Fig 1.
Spectral decomposition of cell edge velocity time series.
(a) A Cos7 fibroblast-like cell with overlaid cell boundaries sampled at 10 sec intervals for 30 min, showing early (blue) and late (red) time points; scale bar = 20 μm. (b) Protrusion activity map displaying the dynamics of all sectors along the cell edge. (c) Edge velocity time series representing the randomly oscillating motion of a particular edge sector (sector No. 30). (d) Empirical mode decomposition (EMD) of time series in (c). (e) Instantaneous frequency distributions of each intrinsic mode function (IMF) calculated by the Hilbert transform. (f) Instantaneous amplitude distributions of each IMF calculated by the Hilbert transform.
Fig 2.
Conservation of frequency distribution among a population of spontaneously protruding Cos7 cells.
(a) Snapshots of active and quiescent Cos7 cell protrusion for 30 min with an increment of 6 min, scale bar = 20μm (see also Video 1 and 3). (b) Histograms of instantaneous frequency distribution for active vs quiescent Cos7 cell. (c) Exponential decrease of instantaneous frequency distributions captured by IMF1-6 for active and quiescent Cos7 cell. Each curve corresponds to the central frequencies of six IMFs computed from a specific sector. The error bar of each IMF indicates the standard error of the instantaneous frequency distribution over all sectors. (d) Cumulative distribution function (CDF) comparison of instantaneous frequency distributions for IMF1 and IMF2 between an active and a quiescent Cos7 cell. P-value is calculated by Kolmogorov–Smirnov (K-S) test. (e) CDF comparison of instantaneous amplitude distribution for IMF1 and IMF2 between an active and a quiescent Cos7 cell. P-value is calculated by K-S test. (f) Heatmaps of KS-statistics for instantaneous frequency distributions among 48 spontaneously protruding Cos7 cells. The sequence of cells is defined in randomized (left) and ascending order (right) of the mean absolute velocity over all cell edge sectors and time points. (g) Heatmaps of KS-statistics for instantaneous amplitude distributions among 48 spontaneously protruding Cos7 cells. The sequences of cells are defined in the same orders as in panel (f).
Fig 3.
Acute photo-inhibition (PI) of Vav2 signaling induces a shift in the instantaneous frequency distribution.
(a) Timing of Rac-GEF Vav2 photo-inhibition using PI Vav2. (b) Comparison of IMF1 instantaneous frequency distributions collected before and during a PI period composed of 1000 msec pulses of light interspersed with 9000 msec darkness, 100 msec pulses of light interspersed with 9900 msec darkness, and 1 msec pulses of light interspersed with 9999 msec darkness (from top to bottom). P-value is calculated by K-S test. Data for IMF2-6 are presented in S4 Fig. (c) Representative scatter plots of instantaneous frequency vs amplitude values of IMF1 before and during a PI period induced by 1000, 100 and 1 msec of light pulses (from top to bottom), respectively.
Fig 4.
Polarity of spontaneously protruding Cos7 cells results in different spectral responses of subcellular regions.
(a) Snapshots of Cos7 cell protrusion at 15 min with red colored windows corresponding to higher motility (≥ 2μm/min) and blue colored windows corresponding to lower motility (< 2μm/min).See also Video 4 and 5. Scale bar = 20μm. Top: active, polarized cell; Bottom: quiescent cell. The solid green box in upper panel indicates the selected protruding cell front, and the dashed green box indicates the selected quiescent cell rear. The solid and dashed orange boxes in lower panel indicate the two subcellular regions of the quiescent Cos7 cell randomly selected for comparison. (b) Protrusion activity maps for active (top) and quiescent (bottom) cells. The solid/dashed green and yellow boxes indicate the time series selected for spectral analysis. (c) K-S test statistics comparing the instantaneous frequency distributions between the indicated subcellular regions. The threshold K-S statistics value of 0.0794 (black dash line) indicates the average difference between whole-cell distributions for a population of cells with homogeneous molecular make-up (mean value of K-S statistics heatmap Fig 2F). The threshold value of 0.227 (red dash line) indicates the average difference between whole-cell distributions of control and Vav2-inhibited cells.
Fig 5.
Spatiotemporal clustering of cell edge motion into spectrally homogeneous regions.
(a) Statistical region merging (SRM) clustering at different Q-values (defining the delicacy of clusters) for a spontaneously protruding Cos7 cell using weighted instantaneous frequencies of all IMFs as a feature vector. (b) Ratio between intra- and inter-region variance as a function of the logarithm of Q. (c) Multiscale clustering using instantaneous amplitudes of all IMFs as a feature vector. (d) Multiscale clustering using weighted instantaneous frequency of only IMF1 as a feature vector.
Fig 6.
Application of merging algorithm before, during, and after optogenetic Vav2 inhibition in two Cos7 cells with distinct initial morphodynamics.
(a) Snapshots of protruding Cos7 cells with strong (top) and weak (bottom) polarity. Scale bar = 25 μm. (b) Top: Protrusion activity map of the Cos7 cell with a strong initial polarity; Bottom: Spectral clustering result (Q = 3). (c) Top: Protrusion activity map of the Cos7 cell with weak polarity; Bottom: Spectral clustering result (Q = 3).
Fig 7.
Regions of spectrally homogeneous cell edge motion have distinct Rac1 signaling programs.
(a) FRET biosensor probing Rac1 activity (yellow-red tones, high activity; green-blue tones, low activity) in a Cos7 cell. The rectangular boxes with white edges overlaid on cell periphery represent the first (outer) and second (inner) layer of sampling windows. The numbers along the cell periphery mark the locations of sectors/windows. Scale bar = 30 μm. (b) Rac1 activity map of a Cos7 cell. (c) Protrusion activity map of a Cos7 cell. (d) SRM identifying four distinct cell edge motion regimens. (e) Quantification of Rac1 activity in the first layer of probing windows for spectral clustering regimens 1–4. (f) Spectral clustering regions in the first layer of probing windows at six time points of the time lapse sequence (see also Video 9 for the full sequence). Scale bar = 30μm. (g-j) Cross-correlation between edge motion and Rac1 activity in the first and second layer of probing windows for regimens 1–4.