Table 1.
Statistical analysis of cancer cell movements on 1D microtracks
| Cell type | MSD (α) | MLE for μ | MLE for μ | Akaike weights | ||||
|---|---|---|---|---|---|---|---|---|
| Power law | Truncated power law | TP | P | LN | SE | E | ||
| PC-3M | 1.58 ± 0.02 | 2.39 ± 0.2, a = 18 | 2.22 ± 0.16, a = 9 | 0.98 | < 0.01 | < 0.01 | < 0.01 | < 0.01 |
| MDA-MB-231 | 1.54 ± 0.01 | 2.58 ± 0.4, a = 12 | 2.49 ± 0.07, a = 6 | > 0.99 | < 0.01 | < 0.01 | < 0.01 | < 0.01 |
| B16-F1 | 1.52 ± 0.02 | 2.50 ± 0.2, a = 3 | 2.99 ± 0.09, a = 6 | 0.57 | 0.20 | 0.23 | < 0.01 | < 0.01 |
| PC-3 | 1.04 ± 0.03 | 3.17 ± 0.5, a = 12 | 3.14 ± 0.19, a = 6 | > 0.99 | < 0.01 | < 0.01 | < 0.01 | < 0.01 |
| MCF-7 | 0.96 ± 0.04 | 4.57 ± 1.1, a = 6 | 4.52 ± 0.9, a = 6 | 0.77 | < 0.01 | < 0.22 | < 0.01 | < 0.01 |
| B16-F0 | 1.05 ± 0.02 | 3.36 ± 1.3, a = 6 | 3.69 ± 0.09, a = 3 | > 0.99 | < 0.01 | < 0.01 | < 0.01 | < 0.01 |
The first column shows exponent α values obtained from mean square displacement vs. time plots shown in Fig. 2c. Other columns show values for μ exponent – both from power law and truncated power law fits – calculated using the maximum likelihood estimates (MLEs), as described in detail in Supplementary Note 1/Supplementary Methods, and Akaike weights (wAIC) for all model comparisons. Parameter a is the lower cutoff parameter determined using reweighted Kolmogorov–Smirnov (KS) statistic as described in56 (see also Supplementary Methods for more details). The 95% confidence intervals (CIs) are shown for all values. For all cell types, truncated power law (TP), power law (P), log-normal (LN), stretched exponential (SE), and exponential (E) distributions were compared. Strongest supported model is highlighted in bold. wAIC comparisons were performed using lower cutoff values a (see Supplementary Tables 1 and 2) that are specified for the truncated power law. Cumulative frequency distributions (CFDs, shown in Fig. 2d–f) for metastatic cells (PC-3M, MDA-MB-231, B16-F1) fit best the truncated power law with 2 < μ < 3 consistent with Lévy walks (see Supplementary Figure 5 and Supplementary Methods for details on all model comparisons); non-metastatic cells (PC-3, MCF-7, B16-F0) fit best truncated power law with μ > 3 consistent with diffusive motion. See Supplementary Movies 1–6. Analyses were based on the following numbers of cells and time points: MDA-MB-231 (n = 69 cells, m = 17,569 time points); MCF-7 (n = 15, m = 4,468); PC-3M (n = 18, m = 4,833); PC-3 (n = 17, m = 5,457); B16-F1 (n = 53, m = 14,640); B16-F0 (n = 62, m = 18,585)