Discrete Modeling of Amoeboid Locomotion and Chemotaxis in Dictyostelium discoideum by Tracking Pseudopodium Growth Direction

Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions

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.

A chemorepellent inhibits local Ras activation to inhibit pseudopod formation to bias cell movement away from the chemorepellent

The ability of cells to sense chemical gradients is essential during development, morphogenesis, and immune responses. Although much is known about chemoattraction, chemorepulsion remains poorly understood. Proliferating Dictyostelium cells secrete a chemorepellent protein called AprA. AprA prevents pseudopod formation at the region of the cell closest to the source of AprA, causing the random movement of cells to be biased away from the AprA. Activation of Ras proteins in a localized sector of a cell cortex helps to induce pseudopod formation, and Ras proteins are needed for AprA chemorepulsion. Here we show that AprA locally inhibits Ras cortical activation through the G protein–coupled receptor GrlH, the G protein subunits Gβ and Gα8, Ras protein RasG, protein kinase B, the p21-activated kinase PakD, and the extracellular signal–regulated kinase Erk1. Diffusion calculations and experiments indicate that in a colony of cells, high extracellular concentrations of AprA in the center can globally inhibit Ras activation, while a gradient of AprA that naturally forms at the edge of the colony allows cells to activate Ras at sectors of the cell other than the sector of the cell closest to the center of the colony, effectively inducing both repulsion from the colony and cell differentiation. Together, these results suggest that a pathway that inhibits local Ras activation can mediate chemorepulsion.