Most proteins have about the same specific refractive index increment, α
(the physical parameter that directly relates refractive index, n
, to protein concentration, C
, where n0
is the refractive index of water). For proteins, α
is around 0.18-0.19 mL/g in the visible wavelength range. Nucleic acids have similar α
at around 0.17-0.18 mL/g [12
]. This small difference makes the interpretation of molecular compositions in the cell a very difficult task. We have previously shown that proteins exhibit large dispersion when the wavelength is close to its absorption peak at 280 nm. Although dispersion for nucleic acids was not calibrated, we expect that it will also be large at close to 260 nm. In this study, we chose 310 nm as one of our imaging wavelengths for three reasons: 310 nm is reasonably close to the peak of dispersion but causes much less damage to the cell, due to more than one order of magnitude lower absorption by both proteins and nucleic acids; the CCD camera has relatively good sensitivity at 310 nm; 310 nm has modest transmission in BK7 glass so that samples can be simply prepared on regular microscope coverslips. The other wavelength is chosen at 400 nm, which is readily available from the OPA output and well within the range of objective lens chromatic aberration correction.
We first calibrated the specific refractive index increment of proteins and nucleic acids using a TIR method [10
], which has higher sensitivity compared to our previous light-scattering based method. Without loss of generality, we used bovine serum albumin (Sigma-Aldrich) and deoxyribonucleic acid sodium salt from salmon testes (Sigma-Aldrich) as our protein and nucleic acid samples, respectively.
shows refractive index measurements of protein and DNA solutions versus concentrations at the two wavelengths. Through linear regression of refractive index against concentration, the specific refractive index increment α
for protein at 310 nm is determined to be 0.208 ± 0.001 mL/g, which is slightly lower than that measured using the light scattering method. At 400 nm, α
for protein is determined to be 0.191 ± 0.001 mL/g. For DNA, α
at 310 nm and 400 nm are 0.218 ± 0.007 mL/g and 0.186 ± 0.014 mL/g, respectively. The fitting error for the DNA measurements are an order of magnitude larger, due to the fact that the maximum concentration we could obtain is <3% and the refractive index change is much smaller. Nonetheless, DNA exhibits larger dispersion relative to proteins at these two wavelengths. We expect RNA will show similar dispersion behavior because its absorption is similar to that of DNA.
Refractive index measured at two wavelengths for (a) protein solutions and (b) DNA solutions versus concentrations and their corresponding linear fits to obtain specific refractive index increments, α.
Next, we studied the dispersion of live HeLa cells. To prepare the sample, HeLa cells were plated onto a coverslip that is fixed onto a homemade aluminum chamber and cultured in Dulbecco's modified eagle medium (DMEM) containing 10% Fetal bovine serum (FBS), penicillin and streptomycin in the incubator (37°, 5% CO2
) for 8 hours. Immediately preceding the experiment, the cells were washed with Phosphate buffered saline (PBS) three times and the cell chamber was then sealed with another coverslip. Because the 400 nm beam is much less damaging to cells, it was used to locate the cell and record the first interferogram; the second interferogram was then recorded at 310 nm. The time interval between these two interferograms is typically <5 s, which can be further shortened to sub-second if the shutters are synchronized with the CCD. To correct for the background phase of the optical system, a background interferogram of a blank area is also taken for both wavelengths. We used the Hilbert transform to obtain the quantitative phases ϕ
of the cell, which can be converted to optical path lengths (OPL
) using the following equation:
is the wavelength, αn
the specific refractive index of one type of biomolecule with average concentration Cn
, and d
the thickness of the cell [13
]. We note that Eq. (1)
is valid only when the medium that the cell immersed in does not contain biomolecules. This is the case in our experiment because all cells are measured in PBS. It is also important to point out that only OPL
difference in the x-y plane is spatially resolved and all the contributions along axial direction is integrated and cannot be separated with current technique.
, show the processed OPL
images of four cells at 310 nm and 400 nm, respectively. As expected, they show very similar features, with slight difference in OPL
due to dispersion. The integration of Cnd
over space is the dry mass Mn
of that particular type of biomolecule:
Fig. 3 Optical path length image of HeLa cells at (a) 310 nm and (b) 400 nm; (c) ratio image of magnification corrected OPL images at 310 nm and 400 nm; (d) composite image of corrected OPL images using red and green channels for 310 nm and 400 nm images, respectively. (more ...)
Therefore OPL images can be directly related to the dry mass of the cell if the composition of the cell is known. Using the wavelength dependence of the specific refractive index α of different types of biomolecules, it is theoretically possible to solve for their dry mass separately. However, due to the complicated composition of cells and insufficient calibration data for all of the biomolecules, calculating the exact dry mass of proteins, nucleic acids, lipids, and polysaccharides would be challenging. Instead, we simply calculate the ratio of the integrated OPL at the two wavelengths and compare that to the calibrated data for proteins and nucleic acids, using the following equation:
We note that the magnifications for the 310 nm and 400 nm images are slightly different and also that there is a spatial offset due to chromatic aberration and imperfect alignment of the two imaging arms. To compensate, the 400 nm phase image was demagnified and spatially shifted to match the phase image at 310 nm. shows the ratio of the two images at the two wavelengths after compensation, while shows the composite image at both wavelengths using different color labels: the 310 nm image is labeled with red color and the 400 nm image is labeled with green color. From , there is some inhomogeneity (with a standard deviation of 0.01-0.02) within the cell but we do not observe the location of the nucleus. The reason for this might be that although DNA is only present in the nucleus, RNA (with a much higher dry mass) is dispersed throughout the cell. Another reason is that laser speckle induced noise in the quantitative phase measurements contributes to fluctuations in the ratio. It is hard to disentangle the contribution of biomolecule spatial distribution and laser speckle noise with the current setup. This problem could potentially be alleviated with phase measurement based on a spatially incoherent source which has much less speckle noise [14
From the matched phase images, we used a custom written image processing script based on watershed algorithm in Matlab (Mathworks) to automatically identify cell borders and calculate the dry mass M, occupied area A and dispersion ratio R
of the cells in each image (the dry mass is calculated using 400 nm OPL
images assuming all biomolecules have the same α
of 0.191 mL/g). We analyzed altogether 54 cells and the statistics of these cells are shown in
as box plots. Both the dry mass and the projected area of the imaged cells have very large variability, with dry mass being more tightly confined compared to the area. This probably occurs because the dry mass of the cell is a well-regulated cell growth parameter, while the cell area depends also on the 3D shape of the cell which could be highly variable among cells. The refractive index increment ratio, R
, is a simplified parameter that reflects the biochemical composition of the cell and therefore has a much narrower distribution. The average dispersion R
of the 54 measured HeLa cells is 1.088 with a standard deviation of 0.013. This number is very close to the dispersion of pure protein solutions at a ratio of 1.089. Considering that mammalian cells typically have approximately 60% of their dry mass composed of proteins, this result is not surprising [15
]. Even though we expect that the presence of nucleic acids might increase the dispersion ratio based on calibration results in the previous section, due to the fact that the amount of total nucleic acids present in mammalian cells is typically less than 5%, this increase is negligible and could be further masked by the smaller dispersion of other biomolecules such as lipids and polysaccharides. For a full characterization of the biochemical composition of cells, a much more detailed calibration of the dispersion of all biomolecules present and quantitative phase images at several wavelengths would be required.
Scatter and box plots of the (a) dry mass (b) projected area (c) dispersion of 54 HeLa cells. The box indicates 25%-75% range and whiskers indicates 5%-95% range.