Simulations of Yeast Endocytosis

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In a paper published recently, we showed that actin nucleator are patterned on the membrane before and during the endocytic event. In particular, actin nucleators form a ring on the membrane around its attachment to the actin cytoskeleton. For this work, the team of Jonas Ries and collaborators imaged over 100000 endocytic sites using super-resolution microscopy.

Using computer simulations, I was able to show that this patterning allows an optimal force generation on the membrane, allowing actin polymerization to generate a force over 1000pN. This work was done using Cytosim, an open-source Cytoskeleton simulator integrating the overdamped Langevin equation.

This simulations sums up some of my interests developed as a Postdoc in François Nédélec’s lab.

I first got interested in endocytosis by interacting with the labs of John Briggs and Marko Kaksonen in EMBL, and in particular with Wanda Kukulski and Andrea Picco. I was really curious to understand what gives the endocytic invaginations their shapes. For this I used a minimal model that minimized the deformation energy. This simple model fitted surprisingly well small membrane invaginations (i.e. until Rvs167, a protein localized at the neck, got involved).

Fig. 1 : Modeling membrane mechanics in yeast endocytosis

As a theoretician joining a biology lab, I was glad to achieve a theory that matched experimental data, but also produced unexpected theoretical results, that could have biological relevance. In particular, we found that membranes under pressure tend to be highly unstable, while neck-localized proteins (such as Rvs167) stabilize the membrane. An interesting prediction that is their removal is sufficient to break the membrane and create a vesicle.

One important result of our work is that a large pulling force, most likely applied by actin, is required to overcome the pressure pushing on the membrane, in order to create an invagination. Order of magnitudes estimates yield around 1000pN of force, while more precise computations based on membrane mechanics predict even larger forces at the peak.

We then wondered how such large forces can be generated by actin, while we expect polymerization and motor forces of a few pN. We realized that the polymerization forces depend on the orientation of the filament with respect to the mechanical constraints. Thus, maximal polymerization forces can be obtained if the filaments are growing nearly orthogonal to the force.

Fig. 2 : Polymerization forces are maximized when filaments are growing orthogonal to the contraint.

At that time, a work by the labs of Marko Kaksonen and Jonas Ries, led by Andrea Picco and Markus Mund, showed that actin was polymerizing close to the membrane, and that some actin-associated molecules formed a ring on the membrane, even before the invagination started. This led them to believe that actin machinery could be highly organized at the membrane, even before the actual endocytic event. For me, it was a crucial finding that could confirm our mechanical theory on how actin can generate enough force to pull on the membrane.

We thus started working with the lab of Jonas Ries that then observed the ring arrangement of many endocytic proteins, in particular actin nucleators. We decided to use this information in a numerical simulation, in addition to our understanding of the membrane and filament mechanics.
The simulation had few constraints : the nucleators form a ring, and the tip of the membrane is bound to actin filaments. As predicted, simulations showed that actin filaments spontaneously orient nearly perpendicularly to the direction of endocytosis, i.e. perpendicularly to the mechanical constraint. While individual filaments could not be directly observed experimentally, the localization of +ends and -ends (observed through the localization of cap proteins and arp2/3 respectively) is in agreement with our theoretical model.

Moreover, we were able to show that a symmetrical ring around the invagination is optimal, maximizing the success rate of simulated endocytosis. This lead us to a unique picture of actin-mediated endocytosis in yeast.

Fig. 3 A new picture of actin-mediated endocytosis in yeast

The article :
Systematic Nanoscale Analysis of Endocytosis Links Efficient Vesicle Formation to Patterned Actin Nucleation
Markus Mund, Johannes Albertus van der Beek, Joran Deschamps, Serge Dmitrieff, Philipp Hoess, Jooske Louise Monster, Andrea Picco, FrançoisNédélec, Marko Kaksonenn, Jonas Ries.

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