Displacement correlations between a single mesenchymal-like cell and its nucleus effectively link subcellular activities and motility in cell migration analysis

Cell migration is an essential process in organism development and physiological maintenance. Although current methods permit accurate comparisons of the effects of molecular manipulations and drug applications on cell motility, effects of alterations in subcellular activities on motility cannot be fully elucidated from those methods. Here, we develop a strategy termed cell-nuclear (CN) correlation to parameterize represented dynamic subcellular activities and to quantify their contributions in mesenchymal-like migration. Based on the biophysical meaning of the CN correlation, we propose a cell migration potential index (CMPI) to measure cell motility. When the effectiveness of CMPI was evaluated with respect to one of the most popular cell migration analysis methods, Persistent Random Walk, we found that the cell motility estimates among six cell lines used in this study were highly consistent between these two approaches. Further evaluations indicated that CMPI can be determined using a shorter time period and smaller cell sample size, and it possesses excellent reliability and applicability, even in the presence of a wide range of noise, as might be generated from individual imaging acquisition systems. The novel approach outlined here introduces a robust strategy through an analysis of subcellular locomotion activities for single cell migration assessment.


SUPPLEMENTARY INFORMATION
Supplementary information 1: Figure S1. One-hour migration movies of 50 cells were analyzed using CN-correlation barcodes to document their migration patterns. Each barcode represents the migration pattern of a randomly selected individual NIH 3T3 fibroblast (RFP-tagged) at one-minute intervals over a one-hour period. Three barcodes are marked as examples of barcodes dominated by a type of subcellular activity in the CN correlation (Region I, II, III, and IV respectively). Four movies (Movie S1-4) correspond to these barcodes. B. The four selected barcodes are chosen based on the most significant occurrence increase of the bar in a specific region (see the main text for explanation).

Supplementary information 2:
Movie S1-S4. Each movie displays a typical cell migration mode in the CCD-NCD // coordinate system as Region I, II, III and IV, respectively. The corresponding barcodes were identified in Figure S1. Each movie records migration of a single RFP-tagged NIH 3T3 fibroblast at 1-min intervals over a one-hour period.
Movie S5. The movie of a single RFP-tagged NIH 3T3 fibroblast was acquired at 1-min intervals over a 500-minute period. This movie was analyzed in Figure 3. Table S1. Error filtered cell migration potential index (CMPI) of 6 different cell types.

Autocorrelation analysis of CN correlation reveals four different cell migratory patterns
We have demonstrated that each CN correlation datum can be mapped to one of the four specific locomotion modes through its location in the CCD vs. NCD // plot using the polar coordinate system. Hence, we obtained CN correlation data from a one-hour cell movie in which the cell performed a distinctive locomotion event. The angular coordinate and the magnitude of the NCD // of the CN correlation data were subjected to autocorrelation analysis to understand whether temporal patterns exist in these two variables during different locomotion events. In the analysis process, the autocorrelation coefficients were computed through using overlapping time intervals, while the CN correlation data were obtained at various time intervals, ranging from one to three minutes.
The autocorrelation of NCD // displayed reasonable results in accordance with their corresponding migration patterns. An active migratory cell showed relatively strong autocorrelation with adjacent time lags. This is expected since during active migration the nucleus should routinely perform translocations with the repeated trailing edge detachments. According to the NCD // autocorrelation result, the nucleus can maintain a relatively similar velocity for approximately three to four minutes, i.e., even though the nucleus might still move in the same direction after four minutes, the nuclear speed can display a significant difference. For an evasive migratory cell, the NCD // autocorrelation was dramatically decreased and the result suggested that there is no clear temporal migratory pattern. A cell undergoing evasive motions displays less persistence to the direction in respect to the active migration. Although the inertia (displaying as the NCD) to resist change from the previous movement plays a critical role in nuclei movement, the magnitude of the NCD // could abruptly change once the cell changes its direction. A sampling cell, on the other hand, has a stationary nucleus (NCD // ∼ 0) regardless of its protrusions occurring in random directions. Hence, the correlogram had random and vigorous oscillation around 0. A 0.24 ± 0.02 0.23 ± 0.02 0.14 ± 0.01 0.10 ± 0.01 0.08 ± 0.00 0.09 ± 0.01 cell with a large-angle protrusion also possessed a largely fluctuating autocorrelation from its CN correlation data as the sampling cells, while displaying obvious autocorrelations when the CN correlation data were obtained at time intervals of 3 minutes. This result can be associated with the cell turning pattern. When a cell proceeds in a large-angle turning event, the inertia of nuclear motion occurs in a regular pattern that can be sustained and observed at the sixth minute (autocorrelation was dropped after six minutes). However, this autocorrelation only can be observed in longer time intervals (3 minutes) in respect to the shorter time intervals (one to two minutes). This is presumably because the continual detachment events, due to cell polarity changes, have a frequency in between two and three minutes and the nuclear motion is controlled by the detachment events. Hence, nuclear motion cannot be smoothly detected in the shorter time intervals.
In contrast to the NCD // autocorrelations, the angular autocorrelations among the four types of migration activities are similar to each other. The autocorrelations decay quickly in different analyses of time intervals, indicating that the angular patterns have no regular trends. Indeed, a cell locomotion event is assembled by various locomotion modes, which can take place without any special order, and it certainly does not require that the component modes consist of a set pattern. Figure S2. Autocorrelations of the CN correlation data representing a specific migratory activity. The NCD // autocorrelation (top) and the angular coordinate autocorrelation (bottom) are calculated from CN correlation data extracted from one-hour cell movies in which the cells are undergoing a specific cell migratory activity. Dots display the autocorrelation results at τ = 1 (blue), 2 (green) and 3 (red) minutes overlapping time intervals, respectively.