Research Article: Membrane Mechanics of Endocytosis in Cells with Turgor

Date Published: October 30, 2015

Publisher: Public Library of Science

Author(s): Serge Dmitrieff, François Nédélec, Helge Ewers

Abstract: Endocytosis is an essential process by which cells internalize a piece of plasma membrane and material from the outside. In cells with turgor, pressure opposes membrane deformations, and increases the amount of force that has to be generated by the endocytic machinery. To determine this force, and calculate the shape of the membrane, we used physical theory to model an elastic surface under pressure. Accurate fits of experimental profiles are obtained assuming that the coated membrane is highly rigid and preferentially curved at the endocytic site. The forces required from the actin machinery peaks at the onset of deformation, indicating that once invagination has been initiated, endocytosis is unlikely to stall before completion. Coat proteins do not lower the initiation force but may affect the process by the curvature they induce. In the presence of isotropic curvature inducers, pulling the tip of the invagination can trigger the formation of a neck at the base of the invagination. Hence direct neck constriction by actin may not be required, while its pulling role is essential. Finally, the theory shows that anisotropic curvature effectors stabilize membrane invaginations, and the loss of crescent-shaped BAR domain proteins such as Rvs167 could therefore trigger membrane scission.

Partial Text: Endocytosis enables cells to internalize extracellular material and to recycle membrane components [1]. During this process, the plasma membrane is deformed into an invagination progressing inwards, which is severed and eventually released in the cytoplasm as a vesicle. Key endocytic components have been identified in several systems. This process usually involves membrane coating proteins (such as clathrin), their adaptors (such as epsins) and actin microfilaments together with associated factors [2]. We focused on the yeast model system, in which endocytosis is well characterized experimentally. The abundance and localization of the principal proteinaceous components have been measured as a function of time both in S. pombe [3, 4] and S. cerevisiae [5, 6]. To understand how these components work together to deform the membrane, it is necessary to consider the physical constraints under which the task is performed in vivo. While in animal cells, invaginations are opposed mostly by membrane tension and elasticity [7], turgor pressure strongly opposes invaginations in plants and fungi. In those cells, the difference of osmolarity with the outside causes a large pressure pushing membrane against the cell wall.

We predict membrane shapes by minimizing a deformation energy, using a Helfrich-type Hamiltonian [24, 34], in which membrane deformations are penalized by a bending rigidity κ and tension σ. We write Π the difference of hydrostatic pressure between the inside and the outside of the cell. In addition, we assume a point force fa pulling the apex of the invagination, to represent the driving force generated by the actin cytoskeleton [6, 13]. We thus implicitly assume that the forces produced by actin polymerization at the base of the invagination, and possibly by myosin motors or other processes, are transmitted to the tip of the invagination over the actin network (see Fig 1). We note κ the rigidity of the membrane together with its coat of proteins [16, 17]. Moreover, we consider that the coat proteins curve the membrane either by scaffolding or inserting themselves in the membrane. We first describe proteins such as clathrin, that induce an isotropic curvature C0, with the same radius of curvature in both directions.

Using a general model for membrane mechanics, we could accurately fit experimental profiles shorter than 80nm, even though we assumed the membrane to be homogeneous, i.e. with constant rigidity and spontaneous curvature over the surface of the deformed membrane. In combination with membrane rigidity, we can expect pressure to be the dominant factor opposing membrane invagination during yeast endocytosis, while membrane tension should be negligible. This statement is derived from the dimension of the invagination, and from the scale of pressure determined experimentally, and is thus independent of the details of the model. We estimated the force required to pull the invagination based on the value of turgor pressure, and on the value of the rigidity that was determined by fitting the experimental curves. While the exact value of the force also depends on other parameters and in particular on the height of the invagination (see Fig 3), its scale is primarily determined by pressure and the width of the invagination. For the measured range of pressure Π ∼ 0.2—1 MPa, the force scale is fΠ ∼ 1000—5000 pN. This is significantly larger than previously estimated (1—1000 pN [13, 48, 49]). The corresponding range of value for the rigidity is κ ∼ 400—2000 kBT. This is much stiffer than a pure lipid bilayer, because the membrane is heavily coated at the endocytic site. It was suggested that phase boundaries could play a role by generating a line tension, favorable to membrane budding. However the typical line tension (of the order of ∼ 0.4 pN [50]) is much smaller than fΠ, and such phenomenon can therefore be discarded.