Cell protrusion and retraction driven by fluctuations in actin polymerization: A two‐dimensional model

Abstract

Animal cells that spread onto a surface often rely on actin-rich lamellipodial extensions to execute protrusion. Many cell types recently adhered on a two-dimensional substrate exhibit protrusion and retraction of their lamellipodia, even though the cell is not translating. Traveling waves of protrusion have also been observed, similar to those observed in crawling cells. These regular patterns of protrusion and retraction allow quantitative analysis for comparison to mathematical models. The periodic fluctuations in leading edge position of XTC cells have been linked to excitable actin dynamics using a one-dimensional model of actin dynamics, as a function of arc-length along the cell. In this work we extend this earlier model of actin dynamics into two dimensions (along the arc-length and radial directions of the cell) and include a model membrane that protrudes and retracts in response to the changing number of free barbed ends of actin filaments near the membrane. We show that if the polymerization rate at the barbed ends changes in response to changes in their local concentration at the leading edge and/or the opposing force from the cell membrane, the model can reproduce the patterns of membrane protrusion and retraction seen in experiment. We investigate both Brownian ratchet and switch-like force-velocity relationships between the membrane load forces and actin polymerization rate. The switch-like polymerization dynamics recover the observed patterns of protrusion and retraction as well as the fluctuations in F-actin concentration profiles. The model generates predictions for the behavior of cells after local membrane tension perturbations.

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

“…To determine if there is any local slowdown in the region of the focal adhesion, in Fig 2B we show the profile of the retrograde flow speed where the retrograde flow speed was averaged over both time and the z-axis. In these flow profiles there is no clear decrease in the retrograde flow inside the focal adhesion region at any value of κ F A , in agreement with experimental results [10] suggest that the actin network in our simulations is sufficiently crosslinked to approximately behave as a uniform elastic gel [55], see Modeling methods and Fig S1.…”

“…We note that this curve is dependent on the simplifying assumptions of our model, including a fixed polymerization (i.e. filament insertion) rate while in reality a reduction of polymerization with force is expected [49,55]. Whether the relationship between the external force at the leading edge the actin network extension speed should be concave or convex for actin networks has been debated [40,41,48,57].…”

WAVE1 and WAVE2 have distinct and overlapping roles in controlling actin assembly at the leading edge

“…These effects may stem from slower actin assembly and protrusion rates ( Yamazaki et al. , 2005 ; Ryan et al. , 2017 ).…”

Building a dendritic actin filament network branch by branch: models of filament orientation pattern and force generation in lamellipodia

“…We can identify a few areas for possible future modeling work. Such work could develop and justify constitutive relationships assumed by models of actin-based motility that start from a more coarse-grained level of description (Barnhart et al 2017;Campas et al 2012;Lewalle et al 2014;Ryan et al 2017;Zhu and Mogilner 2012). For example, work by Falcke and collaborators described protrusive activity and concave force-velocity behavior of lamellipodia considering the actin network as a cross-linked gel connected to the membrane through a layer of polymerizing semiflexible filaments (Dolati et al 2018;Enculescu et al 2010;Zimmermann et al 2010;Zimmermann and Falcke 2014).…”