Unified biophysical mechanism for cell-shape oscillations and cell ingression

Wei-Chang Lo, Craig Madrak, Daniel P. Kiehart, and Glenn S. Edwards

Phys. Rev. E 97, 062414 – Published 22 June 2018

Abstract

We describe a mechanochemical and percolation cascade that augments myosin's regulatory network to tune cytoskeletal forces. Actomyosin forces collectively generate cytoskeletal forces during cell oscillations and ingression, which we quantify by elastic percolation of the internally driven, cross-linked actin network. Contractile units can produce relatively large, oscillatory forces that disrupt crosslinks to reduce cytoskeletal forces. A (reverse) Hopf bifurcation switches contractile units to produce smaller, steady forces that enhance crosslinking and consequently boost cytoskeletal forces to promote ingression. We describe cell-shape changes and cell ingression in terms of intercellular force imbalances along common cell junctions.

Received 14 August 2017

DOI:https://doi.org/10.1103/PhysRevE.97.062414

Physics Subject Headings (PhySH)

Bifurcations Developmental biology Intracellular signalling Morphogenesis Percolation theory

Physics of Living SystemsNonlinear DynamicsInterdisciplinary PhysicsStatistical Physics & ThermodynamicsPolymers & Soft Matter

Authors & Affiliations

Wei-Chang Lo¹, Craig Madrak¹, Daniel P. Kiehart², and Glenn S. Edwards^1,*

¹Physics Department, Duke University, Durham, North Carolina 27708, USA
²Biology Department, Duke University, Durham, North Carolina 27708, USA

^*Corresponding author: GEdwards@phy.duke.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 97, Iss. 6 — June 2018

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Modeling cytoskeleton (2D schematics of 3D structures). Myosin mini-filaments are blue, actin filaments are red, and actin cross-links are black dots. Contractile unit (cross-links enumerated, steady-state deflection shaded) shown (a) in isolation and (b) within a local network. (c) Applied forces acting on an actin-segment at the force-balance condition $T (c_{o}, r) = K (l_{o})$ , where $l_{o}$ is the height of the triangle. $f_{ext, 1}$ and $f_{ext, 2}$ are components (along the segment) of the forces external to the contractile unit. (d) Turnover at one end of a myosin mini-filament. (e), (f) Amnioserosa cell. Light green and dark green borders represent adherens junctions and cell membrane, respectively. The dashed boxes in each lower-left corner correspond to panel (b) (deflections suppressed). Clusters highlighted in gray. Panel (e) has four clusters and panel (f) has one extensively branched cluster. These Mikado representations of the actin (red) filaments were generated as follows. First, a random distribution of points was generated within the hexagon. These points were classified as apicomedial, i.e., relatively central to the hexagon, or as cortical, i.e., near the edges of the hexagon. Then a line was centered on each point. For points within the apicomedial region, the angular orientation was random. For points within the cortical region, the angular orientation was restricted to mostly parallel the edge, but with random variations within the restricted range. The cross-links (black dots) and myosin mini-filaments (blue barbells) were strategically placed in panels (a) and (b) to illustrate cluster formation.
Reuse & Permissions
Figure 2
Characterizing oscillations. (a) Phase portrait, which plots $r \bar{t_{1}}$ (contractility) versus $\frac{1}{\bar{τ} (1 + r)}$ (turnover). $\bar{t_{1}}$ and $\bar{τ}$ are dimensionless versions of $t_{1}$ and τ (Appendix pp1). The bifurcation (sloped) line separates an upper region of oscillating solutions from a lower region of steady solutions. The two sets of oscillating solutions (circles, left set $\frac{1}{\bar{τ}} = 0.5$ , right set $\frac{1}{\bar{τ}} = 1.0$ ) have the same color-coded offsets (0.01, 0.38, and 0.75) above the bifurcation line. Color-coded limit cycles for the (b) left-set and (c) right-set solutions from panel (a). Normalized deflections for the (d) left-set and (e) right-set solutions.
Reuse & Permissions
Figure 3
Switching from oscillations to ingression. (a)–(d) Characterizing switching. Phase portrait (a) including an initial oscillating solution (black) and four final steady solutions (green, purple, blue, and red). Time dependence of the duty ratio (b). Panel (c) tracks the transition from the now unstable limit cycle (black) to the stable fixed point (initial locations of $N$ and $l$ on the limit cycle for clarity). Green solution exhibits critical slowing and has been truncated for clarity. Panel (d) plots the normalized deflection. (e) Recapitulation of the experimental data (fitting parameters listed in Table 1). (f) Magnification factor $M$ .
Reuse & Permissions
Figure 4
Simulations of nonlinear dynamics, where the solutions are color-coded. (a) Phase portrait, where $k_{3} \frac{l_{o}^{2}}{k_{1}} = 15$ ( $k_{3} \frac{l_{o}^{2}}{9 k_{1}} = 15$ for Figs. 2 and 3). The bifurcation line is solid, the threshold for numerical artifact is dashed. Phase plots in terms of (b) normalized concentration $\frac{c}{c_{o}}$ and (c) normalized number $\frac{N}{N_{o}}$ . (d)–(f) Corresponding time series. To facilitate comparison with Ref. [13], these simulations are based on Eq. (A5) with $r$ set to 1, and Eq. (A6) with $r$ set to 0.
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics