Phase correlation imaging of unlabeled cell dynamics

We present phase correlation imaging (PCI) as a novel approach to study cell dynamics in a spatially-resolved manner. PCI relies on quantitative phase imaging time-lapse data and, as such, functions in label-free mode, without the limitations associated with exogenous markers. The correlation time map outputted in PCI informs on the dynamics of the intracellular mass transport. Specifically, we show that PCI can extract quantitatively the diffusion coefficient map associated with live cells, as well as standard Brownian particles. Due to its high sensitivity to mass transport, PCI can be applied to studying the integrity of actin polymerization dynamics. Our results indicate that the cyto-D treatment blocking the actin polymerization has a dominant effect at the large spatial scales, in the region surrounding the cell. We found that PCI can distinguish between senescent and quiescent cells, which is extremely difficult without using specific markers currently. We anticipate that PCI will be used alongside established, fluorescence-based techniques to enable valuable new studies of cell function.


Spatial Light Interference Microscopy (SLIM)
The specimens of interest were imaged with Spatial Light Interference Microscopy (SLIM) (see Ref. [1][2][3] for details). In short, SLIM is white-light illumination, common-path, phase-shifting interferometer, designed as an add-on module to a commercial phase contrast microscope (PCM) (Zeiss Axio Observer Z1). At the light port of PCM, SLIM module is composed of a 4f system (the focal lengths of the Lens L1 and L2 are f1=150 mm and and f2=150 mm). Therefore, the specimen without further magnification is imaged onto a scientific-grade complementary metal oxide semiconductor (sCMOS) camera (Andor, Zyla), which is capable of imaging at 100 frames/s, each frame of 5.5 megapixels. The back focal plane of a phase contrast objective (Zeiss, ph2, 40X, NA=0.75) is projected onto a reflective liquid crystal phase modulator (LCPM). In addition to the conventional /2 phase shift induced by PCM to the unscattered field, the SLIM module introduces three controllable phase shifts in increments of /2 by LCPM such that a unique quantitative phase image is reconstructed from the four interferograms between the scattered and unscattered fields. Note the operation protocol and the environmental control is a standard accessory for the existing commercial microscope base. By moving the objective, the specimen is precisely imaged onto the camera plane. The difference is that the computer synchronization between the phase-shifting control and camera exposure is needed for data acquisition. In order to acquire a sequence of phase images, the acquisition process is repeated. The acquisition speed is only limited by the detector frame rate and the refresh rate of the liquid crystal phase modulation (LCPM in Fig. 1a). Our SLIM system allows fast phase imaging up to 12.5 Hz for each frame consisting of 5.5 megapixels.

Phase Correlation Imaging
In PCI we compute the correlation time map at each pixel from the acquired time-lapse SLIM images, which are essentially cellular dry mass density distributions. Each phase image reflects the optical path length information of living cells, which depends on both the thickness and the refractive index information. Due to intracellular transport, a combination of Brownian and deterministic motion, the phase fluctuates in time. The phase fluctuations around the average can be expressed as , where ϕ(r, t) denotes the phase distribution at time t and the angular bracket indicates temporal average. From the measured phase fluctuation data ( , ) t   r , we calculate its temporal correlation function ( , ) Then the correlation time τ0(x, y) is defined as the decay time, i.e., the standard deviation of the correlation function, defined via the second order moment as, Note that temporal correlation function, g, is the Fourier transform of temporal power spectrum, and the decay rate (x, y) of the power spectrum is proportional to the reciprocal of correlation time τ0(x, y):

Dispersion-relation phase spectroscopy (DPS)
Dispersion-relation phase spectroscopy (DPS) provides an ability to quantify intracellular transport in a label free manner. It has been well documented that intracellular transport includes contributions from both deterministic transport at large scales and diffusive transport at small scales. As the phase image measured by SLIM is related to the thickness and the refractive index, phase image is essentially a dry mass density map and the changes in density satisfy an advectiondiffusion equation. Taking a spatial Fourier transform, the temporal autocorrelation, g, for each spatial frequency mode, q, can be expressed as: , ∆ (4) Where D is diffusion coefficient, v0 is the averaged advection speed, and Δv is the bandwidths of the speed distribution. Thus, the temporal autocorrelation decays exponentially at a rate Γ, Γ q ∆ D The dispersion relationship between the decay rate and spatial mode can be used to estimate the mean diffusion coefficient and the bandwidth of advection speed. In practice, the decay rate Γ is calculated from the time lapse phase images.

Imaging A549 lung cancer cells
The alveolar basal epithelial cell line, A549, was used in this study. The cells were cultured under standard growth conditions in Roswell Park Memorial Institute medium (RPMI). The cells were passaged at 70-90% confluence. For imaging, the cells were passaged to a 30-50% confluence in a glass bottom dish with colorless RPMI. The cells were imaged every 15 seconds for 5 minute intervals on the SLIM system equipped with an incubating chamber.

Imaging quiescent and senescent cells
We utilized WI38 cells to induce quiescence by serum deprivation. Briefly, WI38 cells were grown in media containing 0.1% fetal bovine serum (FBS) for 72hrs to cause a reversible cell cycle arrest or quiescence or G0 4 . To induce senescence by replicative stress, WI38 cells were treated with doxorubicin (DOX) to a final concentration of 100ng/ml for 3 days in the media containing 10% FBS 5,6 .  The appearance of the "fried egg" morphology of cells indicated the induction of cellular senescence. We also utilized the -galactosidase (-gal) staining to confirm cellular senescence 7 [ Fig. S5a]. Moreover, analysis of cellular markers like p21 and p53 either by immunoblotting [ Fig.  S5b] or qPCR analysis (data not shown) further indicated the doxorubicin induced cellular senescence (Demidenko and Blagosklonny, 2008) 6 .
We performed all image processing operations and numerical computations in MATLAB. The histogram, standard deviation (STD), median absolute deviation (MAD) and inter-quartile range (IQR) calculations were done using MATLAB's in-built functions. The histogram normalization was performed to ensure unit area probability density function.

Video Caption
Supplemental Movie 1. Overlay of phase image (red channel) and the correlation time map (green channel) for a A549 lung cancer cell.
Supplemental Movie 1. Overlay of phase image (red channel) and the correlation time map (green channel) for a A549 lung cancer cell.