Morphological entropy encodes cellular migration strategies on multiple length scales

Abstract

Cell migration is crucial for numerous physiological and pathological processes. A cell adapts its morphology, including the overall and nuclear morphology, in response to various cues in complex microenvironments, such as topotaxis and chemotaxis during migration. Thus, the dynamics of cellular morphology can encode migration strategies, from which diverse migration mechanisms can be inferred. However, deciphering the mechanisms behind cell migration encoded in morphology dynamics remains a challenging problem. Here, we present a powerful universal metric, the Cell Morphological Entropy (CME), developed by combining parametric morphological analysis with Shannon entropy. The utility of CME, which accurately quantifies the complex cellular morphology at multiple length scales through the deviation from a perfectly circular shape, is illustrated using a variety of normal and tumor cell lines in different in vitro microenvironments. Our results show how geometric constraints affect the MDA-MB-231 cell nucleus, the emerging interactions of MCF-10A cells migrating on collagen gel, and the critical transition from proliferation to invasion in tumor spheroids. The analysis demonstrates that the CME-based approach provides an effective and physically interpretable tool to measure morphology in real-time across multiple length scales. It provides deeper insight into cell migration and contributes to the understanding of different behavioral modes and collective cell motility in more complex microenvironments.

Fig. 1. Flowchart of CME construction.

a Representative workflow of image processing. The original image was taken with permission from the work and shows that the MDA-MB-231 cell nucleus in red is located in a chamber. Scale bar, 10 µm. b Morphological analysis of the sample in the polar coordinate system (PCS). The green and orange bars represent probability density functions (PDFs) of radial and angular displacements, respectively. c Derivation of the CME based on PDFs and Shannon entropy.

Fig. 2. Biophysical interpretations of the CME metric.

a PDFs of the angular displacement of cell morphology. The inset shows representative single-cell migration modes, adapted from the work under CC–BY license. Scale bar, 10 µm. b PDFs of the radial displacement. c CME components of the two types of migration modes. Data are presented as mean ± sd (standard deviation); n = 10 and 8 for ameboid and mesenchymal modes, respectively; $***p$ < 0.001; t-test; and the lag $dN$ is 4.

Fig. 3. Morphological dynamics of the MDA-MB-231 cell nucleus in a micro-structured channel array.

a Breast cancer cells migrate in a microstructure consisting of sequential channels and chambers, adapted with permission from the work. Nuclei are stained with Hoechst and shown in red. Scale bar, 20 µm. b CME components of angular (red) and radial (blue) displacements as a function of time. The dotted line is a guide for the eye, and the lag $\mathit{dN}$ is 2. c Average of the CME components in b as a function of time. d The scatter of CMEr vs. CMEa. The dotted line is a linear fit to the experimental data, divided into three clusters (see black, red, and blue dots) using K-means clustering. e Three states are indicated by the scatter of CMEr vs. CMEa. Data are presented as mean ± s.d. f Percentage of scatter in each cluster obtained by K-means clustering (orange bars) and manually classifying (green bars).

Fig. 4. Emerging interaction of MCF-10A cells migrating on top of a thick 3D collagen gel.

a Brightfield image series of a typical pair of cells migrating on a collagen gel, adapted with permission from the work. Scale bar, 30 µm. b CME components of the up cell as a function of time. The red and blue lines represent CMEa and CMEr, respectively, and the Spearman’s coefficient is 0.91. c CME components of the down cell as a function of time. The Spearman’s coefficient is 0.85, and the lag $\mathit{dN}$ is 2. d Average of the CME components for the up cell (green line) and the down cell (orange line). The average of CME is artificially divided into four stages according to the trends, i.e., stage I (2 – 34 min), II (36 – 52 min), III (54–70 min), and IV (72–92 min). e Averaged CME in each stage. Data are presented as mean ± s.d.; $**p$ < 0.01, $***p$ < 0.001, n.s. means “not significant”; Kruskal-Wallis test. f Box plots of the CME components in b, c and the average of the components in d. The box plot indicates the mean (small square in the box), the median (black line in the box), the 25th percentile (bottom line of the box), the 75th percentile (top line of the box), and 1.5*IQR (interquartile range, bars). g The scatter of CMEr vs. CMEa. Pearson’s coefficients are 0.97 for the up cell and 0.94 for the down cell. The green and orange lines are linear fits to the corresponding scatter, obeying the functions “y = 0.91x-0.05” (R² = 0.93) and “y = 0.93x-0.08” (R² = 0.88), respectively.

Fig. 5. Transitions from proliferation to invasion of cell spheroids detected by the CME approach.

a Representative fluorescence images of U87 cell spheroids without 7rh treatment. Scale bar, 300 µm. b CME of H1299 cells as a function of time. The red and blue lines correspond to the cases without 7rh and with 7rh treatment. c, d CME of MDA-MB-231 and U87 cells as a function of time. e The scatter of CMEr vs. CMEa for these three types of tumor spheroids. f Slopes of the linear fit for the six cases in e. Data are presented as mean ± s.e.m.; n = 3 independent experiments for each case; and the lag $\mathit{dN}$ is 5.