State of Cell Unjamming Correlates with Distant Metastasis in Cancer Patients

Pathological morphological changes in tumor tissue enable collective cancer cell unjamming, a cellular motility transition. However, fundamental questions remain: Is unjamming essential for tumor progression? Which different unjamming states can be found in patients? Here, vital cell tracking in patient-derived solid tumor explants ($N=16$) reveals that states of cell unjamming can be recognized by elongated cell and nucleus shape (CeNuS) and low nucleus number density. These static variables serve as a morphodynamic link to map the broad range of morphologies and associated motility states found in histological slides of 1380 breast cancer patients to generate a comprehensive state diagram of cancer cell unjamming. An increase in predicted cell motility in primary tumors through unjamming significantly correlates with distant metastases that may even occur a decade later. Patient risk groups are quantified via a decision boundary in the state space found by machine learning. The resulting clinical prognostic potential is evaluated using a range of quantifiers, including Harrel’s concordance index. Using multivariable Cox models, we find that cell unjamming as a prognostic parameter adds a 26% information gain in the concordance index when combined with the established prognostic criteria (tumor diameter, tumor grade, lymph node status) used in the Nottingham index. Unjamming complements the information on affected lymph nodes in patients regarding metastatic risk. The derived state diagram of cancer cell unjamming reconciles conflicting observations regarding shape- or density-induced unjamming and stresses the nuclei’s mechanical importance, which is not considered in current theories of cell unjamming. We conclude that cancer cell unjamming is part of the metastatic cascade; thus, an emergent physical phenomenon contributes to tumor progression.

Popular Summary

With roughly 2 million new cases each year, breast cancer is by far the most common cancer in women. In 2018, more than 600 000 women with breast cancer died, primarily because of the systemic, invasive nature of the disease. Oncologists must decide between a wide range of therapy options and better diagnosis is needed to avoid overtreatment and undertreatment. Cancer cell motility is essential to the spread of cancer to other parts of the body. Current techniques that serve as clinical cell motility markers rely on cancer cell invasion of the nearby lymph and vascular system after cancer cells have already left the tumor mass and permit much ambiguity. There are no early markers for motility within a tumor. Here, we present such a marker that relies on the physics of cancer cell unjamming, which is a collective cell motility transition.

Our unique, simple, biomechanical cell motility marker relies on the squeezed state of a migrating cell in dense tissue and the nucleus number density as discriminators that detect potentially motile cells in static histopathological images of tumors. In a retrospective study with 1380 breast cancer patients, we show that cancer cell unjamming is an early event in the metastatic cascade since it correlates with distant metastasis—a crucial process in cancer aggressiveness and a key prognostic factor for clinical patient outcomes.

Cancer cell unjamming offers complementary information with respect to the invasion state of nearby lymph nodes, the current clinical gold standard. Its prognostic power is comparable with that of lymph node status, so it has the potential to add valuable information to clinical cancer diagnosis. Since unjamming as a mechanical process is relatively agnostic to molecular details of different tumor types, our results should apply to 92% of all cancers.

Figure 1

Cancer cell clusters in patient-derived explants of primary invasive breast cancer stained for actin (green) and DNA (red). White lines emphasize nuclei and cell outlines. The left column (a) represents a region of more roundish cells and nuclei, while the right column (b) contains more elongated cells and nuclei. In both samples, cells are packed close to a volume fraction of 1.

Figure 2

Vital cell tracking in primary breast cancer explants. (a) Explant of a primary breast carcinoma stained with a vital DNA stain. Yellow lines indicate the tracks of the movement of the nuclei in a 150-minute time interval. An unjammed region of uncorrelated cell motion in the lower middle of the sample becomes visible. This region is surrounded by jammed cells. (b) Cell nuclei were segmented, and their corresponding AR was color-coded according to the color map on the right side (red is for high AR, elongated; green is for small AR, round). The region of motile cells exhibits more elongated nuclei shapes with respect to the surrounding neighbors. This analysis is conducted for the same sample as in panel (a) for an $xy$ plane in the middle of the sample. (c) Zoom of individual tracks of a cell nucleus within the region of the motile cancer cells (green outlines) and of a cell nucleus within the surrounding matrix of jammed cells (blue outlines). The observation time is 35 minutes, displayed in 5-minutes time steps. The moving cell is actively deforming and elongating, while the resting one exhibits a constant round shape. (d) Displacement of a motile cell (green line) and a resting cell (blue line). The displacement of the moving cell increases over time and exceeds a typical cell radius (dashed red line, $8\mathrm{\mu }\mathrm{m}$). The displacement of the resting cell only increases for the first 15 minutes due to fluctuations within the cage formed by the surrounding cells.

Figure 3

(a,b) Quantification of the motile and nonmotile regions in vital tumor explants. (a) Measured mean displacements within 3 hours relative to nearest neighbors (cage-relative MSDs). Motile ($N=22$) regions exhibit significantly (2sKS $p<0.0001$) higher displacements above an average cell radius compared to jammed regions ($N=22$) in primary carcinoma (breast, cervix). (b) Nuclei aspect ratios in primary breast carcinoma explants (shown in Fig. 2), which show a more elongated shape for motile ($N=36$) compared to jammed regions ($N=145$). 2sKS test: $p<0.0001$. (c) Relationship between nucleus shape and cell shape. We show the linear correlation between the nucleus and cell aspect ratios, measured in primary breast and cervix cancer, fixated and stained for DNA and actin. The Pearson correlation coefficient is $r=0.73$. (d) Correlation between mean and variance of the nuclei aspect ratios measured in H&E-stained breast cancer sections. One data point corresponds to one patient from the training or test collective ($N=1380$). The Pearson correlation coefficient is $r=0.79$. (e,f) Nucleus packing in histological slides ($N=1380$) of invasive breast cancer. (e) Blue: correlation between the mean cell area and mean nucleus area in histological images of breast cancer patients. The Pearson correlation coefficient is $r=0.86$. The red area shows the correlation of the mean cytoplasmic space (cell area minus nucleus area) and the mean cell area in histological images of invasive breast cancer patients. The Pearson correlation coefficient is $r=0.95$. (f) Correlation of the mean nucleus area and the mean cytoplasmic area in histological images of invasive breast cancer patients. The Pearson correlation coefficient is $r=0.67$. (g) Correlation of individual cell speed measured by nucleus tracking in vital breast cancer explants with a nucleus volume that scales inversely with nucleus number density [compare Fig. 15]. We measure the mean cage relative speed within 2 hours. Cancer cell motility and, thus, unjamming increase with nucleus volume. We use a moving average with a window width of $100\mathrm{\mu }{\mathrm{m}}^3$. Details and filtering can be found in Appendix pp4.

Figure 4

Derivation of the state diagram of cancer cell unjamming. (a) Tracking data in vital tumor explants. The nucleus volume and nucleus ellipsoid shape $s_E$ are used as axes. These structural observables are binned, and the average speed within 2 hours [$\sqrt{\mathrm{MSD}(t=2\mathrm{h})}/(2\mathrm{h})$, where MSD is the cage-relative mean-squared displacement] of the tiles is depicted as a heat map. More elongated nuclei and larger nuclei are strongly correlated with higher motility. The black line corresponds to a binary SVM classification between tiles whose displacements exceed a typical cell radius ($8\mathrm{\mu }\mathrm{m}$) on average and tiles that do not. (b) State diagram of cancer cell unjamming based on histological images from 1380 breast cancer patients connecting tissue morphology with collective cancer cell motility. Nuclei are depicted in purple, and cells are color-coded by a blue-to-green heat map, where blue indicates a jammed state and green a motile state. Note that the diagram does not reflect a linear increase in motility. The region where blue turns to green depicts where we expect the cell unjamming transition to occur. The abscissa varies the cell and nucleus shape (CeNuS) defined in Eq. (1). The ordinate varies the standardized mean cell area ${\overline{A}}_C^{\text{stand}}$, reflecting the inverse nucleus number density. The variables are measured on two-dimensional histological images of tumors. The corresponding three-dimensional observables that we can measure in tracking experiments [in part (a)] are depicted in gray: The nucleus ellipsoid shape corresponds to CeNuS, and the nucleus volume scales with the inverse nucleus number density represented by ${\overline{A}}_C^{\text{stand}}$ in 2D. (c) Seven images of H&E-stained tissue sections of invasive breast cancer associated with the indicated regions demonstrate that real breast cancer patient data span the whole state space. The scale bar equals $50\mathrm{\mu }\mathrm{m}$.

Figure 5

Image analysis of the histopathological H&E-stained slides to map breast cancer patients within our state diagram. (a) Representative native H&E-stained tumor tissue of cancer cell clusters surrounded by stroma. (c) Nuclei segmentation within the cancer cell clusters to measure the nucleus AR. (d) Cell outline segmentation within the cancer cell clusters to measure the shape index. (e) Quantification of the nucleus shape by the AR (${\mathrm{AR}}_N$), the cell shape by the cell shape index ($p$), and of the inverse nucleus number density by the cell area ($A$).

Figure 6

Distant metastasis and clinical relevance of cancer cell unjamming. The distribution of patient outcomes in terms of distant metastasis is displayed with respect to the variables of the state diagram (cell area, CeNuS) for the training collective ($N=688$) and for the test collective ($N=692$). The state diagrams are shown in panels (a) and (c), respectively. Patients who developed distant metastases are indicated by red triangles. Patients who did not develop metastases are indicated by gray circles. The dotted line represents the decision boundary that separates the low-risk patients for distant metastasis (below) from the high-risk group (above) estimated by SVM classification; see Appendix pp9. Kaplan-Meier estimators are used for assessing the quality of our risk stratification based on cancer cell unjamming. The resulting Kaplan-Meier plots are shown in panel (b) for the training set and panel (d) for the test set. They show that the high-risk group (in red) is well separated from the low-risk group (in blue). The log-rank p-value for the training set is $p=0.0012$, and for the test set, $p=0.0080$. In panel (e), we display only the lymph-node-positive ($\mathrm{LN}+$) patients from the test set ($N=252$) to illustrate the complementarity of lymph node status and cell unjamming. The dotted line represents the decision boundary found in the training set, which yields significant separation between risk groups, as seen in the Kaplan-Meier plot in panel (f) (log-rank $p=0.018$). “Patients at risk” indicates the total number of patients who have not been censored or have not developed distant metastasis by a specific follow-up time. In parentheses after the “Patients at risk” is the cumulative number of individuals developing distant metastases later.

Figure 7

Stratification of all lymph-node-positive cases in the training set by the decision boundary in the space of CeNuS and ${\overline{A}}_C^{\text{stand}}$ presented in the main text. The $y$ axis shows the probability of the Kaplan-Meier estimator of developing distant metastasis over time. Log-rank $p=0.01$. “Patients at risk” indicates the total number of patients who have not been censored or have not developed distant metastasis by a specific follow-up time. In parentheses is the cumulative number of individuals who will develop distant metastases at a later time.

Figure 8

Combining LN status with the prognostic unjamming criteria. (a) Training and test sets: The low-risk group consists of the patients whose tumor structure indicates a jammed state and who exhibit no affected lymph nodes (LN-). The high-risk group consists of all other patients. (b) Training and test sets: The high-risk group consists of patients whose tumor structure indicates an unjammed state and who exhibit affected lymph nodes (LN+). The low-risk group consists of all other patients. “Patients at risk” indicates the total number of patients who have not been censored or have not developed distant metastasis by a specific follow-up time. In parentheses is the cumulative number of individuals who will develop distant metastases at a later time.

Figure 9

Comparison of the HER2-segmented cell outlines with the watershed-estimated cell outlines. (a) Exemplary image of the approximated and segmented cell segments (dark masks). (b) Direct correlation of the aspect ratios of the segmented and estimated cell segments ($n=712$). The Pearson correlation coefficient is 0.59. (d) Direct correlation of the cell shape indices of the segmented and estimated cell segments ($n=712$). The Pearson correlation coefficient is 0.42.

Figure 10

Correlation of individual cell motility with its nucleus shape. (a) Visualization of 3D tracking in a breast cancer explant. Stained nuclei are depicted in orange, spots found are depicted in light blue, and the tracks are indicated in green. (b) Structural properties of nuclei estimated with adaptive thresholding followed by watershedding of the thresholded signal around the tracked spots, allowing segmentation of nearby nuclei. The black and white image of the thresholded nuclei contains multiple errors that are filtered in a later step. (c) Mean cage-relative speed of cells within 2-hour lag correlated with the nucleus shape (average over each cell). The nucleus shape is estimated as the shape parameter $s_E=A/V^{2/3}$ of the ellipsoid with the same second moments as the nucleus segment. The colored regions indicate the confidence interval of the plots. The data are averaged using a moving average with a window width of 0.1.

Figure 11

Illustration of the comparison of the annotated tissue type and the tissue type found by the TS algorithm. (a) Red: cancerous regions found by the TS algorithm; white: background; blue: stroma found by the TS algorithm. (b) Annotations for benchmarking the TS algorithm. Red annotated regions represent cancerous regions while blue annotated regions represent regions with no cancer cells.

Figure 12

Clinical relevance of cancer cell unjamming using only nucleus aspect ratio (${\mathrm{AR}}_N$) distributions instead of CeNuS as in Fig. 6. The distribution of patient data is displayed with respect to the variables’ standardized mean cell area ${\overline{A}}_C^{\text{stand}}$ and $2·({\overline{\overline{\mathrm{AR}}}}_N^{\text{stand}}+{\sigma }_{{\mathrm{AR}}_N}^{2\text{stand}})$ (${\mathrm{AR}}_N$ denotes the nucleus aspect ratio distribution per patient) for the training collective with minimal treatment ($N=688$) and in the test collective of the remaining cases ($N=692$). The state diagrams of the training and test sets are shown in panels (a) and (c), respectively. Patients who developed metastases are indicated by red triangles. Patients who did not develop metastases are indicated by gray circles. The dotted line represents the decision boundary that separates the low-risk patients (below) from the high-risk group (above) estimated by SVM classification; see Appendix pp9. Kaplan-Meier estimators are used to assess the quality of the risk stratification. The resulting Kaplan-Meier plots are shown in panel (b) for the training set and panel (d) for the test set. These plots show that the high-risk group (in red) is well separated from the low-risk group (in blue). Log-rank p-value training set $p<0.001$ and test set $p=0.015$. “Patients at risk” indicates the total number of patients who have not been censored or have not developed distant metastasis by a specific follow-up time. In parentheses is the cumulative number of individuals who will develop distant metastases at a later time.

Figure 13

Clinical relevance of cancer cell unjamming using only cell shape index distributions ($p$) instead of CeNuS as in Fig. 6. The distribution of patient data is displayed with respect to the variables’ standardized mean cell area ${\overline{A}}_C^{\text{stand}}$ and $2·({\overline{\overline{p}}}^{\text{stand}}+{\sigma }_p^{2\text{stand}})$ ($p$ denotes the cell shape distribution per patient) for the training collective with minimal treatment ($N=688$) and in the test collective of the remaining cases ($N=692$). The state diagrams of the training and test sets are shown in panels (a) and (c), respectively. Patients who developed metastases are indicated by red triangles. Patients who did not develop metastases are indicated by gray circles. The dotted line represents the decision boundary that separates the low-risk patients (below) from the high-risk group (above) estimated by SVM classification; see Appendix pp9. Kaplan-Meier estimators are used to assess the quality of the risk stratification. The resulting Kaplan-Meier plots are shown in panel (b) for the training set and panel (d) for the test set. These plots show that the high-risk group (in red) is well separated from the low-risk group (in blue). Log-rank test in the training set $p=0.037$ and test set $p=0.044$. “Patients at risk” indicates the total number of patients who have not been censored or have not developed distant metastasis by a specific follow-up time. In parentheses is the cumulative number of individuals who will develop distant metastases at a later time.

Figure 14

Clinical relevance of cancer cell unjamming. The distribution of patient data is displayed with respect to the variables of the state diagram (cell area, CeNuS) for all available cases ($N=1380$). Patients who exhibit no overall survival (death from any cause) are depicted by red triangles. Patients with an overall survival are indicated by gray circles. The dotted line represents the decision boundary that separates the low-risk patients (below) from the high-risk group (above) estimated by SVM classification from the main text in Fig. 6. Kaplan-Meier estimators are used for assessing the quality of the risk stratification based on cancer cell unjamming for the overall survival. The resulting Kaplan-Meier plot is shown in panel (b) and exhibits a log-rank p-value training set $p=0.0313$. “Patients at risk” indicates the total number of patients who have not been censored or have a reported overall death by a specific follow-up time. In parentheses is the cumulative number of individuals who will develop an event (here, overall death) later.

Figure 15

Nucleus packing and spacing in breast cancer cell clusters measured in $N=1380$ patients. (a) Cytoplasmic spacing $d$ (effective distance between nucleus edge and cell edge) directly correlating with the nucleus size. The Gaussian moving average window size is $5\mathrm{\mu }{\mathrm{m}}^2$, and the colored regions correspond to the 95% confidence intervals. (b) Mean nucleus area ${\overline{A}}_N$ inversely scaling with the number density ${\rho }_{2\mathrm{D}}$. The blue line corresponds to a power-law fit: ${\overline{A}}_N\sim {\rho }_{2\mathrm{D}}^{-\alpha }$, where $\alpha =0.71\pm 0.02$. The root-mean-squared error is 0.0001. All observables are ensemble averages for one patient.