Modeling crawling cell movement on soft engineered substrates

Abstract

Self-propelled motion, emerging spontaneously or in response to external cues, is a hallmark of living organisms. Systems of self-propelled synthetic particles are also relevant for multiple applications, from targeted drug delivery to the design of self-healing materials. Self-propulsion relies on the force transfer to the surrounding. While self-propelled swimming in the bulk of liquids is fairly well characterized, many open questions remain in our understanding of self-propelled motion along substrates, such as in the case of crawling cells or related biomimetic objects. How is the force transfer organized and how does it interplay with the deformability of the moving object and the substrate? How do the spatially dependent traction distribution and adhesion dynamics give rise to complex cell behavior? How can we engineer a specific cell response on synthetic compliant substrates? Here we generalize our recently developed model for a crawling cell by incorporating locally resolved traction forces and substrate deformations.The model captures the generic structure of the traction force distribution and faithfully reproduces experimental observations, like the response of a cell on a gradient in substrate elasticity (durotaxis). It also exhibits complex modes of cell movement such as "bipedal" motion. Our work may guide experiments on cell traction force microscopy and substrate-based cell sorting and can be helpful for the design of biomimetic "crawlers" and active and reconfigurable self-healing materials.

Computational approaches to substrate-based cell motility

“…126 The computational model given by Equations (11)- (15) successfully reproduced many features exhibited by moving cells, such as qualitatively correct distributions of actin polarisation and traction forces for keratocyte-like cells (see Figure 4b). In addition to steady cell migration, a variety of complex dynamic propagation modes were discovered, including stick-slip motion 125 (see Figure 4d) and even bipedal motion.…”

“…(b) The actin distribution and the traction force exerted on the substrate of a crawling cell. 126 Motion is to the right. The black solid curves show the contour at phase-field level ρ = 0.25.…”

“…In addition to steady cell migration, a variety of complex dynamic propagation modes were discovered, including stick-slip motion 125 (see Figure 4d) and even bipedal motion. 126 Stick-slip movement is characterized by periodic attachments/detachments of the cell and strong modulations of the propagation speed and shape of the cell. Qualitatively similar behaviour were found for lamellipodia, displaying periodic contractions that depend on the adhesiveness of the substrate, 127 osteosarcoma cells, 128 as well as in filopodia.…”

An introduction to the statistical physics of active matter: motility-induced phase separation and the “generic instability” of active gels

“…Other recent theoretical work on active gel droplets can be found, among others, in Refs. [61][62][63][64][65]. It is clear that a lot of work remains to be done in this area, both in providing a theoretical framework to understand the simulation results, and in taking forward the simulation models to provide more and more realistic descriptions of cell extracts and motile cells.…”

Nematoelastic crawlers

“…As seen in Fig 5a, buckling, originally induced on the entire width of the stripe under the beam, fades away after a few beam passages, as the stripe shifts aside, thereby causing a sharp drop of energy on both edges (Fig 5b). The friction dependence is more straightforward here than in models of crawling cells where an optimal adhesion strength may be chosen [40]. The substrate stiffness (assumed here to be very high) should also affect nemato-elastic crawlers.…”