Fractal dimension is a measure of the texture of an object: as a mass distribution transitions from a fine, smooth structure to a coarser, grainer structure, the fractal dimension increases. We have shown that the mass FD of MCF-7 cells, assessed through the angular light scattering profile, provides an early and sensitive indication of apoptosis. More specifically, in both doxorubicin- and paclitaxel-treated cells the mass FD increases dramatically, with an increase of up to 30% soon after treatment, and remains at an elevated level as the cells undergo apoptosis. Differences for both types of treatment are statistically significant shortly after treatment (1.5−3 hours post-treatment) as well as at later time points, when the cells present more traditional markers of apoptosis induction (12 and 24 hours post-treatment). The fact that statistically significant changes in FD are seen for both treatments indicates that the changes are not drug-specific.
We hypothesized that the mass FD would change as the cells underwent apoptosis due to nuclear fragmentation and/or condensation. Analysis of DAPI-stained images indicated that the box FD did increase to elevated levels at 12 and 24 hours, which could explain the elevated mass FD assessed by a/LCI at those time points. More surprising, and more significant, was the finding of early changes in mass FD, as early as 1.5 hours in 5 nM paclitaxel-treated cells. It is probable that this change occurs due to structural changes in another organelle. Due to the sensitivity of light scattering to mitochondrial morphology (30
), we hypothesized that these organelles were largely responsible for the early, and possibly, later observed changes in mass FD. Our analysis of MitoTracker FM Green-stained cells supports this hypothesis. We see significant changes in box FD after 3 hours of treatment with 5 nM of paclitaxel in the mitochondria images. We note that there is an important distinction between computing box FD using fluorescence images and mass FD using a/LCI. Namely, although microscopic imaging is subject to the diffraction limit (~400 nm), a/LCI is sensitive to changes in structure well below the diffraction limit. With this in mind, we acknowledge that there are a number of other organelles that could experience structural changes due to apoptosis-related events soon after treatment. Mass FD would be sensitive to any changes in sub-cellular organization, even those not necessarily detectable by image analysis, provided that the affected organelles undergo topological changes that result in changes in scattered light. However, our data supports the hypothesis that the nucleus and mitochondria are both, at least partly, responsible for the changes in FD.
Two other noteworthy results are the trends in mass FD for both doxorubicin- and 5 nM paclitaxel-treated cells, and the differences in mass FD between 50 nM and 5 nM paclitaxel-treated cells. First, for both 5 nM paclitaxel- and doxorubicin-treated cells, there is an increase in mass FD up to 3 hours, and then a slight reversal at 6 hours followed by a steady increase through 24 hours. Although these trends are not statistically significant, they do manifest in both treatments. The presence of these trends in both treatments lends credence to the possibility that there are at least two distinct mechanisms responsible for the changes in mass FD which occur in two different temporal windows post-treatment. Additionally, the presence of the trend for both apoptosis-inducing treatments indicates that these two distinct mechanisms are inherent to structural changes that occur during, or leading up to, apoptosis. As previously stated, our analysis indicates that mitochondrial structural changes are partly responsible for at least the early changes in mass FD, while nuclear sub-structure changes are at least partly responsible for later changes in mass FD.
The second noteworthy finding was that 50 nM paclitaxel treatment caused early changes in mass FD which then reverted to nearly the mass FD of control cells at later timepoints. The differences between the mass FD of 50 nM paclitaxel-treated cells and control cells are not statistically significant after three hours. This finding is important because the 50 nM paclitaxel treatment did not result in apoptosis within the observation window. This indicates that the early changes seen in mass FD are not necessarily related to apoptosis, but rather to general structural changes in cellular organelles due to events that may lead to apoptosis. For example, mitochondrial changes that occur in response to cellular stress include mitochondrial swelling, and mitochondrial fission and fusion (2
). One model of apoptosis suggests that mitochondrial fission is required for and precedes the loss of mitochondrial membrane potential during apoptosis. However, there are reports that inhibition of mitochondrial fission does not block Bax/Bak-dependent apoptosis (32
). Our results lend further support to the notion that later changes in FD are related to nuclear fragmentation and apoptosis, but early changes are caused by a different cellular event that may involve mitochondrial fission.
Previous light scattering studies have explored using fractal dimension for detecting apoptosis and dysplasia, but the present study demonstrates stark and statistically significant differences early in treatment, and across multiple treatments. The primary advance that yielded the high degree of sensitivity demonstrated in this study is the use of a T matrix-based ILSA model that accounts for nuclear asphericity. This is in contrast to previous techniques that relied on light scattering model which assumed spherical cell nuclei and organelles. By removing the uncertainty that arises from incompatibility between the shape of the nucleus and the light scattering models previously used in ILSA, we find that the determination of subcellular structures is more accurate and sensitive. Future applications of light scattering can exploit this increase in sensitivity by employing a T matrix-based ILSA algorithm (or another light scattering model appropriate for nuclear shapes) for assessing mass FD. As a general quantitative assessment of changes in cell structure and organization, mass FD presents a potential new avenue for assessing changes in cell function including differentiation, proliferation, apoptosis, and others.
In conclusion, noninvasive, high-throughput light scattering methods such as a/LCI, are a sensitive indicator of subcellular structure. In the present study, we have used a/LCI to measure fractal dimension of subcellular structures to distinguish between cells treated with apoptosis-inducing drugs and control cells. Moreover, the mass fractal dimension of treated and control cells presents significant differences very soon after treatment. Our studies with image analysis of fluorescently tagged organelles indicates that changes in mitochondrial morphology are partly responsible for early changes in fractal dimension, while changes in nuclear structure are largely responsible for later changes in fractal dimension. These findings suggest that light scattering can be a powerful non-invasive tool for monitoring apoptosis in both basic research experiments and clinical treatments.