Minimal Model of Cellular Symmetry Breaking

Abstract

The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechanochemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities. arXiv:1909.12804v1 [physics.bio-ph] 26 Sep 2019 S3 2.3 Components of the Jacobian for l ≥ 2Following the general procedure outlined in Sec. 2.1, we derive in the following the components of the system's Jacobian. The Jacobian diagonalizes in the space of spherical harmonics and contributes for each mode l with J l = J l RR J l Rc J l cR J l cc

Spontaneous polarization and locomotion of an active particle with surface-mobile enzymes

“…The advection of mobile enzymes over the surface by these flows reinforces the initial perturbation, ultimately leading to a self-sustained polarization of the enzyme distribution and steady particle motion. This mechanism bears similarity to other active mechanochemical symmetry-breaking instabilities exploited by cells to divide, polarize or migrate [19][20][21][22]58]. Our results could be useful to design bio-mimicking active particles with an adaptive or controllable propulsion mechanism, which can be dynamically (dis-)engaged by sensing or tuning any of the physical parameters involved in the self-polarization instability, as mapped in the present study.…”

Rayleigh–Plateau instability of anisotropic interfaces. Part 1. An analytical and numerical study of fluid interfaces

“…For a viscous active surface Mietke et al. (2019 a ) and Mietke, Jülicher & Sbalzarini (2019 b ) report a Rayleigh–Plateau instability with mechano-chemical regulation. For a biological tissue composed of multiple cells Hannezo, Prost & Joanny (2012) provide an energy argument based on an effective surface tension.…”

“…Alternatively, proteins which anchor at the plasma membrane can trigger a pearling instability (Tsafrir et al 2001) by bending the membrane and thus inducing a non-zero curvature (Campelo & Hernández-Machado 2007;Jelerčič & Gov 2015). For a viscous active surface Mietke et al (2019a) and Mietke, Jülicher & Sbalzarini (2019b) report a Rayleigh-Plateau instability with mechano-chemical regulation. For a biological tissue composed of multiple cells Hannezo, Prost & Joanny (2012) provide an energy argument based on an effective surface tension.…”

A C++ expression system for partial differential equations enables generic simulations of biological hydrodynamics

“…An important class of models on the scale of cells and multi-cellular tissues is continuum models, formulated as partial differential equations (PDE), that account for the mechanical properties of living matter [ 2 – 4 ]. Coupling biological hydrodynamics with biochemical regulation, such models have been successful at describing the physics underlying biological phenomena such as cell division [ 5 ], zygote polarization [ 6 , 7 ], epithelial tissue folding [ 8 ], and cellular symmetry breaking [ 9 ].…”

“…An important class of models on the scale of cells and multi-cellular tissues is continuum models, formulated as partial differential equations (PDE), that account for the mechanical properties of living matter [2][3][4]. Coupling biological hydrodynamics with biochemical regulation, such models have been successful at describing the physics underlying biological phenomena such as cell division [5], zygote polarization [6,7], epithelial tissue folding [8], and cellular symmetry breaking [9]. Such mechano-chemical models of biological processes are usually nonlinear, either due to nonlinear chemical reaction terms or due to the hydrodynamics itself, e.g., the nonlinear polarity-velocity coupling in active polar fluids.…”