## Materials and Methods
### Quantitative Phase Imaging Setup and Phase Reconstruction  
Our holographic imaging setup is based on a phase shifting inline Mach-Zehnder interferometer. A schematic view of the setup is given in Figure 1c. As a coherent light source, we used a 527 nm, 10 mW He-Ne laser. A high-frequency piezo actuator (New Focus, Irvine, CA, USA, Picomotor 8302) actuated in 1000 steps per second was used for phase-stepping. We developed an algorithm for real-time holographic reconstruction using a continuously shifting piezo actuator and a high speed CMOS camera (ZEISS, Oberkochen, Germany, AxioCam 702 mono). The CMOS camera was synchronized to the motion of the piezo actuator and at each step captured an image. For each frame, we predicted the phase difference between the last two consecutive frames and used the last period of the captured interferograms for holographic reconstruction. Our method is particularly advantageous for dynamic cell cultures where the present fluid flow creates transient deformations in the fringe patterns. In addition, the noise due to commonly-used cell culture containers can be decreased by using several types of filtering algorithms. A watershed algorithm was then applied, based on superpixel segmentation algorithm to continuously track the morphological evolution of individual cells and evaluate the morphological transition during the EMT phase [20]. Assembled experimental setup can be seen in Figure 1d.  
The intensity distribution of a given interferogram obtained from the Mach-Zehnder interferometer can be expressed as follows [21]:  
\[I_{ij}=A_{ij}+B_{ij}\cos(\theta_{j}+\delta_{j}) \tag{1}\]  
where \(i\) represents the \(i\)th phase-shifted interferogram (\(i=1,2,\ldots,M\)) and \(j\) denotes the individual pixel locations in each image (\(j=1,2,\ldots,N\)). Here \(A_{ij}\) is the background intensity, \(B_{ij}\) is the modulation amplitude, \(\Phi_{j}\) is the angular phase information, and \(\delta_{i}\) is the phase-shift amount of each frame.  
We assume that the background intensity and modulation amplitude does not have intraframe variation, which is a reasonable assumption under stable imaging conditions. Then, Equation (1) can be expressed as [17]:  
\[I_{ij}^{t}=a_{j}+b_{j}\cos(\delta_{j})+c_{j}\sin(\delta_{j}) \tag{2}\]by defining \(a_{j}=A_{ij}\), \(b_{j}=B_{ij}\cos(\Phi_{j})\), and \(c_{j}=-B_{ij}\sin(\Phi_{j})\). Using M images and N pixels we can use an over-determined least-squares method to solve for the unknown variables. The least-squares error \(S_{j}\) can be written as:  
\[S_{j}=\sum_{i=1}^{M}(I_{ij}^{t}-I_{ij})^{2}=\sum_{i=1}^{M}(a_{j}+b_{j}\cos( \delta_{i})+c_{j}\sin(\delta_{i})-I_{ij})^{2} \tag{3}\]  
where \(I_{ij}\) is the experimentally measured intensity of the interferogram.  
Least-squares criteria can be written as:  
\[\frac{\partial S_{j}}{\partial a_{j}}=0,\quad\frac{\partial S_{j}}{\partial b _{j}}=0,\quad\frac{\partial S_{j}}{\partial c_{j}}=0, \tag{4}\]  
which yields:  
\[\{X_{j}\}=[A]^{-1}\{B_{j}\} \tag{5}\]  
where,  
\[A=\begin{bmatrix}M&\sum_{i=1}^{M}\cos\delta_{i}&\sum_{i=1}^{M}\sin\delta_{i} \\ \sum_{i=1}^{M}\cos\delta_{i}&\sum_{i=1}^{M}\cos^{2}\delta_{i}&\sum_{i=1}^{M} \cos\delta_{i}\sin\delta_{i}\\ \sum_{i=1}^{M}\sin\delta_{i}&\sum_{i=1}^{M}\sin\delta_{i}\cos\delta_{i}&\sum_{ i=1}^{M}\sin^{2}\delta_{i}\end{bmatrix} \tag{6}\]  
\[\{X_{j}\}=\{a_{j}\quad b_{j}\quad c_{j}\}^{T}, \tag{7}\]  
\[\{B_{j}\}=\left\{\sum_{i=1}^{M}I_{ij}\quad\sum_{i=1}^{M}I_{ij}\cos\delta_{i} \quad\sum_{i=1}^{M}I_{ij}\sin\delta_{i}\right\}^{T}. \tag{8}\]  
From these equations, the unknowns \(a_{j}\), \(b_{j}\) and \(c_{j}\) can be solved using:  
\[\Phi_{j}=tan^{-1}(-c_{j}/b_{j}) \tag{9}\]  
Additionally, the amplitude term is found as,  
\[D_{j}=\sqrt{\frac{\left[\left(\sum_{i=1}^{N}I_{ij}\right)/N\right]-\sqrt{ \Delta}}{2}} \tag{10}\]  
where  
\[\Delta=(\frac{\sum_{i=1}^{N}I_{ij}}{N}). \tag{11}\]