared. We can clearly see processes emanating from the cell body as birefringent “arms.” Two distinct features are seen: (1) The processes appear as twisted bright fibers, in contact to the smooth, bright edges of elongated muscle cells. (2) One of the arms has a pink color, which is quite different from the other arms. This pink color may indicate a difference in the chemical components on the surface of one process compared with the other processes, which would affect the local alignment of the liquid crystal. Theory To explain the liquid-crystal images of cells, there are three key theoretical questions. First, what is the interaction between cell surfaces and liquid crystals, which determines the orientation of the liquid crystals at the cell surface? Second, how does the orientation induced by the cell surface extend into the interior of the liquid crystal? Third, how does the configuration of the liquid crystal director affect the transmission of light? The second and third questions involve issues of liquid-crystal science, which we address in this section. The first question involves the connection between liquid-crystal science and biology. Although we do not have a definite answer, we discuss the possibilities in the next section. We consider the geometry of Figure 1. A cell is adsorbed on the microscope slide, and the nematic liquid crystal fills the space between the cell and the coverslip. Light propagates upward through the polarizer, then through the liquid crystal which may rotate its plane of polarization, and then out through the analyzer. The optical properties of the liquid crystal are determined by the director n(r), which represents the local orientation of the molecules. This director must satisfy certain boundary conditions along the surfaces of the microscope slide, the coverslip, and the cell itself. Along the glass slide and coverslip, the anchoring is homeotropic; i.e., the director points perpendicular to these surfaces, along the z axis. As a working model, we suppose that anchoring along the cell surface is also homeotropic, so that the director points radially outward. Possible mechanisms for this anchoring will be discussed in the next section.
∫d3r (∂Rnβ)(∂Rnβ)
(1)
implicitly summed over vector indices R and β. We minimize this free energy for two geometries. Case 1: Muscle Cell. We model a muscle cell by a half-cylinder extended along the y axis. Because of the symmetry of the boundary conditions, the liquid-crystal director lies in the xz plane and depends only on the x and z coordinates. For that reason, we write it as n ) (sin θ, 0, cos θ), where θ(x,z) is the angle of the molecules with respect to the z axis. In terms of θ(x,z), the free energy becomes
1 F) K 2
∫d3r |∇θ|2
(2)
Minimizing this free energy over θ(x,z) gives Laplace’s equation
∇2θ(x,z) ) 0
(3)
Note that the elastic constant K drops out of this equation, and hence the solution depends only on the geometry and not on the energetics. To solve Laplace’s equation with the appropriate geometry, we discretize the xz plane as a two-dimensional square lattice with lattice constant 1 µm. The liquid-crystal domain is a rectangle of size 60 µm × 30 µm, with a semicircular cut-out of radius 10 µm to represent the cell. Within the liquid-crystal domain, there is a variable director on each lattice site. Just outside this domain, there is a fixed director on each lattice site, pointing in the orientation given by the boundary conditions. We use a relaxation algorithm, which converges rapidly to the solution shown in Figure 5a. Far from the cell, the director is vertical, as given by the boundary conditions on the microscope slide and coverslip. At the cell surface, the director points radially outward. Moving away from the cell surface, the director relaxes toward the vertical orientation, with a relaxation length of order the cell radius. Once we have derived the director configuration, we can calculate the transmission of light through the material. In regions where the director is tilted with respect to the z axis, the liquid crystal is optically birefringent, so it rotates the polarization of light and allows some transmission through crossed polarizers. By comparison, in regions where the director is vertical, the liquid crystal is optically isotropic for light propagating in the z direction, so there is no transmission through crossed polarizers. Hence, the important parameter is the effective birefringence
∆neff(θ) )
(
)
sin2θ cos2θ + ne2 no2
-1/2
- no ≈ ∆nsin2θ (4)
where ne and no are the extraordinary and ordinary refractive indices of the liquid crystal and ∆n ) ne - no is the birefringence. We integrate the effective birefringence over z to obtain the phase retardation
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Figure 5. (a) Minimum-energy configuration for the liquidcrystal director above a muscle cell (modeled as a half-cylinder) in the xz plane. (b) Corresponding profile of the transmitted intensity in the xy plane.
δ(x) )
2π λ
∫∆neff(θ(x,z)) dz
(5)
where λ is the wavelength of the light. The intensity transmitted through the crossed polarizers is then
( )
I(x) ) I0 sin2
δ(x) sin2(2(φ - φ0)) 2
(6)
where I0 is the incoming intensity and (φ - φ0) is the constant orientation of the crossed polarizers with respect to the xz plane. From the director configuration in Figure 5a, we derive the transmitted intensity profile shown in Figure 5b. This profile shows the xy plane, as seen from above. The optical transmission is represented by a gray scale. We assume the optical wavelength λ ) 0.5 µm and the birefringence ∆n ) 0.17 (appropriate for the liquid crystal 5CB at room temperature). The transmission is zero far from the cell, and it is also zero at the center of the cell, where the director is vertical. The transmission is nonzero near the edges of the cell, where the director is tilted. Hence, there are two broad bright bands along the two edges. The width of the bright bands is of order the cell radius. Note that each band has a striped structure: bright at δ(x) ) π, dark at δ(x) ) 2π, bright at δ(x) ) 3π, back to dark at δ(x) ) 2π, and bright at δ(x) ) π. The theoretical image of Figure 5b is quite similar to the experimental images of muscle cells shown in Figure 2a. Like the theoretical image, the experimental images show two broad bright bands along the two edges of the cells, with a dark region at the center of the cell and a dark background far from the cell. This consistency indicates that our assumption for the anchoring of the liquid crystal at the cell surface is appropriate. The only difference between theory and experiment is that the experimental images do not show the dark structure within the bright bands. This difference suggests that the
Figure 6. (a) Minimum-energy director configuration above a fat cell (modeled as a hemisphere) in terms of the cylindrical coordinates F ) (x2 + y2)1/2 and z. (b) Corresponding profile of the transmitted intensity in the xy plane.
actual birefringence ∆n is less than 0.17, perhaps because of imperfect alignment, so that the image never goes beyond the first peak at δ(x) ) π. Case 2: Fat Cell. We model a fat cell by a hemisphere on the xy plane. In the liquid crystal above the fat cell, the director can be written in general as n ) (sin θ cos φ, sin θ sin φ, cos θ), where θ is the polar angle with respect to the z axis and φ is the azimuthal angle in the xy plane. In terms of these angles, the free energy of eq 1 becomes
1 F) K 2
∫d3r [|∇θ|2 + sin2θ|∇φ|2]
(7)
It is most convenient to analyze the director configuration in this case using cylindrical coordinates. Because this case has radial symmetry, we have |∇φ|2 ) F-2, where F ) (x2 + y2)1/2. Minimizing the free energy over θ(F,z) then gives the Euler-Lagrange equation
∇2θ )
∂2θ 1 ∂θ ∂2θ 1 + + ) sin 2θ ∂F2 F ∂F ∂z2 F2
(8)
We solve this differential equation through a lattice relaxation technique analogous to case 1 above. The results of this calculation, shown in Figure 6a, are similar to the previous case. Again, the director is vertical at the center of the cell, tilted near the edge of the cell, and vertical again far from the cell. The relaxation length around the cell edge is comparable to the cell radius. From this director configuration, we can calculate the transmitted intensity profile around a fat cell. In this calculation, there is one important difference between fat and muscle cells: For a muscle cell, the azimuthal angle (φ - φ0) between the director and the polarizers is constant, but for a fat cell, this angle rotates through 360° about the cell. As a result, the transmitted intensity profile around a fat cell has the form shown in Figure 6b. The transmission is zero far from the cell and at the center of the cell. It is also zero along four lines extending outward from the
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center, where the molecules are tilted in a direction φ aligned with the crossed polarizers. The transmission is nonzero where the molecules are tilted in other directions. Hence, there are four bright lobes around the edge of the cell. The radial width of the lobes is of order the cell radius, and the angular width is 90°. The theoretical image of Figure 6b is comparable to the experimental images of fat cells in Figure 3a. The experimental images also show four bright lobes around the edge of the cell, with a radial width similar to the cell radius and angular width of 90°. The dark structure within the lobes shows that the phase retardation δ is near 2π in the center of the lobes, as in the theoretical calculation. The consistency between the theoretical and experimental images of fat cells as well as muscle cells provides another confirmation of our assumption for the anchoring of the liquid crystal at the cell surface. Apart from the specific calculations for the experimental cases of muscle and fat cells, we can use our model to estimate the optimum resolution that can be achieved by the liquid-crystal imaging technique. Consider a cell, or a bump on a cell, with a radius r. The nematic director field distorts around that bump over a length scale r, as we have calculated above. This distortion in the director field leads to a local phase retardation δ, which can be estimated as
δ≈
2π r∆n λ 2
(9)
where the factor of 1/2 is an estimate of sin2θ in the middle of the distortion. The resulting optical intensity transmitted through the liquid crystal is
(2δ) ≈ I sin (πr∆n 2λ )
I ) I0 sin2
2
0
(10)
We estimate that this intensity is detectable if it exceeds half of the incident light intensity,
I>
I0 2
(11)
By combining eqs 9-11, we find that the intensity is detectable if
r>
λ 2∆n
(12)
Hence, this length scale is the optimum resolution of the technique. Note that the optimum resolution of eq 12 scales with the optical wavelength λ and inversely with the liquidcrystal birefringence ∆n. For the liquid crystal 5CB at room temperature, we have λ ) 0.5 µm and ∆n ) 0.17, which gives an optimum resolution of 1.5 µm. This calculation shows the importance of using a high-birefringence liquid crystal, to get the best possible resolution from this technique. Discussion and Conclusions In this paper, we have demonstrated that muscle cells, fat cells, and neurons can be imaged using liquid crystals as an optical amplification medium. We have also shown
that the images of muscle and fat cells can be explained by a theoretical model, which assumes homeotropic anchoring of the liquid-crystal director along the cell surfaces. It is interesting to note that the images of neurons are not consistent with this model: The neuron images are bright in the center of the cell body and the center of the processes, while the predicted images are dark in the center because the director points vertically upward there. Hence, the director anchoring along the surface of neurons is probably not homeotropic. These results lead to two questions. First, what is the interaction of liquid crystals with muscle and fat cells, which leads to homeotropic anchoring of the director? Second, why is there a different interaction of liquid crystals with neurons, which leads to different orientational anchoring? To address these questions, we must consider the nature of a cell surface. It is well-known that the cell surface is a complex structure consisting of phospholipids, integral proteins, and carbohydrates.12 The ratio of lipids, proteins, and carbohydrates varies from one cell type to another. In general, the cell surface carries a fixed negative electric charge, with an overall charge density on the order of 10-2 C m-2.13 This charge density gives a large electric field pointing radially inward toward the cell. The electrostatic interaction of the dipole moment of the liquid crystal with this electric field should favor a homeotropic orientation of the director. In addition to this electrostatic interaction, there can also be a hydrophobic interaction between the hydrocarbon chains of the liquid crystal and the carbohydrates of the cell surface, because the liquidcrystal molecules can penetrate into the carbohydrates. The hydrophobic interaction may favor a nonhomeotropic orientation of the liquid crystal. Furthermore, the relative strength of the electrostatic and hydrophobic interactions may depend on cell type, because of the different structure of neurons compared with muscle and fat cells. This change in the dominant interaction may give the crossover between homeotropic anchoring and anchoring in other orientations. To assess these possible mechanisms for liquid-crystal alignment at cell surfaces, we will need to carry out experiments on selected cells whose surfaces are predominantly covered with lipids, integral proteins, or carbohydrates. A further approach will be to treat cells with enzymes that affect the structure and properties of cell surfaces in well-defined ways. As a final point, it is important to investigate the feasibility of using the same technique to probe biochemical reactions occurring at cell surfaces, such as ligand-receptor interactions. The first issue to be addressed for work in this direction is the biocompatibility of the liquid crystals with cells, to image living as well as immobilized cells. Design and synthesis of such biocompatible liquid crystals are underway. Acknowledgment. We would like to thank N. A. Abbott and D. A. Stenger for useful discussions and K. Shaffer for neutron cultures. Financial support of the Defense Advanced Research Projects Agency (DARPA) is gratefully acknowledged. LA0264062 (11) de Genns, P. G.; Prost, J. The Physics of Liquid Crystals, 2nd ed.; Oxford University Press: Oxford, 1993; Section 3.1. (12) Jenings, M. L. Annu. Rev. Biochem. 1989, 58, 999-1027. (13) Zhang, P.-C.; Keleshian, A. M.; Sachs, F. Nature (London) 2001, 413, 428-432.
