## 4 Discussion  
The hallmarks of transitions along the EMP spectrum include changes in the expression of specific extracellular matrix components, cell surface markers, cytoskeleton components, and transcription factors. However, the identity and uniformity of these molecular changes, as well as the rate in which these changes occur, vary dependent on cell line and condition. In addition, several canonical EMP regulating transcription factors (i.e., Twist1/2, Zeb1/2, Snail, and Slug) frequently undergo nuclear translocation instead of a change in expression. Therefore, assays that monitor either a single time-point, average a population of cells, or provide qualitative metrics, each miss critical information regarding EMP transitions. Another hallmark of EMP transitions is a change in morphology. Here we have exploited this hallmark to establish a label-free and non-invasive assay to quantify the kinetics, heterogeneity, and degree of the transition. Morphological parameters as determined using quantitative phase imaging (QPI) techniques such as DHC have previously been used to distinguish between normal cells and cancer cells as well as to distinguish cancer in situ from metastatic cancer cells [30] with high sensitivity and specificity. Further, DHC has proven to be a powerful method to evaluate toxicity using morphological data [31]. Since the DHC platform used here can be used inside a cell incubator, it is a powerful method to monitor individual cells throughout a morphological transition [24]. In this study, we have used DHC to investigate morphological differences between different cell states over time. To apply DHC-derived feature classification to a cell state transition, we used the well-established model of treating epithelial NMuMG cells with TGF\(\beta\) to induce EMT [29]. We show that morphological parameters could clearly distinguish between epithelial and mesenchymal NMuMG cells (Figures 1 and 2). One useful aspect of the approach presented here is the ability to follow changes in morphology over time using time-lapse imaging. Changes in morphology compared to untreated cells were observed within five hours after TGF\(\beta\) addition (Figure 3). This observation is consistent with a previous report noting changes in micromotility within 5-7 h of treating NMuMG cells with TGF\(\beta\)[32]. We further observed the difference in morphology between non-treated cells and TGF\(\beta\)-treated cells to peak at approximately 16 h after addition of TGF\(\beta\) (Figure 3). This ability to monitor both when the transition initiates and peaks permits more refined selection of time-points for molecular assays. A previous report has demonstrated that DHC-derived classifiers trained on established, but unrelated, epithelial and mesenchymal cell lines can be used to infer the EMP status of independent uncharacterized lines [25]. Our presented work further advances the application of DHC feature-based classification of EMP in four important aspects. The first, as discussed above, is the addition of kinetics. Through utilizing a well-defined system of EMT, we demonstrate distinct DHC-derived features in the epithelial and mesenchymal states of precisely the same cells, proving the differences are the consequence of cell state, not genetic differences between cell lines (Figures 1-3). The second is the inclusion of both degree and heterogeneity of EMP (Figure 3). Each cell within a culture can occupy a different state in the EMP spectrum--a phenomena that can be captured by the EMP score generated here, but may be lost with application of binary \"E or M\" classifiers. An important third advancement is the demonstration that EMP classifiers trained on one cell line are not universally applicable across cell types and species (Figures 4 and 5). This result is fully expected based upon known molecular and morphological diversity across lines.