Universal features of cell polarization processes

Abstract

Cell polarization plays a central role in the development of complex organisms. It has been recently shown that cell polarization may follow from the proximity to a phase separation instability in a bistable network of chemical reactions. An example which has been thoroughly studied is the formation of signaling domains during eukaryotic chemotaxis. In this case, the process of domain growth may be described by the use of a constrained time-dependent Landau-Ginzburg equation, admitting scale-invariant solutionsà la Lifshitz and Slyozov. The constraint results here from a mechanism of fast cycling of molecules between a cytosolic, inactive state and a membrane-bound, active state, which dynamically tunes the chemical potential for membrane binding to a value corresponding to the coexistence of different phases on the cell membrane. We provide here a universal description of this process both in the presence and absence of a gradient in the external activation field. Universal power laws are derived for the time needed for the cell to polarize in a chemotactic gradient, and for the value of the smallest detectable gradient. We also describe a concrete realization of our scheme based on the analysis of available biochemical and biophysical data.

A Bistable Model of Cell Polarity

“…Thus, large patches grow at the expense of smaller patches until a single patch survives. This kind of competitive growth of patches has been known for a long time in the physics of materials as Lifshitz-Slyozov coarsening [2], [3], [20], [21]. The corresponding dynamics may be understood via a simple physical analogy with the nonequilibrium process taking place during the formation of precipitate from a supersaturated solution (see Fig.…”

Continuum model of cell motility and chemotaxis

“…the chemotactic velocity v ch being assumed to be collinear to ∇γ A (see (5) of [32]). Since, if ρ is a constant, we can write the conservation of mass in the form…”

“…Essentially, this phenomenon depends on two properties of cells. First, cell membrane is capable of sensing spatial gradients of attractant or repellent chemicals in the external environment, providing in particular a direction for migration, for example, towards nutrients [3][4][5]. Moreover, cells behave as self-propelled or active particles, which means that they can transform their internal energy into energy of motion.…”

“…[2,5,3] are modelled by a rigid body structure assigned to each particle. As a consequence, the rotational motion of particles is explicitly considered, thus providing a more realistic model for the description of cells.…”

Symmetry breaking mechanism for epithelial cell polarization

“…Fast diffusion of PI3K and PTEN enzymes in the cy-tosol, and the conservation law [PIP2] + [PIP3] = c allow to effectively describe the state of the cell membrane in terms of the configuration of the single-component concentration field [19,25]:…”