Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells

Abstract

Amoeboid movement is one of the most widespread forms of cell motility that plays a key role in numerous biological contexts. While many aspects of this process are well investigated, the large cell-to-cell variability in the motile characteristics of an otherwise uniform population remains an open question that was largely ignored by previous models. In this article, we present a mathematical model of amoeboid motility that combines noisy bistable kinetics with a dynamic phase field for the cell shape. To capture cell-to-cell variability, we introduce a single parameter for tuning the balance between polarity formation and intracellular noise. We compare numerical simulations of our model to experiments with the social amoeba Dictyostelium discoideum. Despite the simple structure of our model, we found close agreement with the experimental results for the center-of-mass motion as well as for the evolution of the cell shape and the overall intracellular patterns. We thus conjecture that the building blocks of our model capture essential features of amoeboid motility and may serve as a starting point for more detailed descriptions of cell motion in chemical gradients and confined environments.

Cell motility dependence on adhesive wetting

“…To accurately capture cell shape and its deformations, we use the phase field approach in which an auxiliary field φ(r, t) is introduced to distinguish between the interior (φ = 1) and exterior (φ = 0). This approach allows us to efficiently track the cell boundary which is determined by φ(r, t) = 1/2 [12,20,24,25,27,28]. In our model, boundary motion is driven by fluid flow which is determined by adhesion, friction, membrane forces and active protrusion.…”

Comparative mapping of crawling-cell morphodynamics in deep learning-based feature space

“…still images provided morphodynamic basis for the random walk trajectory previously approximated by a particle model (1). The main difference between existing models and the present model is that while previous models were either rule-based dynamics (37,47), excitable and oscillatory dynamics (14,40,48) or the wave-pinning dynamics (38,39) transition from a circular to amoeboid then to a keratocyte-like shape by the increase in the protrusion force ( Fig. 2f.…”

“…The present framework of data analysis potentially provides means to test and improve specific models of migrating cells. Distinctions between various excitable (14,41,61) and cell polarity models (38,62,63) will become more relevant as we proceed further to analyze detailed geometries and dynamics associated with specific cells and conditions. For example, our ideal cell model gave more frequent rise to pseudopods from the tail region compared to the real cell data.…”

“…Cdc42 in neutrophils and Ras/Rap in Dictyostelium are also known to act positively to strengthen Rac and Rho and hence cell polarity (16,(34)(35)(36). Mathematical models of random turning and persistent migration thusfar have descried the outcome of either excitability-based (14,37) or polarity-based regulation (38), however realistic shapes resulting from the interplay of cell polarity and pseudopods have not been addressed not to mention the lack of systematic and quantitative morphology comparison between simulations and real data. In this work, to overcome these shortcomings, we first developed a framework that employs deep learning based classifier to obtain objective measures for shape comparison.…”

REMI-seq: Development of methods and resources for functional genomics inDictyostelium

“…Almost all Dictyostelium cell motility assays are based on starved mid-aggregation stage cells undergoing chemotaxis to cAMP or chemotaxis of bacterially grown-cells to folate. Developed cells show a significantly higher speed and directionality of movement compared to those in growth phase (Varnum, Edwards and Soll, 1986;Alonso, Stange and Beta, 2018). This difference may arise due to the influence of different molecular pathways controlling chemotaxis (Nichols, Veltman and Kay, 2015).…”