Roles of Membrane Mechanics-mediated Feedback in Membrane Traffic

Abstract

Synthesizing the recent progresses, we present our perspectives on how local modulations of membrane curvature, tension, and bending energy define the feedback controls over membrane traffic processes. We speculate the potential mechanisms of, and the control logic behind, the different membrane mechanics-mediated feedback in endocytosis and exo-endocytosis coupling. We elaborate the path forward with the open questions for theoretical considerations and the grand challenges for experimental validations.

Introduction

A remarkable feature of membrane traffic processes is that while each event hinges on complicated interactions between hundreds of different types of molecules, these molecular players all follow a robust order in time and space (e.g., in endocytosis [1]). A fundamental and unsolved question is: Given the everlasting noises inside cell, what underlies the robust spatial-temporal pattern for these many proteins and lipids? While specific protein-protein and protein-lipid interactions are certainly integral part of the picture, the real question is: Are these specific molecular interactions sufficient to ensure the robust spatial-temporal regulation?

To better appreciate the gravity of this question, let us have a real-life analogy: In a telephone game, the message progressively deviates from the original one as it passes through the participants. Obviously, feedback control is necessary to ensure the fidelity of information transmission, which is the focal point of systems biology. However, a membrane traffic event is a small system: For each endocytic or exocytic site, it only involves a limited number of molecules (typically 10’s to low 100’s) for each key component [2–4], and therefore is subjected to the intrinsic small-number fluctuations [5], which could ripple through the feedback scheme and amplify the uncertainty in the outcome. Consequently, a pure biochemical feedback control may not be reliable to ensure the fidelity. In fact, how to achieve a reliable outcome of a feedback scheme in a small system is a central question that any cellular process must address.

Membrane traffic utilizes the membrane-bound biochemical reactions to drive drastic membrane shape changes and hence is inherently mechanochemical in nature. An overarching question is: Do the regulatory mechanisms of membrane traffic only direct from biochemical reactions to the membrane mechanics, or the membrane mechanics also feedback to the biochemical reactions?

It was proposed that membrane mechanics and the membrane-bound biochemical reaction form a mechanochemical feedback to ensure the robustness of endocytosis [6]. Hereby, membrane curvature may serve as a stable spatial cue that quenches the intrinsic small-number-fluctuations in endocytosis [6–8]. While this notion gains more and more support from emerging data, it precipitates the mechanistic questions in two directions. First, which element of membrane mechanics directly feedback to the biochemistry in endocytosis? Is it the membrane curvature, membrane tension, or both? Note that we define the membrane tension as the sum of two primary sources: the intrinsic membrane tension of the lipid bilayer and the cortical tension arising from cytoskeleton–membrane adhesion [9]. Second, endocytosis is reported to spatial-temporally couples to exocytosis [10]. The questions are: What determines the defined spatial-temporal pattern of exo-endocytosis coupling? And how does the mechanochemical feedback of endocytosis contribute to the coupling? In this essay, we elaborate our perspectives in the context of the two questions.

Curvature-mediated mechanochemical feedback

The physical basis of curvature-mediated feedback of endocytosis lies in the curvature sensitivities evidenced in many of the key endocytic proteins [11,12]. In the simplest picture (Figure 1a), these membrane proteins have their preferred shape and hence membrane curvature. When such a protein binds to the membrane, it “feels” happier (with higher on rate, or lower off rate, or both), if the underlying membrane shape fits to its preferred shape. This is a curvature-sensing effect; likewise, membrane curvature provides the spatial cue so that different endocytic proteins will preferentially localize to the different locations along the membrane invagination at an endocytic site. Conversely, the more these proteins bind to the membrane, the more will they sculpt the local membrane in accordance with their preferred shape (aka a curvature-sculpting effect). As such, curvature sensing and sculpting form positive feedback. The theoretical model based on this curvature-mediated feedback can quantitatively explain the sequential recruitments of key endocytic proteins in coupling with the drastic membrane shape changes, leading to a robust vesicle scission event both in yeast and mammalian cell endocytosis [6]. It was therefore posited that the curvature-mediated feedback mechanism defines a coherent theme of endocytosis, and different types of endocytosis (e.g., clathrin-(in)dependent, dynamin-(in)dependent or not) utilize the distinct sets of proteins with differential curvature sensitivities under this framework [13].

Figure 1.

Curvature-mediated feedback as a central theme of membrane traffic processes. a) Positive feedback loop between curvature sensing and curvature sculpting effects of membrane proteins. b) Curvature-sensitive proteins may control the local membrane mechanics (e.g., membrane tension and/or bending modulus). Curvature-sensitive proteins may directly influence the local membrane tension via affecting the hydrophobicity of membrane-water interface via lipid-binding, or indirectly do so by modulating actin cytoskeletons.

Since the model was published in 2009, the results of experimental testing are consistent with the predictions so far. Particularly, experimentalists can create the curvature patterns on a substrate: When the cell adheres onto such a substrate, the shape of the cell membrane will adopt to the local curvature. It was reported that the endocytosis preferentially initiates at the location of a higher curvature, providing a strong support for the notion of curvature-sensing effects in endocytosis [14,15].

What about curvature-sculpting effects, the other half of the proposed feedback in endocytosis? While there is a plethora of in vitro GUV data demonstrating the strong curvature-sculpting activities of purified BAR or F-BAR domain proteins [16–19], the unequivocal in vivo evidence is still at large due to several reasons. For instance, the curvature-sculpting effect by a protein is subject to the membrane mechanics itself. Intuitively, the stiffer the membrane is, the harder for the curvature-sensitive proteins to deform it. Therefore, blocking the curvature-sculpting by increasing the membrane tension will inhibit the curvature-mediated positive feedback and, ultimately, diminish the curvature-sensing effect [20,21]. Conversely, the more scarce or more structurally flexible the curvature-sensitive proteins are, the less likely will they impose their preferred curvature onto the underlying membrane. Consequently, the manifestation of curvature-sculpting activities hinges on the balance between the curvature-deforming power of the proteins and the deformability of the membrane. From this viewpoint, it may provide an explanation for the involvement of actin cytoskeleton and motors in endocytosis [22,23]: When the cell membrane is harder to deform by the curvature-sensitive proteins themselves, the cytoskeletons may join the forces to deform the membrane; in doing so, however, it may mask the curvature-sculpting activities of BAR-domain proteins in vivo. One may soften the cell membrane by surfactants or osmotic treatments to delineate the curvature-sculpting effects. But these experiments are global perturbations and may introduce adverse effects. A sensible way to test the curvature-sculpting effect in endocytosis is to locally soften/stiffen the cell membrane and compare the extension and the rate of the resulting membrane invagination at the endocytic site with the wildtype. This proposal calls for the novel experimental approaches for local perturbations of cell membrane mechanics in vivo. Taken together, while the curvature-mediated feedback provides a potential overarching framework of endocytosis, the jury is still out.

Roles of membrane tension

Membrane tension is known to regulate endocytosis [24–29]; however, its mechanistic roles are not well-understood. Is membrane tension simply a global constant controlling the deformability of cell membrane, as in the proposed curvature-mediated feedback model? Or is it locally modulated at the endocytic site over time? The in vitro data indicate that the membrane-binding of some BAR-domain proteins may impact the effective membrane tension [30,31]. Hence, it is physically possible that during endocytosis the curvature-sensitive proteins decreases the local membrane tension, which may facilitate the membrane shape deformation that further promotes the recruitment of curvature-sensitive proteins (Figure 1b, the 1^st mechanism). This may provide a more elaborate scheme of endocytosis, in which membrane tension is locally modulated to potentiate the curvature-mediated positive feedback. If so, then, the membrane tension is expected to decrease locally at the endocytic site and the associated spatial heterogeneity is expected to persist at endocytic timescale (typically ~ 10’s seconds). Can this idea be tested experimentally in vivo?

In a recent experiment, Zhi and his colleagues developed a novel dual-trap optical tweezer assay to monitor how the local perturbation of membrane tension propagates along the cell membrane in a living cell [32]. They perturbed the membrane tension by pulling a membrane tether from the cell and recorded the local membrane tension by a second tether at a desired distance from the first one on the same cell. On the cell membrane bleb that is detached from actin cortex, rapid equilibration of membrane tension is observed. In contrast, on the cell membrane that attaches to actin cortex, the propagation of membrane tension is very slow. Therefore, membrane tension could remain spatially heterogeneous on the cell membrane in vivo.

Physically, the intrinsic membrane tension of a lipid bilayer arises from the thermodynamic driving forces that minimize the unfavorable contacts between the hydrophobic cores of the lipids and the aqueous solution [33]. Hence, the membrane region with a higher tension presents more unfavorable exposures of the lipids to water, which “attract” more lipids toward it to minimize the free energy. This leads to the in-plane lipid flow (aka Marangoni flow) that rapidly homologizes the intrinsic membrane tension, according to the experiment [32] (Figure 2). The intrinsic membrane tension also intimately links to the membrane shape: Bending a lipid bilayer splays the lipid molecules, exposes more of their hydrophobic cores to the water, resulting in a higher membrane tension. This was nicely captured by the elastic theory by Lipowsky [34]. The key question is: How long will this gradient of membrane tension persist? Many follow-up theory papers modeled the dynamics of curvature-mediated membrane tension gradient. Their main conclusion is that the resulting spatial gradient of membrane tension by curvature-sensitive proteins will persist even after 10 seconds on a 1-micron membrane patch (e.g., [35]). In a stark contrast, however, the recent experiments demonstrated that the membrane tension equilibrates rapidly (less than 1 second for > 10-micron distance) on a GUV, or a cell membrane bleb delaminated from actin cortex [32]. The rapid relaxation is due to the in-plane lipid flow that brings more lipids from the low-tension region to the high-tension region; and the resulting redistribution in the lipid density equilibrates the membrane tension (Figure 2). Critically, in these experiments one used a micropipette to pull out a membrane tubule to modulate the local membrane tension, which is equivalent to sculpting a membrane curvature by curvature-sensitive proteins as modeled in the above theoretical models.

Figure 2.

Lipid flow equilibrates imposed membrane tension gradient. A) When a higher tension is externally imposed on the right, it introduces the increasing membrane tension gradient toward the right. This induces the lipid flow to the right. Hereby, the membrane tension is the sum of the intrinsic membrane tension of the lipid bilayer and the externally imposed tension. B) As more lipids move from left to the right, the inter-spacing between the lipids increases on the left while decreasing on the right. The increased inter-spacing exposes more hydrophobic core of the lipids and hence the intrinsic membrane tension on the left increases. Conversely, the decreased inter-spacing further minimizes the hydrophobic exposure of the lipids and therefore, the intrinsic membrane tension on the right decreases. Because the imposed higher tension persists on the right, its overall tension is still higher than the left. Consequently, the lipid flow continues until the intrinsic membrane tension on the left equals the sum of the intrinsic and the imposed tensions on the right. At this point, the system reaches the equilibrium. We note that the above schematics reflects a simplified picture of lipid flow, which may display more complex spatial-temporal flow pattern depending on the dimensionality of the system and experimental conditions.

Why is there such a fundamental discrepancy between theory and experiment, even though the above theoretical models did describe the in-plane lipid flow driven by the membrane tension gradient? The issue seems to stem from some unphysical assumptions in the models. For example, these models assume a uniform lipid density in the membrane and, likewise, impose a fixed value of membrane tension at the boundary of the simulated membrane patch [35]. These models thus neglect the redistribution of lipid density by in-plane lipid flow and the associated membrane tension equilibration [35]. These unphysical assumptions will cause the persistence of membrane tension gradient, which is therefore inconsistent with the experiments [32].

Taken together, if the membrane tension gradient emerges from a highly curved membrane shape, it should equilibrate at biologically relevant timescales, due to the rapid equilibration from the in-plane lipid flows.

On a cell membrane, however, the membrane tension has a more complicated picture, because it is additionally controlled by the mechanics of the actin cortex underneath the membrane [9,36,37]. These cytoskeleton-membrane attachments compartmentalize the membrane tension by hindering the in-plane lipid flow. Conceivably, the propagation speed and, hence, the spatial distribution of membrane tension critically hinge on the lifetime and abundance of these cytoskeleton-membrane attachments as well as the contractile mechanics of the actin cortex itself. This may explain the diverse behaviors of membrane tension propagation observed in the different regions of the same cell [32], with different cell types [38], and by different methods of force perturbations [39]. Of course, more rigorous theoretical modeling – that goes beyond the above intuitive arguments (e.g., [40]) – are needed to quantitatively account for these disparate experimental observations on a coherent basis.

Looping back to endocytosis, the actin cortex remodels extensively at the endocytic sites [22,23]. Putting the above observations into perspectives, the question is: Is it possible that the cell remodels the actin cortex to actively control the local membrane tension and modulate its transmission across the entire cell membrane, in addition to generating mechanical forces (if any)? There are at least two possibilities. First, some of BAR-domain proteins themselves can impact the membrane tension, perhaps by modulating the hydrophobicity of the membrane-water interface via lipid-binding. For instance, recent in vitro experiments indicated that accumulation of some F-BAR domain proteins on a membrane tubule may slow down the equilibration of the tension gradient [30]. While the curvature-mediated membrane tension gradient does not persist at a biologically relevant timescale as elaborate above, specific protein-lipid interactions may hold the lipids and hence counteract the redistribution of lipid density driven by the tension gradient. Notably, these effects are different from the membrane curvature, although they both stem from the same curvature-sensitive protein. In this sense, a recent theory work on some flavors of this idea explicitly [40]. Second, many of the BAR-domain proteins can directly interact with F-actin [41]. As such, the cell may utilize the curvature-sensitivities of endocytic proteins to weaken the actin cortex and hence lower the associated membrane tension at an endocytic site (Figure 1b, the 1^st mechanism). Given the limited number of molecules involved per endocytic site in vivo [2–4], the curvature-sculpting power of endocytic proteins may not be as strong as those evidenced in vitro, where the proteins are always abundant. The local softening of the cell membrane will therefore facilitate the curvature-sculpting activities of the endocytic proteins, potentiate the curvature-mediated positive feedback, and provide an extra regulatory layer for a robust endocytosis.

This new proposal, if holds up, may have broad implications in the molecular logic behind the BAR-domain proteins-actin cytoskeleton interplays in many cellular processes [41]. Likewise, the local membrane tension may be modulated distinctly to fulfill different functions from endocytosis. For instance, in the membrane shape-mediated actin and F-BAR waves [42], the F-BAR/N-WASP axis not only underlies the curvature-mediated feedback but promotes F-actin polymerization. Rather than directly generating forces to deform the membrane, the actin polymerization is proposed to increase the local membrane tension by thickening the cortex, which regulates the curvature-mediated positive feedback (Figure 1b, the 2^nd mechanism). Consistently, a recent cryo-EM study demonstrated that the F-actin polymerization in the actin wave of a Dictyostelium cell backfills the cell protrusion, instead of driving it [43]. Therefore, such a local control of membrane tension may provide a general mechanism for membrane-bound cellular processes and call for novel methods of experimental testing.

In this regard, the recent progress in the experimental approaches (e.g., [32,38,40,44]) provides a great starting point to resolve the spatial-temporal patterns of membrane tension at a subcellular level and address these exciting possibilities. Depending on the outcomes of these experimental findings, we may need to revisit the curvature-mediated feedback model of endocytosis by incorporating more elaborate roles of membrane tension and actin cortex.

Membrane mechanics-mediated feedback in exo-endocytosis coupling

Endocytosis couples with exocytosis to maintain the constant area of cell membrane. While membrane mechanics was proposed to mediate such a coupling at a whole cell-level [45], the exact physical mechanisms are unknown. Particularly, it is not understood why endocytosis and exocytosis events are next to each other with defined spatial-temporal patterns [10,46–48].

Membrane tension was proposed to act as a mediator for the two membrane traffic events [45]. That is, addition of the extra membrane from an exocytosis event causes the relaxation of the local membrane tension, which propagates and triggers an endocytosis event at some distance away. If so, then the membrane tension should propagate at a proper speed: If the propagation is too fast, then the membrane tension will become uniform, even before the endocytic machinery can respond. If it is too slow, then the membrane tension modulation cannot be efficiently transmitted to other locations on a cell membrane and, hence, the endocytosis event may not spatially couple to the exocytosis event. Given the disparate speeds of membrane tension propagation observed in different experiments [32,38,39], how endocytosis couples with exocytosis and the role of membrane mechanics in this coupling remain open questions.

Exploiting membrane traffic of synaptic vesicles (SVs) in neurons as a model system, the recent study, synergizing theory and experiment, sheds some new lights on the roles of membrane mechanics in the exo-endocytosis coupling [49]. In neurons, tight coupling between SV exocytosis and endocytosis is essential for maintaining synaptic transmission [50–54], and is uniquely ultrafast with the ordered spatial pattern [47,48]. That is, SVs fuse onto the plasma membrane of presynaptic terminal (termed “active zone”, AZ); the SV exocytosis triggers the ultrafast endocytosis, which is at ~ 100 nm away from the SV fusion sites and completes within ~ 100 milli-seconds; this endocytosis clears out the SV release sites timely on AZ for the next round of exocytosis [55]. Interestingly, the ultrafast endocytosis depends on the same endocytic machinery for conventional endocytosis, including F-actin, BAR-domain proteins, and dynamin etc [47,56].

According to the curvature-mediated feedback model of endocytosis [6], the timescale of endocytosis depends on two factors: the recruitment rate of endocytic proteins onto the membrane and the dynamical pace of membrane shape changes. Given the typical intracellular concentrations of endocytic proteins and membrane mechanics, the endocytic timescale is predicted to be ~ 10’s seconds, which are consistent with the experimental measurements across different cell lines [13]. Therefore, the mystery here is: How does same machinery drive the endocytosis 100–1000 times faster in neurons than in other cell types?

One way to speed up endocytosis is to increase the local concentrations of endocytosis proteins. Indeed, dynamin is reported to constitutively forms high-density droplets at the edge of AZ that poise ready for rapid execution of endocytosis [57]. Additionally, other endocytosis proteins such as endophilin also compartmentalizes with a high concentration at presynaptic terminals that are facilitated by the SV vesicle clusters [58–60]. Although these observations may account for the rapid vesicle fission, it does not explain how the location and timing of the ultrafast endocytosis couple to the SV exocytosis. Crucially, while dispersing the dynamin droplet slowed down the SV endocytosis by 100 times, the endocytic membrane pits still emerged within 100 milli-seconds after the SV fusions and ~ 100 nm away from the fusion sites [57], just like the WT. This suggests that upon SV fusion the endocytic membrane pits emerge first, which then invoke the curvature-mediated feedback with the endocytic proteins, leading to vesicle scission. Therefore, the real question is: How does the SV exocytosis drive the ultrafast formation of endocytic pits without the endocytic machinery?

Can SV exocytosis perturb the membrane tension that triggers the ultrafast endocytosis? According to the membrane tether measurement at the presynaptic terminal of small central hippocampal neurons, the membrane tension propagates at the speed of ~ 20 micron/s [38], which will traverse the 100 nm distance in ~ 5 milli-seconds. Hence, the membrane tension gradient (if exists) will disappear long before the endocytic pits emerge. If membrane tension gradient triggers the ultrafast endocytosis, then there must exist some factor(s) that meets the following requirements: 1) It is activated by the membrane tension; 2) it must maintain the activated state even after the tension trigger stops, which is ~ 5 milli-seconds after the SV fusions; 3) this activated state causes the membrane invagination after ~ 50 milli-seconds and at a location of ~ 100 nm away from the SV fusion sites, and 4) it must become de-activated after the endocytosis is completed at ~ 100 milli-seconds so that it will not initiate another round endocytosis without new SV fusions. Note that, the above requirement 2) entails some self-reinforcing effect to sustain the activated state of the hypothetical factor for ~ 50 −100 milli-seconds after the trigger disappears; and the requirement 4) dictates that such positive feedback must be turned off after endocytosis. Can this scenario be possible? None of the key endocytic proteins or lipids is known to simultaneously meet the above four requirements with the ultrafast sub-second timescales. However, this could just mean that we have not found this hypothetical factor, which may suggest a new future direction. Nevertheless, our current knowledge suggests that membrane tension may not provide the spatial cue of SV exo-endocytosis coupling.

Instead, the theory in the recent work suggests another possibility [49] (Figure 3): The flattening of exocytosed SV compresses the membrane on AZ and causes the ultrafast formation of endocytic pits, akin to a buckling instability. This buckling instability requires two conditions. First, it causes higher energy penalty to bend SV membrane than the AZ membrane (i.e., a higher bending modulus for SV); this way, it is energetically favorable for the SVs to flatten out while squeezing the AZ membrane into endocytic pits. Second, the total membrane area should be conserved to rectify the buckling instability. With the realistic model parameters, this theoretical model can quantitatively recapitulate the observed spatial-temporal pattern of ultrafast endocytic pit formation in coupling to the SV exocytosis [49]. Importantly, the STED imaging in the same study showed that F-actin forms a dense ring-like structure surrounding the AZ [49], suggesting that the actin cortex may act as a barrier conserve the total membrane area at the AZ, by preventing the lipids and proteins from flowing out of AZ. Likewise, disrupting the F-actin at the AZ periphery is predicted to inhibit the ultrafast endocytosis upon SV exocytosis, whereas preserving the F-actin structure by freezing the dynamical exchange of actin monomers is expected to leave the ultrafast endocytosis unaltered. Indeed, the ultrafast endocytosis was completely abolished by the Latrunculin A treatment that disassembled F-actin, while it persisted in these neurons with Jasplakinolide treatments that froze the F-actin structures [49].

Figure 3.

Schematics of membrane compression model of ultrafast exo-endocytosis on presynaptic terminals of neurons. The model hinges on two key ingredients. First, synaptic vesicle (SV) membrane is assumed to be much stiffer than the active zone (AZ) membrane, because SV membrane is highly enriched in cholesterols and coated by dense membrane proteins, both of which are known to rigidify the membrane. Second, the total area of the membrane is conserved so that the lipids and proteins are prevented from flowing out of the AZ. This conservation is mediated by the thick actin cortex surrounding the AZ as demonstrated by the STED imaging.

These findings reveal several salient features for the ultrafast endocytosis in neurons. First, instead of membrane tension, it is the local variations of membrane bending energy that spatial-temporally coordinate SV exocytosis with endocytosis. Second, the ultrafast endocytosis hinges on the stability of actin cortex surrounding the exocytosis and endocytosis sites, whereas conventional endocytosis entails local remodeling of actin cortex. Third, in the ultrafast endocytosis the membrane pit forms first, and then the high-density dynamin droplet deforms the membrane pit via curvature-mediated feedback and pinch off the vesicle rapidly. In contrast, conventional endocytosis starts with a flat membrane and exploits the curvature-mediated feedback from scratch; hence, it takes a much longer time to pinch off the vesicle. Together, this recent work highlights the importance of local control over membrane mechanics in exo-endocytosis coupling, and calls for better experimental approaches (e.g., AFM) to precisely measure the membrane mechanics at 100 nm-scale in situ.

As different as can be, ultrafast and conventional endocytosis commonly share many key players of endocytic machinery. This precipitates many fascinating questions. For instance, external parameters (e.g., decreasing temperature from 37°C to 20°C) significantly slow down the endocytic timescale in neurons [61]. Given membrane fluidity is known to undergo phase transition around 30°C [62,63], the question is: Does the transition of membrane fluidity differentially regulate the bending moduli of SV and AZ membrane so that it critically impacts the ultrafast endocytosis? Moreover, how does the local modulation of membrane mechanics (curvature, tension, bending energy etc) adapt to the exo-endocytosis coupling in other systems (e.g., secretory cells [52]), where the dimensions and rates of exocytosis and endocytosis are different from neurons? Fundamentally, what are the overarching principles that the same endocytic players take on different modalities, modulating the endocytic timescales over three-orders-of-magnitude? It will be exciting to address these questions in future endeavors.

Conclusions

Spatial-temporal modulation of the local membrane mechanics is integral of the feedback control over membrane traffic processes. The membrane mechanics-mediated feedback defines a central theme for membrane-bound cellular processes. This concept challenges experimentalists to come up with better tools to resolve the finer details and compels theorists to construct more meaningful mathematical models to engage with experiments. Together, we are on an exciting path toward deciphering the organizational logic of how molecular specifics intersects with membrane mechanics to drive robust membrane traffic processes.