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Comparison of experimental and simulated cell trajectories (A). Examples of cell trajectories from wild-type cells in an MZoep host from low-magnification experiments (top) and from model simulations with the fitted parameters (bottom). All experimental (three-dimensional) trajectories were projected to the primary two-dimensional plane of their motion and rotated so that their average direction of migration aligns with the y-axis as in the simulations. Frames were captured at 90 s intervals for 3 h (~5.5–8.5 hpf). The red symbols indicate the points along the trajectory identified as tumbling events using the algorithm introduced in Sec. I C. Simulated cell trajectories corresponding to different experimental conditions (B). Examples of simulated cell trajectories for different values of model parameter τr with other parameters as fitted for wt cells in an MZoep embryo. (left) τr as fitted to the wt cells (τr = 8 min). (center) For long runs (τr = 25 min), which yield T r = T t - values consistent with results obtained from CAEzrin cells, and (right) short runs (τr = 4 min), which yield T r = T t , values consistent with the ones measured for ezrin-MO cells. (PDF 1651 kb)

Supplementary Methods. Supplementary methods file with detailed description of: 1. Data analysis: (A) Automatic Protrusion Analyzer (APA) software. (B) Polar Order Parameter (POP) used to characterize the distribution of orientations of protrusions of the model. (C) Automatic detection of run and tumbles. 2. Model of cell migration: (A) Cell migration model description [41â 44]. (B) Parameterization of the computational model using experimental measurements [45]. (C) Model Predictions â Distance to target and position variance [31]. (PDF 203 kb)

Frequency of actin-rich protrusions, orientation of cell protrusions, and summary of POP values. (A) Frequency of actin-rich protrusions in control and ezrin-MO-injected mesendoderm cells. Arbitrary units (AU) are used as actin-rich protrusions are weighted with the intensity of the Lifeact signal in the protrusion. (B) Orientation of blebs with respect to the local migration axis. POP: Mean ± SEM of the magnitude of the polar order parameter. Number of analyzed cells = 17 for wt, 6 for ezrin-MO, and 6 for CAEzrin. Number of blebs n = 349 for wt, 163 for ezrin-MO, and 6 for CAEzrin. Statistical significance was determined comparing the mean ± SEM of the magnitude of the POP of the angular distributions. (C) Orientation of bleb and actin-rich protrusion formation with respect to the Yolk-ectoderm axis. For all experimental conditions, protrusions are almost exclusively oriented perpendicular to the Yolk-ectoderm axis, indicating that protrusions are formed into the extracellular space between the Yolk cell and the overlaying ectoderm layer. (D) Mean values ± SEM of the magnitude of the POP of the angular distributions of the analyzed protrusions. Green shaded area covers the wt mean ± SEM. Number of analyzed cells = 17 for wt, 6 for ezrin-MO, and 6 for CAEzrin. Number of actin-rich protrusions = 10853 for wt, 1501 for ezrin-MO, 1160 and 2549 for CAEzrin. Number of blebs n = 349 for wt and 163 for ezrin-MO. For CAEzrin only 6 blebs were observed so the POP was not calculated. (PDF 600 kb)

Durations of run and tumble phases. Distribution of run and tumble durations as detected by our algorithm from low-magnification movies of wt cells transplanted in a MZoep host. Frames were captured at 90 s intervals for 3 h (~5.5–8.5 hpf). The inset shows the same data in a semi-logarithmic plot, where a line indicates an exponential relationship. Exponentially distributed times are expected in a run and tumble trajectory if we assume a simple two-state Markov processes, namely a process that undergoes transitions from one state to another where the probability distribution of the next state depends only on the current state and not on the sequence of events that preceded it [41]. (PDF 103 kb)

Accuracy of protrusion detection using the Automatic Protrusion Analyzer (APA). APA accurately detects 83 % of the blebs formed by the cells as validated by two independent experimentalists. The majority of false positive detected blebs consisted of the same bleb being detected at more than one time point. Number of analyzed cells = 28. Manual control was also performed for actin-rich protrusions and detection was found to be accurate for more than 99 % of the protrusions and for this reason we do not provide the results of the manual segmentation here. (PDF 148 kb)

Frequency of actin-rich protrusions, orientation of cell protrusions, and summary of POP values. (A) Frequency of actin-rich protrusions in control and ezrin-MO-injected mesendoderm cells. Arbitrary units (AU) are used as actin-rich protrusions are weighted with the intensity of the Lifeact signal in the protrusion. (B) Orientation of blebs with respect to the local migration axis. POP: Mean ± SEM of the magnitude of the polar order parameter. Number of analyzed cells = 17 for wt, 6 for ezrin-MO, and 6 for CAEzrin. Number of blebs n = 349 for wt, 163 for ezrin-MO, and 6 for CAEzrin. Statistical significance was determined comparing the mean ± SEM of the magnitude of the POP of the angular distributions. (C) Orientation of bleb and actin-rich protrusion formation with respect to the Yolk-ectoderm axis. For all experimental conditions, protrusions are almost exclusively oriented perpendicular to the Yolk-ectoderm axis, indicating that protrusions are formed into the extracellular space between the Yolk cell and the overlaying ectoderm layer. (D) Mean values ± SEM of the magnitude of the POP of the angular distributions of the analyzed protrusions. Green shaded area covers the wt mean ± SEM. Number of analyzed cells = 17 for wt, 6 for ezrin-MO, and 6 for CAEzrin. Number of actin-rich protrusions = 10853 for wt, 1501 for ezrin-MO, 1160 and 2549 for CAEzrin. Number of blebs n = 349 for wt and 163 for ezrin-MO. For CAEzrin only 6 blebs were observed so the POP was not calculated. (PDF 600 kb)

Accuracy of protrusion detection using the Automatic Protrusion Analyzer (APA). APA accurately detects 83 % of the blebs formed by the cells as validated by two independent experimentalists. The majority of false positive detected blebs consisted of the same bleb being detected at more than one time point. Number of analyzed cells = 28. Manual control was also performed for actin-rich protrusions and detection was found to be accurate for more than 99 % of the protrusions and for this reason we do not provide the results of the manual segmentation here. (PDF 148 kb)

Durations of run and tumble phases. Distribution of run and tumble durations as detected by our algorithm from low-magnification movies of wt cells transplanted in a MZoep host. Frames were captured at 90 s intervals for 3 h (~5.5–8.5 hpf). The inset shows the same data in a semi-logarithmic plot, where a line indicates an exponential relationship. Exponentially distributed times are expected in a run and tumble trajectory if we assume a simple two-state Markov processes, namely a process that undergoes transitions from one state to another where the probability distribution of the next state depends only on the current state and not on the sequence of events that preceded it [41]. (PDF 103 kb)

Computational model description and supplementary results. (A) Schematic visualization of the simulation set-up: three-dimensional model where the cell is confined in the z-direction to the mesoendodermal layer of height ΔME. The red arrow indicates the direction of polarization within the layer. (B) Schematic visualization of example model trajectories in the mesoendodermal plane (xy) in the tumble and run phases. The arrow in the run panel indicates the direction of the run determined by the polar angle 'φD = 0, which sets the average direction of migration during the run. The dashed lines indicate the instantaneous movement angle 'φ(t0) at time t0. Impact of orientation error ε on the model results (C–E). Distance to target and spatial variance of the cells at t = 90 min as a function of the scaled avg. run time τr for different values of the reorientation error towards the target ε (value estimated for wt cells and used in the main text ε = 0:2, Fig. 5); (C) ε = 0:1, (D) ε = 0:3, and (E) ε = 0:4. Average relative error versus run time (F). Average relative error E rel defined as the mean observable deviation (Additional file 1: Table S2) between model simulations and experimental results (wt cells in MZoep host). All model parameters as fitted to experimental data with the average run time being varied around the fitted value as in Fig. 5b. The vertical line represents the threshold value 0.1, which defines the shaded ‘consistency region’ in Fig. 5b. (PDF 1475 kb)