1. Introduction

Angularly-resolved light scattering has been well-established as an early detector of subtle size changes in organelles, such as nuclear swelling indicative of pre-cancer [1]. Non-nuclear organelles can also be important indicators of cellular state. For example, mitochondria respond to changes in metabolic demand by undergoing fission and fusion [2]. Angular light scattering has been used to detect mitochondria rounding up during calcium overload [3] and swelling in response to oxidative stress induced by photodynamic insult [4].

Leveraging Mie theory [5] allows for inverting angular scattering to estimate scatterer sizes. Studying organelle sizes and dynamics at the single cell level provides powerful capabilities compared to obtaining measurements averaged over large ensembles of cells. For example, tracking individual cells over time would enable the study of heterogeneity in cellular processes such as cell division, immune response, and apoptosis. Previous angular scattering work on sizing non-nuclear organelles has used scattering from cellular ensembles and utilized assumptions about the functional form of scatterer size distributions [6]. Sizing based on scattering from single cells has been demonstrated on larger scatterers such as nuclei or the cells themselves [7–9]. However, sizing populations of smaller organelles in single cells is challenging due to the smaller number of scatterers, correspondingly weaker signal and the need to isolate scattering from a single cell. We strive to bring the capability to assess non-nuclear organelle size distributions to the single-cell level.

Although elastic light scattering requires no staining and has no photo-bleaching risk like fluorescence-based imaging, it lacks specificity, since scattered light is collected from all sources of refractive index contrast. In addition to the organelle scattering, light is also scattered by the index contrast between the cell’s cytosol and its immersion medium. This signal is highly sensitive to the cell’s shape and size, and can obscure the scattering from the contrast between the organelles and cytosol. Since this whole-cell contribution changes the shape of the angular scattering pattern, it has the potential to significantly bias estimates of organelle size distributions. To address this concern, we present a physical method of reducing the whole-cell refractive index (RI) contrast, and therefore its scattering, by physically matching the immersion medium’s RI to the index of the cell’s cytosol. This reduces scattered light from the cell itself and improves isolation of the organelles’ angular scattering.

1.1 Refractive index-matching in live cells

Tuning the RI of a live cell’s immersion medium was introduced by Barer and Joseph in the late 1950s for performing immersion refractometry on rod and cone cells [10,11]. In this technique, different organelles’ images lose contrast at different RI tunings of the immersion medium, enabling RI values of organelles to be estimated. This early work tuned the concentration of the protein albumin to vary the RI of the immersion medium.

Boothe et al. [12] more recently introduced RI tuning using iodixanol, an inorganic chemical commercially available as Optiprep. In this case the goal was to reduce aberrations from RI mismatches at cell boundaries and thus improve imaging deeper into tissues. The authors demonstrated continuous tuning of a solution’s RI by diluting 60% stock iodixanol in water. They empirically determined that the relationship between iodixanol concentration and the solution’s RI ($n$) at $\lambda =589.3$ nm is well-described by the linear function

1.2 Angular light scattering

Drezek et al. [13] highlighted the impact of immersion medium RI on angular scattering by simulating angular scattering from the same cell with a cytosol RI $n_c=1.37$ immersed in media with $n_m=1.35$ and $n_m=1.37$. Results showed increased low-angle forward-scatter for the cell with $n_m=1.35$ due to the presence of whole-cell scattering. They emphasized the value of matching the RI of the immersion medium to the cell’s cytosol when performing goniometric measurements on cell suspensions in order to isolate the organelle signal from whole-cell scattering. By immersing cells in protein solutions with slightly elevated RI values up to 1.345, Mourant et al. [14] experimentally measured such a reduction in whole-cell angular scattering.

Despite this evidence that whole-cell scattering can contribute significantly, the seminal experimental angular-scattering papers on non-nuclear organelle sizing assign whole-cell scattering a secondary role in the calculation of Mie-derived size estimates. Working with M1 and MR1 rat embryo fibroblast cells, Mourant et al. [15] suggested that cell shape did not contribute strongly to the angular scattering between 5 and 180 degrees. In a later paper [16], the same group was able to fit size distributions from intact cells using a bimodal log normal model that did not include any cell-sized scatterers. Similarly, Wilson et al. [4] showed empirically for EMT6 mouse mammary carcinoma cells that the angular scattering was modeled to within the noise by a combination of two log-normal size distributions, both with peaks well below the size of nuclei or cells. The authors concluded that 65% of the light scattering between 5 and 90 degrees from intact cells was from mitochondria-sized scatterers with diameters between 1-3 $\mu$m.

To address this discrepancy in the literature on the influence of whole-cell scattering upon organelle size estimates, we report here on experimental measurements of angular scattering from live single cells immersed sequentially in traditional aqueous media and in media closely RI-matched to the cell’s cytosol, in analogy to Drezek et al.’s simulations. This provides a direct estimate of the whole-cell contribution’s angular dependence and its strength relative to the organelle contribution.

2. Methods

2.1 Cell preparation and measurements

Cells from the 4T1 mouse mammary adenocarcinoma cell line (Caliper Life Sciences, Hopkinton, MA) were frozen after three initial passages. Cells were maintained in media consisting of RPMI (Gibco, Invitrogen Inc., Carlsbad, CA), 10% fetal bovine serum, and 1% penicillin/streptomycin. 67NR cells were purchased from the Animal Model & Therapeutic Evaluation Core (AMTEC), Barbara Karmanos Cancer Institute, Wayne State University. The 67NR cell line is a sister cell population to the 4T1 cell line, both derived from a single spontaneous Balb/cfC3H. The 67NR cells were frozen after three initial passages and were maintained in media consisting of Dulbecco’s Modified Eagle Medium (DMEM, Gibco 11965092), 10% fetal bovine serum, 1% 2mM L-glutamine (Cellgro 25-005-Cl), and 0.1% 1mM Mixed Nonessential Amino Acids (Gibco 11140). All cells were maintained in an incubator at 37$^{\circ }$C, 5% CO$_2$, and 95% relative humidity. Prior to imaging, $1\times {10}^4$ cells were seeded on 25mm diameter No. 1.5 thickness coverslips (Thermo Scientific) in a 6-well plate. Each well was filled with 2mL with the respective media depending on the cell type. Cells were then incubated at 37$^{\circ }$C, 5% CO$_2$, and 95% relative humidity for 24 hours.

For imaging, the coverslip was sandwiched in an Attofluor cell chamber, immersed in 1.3 mL of the imaging solution, and finally covered with an 18mm $\times$ 18mm thickness No. 1 top coverslip (Fisherbrand 12-542A) to ensure planar illumination before being placed on the inverted microscope. The Attofluor chamber was secured to the microscope stage with double-sided tape, which was sufficient to hold the sample in place when switching immersion media so that the same cell can be re-imaged. To switch immersion media, the top coverslip was removed, the original media was aspirated and immediately replaced with the new immersion media, and the top coverslip was replaced. The challenge of changing immersion media with a manual pipette without nudging the sample limited the number of cells for which unmatched and RI-matched data were successfully obtained. Additionally, some image pairs were rejected because the difference in cell shape was judged to be much more extensive than typical. Such changes were assumed to be caused by particularly rapid evolution of the cell or by a disturbance from the manual aspiration step of the media switch.

2.2 Refractive index-matching

Although the cytosol RI values were not directly measured, we observed reasonable RI-matching conditions to occur (as defined by minimal cytosol:media image contrast using 780 nm illumination; see Sec. 1.1) for a solution of 23.1% iodixanol in cell media. Measurements on an Abbe refractometer verified that this procedure repeatably yields a solution with an RI of 1.372+/−0.001 as measured at 588 nm, which is consistent with cytoplasm RI values reported in the literature [13]. This protocol was sufficient to provide significantly closer index matching at 780 nm compared to using traditional media, as will be shown.

2.3 Complex field imaging

Experimental measurements of single cells were made on a system described by Draham et al. [17], using an LED at 780 nm (Thorlabs, LED780L) for illumination. The complex field of scattered light from cells on a cover slip was obtained using a Fourier phase microscope (FPM) [18], which is shown in Fig. 1. Unscattered light is focused onto the center of a spatial light modulator (SLM), which is conjugate to the back focal plane of the microscope objective. Here, the unscattered light is repurposed as a reference wave and phase-shifted by a small central region of the SLM. The intermediate image of the sample at location O’ is relayed to the CCD camera at O’, where intensity interferograms are recorded for each of the four phase shifts $\phi =\frac {m\pi }{2}$ applied by the spatial light modulator, for $m = 0,1,2,3$. The complex field of light scattered by the sample can then be recovered by the four-bin phase shifting algorithm [19]. The four intensity images are

 

Fig. 1. Diagram of a Fourier phase microscope. Unscattered light (red) is focused to the center of the back focal plane (F) and then relayed to the center pixels of a spatial light modulator (SLM) at position F’, where four sequential phase shifts are applied to the unscattered light only. Scattered light (grey) is imaged to an intermediate image plane (O’) and relayed to the CCD camera where it interferes with the scattered light, producing four sequential interferograms. SLM: spatial light modulator. CCD: Charge coupled device.

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Two-dimensional maps of a single cell’s angular scattering are obtained by digitally selecting the cell’s image region, computing a two-dimensional fast Fourier transform, and taking the intensity values. Azimuthally averaging yields a one-dimensional plot of scattered intensity versus polar angle $\theta$. The angular range subtended by the SLM’s shifting pixels determines the minimum $\theta$ that is detected by FPM; this was less than 5 degrees and thus did not affect the angular range most useful for sizing organelle-sized scatterers [17].

When comparing angular scattering from the same cell in different immersion media, we normalize the intensities so that the total scattering between 35 and 55 degrees is the same for both cases. This angular regime is expected to be dominated by organelle scattering (c.f. Reference [13]), and the RI contrast between organelles and cytosol is relatively constant between the two scenarios since iodixanol does not penetrate the cell (see however section 4.3 for discussion about secondary effects of iodixanol upon organelles due to osmolality). The normalization thus enforces the approximation that the amount of organelle scattering is unchanged. To quantify the differences at angles where whole-cell scattering is expected to be non-negligible, we calculate the total scattered intensity over the range $5^\circ$–$20^\circ$ for the unmatched and RI-matched cases and define their ratio to be

2.4 Phase contrast theory

In his early immersion refractometry work, Barer [11] reported that matching the RI of immersion media to the cell’s cytosol increased the ability to see internal organelle structure in phase contrast images of spherical cells. Similarly, when imaged in standard media with $n_m=1.33$, we have observed that the scattered-field quantitative phase image of a cell tends to appear flat, with only small percent variation in phase values. We provide here a simple phasor-based description of this phenomenon, most applicable for a flat adherent cell as depicted in 2(a). In such cells, variations in the cell’s thickness versus lateral position are assumed to be more slowly varying than organelle-scale variations. The complex field value at any pixel potentially contains contributions from two sources:

 

Fig. 2. (a) Depiction of the transverse plane, showing organelle scattering from contrast between the organelle and cytosol, and between the cytosol and immersion media. (b) Depiction of the image plane, with scattering from regions of cytosol alone (e.g. box 1) and combined cytosol and organelle (box 2). (c) Complex phasors associated with scattering by cytosol (blue) and six different locations on organelles (green). When the blue phasor is added to the cluster of green ones, the resultant vectors span a narrow range of phase angles in the complex plane. (d) Organelle field values from (c) are shifted to the origin when the cytosol scattering is suppressed by RI-matching, resulting in a larger range of phase values.

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Figure 2(a), depicting the side view of a cell illuminated by a plane wave, emphasizes that both organelle and whole-cell scattering can contribute to the same $(x,y)$ region of a cell’s image. As shown in Fig. 2(b), some regions of the image could contain only whole-cell scattering (e.g. box 1), while others could additionally include organelle scattering (e.g. box 2).

If over a micron-scale area the whole-cell scattering is approximately constant and at least comparable to the organelle contribution, then the cluster of phasor values will be significantly offset from the origin of the complex plane. Such an offset, shown as the blue vector in 2(c), causes the cluster of complex field values to subtend a small angular range and therefore have a small range of phase values. However, if the whole-cell scattering is removed by RI-matching, this phasor cluster is then shifted to the origin, as depicted in Figure (d). This allows the phase values to occupy the full range of 2$\pi$ radians, potentially increasing the degree of phase contrast as in Barer’s observations.

3. Results

3.1 Scattering from an elongated 67NR cell

Figure 3 shows one 67NR cell imaged in both standard cell media and a RI-matching solution with $n_m=1.37$. The amplitude and phase of the scattered field for each condition are shown in Fig. 3. The internal structure of the cell has higher contrast in the index-matched phase image (d) compared to the unmatched case (c). Additionally, the cell interior and the border have higher amplitudes in the unmatched (a) compared to the matched case (b).

 

Fig. 3. Amplitude (a,b) and phase (c,d) images of the same 67NR cell immersed in cell media (a,c) with $n_m=1.33$ and in RI-matched solution (b,d) of iodixanol mixed with media to achieve $n_m = 1.37$.

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The corresponding angular scattering intensity images are shown in Fig. 4(a) and (b). There is a bright streak visible in the angular scattering from the unmatched cell in (a), perpendicular to the cell’s orientation in Fig. 3(a). This effect is significantly reduced for the index-matched cell in Fig. 4(b). To assess the relative strength of the streak, Fig. 4(c) shows an azimuthal line-through at a polar deflection of 12 degrees, indicated by the red circles in (a-b). The streak intensity has a peak more than 5 times higher for the unmatched cell compared to the matched cell. Finally, Fig. 4(d) shows the azimuthally averaged 1D angular scattering intensity across all polar angles. Higher scattering from the unmatched cell is seen at angles less than 25 degrees. The ratio of the unmatched and matched scattering intensity between 5 and 20 degrees (c.f. Equation (5)) is $\alpha =4.51$.

 

Fig. 4. Angular scattering intensity of light scattered from the 67NR cell shown in Fig. 3, immersed in (a) traditional media, with a visible streak, and (b) RI-matching solution. Small and large white dashed circles indicate polar deflection angles of 5 and 55 degrees, respectively. (c) 1D azimuthal line-throughs of the angular scattering at 12 degrees, indicated by the red circles in (a) and (b), showing that the streak intensity is much higher for the cell immersed in media. (d) Azimuthally averaged 1D scattered intensity for the cell immersed in media and RI-matched solution, showing higher scattering for the cell in media at lower angles outside of the normalization range.

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3.2 Scattering from a non-elongated 4t1 cell

Results for a 4t1 cell in both media and RI-matched solution are shown in Fig. 5. Just as for the 67NR cell, this cell was RI-matched by using immersion media with a RI close to 1.37. This cell’s image is more circular compared to the elongated 67NR cell shown in Fig. 3. The amplitude image of the unmatched cell in Fig. 5(a) contains a strong halo effect at the cell borders that is less apparent in the matched condition (b). The corresponding angular scattering is shown in Fig. 6. Although the 2D angular scattering in (a) does not have the bright streak characteristic of an elongated cell, the angular scattering intensity is higher at the low angles at the center of the plot compared to the matched cell’s scattering in (b). This is easier to see in the azimuthally averaged 1D plot in (c), where the scattering is higher at low angles for the unmatched compared to the RI-matched condition. The low angle scattering ratio for this 4t1 cell is $\alpha =1.81$.

 

Fig. 5. Amplitude (a,b) and phase (c,d) images of the same 4t1 cell immersed in cell media (a,c) with $n_m=1.33$ and in RI-matching solution (b,d) of iodixanol mixed with media to achieve $n_m = 1.37$.

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Fig. 6. Angular scattering intensity of light scattered from the 4t1 cell shown in Fig. 5, immersed in (a) cell media and (b) RI-matching solution. (c) Azimuthally averaged 1D scattered intensity for the cell showing higher low-angle scattering for the cell in media. White dashed circles indicate 5/55 degrees.

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3.3 Measurements of $\alpha$ for multiple cells

As noted above, the challenging nature of aspirating and replacing cell media without moving the sample limited the number of cells for which corresponding images were obtained both before and after RI matching. Table 1 shows the mean ($\mu _\alpha$) and standard deviation ($\sigma _\alpha$) of $\alpha$ for the $N$ cells of each cell type. Similar to the example cell images in Fig. 3 and 5, the 67NR cells were elongated and the 4t1 cell images had high circular symmetry.

Table 1. Distribution of $\alpha$ measurements on multiple cells.

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The particular 67NR and 4t1 cells shown in Figs. 3–6 had the shortest time lapses between their two images. Using smallest time lapse as a proxy for least cellular change, we selected these cells in order to get as close as possible to the ideal scenario of only the external medium itself changing.

3.4 Phase contrast

As was seen in images (c) and (d) of Fig. 3, the contrast in the phase image increased upon RI-matching. These images are reproduced as panels (a) and (b) of Fig. 7, along with insets showing detail in the same subregion of each image. Figure 7(c) shows phasor values for pixels in the inset regions of (a) and (b). Both data clouds have similar spread, but the matched one is centered on the origin while the unmatched one is noticeably displaced. The resulting histogram of phase values in (d) exhibits a much larger range of phase values for the matched case than the unmatched.

 

Fig. 7. Scattered field phase images of the same cell immersed in (a) unmatched media with $n_m=1.33$ and (b) in index-matched media with $n_m=1.37$, with selected region enlarged and shown in inset. (c) Phasor diagrams of the complex field values from the selected region for both the matched and unmatched cases, and (d) histogram of the corresponding phases.

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4. Discussion

4.1 Whole-cell scattering

The presented results demonstrate that whole-cell RI contrast with a traditional immersion medium can result in significant amounts of light scattering at angles between 5 and 20 degrees. The evidence is that the scattering in this low-angle domain is markedly reduced when an index-matching immersion medium is used. As indicated in Table 1, all cells analyzed experienced a reduction in low-angle scattering upon RI matching, with $\alpha$ values of at least 1.47. In other words, each cell’s low-angle scattering was increased by at least 47% when a traditional (non-RI-matched) medium was used instead of an RI-matched one.

These effects were seen for two different cell types. For the 67NR cells, which were all elongated in the image plane, the average scattering reduction was $\alpha = 2.79\pm 1.24$. Because of the elongation in shape, the 2D angular scattering patterns for these cells contain streaks that correspond to Fourier transforms of those shapes. In Fig. 4(a), the bright streak perpendicular to the cell’s long axis direction (c.f. Fig. 3(a)) corresponds to light diffracted due to index contrast between cytosol and immersion fluid. When RI-matching is achieved using iodixanol, this diffraction effect is significantly reduced, as evidenced by the much weaker streak in Fig. 4(b) and the lower peaks in (c). This provides direct visual evidence that the amplitude of whole-cell scattering has decreased. Unlike the streak, the elongation of the individual speckle grains in the 67NR cell’s angular scattergrams in Figs. 4(a,b) is observed to be similar under traditional and RI-matched conditions. This result is as expected. The speckle grain shape is caused by interference between all the individual organelle-sized scatterers, which are distributed throughout the asymmetric cell area. Since this scattering happens inside the cell and is related to organelle locations, changing the extracellular fluid should not have a noticeable influence.

For the more circular 4t1 cells, the average scattering reduction was $\alpha = 1.88\pm 0.32$. The smaller $\sigma _{\alpha }$ value for the 4t1 cells (c.f. Table 1) is likely due to the circular shapes being more similar to each other, compared to the changes in elongation for the 67NR cells. Note that although the 2D scattering patterns from these symmetrical cells exhibited no streaks, whole-cell scattering was still reduced in each cell. This suggests that measurements of multicell suspensions, with averaging over orientations and shapes, should also contain significant amounts of whole-cell scattering if RI matching is not used.

Using RI-matching to reduce whole-cell angular scattering and improve estimates of organelle size distribution would be straightforward to implement. Once a suitable RI-matching medium has been predetermined for a cell type of interest, measurements need only be performed in that one fluid. Unlike the experiments described above, no switching between different immersion media would be required. This simplification opens the possibility of high-volume flow cytometry measurements of single-cell organelle size distribution. We also note that continuous RI tuning could be implemented to more closely match the cytopsol RI of individual cells. For example, immersion refractometry on single bacterial cells has recently been implemented with on-chip, optofluidic-based instrumentation, using a chaotic micromixer to continuously vary the immersion media’s RI by controlling the concentration of Ficoll solution in water [8].

4.2 Comparison to angular scattering literature

Our finding that index-matching reduces scattering at low angles by suppressing whole-cell scattering corroborates the simulation work by Drezek et al. [13]. Our results influence the interpretation of organelle population size parameters derived from angular scattering experiments that contain substantial whole cell scattering. Although angular scattering from multi-cell suspensions has been modeled to within the noise using two log-normal distributions with peaks characteristic of mitochondria and smaller organelles [6,16], whole-cell scattering in such experiments could influence the shape of the angular signature and therefore also the size estimates obtained from Mie theory-based fits.

4.3 Iodixanol effects upon cells

Since iodixanol does not penetrate into living cells [12], it directly modifies only the immersion fluid’s RI. However, Barer et al. pointed out the importance of maintaining osmotic pressure as the immersion fluid is modified, to prevent components of the cell from swelling or shrinking and therefore undergoing changes in internal RI and volume [11]. This ensures that the cell’s state is not changed upon immersion in the RI-matched media, which is important if the goal is to study the size distribution of the cell’s organelles. The approximately linear relationship between osmolality and solution concentration means that the change in osmotic pressure can be offset by changing the salt concentration of the media [11,12]. While we have not yet matched osmotic pressure in this work, the fact that the shape of the angular scattering remains relatively unchanged upon RI-matching at high angles (35 to 55$^\circ$), where organelle-sized scattering dominates, suggests that it is the reduction in whole-cell scattering rather than effects due to osmotic pressure that is primarily responsible for the scattering changes in Figs. 4 and 6. This claim is also supported by the strong reduction in streak intensity in Fig. 4 upon index-matching, which is clearly related to the cell’s shape and scattering. Future work will include modifying the salt concentration of the immersion media to maintain consistency in osmotic pressure and therefore in cell volume and RI, enabling better comparisons between structure in matched and unmatched conditions.

4.4 Phase image contrast

As noted earlier, Barer demonstrated that RI-matching the immersion medium to the cytosol increased the ability to see internal structure in phase contrast images of spherical cells [11]. In the present work, we analogously observed that RI-matching increased the spread in phase values and gave the impression of greater internal structure (c.f. Fig. 5). We note that in this case phase images were associated with only the scattered light. The increased contrast in such images does not imply a correspondingly substantial change in the thickness profile of a cell. That profile, associated with the quantitative phase of the total transmitted light field through the cell at each $(x,y)$ pixel, is strongly influenced by unscattered light.

The increase in phase range was also consistent with the previously described model of complex field values shifting closer to the origin upon removal of a constant, strong whole-cell scattering contribution. In the experiments performed here, whole-cell scattering was removed physically, by RI-matching. Within the approximation that whole-cell scattering is constant, we note that the model implies the possibility of a purely digital approach, eliminating the need for RI-matching. One would simply calculate all the phasors associated with a cell image and then recenter the data cloud at the origin of the complex plane, thereby removing the whole-cell constant. However, in a real cell, the whole-cell contribution will not be constant in $(x,y)$, due to variations in the cell’s thickness or the cytosol’s RI. As proposed earlier, we conjecture that these spatial variations will be at lower frequencies than those associated with organelles. Future work will involve attempts to “digitally index-match” the cell by subtracting off suitably local estimates of the whole-cell contribution at each pixel. One method of assessing the power of this method would be to compare the 1D angular scattering of the physically matched cell with that of the digitally matched cell.

5. Conclusion

We demonstrate that combining iodixanol in solution with cell media is a simple and effective method of matching the RI of a cell’s immersion medium to its cytosol and thereby reducing whole-cell scattering. Furthermore, through comparison of the same cell’s scattering in both RI-matched and unmatched media, we show that the effect of the whole-cell contribution can be significant at angles up to 20 degrees. To our knowledge, this is the first experimental comparison of angular scattering from the same cell immersed in both RI-matched and unmatched media. Reducing whole-cell scattering also improves the isolation of organelle signal, enabling more accurate assessment of organelle size distributions. Additionally, we provide a simple, phasor-based explanation for the increased contrast in the phase images due to index-matching, suggesting the potential for digital RI-matching to achieve results similar to that of the physical method.