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. 2015 Feb 3;108(3):508-19.
doi: 10.1016/j.bpj.2014.11.3481.

On the modeling of endocytosis in yeast

Tao Zhang  1 , Rastko Sknepnek  2 , M J Bowick  1 , J M Schwarz  3
Affiliations

On the modeling of endocytosis in yeast

Tao Zhang et al. Biophys J. .

Abstract

The cell membrane deforms during endocytosis to surround extracellular material and draw it into the cell. Results of experiments on endocytosis in yeast show general agreement that 1) actin polymerizes into a network of filaments exerting active forces on the membrane to deform it, and 2) the large-scale membrane deformation is tubular in shape. In contrast, there are three competing proposals for precisely how the actin filament network organizes itself to drive the deformation. We use variational approaches and numerical simulations to address this competition by analyzing a meso-scale model of actin-mediated endocytosis in yeast. The meso-scale model breaks up the invagination process into three stages: 1) initiation, where clathrin interacts with the membrane via adaptor proteins; 2) elongation, where the membrane is then further deformed by polymerizing actin filaments; and 3) pinch-off. Our results suggest that the pinch-off mechanism may be assisted by a pearling-like instability. We rule out two of the three competing proposals for the organization of the actin filament network during the elongation stage. These two proposals could be important in the pinch-off stage, however, where additional actin polymerization helps break off the vesicle. Implications and comparisons with earlier modeling of endocytosis in yeast are discussed.

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Figures

Figure 1
Figure 1
An electron micrograph image of a deformed membrane during endocytosis in S. cerevisiae. The image is reprinted with permission from Kukulski et al. (2). Scale bar, 100 nm.
Figure 2
Figure 2
Schematic for endocytosis in yeast using Proposal 1 for the actin filament organization. (a) Clathrin (purple) attaches to the membrane (black/blue) via proteins Sla1 and Ent1/2 (not depicted here) and the protein Sla2 (green/brown) is recruited near the clathrin. (b) Actin (red) attaches to the membrane near the edge of the clathrin bowl via Sla2 and lengthens due to polymerization to initiate tube formation. (c) Actin continues to polymerize and lengthen the tube. (d) BAR proteins (orange) become prominent and surround part of the tube (and the actin). Gray arrows denote the direction of the actin force on the membrane. Note that potential additional actin filaments rooted in the surrounding cytoskeleton and extending toward the invagination site have not been drawn.
Figure 3
Figure 3
(a) Schematic depicting Proposal 2, where the actin filaments are tethered to the rest of the cytoskeleton, as denoted by the two black Xs, and polymerize inward toward the invagination site. (b) Schematic representing Proposal 3, where there are two local anchoring regions such that two actin networks form to drive tube formation. Gray arrows denote the direction of the actin force on the membrane.
Figure 4
Figure 4
(a) Cell membrane profile, or z(x,y = 0), for the parameters stated in the text. The red area denotes the clathrin-bound part of the membrane, and the blue denotes the bare membrane. (b) Top view of the two-component membrane model using simulated annealing Monte Carlo methods. (c) Side view of the same configuration. Both images have been rescaled accordingly for presentation purposes. (d) Comparison of the maximum depth (or depth) obtained from the numerical simulation (symbols) with the analytical solution (line) for the intiation stage. All the parameters, except for the varying C01, are the same as the κG = 0 curve in a. To see this figure in color, go online.
Figure 5
Figure 5
(a) Simulation results for Model 1 with total applied force Ft = 10 pN. The total force is applied to only the yellow part of the membrane (at the vertices). Red denotes the Sla1/Ent1/2 bound part of the membrane and blue denotes the bare membrane. (b) Same as (a), but with applied force Ft = 50 pN; (c) Comparison of the depth as a function of Ft for three different models with zero and nonzero turgor pressure, p. Again, the error bar is of the order of the symbol size. The arrow pointing downward denotes the value of Feq for reference. To see this figure in color, go online.
Figure 6
Figure 6
(a–c) The pearling instability for a cylindrical membrane with increasing surface tension going from left to right, or σRo2/κ=0.267,2.67, and 4.15 respectively. The top and red parts of the tube are fixed.
See this image and copyright information in PMC

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