Symmetry breaking mechanism for epithelial cell polarization

A non local model for cell migration in response to mechanical stimuli

Cell migration is one of the most studied phenomena in biology since it plays a fundamental role in many physiological and pathological processes such as morphogenesis, wound healing and tumorigenesis. In recent years, researchers have performed experiments showing that cells can migrate in response to mechanical stimuli of the substrate they adhere to. Motion towards regions of the substrate with higher stiffness is called durotaxis, while motion guided by the stress or the deformation of the substrate itself is called tensotaxis. Unlike chemotaxis (i.e. the motion in response to a chemical stimulus), these migratory processes are not yet fully understood from a biological point of view. In this respect, we present a mathematical model of single-cell migration in response to mechanical stimuli, in order to simulate these two processes. Specifically, the cell moves by changing its direction of polarization and its motility according to material properties of the substrate (e.g., stiffness) or in response to proper scalar measures of the substrate strain or stress. The equations of motion of the cell are non-local integro-differential equations, with the addition of a stochastic term to account for random Brownian motion. The mechanical stimulus to be integrated in the equations of motion is defined according to experimental measurements found in literature, in the case of durotaxis. Conversely, in the case of tensotaxis, substrate strain and stress are given by the solution of the mechanical problem, assuming that the extracellular matrix behaves as a hyperelastic Yeoh's solid. In both cases, the proposed model is validated through numerical simulations that qualitatively reproduce different experimental scenarios.

Physics of compartmentalization: How phase separation and signaling shape membrane and organelle identity

Compartmentalization of cellular functions is at the core of the physiology of eukaryotic cells. Recent evidences indicate that a universal organizing process - phase separation - supports the partitioning of biomolecules in distinct phases from a single homogeneous mixture, a landmark event in both the biogenesis and the maintenance of membrane and non-membrane-bound organelles. In the cell, 'passive' (non energy-consuming) mechanisms are flanked by 'active' mechanisms of separation into phases of distinct density and stoichiometry, that allow for increased partitioning flexibility and programmability. A convergence of physical and biological approaches is leading to new insights into the inner functioning of this driver of intracellular order, holding promises for future advances in both biological research and biotechnological applications.

A Polarizing Issue: Diversity in the Mechanisms Underlying Apico-Basolateral Polarization In Vivo

Polarization along an apico-basolateral axis is a hallmark of epithelial cells and is essential for their selective barrier and transporter functions, as well as for their ability to provide mechanical resiliency to organs. Loss of polarity along this axis perturbs development and is associated with a wide number of diseases. We describe three steps involved in polarization: symmetry breaking, polarity establishment, and polarity maintenance. While the proteins involved in these processes are highly conserved among epithelial tissues and species, the execution of these steps varies widely and is context dependent. We review both theoretical principles underlying these steps and recent work demonstrating how apico-basolateral polarity is established in vivo in different tissues, highlighting how developmental and physiological contexts play major roles in the execution of the epithelial polarity program.

Curvature-driven positioning of Turing patterns in phase-separating curved membranes

We introduce a new finite difference scheme to study the dynamics of Turing patterns of a two-species activator-inhibitor system embedded on a phase-separating curved membrane, modelling for instance a lipid bilayer. We show that the underlying binary fluid can strongly affect both the dynamical and the steady state properties of the ensuing Turing patterns. Furthermore, geometry plays a key role, as a large enough local membrane curvature can both arrest the coarsening of the lipid domains and position the patterns selectively at areas of high or small local curvature. The physical phenomena we observe are due to a minimal coupling, between the diffusivity of the Turing components and the local membrane composition. While our study is theoretical in nature, it can provide a framework within which to address intracellular pattern formation in systems of interacting membrane proteins.

Dynamic membrane patterning, signal localization and polarity in living cells

We review the molecular and physical aspects of the dynamic localization of signaling molecules on the plasma membranes of living cells. At the nanoscale, clusters of receptors and signaling proteins play an essential role in the processing of extracellular signals. At the microscale, "soft" and highly dynamic signaling domains control the interaction of individual cells with their environment. At the multicellular scale, individual polarity patterns control the forces that shape multicellular aggregates and tissues.

Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures

The growth of a well-formed epithelial structure is governed by mechanical constraints, cellular apico-basal polarity, and spatially controlled cell division. Here we compared the predictions of a mathematical model of epithelial growth with the morphological analysis of 3D epithelial structures. In both in vitro cyst models and in developing epithelial structures in vivo, epithelial growth could take place close to or far from mechanical equilibrium, and was determined by the hierarchy of time-scales of cell division, cell-cell rearrangements, and lumen dynamics. Equilibrium properties could be inferred by the analysis of cell-cell contact topologies, and the nonequilibrium phenotype was altered by inhibiting ROCK activity. The occurrence of an aberrant multilumen phenotype was linked to fast nonequilibrium growth, even when geometric control of cell division was correctly enforced. We predicted and verified experimentally that slowing down cell division partially rescued a multilumen phenotype induced by altered polarity. These results improve our understanding of the development of epithelial organs and, ultimately, of carcinogenesis.

A bistable model of cell polarity

Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

The shade avoidance syndrome: a non-Markovian stochastic growth model

Plants at high population density compete for light, showing a series of physiological responses known as the shade avoidance syndrome. These responses are controlled by the synthesis of the hormone auxin, which is regulated by two signals, an environmental one and an internal one. Considering that the auxin signal induces plant growth after a time lag, this work shows that plant growth can be modelled in terms of an energy-like function extremization, provided that the Markov property is not applied. The simulated height distributions are bimodal and right skewed, as in real community of plants. In the case of isolated plants, theoretical growth dynamics and speed correctly fit Arabidopsis thaliana experimental data reported in literature. Moreover, the growth dynamics of this model is shown to be consistent with the biomass production function of an independent model. These results suggest that memory effects play a non-negligible role in plant growth processes.