Four different mechanisms for switching cell polarity

The influence of polarized membrane ion carriers and extracellular electrical/pH gradients on cell ionic homeostasis and locomotion

Anisotropic environmental signals or polarized membrane ion/solute carriers can generate spatially-varying intracellular gradients, leading to polarized cell dynamics. For example, directional migration of neutrophils, galvanotaxis of glioblastoma, and water flux in kidney cells, all result from the polarized distribution of membrane ion carriers and other intracellular components. The underlying physical mechanisms behind how polarized ion carriers interact with environmental signals are not well studied. Here, we use a physiologically-relevant, physics-based mathematical model to reveal how ion carriers generate intracellular ionic and voltage gradients. The model is able to discern the contribution of individual ion carriers to the intracellular pH gradient, electric potential, and water flux. We discover that an extracellular pH gradient leads to an intracellular pH gradient via chloride-bicarbonate exchangers, whereas an extracellular electric field leads to an intracellular electric potential gradient via passive potassium channels. In addition, the mechanical-biochemical coupling can modulate actin distribution and flow, and create biphasic dependence of the cell speed on water flux. Moreover, we find that F-actin interaction with NHE alone can generate cell movement, even when other ion carriers are not polarized. Taken together, the model shows the importance of cell ion dynamics in modulating cell migration and cytoskeletal dynamics.

Forced and spontaneous symmetry breaking in cell polarization

How does breaking the symmetry of an equation alter the symmetry of its solutions? Here, we systematically examine how reducing underlying symmetries from spherical to axisymmetric influences the dynamics of an archetypal model of cell polarization, a key process of biological spatial self-organization. Cell polarization is characterized by nonlinear and non-local dynamics, but we overcome the theory challenges these traits pose by introducing a broadly applicable numerical scheme allowing us to efficiently study continuum models in a wide range of geometries. Guided by numerical results, we discover a dynamical hierarchy of timescales that allows us to reduce relaxation to a purely geometric problem of area-preserving geodesic curvature flow. Through application of variational results, we analytically construct steady states on a number of biologically relevant shapes. In doing so, we reveal non-trivial solutions for symmetry breaking.

Oscillations and bifurcation structure of reaction-diffusion model for cell polarity formation

We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by (Otsuji et al., PLoS Comp Biol 3:e108, 2007). The system is a useful model for understanding cell polarity formation. We show that this model exhibits four different spatiotemporal patterns including two types of oscillatory patterns, which can be regarded as cell polarity oscillations with the reversal and non-reversal of polarity, respectively. The trigger causing these patterns is a diffusion-driven (Turing-like) instability. Moreover, we investigate the effects of extracellular signals on the cell polarity oscillations.