Force required for endocytic vesicle formation analyzed by FRET-based force sensors

Mechanical forces exerted by multiprotein machines are essential for many cellular processes. One of the best-studied examples is membrane reshaping during clathrin- mediated endocytosis, a principal vesicle trafficking route responsible for molecular uptake, signaling, and membrane homeostasis. During endocytosis, a small area of the plasma membrane reshapes from a flat sheet to a closed vesicle. This reshaping requires mechanical force, which is provided by multiple endocytic proteins and actin polymerization. Several theoretical models have been proposed to describe force requirements of endocytosis (Lacy et al., 2018). However, to understand force-dependent endocytic vesicle formation, applied forces need to be analyzed in vivo to report real force values and key involved factors. To achieve that, we used FRET (Förster Resonance Energy Transfer) tension sensors (Freikamp et al., 2016), which allow the measurement of forces in the range of piconewtons (pN) in vivo, and inserted them into the yeast protein Sla2. Sla2 is part of the essential Sla2-Ent1 (Hip1R-epsin 1-3 in human) protein linker transmitting force of the polymerizing actin cytoskeleton to the plasma membrane during endocytosis (Skruzny et al., 2012, 2015). We followed forces transmitted over Sla2 in real time during individual endocytic events and measured force of approx. 10 pN per Sla2 molecule, hence 450-1330 pN per endocytic event. Next, we analyzed the role of the actin cytoskeleton and followed force transmission in cells absent of the negative regulator of actin polymerization Bbc1. Despite the enlarged endocytic actin cytoskeleton, less force was transmitted over the force sensor prior to vesicle scission. We propose that an excess of dense actin meshwork in bbc1Δ cells directly physically remodel the long invaginating membrane. Finally, force transmission was followed in cells missing BAR-domain protein Rvs167 during unsuccessful endocytic events characterized by initial membrane bending followed by retraction back to the flat membrane profile. Only force similar to force of early membrane bending in wild-type cells was observed. This suggests that stabilization of the deeply invaginated membrane provided by BAR-domain proteins is essential to facilitate productive force transmission around the time of vesicle scission. In addition, we analyzed the role of physical conditions in force-dependent steps of endocytosis. First, we counteracted the high turgor pressure of the yeast cytoplasm by exposing cells to hypertonic conditions. We observed an overall decrease in the force required for membrane invagination. Similarly, we reduced plasma membrane tension by incorporation of soluble lipid into the membrane and again detected less force transmitted over the Sla2 force sensor. We also analyzed the capacity of the endocytic force-generating machinery in hypotonic conditions, which should increase cell turgor opposing endocytosis. We exposed cells to increasing osmotic shifts and observed an increase in number of arrested endocytic sites. When we followed force transmission of remaining completed endocytic events, we detected force similar to untreated cells. The observed endocytic block and unchanged force transmission suggest that the actin cytoskeleton can provide only limiting force for endocytosis. We believe that our data will form a base of biomechanical model of endocytic vesicle formation, essential to understand how the endocytic machinery works in physiological and pathological conditions. Moreover, our data could be highly valuable for the understanding of other force-dependent membrane remodeling processes in the cell

A master equation approach to actin polymerization applied to endocytosis in yeast

<div><p>We present a Master Equation approach to calculating polymerization dynamics and force generation by branched actin networks at membranes. The method treats the time evolution of the F-actin distribution in three dimensions, with branching included as a directional spreading term. It is validated by comparison with stochastic simulations of force generation by actin polymerization at obstacles coated with actin “nucleation promoting factors” (NPFs). The method is then used to treat the dynamics of actin polymerization and force generation during endocytosis in yeast, using a model in which NPFs form a ring around the endocytic site, centered by a spot of molecules attaching the actin network strongly to the membrane. We find that a spontaneous actin filament nucleation mechanism is required for adequate forces to drive the process, that partial inhibition of branching and polymerization lead to different characteristic responses, and that a limited range of polymerization-rate values provide effective invagination and obtain correct predictions for the effects of mutations in the active regions of the NPFs.</p></div