Pattern formation by curvature-inducing proteins on spherical membranes

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/proteinpoor 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. protein patterns on the surface of other types of cells, as well as in model systems consisting of lipid vesicles and proteins. In this work, we will explore in full generality and detail the predictions of such a model.The basic idea behind the model is presented in figure 1. A closed, initially spherical membrane contains proteins that impose a spontaneous curvature C p on the membrane (in general, the proteins might be attached to the membrane from the cytoplasmic or the exoplasmic sides, or they might be transmembrane proteins embedded in the membrane) [13,14]. If the proteins did not induce any curvature, a random, homogeneous distribution of proteins would be favoured by thermal fluctuations, that is, entropic forces (in the absence of direct attractive protein-protein interactions). However, if the curvature induced by the proteins is large enough, bending contributions to the free energy of the system can lead to an effective attraction between proteins and to the formation of spatially inhomogeneous patterns in protein distribution and membrane curvature. The details of membrane-mediated protein-protein interactions have been thoroughly studied in the past [15][16][17][18]. Furthermore, we will consider the possibility of geometric constraints on the membrane, such as the tethering of the membrane to a rigid cell wall/cortex or the existence of a membrane area reservoir at nonzero tension. Interestingly, it was recently shown that solid particles such as proteins can sense the local membrane curvature imposed by geometric constraints on the membrane [19].Here, we have found that, in realistic situations, spontaneous pattern formation can be induced either by an increase in the surfac...

A Rationale for Mesoscopic Domain Formation in Biomembranes

“…The second maximum of the structure factor then obeys qc2≥κC12/(2b). This confinement can also be seen as a model for the cell wall pinning by proteins and/or tethering to the actin cortex [87,88] (the membrane tension was restored in [88], and the analytical treatment was performed in spherical geometry there).…”

Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

“…In this equation, k T B is the thermal energy, a p is the area on the membrane of a single protein so that f/a p is the number density, the term involving f m (a saturation area fraction) accounts for the entropy of uncovered spaces, χ determines the strength and sign (attractive or repulsive) of protein-protein interactions, and μ 0 is a reference chemical potential. Variants of this model have been used to understand the linear stability of fully mixed states [42,43] or to examine protein sorting by curvature at fixed shape [18,44,47].…”

“…These models suggest that, rather than two different mechanisms, curvature sensing and generation are two manifestations of the same mechanochemical coupling. They have provided a background to understand the emergence of heterogeneous proteinrich curved domains using linear stability analysis [42,43], or curvature sorting of proteins in equilibrium and at fixed shape between tubes and vesicles [18,[44][45][46] or on wavy surfaces [47]. Also in equilibrium, proteinmembrane interactions allowing for shape changes were studied in [48].With a few exceptions under rather restrictive conditions [49,50], previous theories of the interaction between curved proteins and membranes have focused on equilibrium.…”

“…into(43) and choosing the test function ψ=B I , we obtain N discrete equations for f J , I=1, K N as…”

A rationale for mesoscopic domain formation in biomembranes

“…The second maximum of the structure factor then obeys q 2 c ≥ κC 2 1 /(2b). This confinement can also be seen as a model for the cell wall pinning by proteins and/or tethering to the actin cortex [87,88] (the membrane tension was restored in [88], and the analytical treatment was performed in spherical geometry there).…”