Vesiculation pathways in clathrin-mediated endocytosis
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eLife Assessment
This valuable study proposes a theoretical model of clathrin coat formation based on membrane elasticity that seeks to determine whether this process occurs by increasing the area of a protein-coated patch with constant curvature, or by increasing the curvature of a protein-coated patch that forms in an initially flat conformation (so called constant curvature or constant area models). Identifying energetically favorable pathways and comparing the obtained shapes with experiments provides solid support to the constant-area pathway. This work will be of interest for biologists and biophysicists interested in membrane remodelling and endocytosis. It provides an innovative approach to tackle the question of constant curvature vs. constant area coat protein formation, although some of the model's assumption are only partially supported by experimental evidence.
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Abstract
Abstract
During clathrin-mediated endocytosis, a patch of flat plasma membrane is internalized to form a vesicle. In mammalian cells, how the clathrin coat deforms the membrane into a vesicle remains unclear and two main hypotheses have been debated. The “constant area” hypothesis assumes that clathrin molecules initially form a flat lattice on the membrane and deform the membrane by changing its intrinsic curvature while keeping the coating area constant. The alternative “constant curvature” hypothesis assumes that the intrinsic curvature of the clathrin lattice remains constant during the formation of a vesicle while the surface area it covers increases. Previous experimental studies were unable to unambiguously determine which hypothesis is correct. In this paper, we show that these two hypotheses are only two extreme cases of a continuum of vesiculation pathways if we account for the free energies associated with clathrin assembly and curvature generation. By tracing the negative gradient of the free energy, we define vesiculation pathways in the phase space of the coating area and the intrinsic curvature of clathrin coat. Our results show that, overall, the differences in measurable membrane morphology between the different models are not as big as expected, and the main differences are most salient at the early stage of endocytosis. Furthermore, the best fitting pathway to experimental data is not compatible with the constant-curvature model and resembles a constant-area-like pathway where the coating area initially expands with minor changes in the intrinsic curvature, later followed by a dramatic increase in the intrinsic curvature and minor change in the coating area. Our results also suggest that experimental measurement of the tip radius and the projected area of the clathrin coat will be the key to distinguish between models.
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eLife Assessment
This valuable study proposes a theoretical model of clathrin coat formation based on membrane elasticity that seeks to determine whether this process occurs by increasing the area of a protein-coated patch with constant curvature, or by increasing the curvature of a protein-coated patch that forms in an initially flat conformation (so called constant curvature or constant area models). Identifying energetically favorable pathways and comparing the obtained shapes with experiments provides solid support to the constant-area pathway. This work will be of interest for biologists and biophysicists interested in membrane remodelling and endocytosis. It provides an innovative approach to tackle the question of constant curvature vs. constant area coat protein formation, although some of the model's assumption are only …
eLife Assessment
This valuable study proposes a theoretical model of clathrin coat formation based on membrane elasticity that seeks to determine whether this process occurs by increasing the area of a protein-coated patch with constant curvature, or by increasing the curvature of a protein-coated patch that forms in an initially flat conformation (so called constant curvature or constant area models). Identifying energetically favorable pathways and comparing the obtained shapes with experiments provides solid support to the constant-area pathway. This work will be of interest for biologists and biophysicists interested in membrane remodelling and endocytosis. It provides an innovative approach to tackle the question of constant curvature vs. constant area coat protein formation, although some of the model's assumption are only partially supported by experimental evidence.
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Reviewer #1 (Public review):
Summary:
The authors develop a set of biophysical models to investigate whether a constant area hypothesis or a constant curvature hypothesis explains the mechanics of membrane vesiculation during clathrin-mediated endocytosis.
Strengths:
The models that the authors choose are fairly well-described in the field and the manuscript is well-written.
Weaknesses:
One thing that is unclear is what is new with this work. If the main finding is that the differences are in the early stages of endocytosis, then one wonders if that should be tested experimentally. Also, the role of clathrin assembly and adhesion are treated as mechanical equilibrium but perhaps the process should not be described as equilibria but rather a time-dependent process. Ultimately, there are so many models that address this question that …
Reviewer #1 (Public review):
Summary:
The authors develop a set of biophysical models to investigate whether a constant area hypothesis or a constant curvature hypothesis explains the mechanics of membrane vesiculation during clathrin-mediated endocytosis.
Strengths:
The models that the authors choose are fairly well-described in the field and the manuscript is well-written.
Weaknesses:
One thing that is unclear is what is new with this work. If the main finding is that the differences are in the early stages of endocytosis, then one wonders if that should be tested experimentally. Also, the role of clathrin assembly and adhesion are treated as mechanical equilibrium but perhaps the process should not be described as equilibria but rather a time-dependent process. Ultimately, there are so many models that address this question that without direct experimental comparison, it's hard to place value on the model prediction.
While an attempt is made to do so with prior published EM images, there is excessive uncertainty in both the data itself as is usually the case but also in the methods that are used to symmetrize the data. This reviewer wonders about any goodness of fit when such uncertainty is taken into account. -
Reviewer #2 (Public review):
Summary:
In this manuscript, the authors employ theoretical analysis of an elastic membrane model to explore membrane vesiculation pathways in clathrin-mediated endocytosis. A complete understanding of clathrin-mediated endocytosis requires detailed insight into the process of membrane remodeling, as the underlying mechanisms of membrane shape transformation remain controversial, particularly regarding membrane curvature generation. The authors compare constant area and constant membrane curvature as key scenarios by which clathrins induce membrane wrapping around the cargo to accomplish endocytosis. First, they characterize the geometrical aspects of the two scenarios and highlight their differences by imposing coating area and membrane spontaneous curvature. They then examine the energetics of the process …
Reviewer #2 (Public review):
Summary:
In this manuscript, the authors employ theoretical analysis of an elastic membrane model to explore membrane vesiculation pathways in clathrin-mediated endocytosis. A complete understanding of clathrin-mediated endocytosis requires detailed insight into the process of membrane remodeling, as the underlying mechanisms of membrane shape transformation remain controversial, particularly regarding membrane curvature generation. The authors compare constant area and constant membrane curvature as key scenarios by which clathrins induce membrane wrapping around the cargo to accomplish endocytosis. First, they characterize the geometrical aspects of the two scenarios and highlight their differences by imposing coating area and membrane spontaneous curvature. They then examine the energetics of the process to understand the driving mechanisms behind membrane shape transformations in each model. In the latter part, they introduce two energy terms: clathrin assembly or binding energy, and curvature generation energy, with two distinct approaches for the latter. Finally, they identify the energetically favorable pathway in the combined scenario and compare their results with experiments, showing that the constant-area pathway better fits the experimental data.
Strengths:
The manuscript is well-written, well-organized, and presents the details of the theoretical analysis with sufficient clarity.
The calculations are valid, and the elastic membrane model is an appropriate choice for addressing the differences between the constant curvature and constant area models.
The authors' approach of distinguishing two distinct free energy terms-clathrin assembly and curvature generation-and then combining them to identify the favorable pathway is both innovative and effective in addressing the problem.
Notably, their identification of the energetically favorable pathways, and how these pathways either lead to full endocytosis or fail to proceed due to insufficient energetic drives, is particularly insightful.Weaknesses:
Membrane remodeling in cellular processes is typically studied in either a constant area or constant tension ensemble. While total membrane area is preserved in the constant area ensemble, membrane area varies in the constant tension ensemble. In this manuscript, the authors use the constant tension ensemble with a fixed membrane tension, σe. However, they also use a constant area scenario, where 'area' refers to the surface area of the clathrin-coated membrane segment. This distinction between the constant membrane area ensemble and the constant area of the coated membrane segment may cause confusion.
As mentioned earlier, the theoretical analysis is performed in the constant membrane tension ensemble at a fixed membrane tension. The total free energy E_tot of the system consists of membrane bending energy E_b and tensile energy E_t, which depends on membrane tension, σe. Although the authors mention the importance of both E_b and E_t, they do not present their individual contributions to the total energy changes. Comparing these contributions would enable readers to cross-check the results with existing literature, which primarily focuses on the role of membrane bending rigidity and membrane tension.
The authors introduce two different models, (1,1) and (1,2), for generating membrane curvature. Model 1 assumes a constant curvature growth, corresponding to linear curvature growth, while Model 2 relates curvature growth to its current value, resembling exponential curvature growth. Although both models make physical sense in general, I am concerned that Model 2 may lead to artificial membrane bending at high curvatures. Normally, for intermediate bending, ψ > 90, the bending process is energetically downhill and thus proceeds rapidly. the bending process is energetically downhill and thus proceeds rapidly. However, Model 2's assumption would accelerate curvature growth even further. This is reflected in the endocytic pathways represented by the green curves in the two rightmost panels of Fig. 4a, where the energy steeply increases at large ψ. I believe a more realistic version of Model 2 would require a saturation mechanism to limit curvature growth at high curvatures.
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