Abstract
Spatial organisation is a hallmark of all living cells, and recreating it in model systems is a necessary step in the creation of synthetic cells. It is therefore of both fundamental and practical interest to better understand the basic mechanisms underlying spatial organisation in cells. In this work, we use a continuum model of membrane and protein dynamics to study the behaviour of curvature-inducing proteins on membranes of spherical shape, such as living cells or lipid vesicles. We show that the interplay between curvature energy, entropic forces, and the geometric constraints on the membrane can result in the formation of patterns of highly-curved/protein-rich and weakly-curved/protein-poor domains on the membrane. The spontaneous formation of such patterns can be triggered either by an increase in the average density of curvature-inducing proteins, or by a relaxation of the geometric constraints on the membrane imposed by the membrane tension or by the tethering of the membrane to a rigid cell wall or cortex. These parameters can also be tuned to select the size and number of the protein-rich domains that arise upon pattern formation. The very general mechanism presented here could be related to protein self-organisation in many biological processes, ranging from (proto)cell division to the formation of membrane rafts.
Highlights
Spatial organisation into inhomogeneous patterns is an essential feature of living organisms, from the macroscale to the cellular level
Estimation and control of model parameters in real systems We have shown above that pattern formation in a spherical membrane containing curvature-inducing proteins is controlled by the four dimensionless parameters W, K, T and P, which represent the number of curvatureinducing proteins on the membrane, the strength of the membrane tethering to the cell wall/cortex, the membrane tension, and the correlation length of protein fluctuations, respectively
Pattern formation arises from the interplay between membrane curvature energy, protein density fluctuations, and geometric constraints such as membrane tension and confinement forces due to the tethering of the membrane to the cell wall/cortex
Summary
Spatial organisation into inhomogeneous patterns is an essential feature of living organisms, from the macroscale to the cellular level. Organisation of the plasma membrane and the cytoplasm into specialised domains is more commonly referred to as cell polarity [1, 2]. As early as in 1952, Turing realised [3] that very simple systems that are initially in a spatially homogeneous state can spontaneously self-organise into spatially inhomogeneous patterns. It is generally believed [1, 2] that the generation of polarity in cells is the result of a tightly-controlled orchestration involving complex signalling networks and active processes such as the reorganisation of the cellular cytoskeleton. The underlying mechanisms in these systems are not well understood
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