Nascent clathrin lattices spontaneously disassemble without sufficient adaptor proteins

TL;DR: In this paper, the authors combine experimental data with microscopic reaction-diffusion simulations and theory to quantify mechanisms of stable vs unstable clathrin assembly on membranes, showing that adaptor binding and dimensional reduction on the 2D surface are necessary to reproduce the cooperative kinetics of assembly.

Abstract: Clathrin-coated structures must assemble on cell membranes to perform their primary function of receptor internalization. These structures show marked plasticity and instability, but what conditions are necessary to stabilize against disassembly have not been quantified. Recent in vitro fluorescence experiments have measured kinetics of stable clathrin assembly on membranes as controlled by key adaptor proteins like AP-2. Here, we combine this experimental data with microscopic reaction-diffusion simulations and theory to quantify mechanisms of stable vs unstable clathrin assembly on membranes. Both adaptor binding and dimensional reduction on the 2D surface are necessary to reproduce the cooperative kinetics of assembly. By applying our model to more physiologic-like conditions, where the stoichiometry and volume to area ratio are significantly lower than in vitro, we show that the critical nucleus contains ~25 clathrin, remarkably similar to sizes of abortive structures observed in vivo. Stable nucleation requires a stoichiometry of adaptor to clathrin that exceeds 1:1, meaning that AP-2 on its own has too few copies to nucleate lattices. Increasing adaptor concentration increases lattice sizes and nucleation speeds. For curved clathrin cages, we quantify both the cost of bending the membrane and the stabilization required to nucleate cages in solution. We find the energetics are comparable, suggesting that curving the lattice could offset the bending energy cost. Our model predicts how adaptor density controls stabilization of clathrin-coated structures against spontaneous disassembly, and shows remodeling and disassembly does not require ATPases, which is a critical advance towards predicting control of productive vesicle formation. Significance StatementStochastic self-assembly of clathrin-coated structures on the plasma membrane is essential for transport into cells. We show here that even with abundant clathrin available, robust nucleation and growth into stable structures on membranes is not possible without sufficient adaptor proteins. Our results thus provide quantitative justification for why structures observed to form in vivo can still spontaneously disassemble over many seconds. The ATPases that drive clathrin disassembly after productive vesicle formation are therefore not necessary to control remodeling during growth. With parameterization against in vitro kinetics of assembly on membranes, our reaction-diffusion model provides a powerful and extensible tool for establishing determinants of productive assembly in cells.

Summary

Introduction

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Figures

Figure 1. The structure-resolved reaction-diffusion model for clathrin recruitment and assembly on membranes captures structure, valency, and excluded volume. Clathrin trimers are initialized in

Figure 4. Clathrin lattices face an initial barrier to growth, with a stable size reached only after significant growth. A) The probability of observing clathrin lattices of size n can be converted to an energy-like metric -ln(P(n)), which at equilibrium is a true free energy. An initial barrier to nucleation plateaus, followed by a flat region, where structures have comparable probability. Growth phase (yellow) samples intermediate size lattices, while at equilibrium only small and large clusters are visible. Full

Figure 3. Clathrin lattices at physiologic-like geometries fail to assemble until adaptor concentration reaches 0.6µM. A) Kinetics of largest clathrin lattice assembly is faster and reaches larger sizes with

Table 1. The varying parameters in the model and optimal values to reproduce the experimental kinetics

Figure 5. Curved-cage assembly in solution requires added stabilization, which is comparable to membrane bending energies A) Clathrin cages with adaptors present do not form in solution (black dots), using same model as on the membrane (open circles). With added stabilization via clathrin-

Full text

1
Nascent clathrin lattices spontaneously disassemble without sufficient adaptor
proteins
Si-Kao Guo
1
, Alexander J. Sodt
2
, Margaret E. Johnson
1
*
1
TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St, Baltimore,
MD 21218.
2
Eunice Kennedy Shriver National Institute of Child Health and Human Development
*Corresponding Author: margaret.johnson@jhu.edu
Keywords: reaction-diffusion simulations, self-assembly, dimensional reduction, membrane mechanics,
clathrin-mediated endocytosis
Classification: Biological Sciences: Biophysics and Computational Biology
.CC-BY-ND 4.0 International licenseavailable under a
was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprint (whichthis version posted April 20, 2021. ; https://doi.org/10.1101/2021.04.19.440502doi: bioRxiv preprint

2
Abstract
Clathrin-coated structures must assemble on cell membranes to perform their primary function of
receptor internalization. These structures show marked plasticity and instability, but what conditions are
necessary to stabilize against disassembly have not been quantified. Recent in vitro fluorescence
experiments have measured kinetics of stable clathrin assembly on membranes as controlled by key
adaptor proteins like AP-2. Here, we combine this experimental data with microscopic reaction-diffusion
simulations and theory to quantify mechanisms of stable vs unstable clathrin assembly on membranes.
Both adaptor binding and dimensional reduction on the 2D surface are necessary to reproduce the
cooperative kinetics of assembly. By applying our model to more physiologic-like conditions, where the
stoichiometry and volume to area ratio are significantly lower than in vitro, we show that the critical
nucleus contains ~25 clathrin, remarkably similar to sizes of abortive structures observed in vivo. Stable
nucleation requires a stoichiometry of adaptor to clathrin that exceeds 1:1, meaning that AP-2 on its
own has too few copies to nucleate lattices. Increasing adaptor concentration increases lattice sizes and
nucleation speeds. For curved clathrin cages, we quantify both the cost of bending the membrane and
the stabilization required to nucleate cages in solution. We find the energetics are comparable,
suggesting that curving the lattice could offset the bending energy cost. Our model predicts how
adaptor density controls stabilization of clathrin-coated structures against spontaneous disassembly,
and shows remodeling and disassembly does not require ATPases, which is a critical advance towards
predicting control of productive vesicle formation.
.CC-BY-ND 4.0 International licenseavailable under a
was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprint (whichthis version posted April 20, 2021. ; https://doi.org/10.1101/2021.04.19.440502doi: bioRxiv preprint

3
Significance Statement
Stochastic self-assembly of clathrin-coated structures on the plasma membrane is essential for transport
into cells. We show here that even with abundant clathrin available, robust nucleation and growth into
stable structures on membranes is not possible without sufficient adaptor proteins. Our results thus
provide quantitative justification for why structures observed to form in vivo can still spontaneously
disassemble over many seconds. The ATPases that drive clathrin disassembly after productive vesicle
formation are therefore not necessary to control remodeling during growth. With parameterization
against in vitro kinetics of assembly on membranes, our reaction-diffusion model provides a powerful
and extensible tool for establishing determinants of productive assembly in cells.
.CC-BY-ND 4.0 International licenseavailable under a
was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprint (whichthis version posted April 20, 2021. ; https://doi.org/10.1101/2021.04.19.440502doi: bioRxiv preprint

4
INTRODUCTION
In cells, clathrin-coated structures assemble into membrane bound puncta
1
that proceed to productive
vesicles only about half the time
2
, otherwise, they disassemble. These structures are observed to
contain at least ~20 clathrin
1
; are they dynamic
3
and unstable? Many proteins have been shown to tune
the frequency and probability of disassembly in these transition structures
1,2,4,5
, but none of these
proteins are physical drivers of disassembly. The clathrin uncoating machinery, which is capable of
driving disassembly
6,7
, is rarely seen at maturing clathrin-coated structures
8,9
. A fundamental question
thus remains, what physically stabilizes clathrin-coated structures against disassembly, and to what
extent? Addressing this question will help to establish under what conditions early clathrin-coated
structures develop into productive vesicles. Here, our simulations of clathrin recruitment and assembly
on membranes reproduce in vitro kinetic data, validating a model that then establishes how the key
parameters of adaptor density, volume to area (V/A) ratio, and clathrin concentration determine the
kinetics and critical nuclei of clathrin-coated structures on membranes.
Experiments in vitro have shown that clathrin-coated structures can assemble robustly on membranes
with clathrin and a minimal set of components, requiring a cytosolic adaptor that localizes clathrin to the
membrane and membrane binding sites that localize adaptors to the membrane, which physiologically is
the essential lipid PI(4,5)P
2
10-12
. In addition, the in vitro clathrin assembles both flat and vesicle-shaped
lattices, just as is observed in vivo
13,14
. What these experiments have not probed, however, is what
stoichiometry of clathrin, adaptors, and membrane area determines the transition from unstable to
stable clathrin coats, as all conditions studied report equilibrium, highly stabilized lattices. Even when
component concentrations are comparable to in vivo reported values, the V/A ratio is typically orders of
magnitude higher than in cells, which can dramatically increase stability of membrane associated
complexes
15
. In vivo experiments have provided more detailed insight into the dynamics of clathrin coat
nucleation and budding
3,16
, but the number of factors that are known to contribute to clathrin-mediated
endocytosis in cells, including enzymatic activity
17,18
, makes it impossible to estimate the critical nucleus
of clathrin and adaptors that is stabilized against disassembly. The composition of successful productive
vesicles
19
demonstrates that a diversity of adaptor and receptor compositions result in productive
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5
budding, and the goal of our study is to establish minimal criteria for stable nucleation and growth
dependent on adaptor concentration, out of equilibrium.
Kinetic measurements have provided a powerful variable to assess both models and mechanisms of
solution assembly in diverse filament forming
20,21
, aggregating
22,23
, and capsid forming systems
24
. With
recent kinetic experiments, Sarkar and Pucaydil
25
provided insight not only on the initial conditions that
can drive stable clathrin lattice formation on membranes, but constraints on rates of growth, while
previous biochemical experiments constrain the relative free energy of clathrin-clathrin
26
and clathrin-
adaptor
27
interactions. The kinetic experiments used initial conditions that again drove stable lattices,
and could not test the requirements for stable vs unstable lattices. To assess the size and speed of stable
nuclei as they might occur in the cell, we need to mimic the lower V/A ratio of the cell, recreating these
experiments in silico at new conditions that are challenging experimentally. A great advantage of the
type of microscopic spatial modeling here is that instead of requiring experiments at many distinct
concentrations in order to fit rate equations to the data
23
, our explicit physical models tightly constrain
the subset of rate constants that can quantify the data.
Modeling has played an important role in understanding principles of clathrin-coated assembly, but has
yet to characterize the kinetics of assembly, due to the challenges of capturing molecular structure at
mesoscopic length (
!
m) and time (minutes) scales. We achieve this here using recently developed
structure-resolved reaction-diffusion software
28
, which captures coarse molecular structure
29
for multi-
component systems in 3D
30
, 2D
31
, and transitioning between
32
. Critically, dimensional reduction, or the
change in search space and dynamics that accompanies transitions from 3D to 2D
33
, is rigorously
accounted for in our model, which will quantitatively impact stability
15
and kinetics
34
of assembly steps.
Our model produces energetics of clathrin cages similar to purely statistical mechanical models
35-39
,
although those models lack temporal resolution and molecular detail. Our model produces similar
structures to previous spatial simulations in solution
40-42
, but with membrane included these simulations
were too expensive to characterize experimental kinetics
43
. We here estimate the energetic balance of
curved cage formation and membrane bending by determining the minimum energy membrane shape
compatible with curved solution cages. Similarly to other approaches
44-46
, we do not dynamically couple
cage assembly to vesicle formation. Yet we are uniquely able to capture kinetics of localization and
assembly on membrane by tracking flat lattice assembly, which is consistent with observed early growth
13
. Our model provides a starting point to move beyond non-spatial kinetic models
47,48
or force-balanced
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was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
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Frequently asked questions

Q1. What are the contributions in "Nascent clathrin lattices spontaneously disassemble without sufficient adaptor proteins" ?

In this paper, a model for clathrin-coated structures is proposed to determine the transition from unstable to stable lattices. 

Q2. What are the future works in "Nascent clathrin lattices spontaneously disassemble without sufficient adaptor proteins" ?

The behavior of these additional adaptor protein types is consistent with their model prediction that AP-2 needs help to nucleate stable lattices, and in future work the authors will consider how explicit cross-linking can enhance local concentrations to drive nucleation and growth in time and space. 

Q3. What is the limitation of the model?

A limitation of their model is the clathrin-coat assembly is not dynamically coupled to themembrane remodeling to form spherical vesicles. 

Q4. What is the role of a lipid adaptor in clathrin-co?

Experiments in vitro have shown that clathrin-coated structures can assemble robustly on membraneswith clathrin and a minimal set of components, requiring a cytosolic adaptor that localizes clathrin to themembrane and membrane binding sites that localize adaptors to the membrane, which physiologically is the essential lipid PI(4,5)P2 10-12. 

Q5. What is the kinetics of the clathrin-adaptor?

The reflection of all the clathrin sites off of the membrane surface can reduce reactive flux between the reactive binding sites of clathrin-adaptor. 

Q6. How much lag does clathrin localize to the membrane?

In these in vitro simulations, the localizationtime of clathrin to the membrane contributes about 40% of the lag (first term in Eq 2), and is, as expected,most sensitive to both the rate of clathrin binding to adaptor and the density of adaptor on the membrane. 

Q7. What is the minimum requirement to overcome the barrier to nucleate structures on a membrane?

A minimal requirement toovercome this barrier to nucleate structures on a membrane is a sufficient concentration of adaptorproteins that can link clathrin to the membrane, allowing assembly to cooperatively benefit fromincreased (adaptor-driven) stability and dimensional reduction. 

Q8. At what concentration of AP-2 do the hallmark lag and growth phases require?

At thisclathrin concentration, the hallmark lag and growth phases require a clathrin to adaptor ratio of ~1:1(reached at 0.7-0.8µM of adaptor). 

Q9. What is the stress balance for the curved lattices?

This stress balance is the basis for usingseparate rates for the curved lattices in solution vs expected values on the membrane, which would thenbe more similar to flat lattice values. 

Q10. How do the authors predict how a single adaptor type would grow?

By increasing the local density of clathrin-recruitment sites, the authors predict thiscross-linking would then help nucleate stable lattices at lower concentrations than occur for a singleadaptor type. 

Q11. What is the way to assess the size and speed of stable lattices?

To assess the size and speed of stablenuclei as they might occur in the cell, the authors need to mimic the lower V/A ratio of the cell, recreating theseexperiments in silico at new conditions that are challenging experimentally. 

Q12. What is the rate of AP-2 to lipid binding?

The authors note that the recruitment of AP-2 to lipids is not rate-limiting in these simulations, as PI(4,5)P2 coverage is ~20000µm-2 (1%), and the rate of AP-2 to lipid binding is fast, 0.3s-1µM1 (Table S2). 

Q13. What is the energy per clathrin needed to bend the membrane?

their energetic calculations using ourassembled clathrin structures and a deformable membrane model demonstrate that the energy perclathrin needed to bend the membrane is comparable to the clathrin curvature free energy. 

Q14. What is the probability of observing a cluster with size n?

P(n) is the probabilities of observing a cluster with size n and can be calculated from summing T(Dt) over the column n, and then normalizing over all n. 

Q15. What is the effect of AP-2 on the binding kinetics of additional interactions?

The binding kinetics of additional interactions can also be significantly more dynamic thanAP-2; the proteins FCho1 and eps15 form clusters with AP-2 that helps initiate sites of clathrin-coatedstructure formation in cells, and yet both FCHo1 and eps15 are largely absent from completed vesicles, indicating the transience of their clathrin contacts63-65. 

Q16. What is the sensitivity of the growth rate k E to the parameters in Table?

Growth kinetics is controlled primarily by recruitment from adaptorsFigure 2D shows, in red, the sensitivity of the initial growth rate 𝑘 × 𝐸 to the parameters in Table 1.