Artificial non-polarized cell track with <i>T</i> = 500<i>s</i> based on a Hawkes process.

(A, B) Contour dynamics (left, colored contours), the center of mass trajectory (right, colored line), and the trace of the entire cell track(right, gray area). (C, D) In the second row, kymographs of the local motion f and its protrusion component fprot are displayed. Point events realized by the underlying Hawkes process are depicted as circles in the protrusion kymograph. (E, F) In the third row, kymographs of the other two components fAAF and fAPCSF are shown. Finally, in panels (G, H), the evolution of the contour area as well as the contour arc length are presented.</p

Contour dynamics of non-polarized cell tracks based on a Hawkes process as shown in Fig 6.

The cell tracks are displayed at tenfold speed. (MP4)</p

Supporting formulas and computations.

Amoeboid cell motility is relevant in a wide variety of biomedical processes such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that visually resemble experimental data very closely. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to common biomarkers: the F-actin density close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward, and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism Dictyostelium discoideum. An implementation of the model is provided within the open-source software package AmoePy, a Python-based toolbox for analyzing and simulating amoeboid cell motility.</div

Contour dynamics with corresponding kymographs of a polarized cell track based on a Hawkes process as shown in Fig 4.

The point events generated by the Hawkes process are depicted as white circles. The cell track is displayed at a fivefold speed. (MP4)</p

Comparison of local motion kymographs for different non-polarized cell tracks generated with different temporal resolutions: .

Comparison of local motion kymographs for different non-polarized cell tracks generated with different temporal resolutions: .</p

Computation of relative fluorescence intensity for experimental microscopy data and tenfold upsampled data via ellipses along the cell contour.

Computation of relative fluorescence intensity for experimental microscopy data and tenfold upsampled data via ellipses along the cell contour.</p

Collection of five non-polarized cell tracks based on Poisson point processes as protrusion process and the corresponding kymographs displayed as in Fig 3.

Collection of five non-polarized cell tracks based on Poisson point processes as protrusion process and the corresponding kymographs displayed as in Fig 3.</p

Model components extracted from experimental cell track of Fig 7 and their proportion on the overall velocity of the contour dynamics for two pairs of model weights.

The model weights were estimated by minimizing sums of squared residuals: S (left column) and S+ (right column), see S1 Text for more details. (PDF)</p

Inferring protrusion component from <i>D. discoideum</i> cell track.

(A) Persistently motile cell track for T = 500s. (B) Microscopy image with fluorescence intensity (mRFP tagged LifeAct as marker for filamentous actin, white to green color scheme) and segmented cell contours (red lines, every tenth shown). (C) Local motion kymograph showing expansions (red areas) and retractions (blue areas). (D) Relative fluorescence intensity as in panel (B) with regions of high and low F-actin density displayed in red and blue, respectively. (E) The underlying protrusion component inferred from our model for a given set of model parameters. The resulting propagation of virtual markers from one contour to the next one is depicted as black circles in panel (B). (F) The contour area with predefined reference area Aref = 91.23μm2 (dashed gray line). Finally, regions of interest are displayed as black and white dashed boxes.</p

Collection of five polarized cell tracks based on Poisson point processes as protrusion process and the corresponding kymographs displayed as in Fig 4.

Collection of five polarized cell tracks based on Poisson point processes as protrusion process and the corresponding kymographs displayed as in Fig 4.</p