publications

2024

1. Stability vs flexibility: reshaping monolayer and bilayer archaeal membranes in silico

   Miguel Amaral ,  Felix Frey ,  Xiuyun Jiang ,  Buzz Baum , and 1 more author

   bioRxiv, Oct 2024

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   Across the tree of life, distinct designs of cellular membranes have evolved that are both stable and flexible. In bacteria and eukaryotes this trade-off is accomplished by single-headed lipids that self-assemble into flexible bilayer membranes. By contrast, archaea in many cases possess both bilayer and double-headed, monolayer spanning bolalipids. This composition is believed to enable extremophile archaea to survive harsh environments. Here, through the creation of a minimal computational model for bolalipid membranes, we discover trade-offs when forming membranes using lipids of a single type. Similar to living archaea, we can tune the stiffness of bolalipid molecules. We find that membranes made out of flexible bolalipid molecules resemble bilayer membranes as they can adopt U-shaped conformations to enable higher curvatures. Conversely, stiffer bolalipid molecules, like those found in archaea at higher temperatures, preferentially take on a straight conformation to self-assemble into liquid membranes that are stable, stiff, prone to pore formation, and which tear during membrane reshaping. Strikingly, however, our analysis reveals that it is possible to achieve the best of both worlds – membranes that are fluid, stable at high temperatures and flexible enough to be reshaped without leaking – through the inclusion of a small fraction of bilayer lipids into a bolalipid membrane. Taken together, our study compares the different membrane designs across the tree of life and indicates how combining lipids can be used to resolve trade-offs when generating membranes for (bio)technological applications.

2. Endosomal membrane budding patterns in plants

   Ethan Weiner ,  Elizabeth Berryman ,  Felix Frey ,  Ariadna González Solı́s , and 4 more authors

   Proc. Natl. Acad. Sci. U.S.A., Oct 2024

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   Multivesicular endosomes (MVEs) sequester membrane proteins destined for degradation within intralumenal vesicles (ILVs), a process mediated by the membrane-remodeling action of Endosomal Sorting Complex Required for Transport (ESCRT) proteins. In Arabidopsis, endosomal membrane constriction and scission are uncoupled, resulting in the formation of extensive concatenated ILV networks and enhancing cargo sequestration efficiency. Here, we used a combination of electron tomography, computer simulations, and mathematical modeling to address the questions of when concatenated ILV networks evolved in plants and what drives their formation. Through morphometric analyses of tomographic reconstructions of endosomes across yeast, algae, and various land plants, we have found that ILV concatenation is widespread within plant species, but only prevalent in seed plants, especially in flowering plants. Multiple budding sites that require the formation of pores in the limiting membrane were only identified in hornworts and seed plants, suggesting that this mechanism has evolved independently in both plant lineages. To identify the conditions under which these multiple budding sites can arise, we used particle-based molecular dynamics simulations and found that changes in ESCRT filament properties, such as filament curvature and membrane binding energy, can generate the membrane shapes observed in multiple budding sites. To understand the relationship between membrane budding activity and ILV network topology, we performed computational simulations and identified a set of membrane remodeling parameters that can recapitulate our tomographic datasets.

3. Coat stiffening explains the consensus pathway of clathrin-mediated endocytosis

   Felix Frey ,  and  Ulrich S. Schwarz

   preprint: arXiv, May 2024

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   Clathrin-mediated endocytosis is the main pathway used by eukaryotic cells to take up extracellular material, but the dominant physical mechanisms driving this process are still elusive. Recently several high-resolution imaging techniques have been used on different cell lines to measure the geometrical properties of clathrin-coated pits over their whole lifetime. Here we first show that all datasets follow the same consensus pathway, which is well described by the recently introduced cooperative curvature model, which predicts a flat-to curved transition at finite area, followed by linear growth and subsequent saturation of curvature. We then apply an energetic model for the composite of plasma membrane and clathrin coat to the consensus pathway to show that the dominant mechanism for invagination is coat stiffening, which results from cooperative interactions between the different clathrin molecules and progressively drives the system towards its intrinsic curvature. Our theory predicts that two length scales determine the time course of invagination, namely the patch size at which the flat-to-curved transition occurs and the final pit radius.

2023

1. Clathrin coats partially preassemble and subsequently bend during endocytosis

   Markus Mund ,  Aline Tschanz ,  Yu-Le Wu ,  Felix Frey , and 5 more authors

   J. Cell Biol., Mar 2023

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   Eukaryotic cells use clathrin-mediated endocytosis to take up a large range of extracellular cargo. During endocytosis, a clathrin coat forms on the plasma membrane, but it remains controversial when and how it is remodeled into a spherical vesicle. Here, we use 3D superresolution microscopy to determine the precise geometry of the clathrin coat at large numbers of endocytic sites. Through pseudo-temporal sorting, we determine the average trajectory of clathrin remodeling during endocytosis. We find that clathrin coats assemble first on flat membranes to 50% of the coat area before they become rapidly and continuously bent, and this mechanism is confirmed in three cell lines. We introduce the cooperative curvature model, which is based on positive feedback for curvature generation. It accurately describes the measured shapes and dynamics of the clathrin coat and could represent a general mechanism for clathrin coat remodeling on the plasma membrane.

2. Branched actin cortices reconstituted in vesicles sense membrane curvature

   Lucia Baldauf* ,  Felix Frey* ,  Marcos Arribas Perez ,  Timon Idema , and 1 more author

   Biophys. J., Feb 2023

   *contributed equally

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   The actin cortex is a complex cytoskeletal machinery that drives and responds to changes in cell shape. It must generate or adapt to plasma membrane curvature to facilitate diverse functions such as cell division, migration, and phagocytosis. Due to the complex molecular makeup of the actin cortex, it remains unclear whether actin networks are inherently able to sense and generate membrane curvature, or whether they rely on their diverse binding partners to accomplish this. Here, we show that curvature sensing is an inherent capability of branched actin networks nucleated by Arp2/3 and VCA. We develop a robust method to encapsulate actin inside giant unilamellar vesicles (GUVs) and assemble an actin cortex at the inner surface of the GUV membrane. We show that actin forms a uniform and thin cortical layer when present at high concentration and distinct patches associated with negative membrane curvature at low concentration. Serendipitously, we find that the GUV production method also produces dumbbell-shaped GUVs, which we explain using mathematical modeling in terms of membrane hemifusion of nested GUVs. We find that branched actin networks preferentially assemble at the neck of the dumbbells, which possess a micrometer-range convex curvature comparable with the curvature of the actin patches found in spherical GUVs. Minimal branched actin networks can thus sense membrane curvature, which may help mammalian cells to robustly recruit actin to curved membranes to facilitate diverse cellular functions such as cytokinesis and migration.

3. Biomimetic actin cortices shape cell-sized lipid vesicles

   Lucia Baldauf ,  Felix Frey ,  Marcos Arribas Perez ,  Miroslav Mladenov , and 3 more authors

   preprint: bioRxiv, Jan 2023

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   Animal cells are shaped by a thin layer of actin filaments underneath the plasma membrane known as the actin cortex. This cortex stiffens the cell surface and thus opposes cellular deformation, yet also actively generates membrane protrusions by exerting polymerization forces. It is unclear how the interplay between these two opposing mechanical functions plays out to shape the cell surface. To answer this question, we reconstitute biomimetic actin cortices nucleated by the Arp2/3 complex inside cell-sized lipid vesicles. We show that thin Arp2/3-nucleated actin cortices strongly deform and rigidify the shapes of giant unilamellar vesicles and impart a shape memory on time scales that exceeds the time of actin turnover. In addition, actin cortices can produce finger-like membrane protrusions, showing that Arp2/3-mediated actin polymerization forces alone are sufficient to initiate protrusions in the absence of actin bundling or membrane curving proteins. Combining mathematical modeling and our experimental results reveals that the concentration of actin nucleating proteins, rather than actin polymerization speed, is crucial for protrusion formation. This is because locally concentrated actin polymerization forces can drive a positive feedback loop between recruitment of actin and its nucleators to drive membrane deformation. Our work paints a picture where the actin cortex can either drive or inhibit deformations depending on the local distribution of nucleators.

2022

1. Membrane area gain and loss during cytokinesis

   Felix Frey ,  and  Timon Idema

   Phys. Rev. E, Aug 2022

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   In cytokinesis of animal cells, the cell is symmetrically divided into two. Since the cell’s volume is conserved, the projected area has to increase to allow for the change of shape. Here we aim to predict how membrane gain and loss adapt during cytokinesis. We work with a kinetic model in which membrane turnover depends on membrane tension and cell shape. We apply this model to a series of calculated vesicle shapes as a proxy for the shape of dividing cells. We find that the ratio of kinetic turnover parameters changes nonmonotonically with cell shape, determined by the dependence of exocytosis and endocytosis on membrane curvature. Our results imply that controlling membrane turnover will be crucial for the successful division of artificial cells.

2. A systematic review and comparison of automated tools for quantification of fibrous networks

   Judith J. Vries ,  Daphne M. Laan ,  Felix Frey ,  Gijsje H. Koenderink , and 1 more author

   Acta Biomater., Dec 2022

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   Fibrous networks are essential structural components of biological and engineered materials. Accordingly, many approaches have been developed to quantify their structural properties, which define their material properties. However, a comprehensive overview and comparison of methods is lacking. Therefore, we systematically searched for automated tools quantifying network characteristics in confocal, stimulated emission depletion (STED) or scanning electron microscopy (SEM) images and compared these tools by applying them to fibrin, a prototypical fibrous network in thrombi. Structural properties of fibrin such as fiber diameter and alignment are clinically relevant, since they influence the risk of thrombosis. Based on a systematic comparison of the automated tools with each other, manual measurements, and simulated networks, we provide guidance to choose appropriate tools for fibrous network quantification depending on imaging modality and structural parameter. These tools are often able to reliably measure relative changes in network characteristics, but absolute numbers should be interpreted with care.

2021

1. More than just a barrier: using physical models to couple membrane shape to cell function

   Felix Frey ,  and  Timon Idema

   Soft Matter, Dec 2021

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   The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

2020

1. Eden growth models for flat clathrin lattices with vacancies

   Felix Frey ,  Delia Bucher ,  Kem A Sochacki ,  Justin W Taraska , and 2 more authors

   New J. Phys., Jul 2020

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   Clathrin-mediated endocytosis is one of the major pathways by which cells internalise cargo molecules. Recently it has been shown that clathrin triskelia can first assemble as flat lattices before the membrane starts to bend. However, for fully assembled clathrin lattices high energetic and topological barriers exist for the flat-to-curved transition. Here we explore the possibility that flat clathrin lattices grow with vacancies that are not visible in traditional imaging techniques but would lower these barriers. We identify the Eden model for cluster growth as the most appropriate modeling framework and systematically derive the four possible variants that result from the specific architecture of the clathrin triskelion. Our computer simulations show that the different models lead to clear differences in the statistical distributions of cluster shapes and densities. Experimental results from electron microscopy and correlative light microscopy provide first indications for the model variants with a moderate level of lattice vacancies.

2. Forces during cellular uptake of viruses and nanoparticles at the ventral side

   Tina Wiegand ,  Marta Fratini ,  Felix Frey ,  Klaus Yserentant , and 11 more authors

   Nat. Commun., Dec 2020

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   Many intracellular pathogens, such as mammalian reovirus, mimic extracellular matrix motifs to specifically interact with the host membrane. Whether and how cell-matrix interactions influence virus particle uptake is unknown, as it is usually studied from the dorsal side. Here we show that the forces exerted at the ventral side of adherent cells during reovirus uptake exceed the binding strength of biotin-neutravidin anchoring viruses to a biofunctionalized substrate. Analysis of virus dissociation kinetics using the Bell model revealed mean forces higher than 30 pN per virus, preferentially applied in the cell periphery where close matrix contacts form. Utilizing 100 nm-sized nanoparticles decorated with integrin adhesion motifs, we demonstrate that the uptake forces scale with the adhesion energy, while actin/myosin inhibitions strongly reduce the uptake frequency, but not uptake kinetics. We hypothesize that particle adhesion and the push by the substrate provide the main driving forces for uptake.

3. Competing pathways for the invagination of clathrin-coated membranes

   Felix Frey ,  and  Ulrich S. Schwarz

   Soft Matter, Dec 2020

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   Clathrin-mediated endocytosis is the major pathway by which eukaryotic cells take up extracellular material, but it is still elusive which physical pathways are being taken during membrane invagination. From a continuum point of view, it can be driven by increases in coat stiffness, preferred curvature or line tension. Here we develop a comprehensive theoretical framework that can be solved analytically and that predicts the consequences of these different scenarios. We find that for the case of increasing stiffness or preferred curvature, curvature will be acquired gradually with growth, while for increasing line tension, the lattice must have grown to a certain size before a flat-to-curved transition can occur. At low membrane tension, the critical value for coat stiffness is 30 kBT, for preferred curvature it is 200 nm, and for line tension it is 6 pN. For high membrane tension, critical coat stiffness is 150 kBT and critical preferred curvature is 70 nm. In the mixed case when a coat with finite rigidity but increasing line tension is considered, a cup-to-sphere transition can occur for a line tension of 6 pN. The flat-to-curved and the cup-to-sphere transitions driven by line tension are both suppressed by high membrane tension.

2019

1. Physical models for uptake processes at the cell membrane

   Felix Frey

   PhD thesis, Jun 2019

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   All biological cells are enclosed by a fluid membrane and have to continuously transport information and material across this interface. Cells have developed multiple strategies by which they take up small particles. In this thesis, I use theoretical models from statistical physics and computer simulations to investigate two of these strategies, namely receptor-mediated endocytosis driven by adhesion energy and clathrin-mediated endocytosis driven by the polymerisation energy of supramolecular assembly. For receptor-mediated uptake, I focus on systems with sizes in the order of 10 − 300 nm, few tens of cell surface receptors and address stochastic effects. We show how the stochastic dynamics of uptake is influenced by particle geometry and compare theoretically predicted adhesion energies to experimental data. For clathrin-mediated endocytosis we demonstrate by combining different experimental data sets with physical models how clathrin triskelia assemble and rearrange during endocytosis. Using computer simulations we show that flat clathrin lattices grow sparsely and that an increasing clathrin density could drive a flat-to-curved transition of clathrin lattices. Together, these results demonstrate how physical models can help to understand the complex biological process of cellular uptake.

2. Stochastic Dynamics of Nanoparticle and Virus Uptake

   Felix Frey ,  Falko Ziebert ,  and  Ulrich S. Schwarz

   Phys. Rev. Lett., Feb 2019

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   The cellular uptake of nanoparticles or viruses requires that the gain of adhesion energy overcomes the cost of plasma membrane bending. It is well known that this leads to a minimal particle size for uptake. Using a simple deterministic theory for this process, we first show that, for the same radius and volume, cylindrical particles should be taken up faster than spherical particles, both for normal and parallel orientations. We then address stochastic effects, which are expected to be relevant due to small system size, and show that, now, spherical particles can have a faster uptake because the mean first passage time profits from the multiplicative noise induced by the spherical geometry. We conclude that stochastic effects are strongly geometry dependent and may favor spherical shapes during adhesion-driven particle uptake.

3. Dynamics of particle uptake at cell membranes

   Felix Frey ,  Falko Ziebert ,  and  Ulrich S. Schwarz

   Phys. Rev. E, Nov 2019

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   Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While the shape of the free membrane does not play an important role for tensed and loose membranes, in the intermediate regime it leads to an important energy barrier. Here we show that this barrier is similar to but different from an effective line tension and suggest a simple analytical approximation for it. We then explore the rich dynamics of uptake for particles of different shapes and present the corresponding dynamical state diagrams. We also extend our model to include stochastic fluctuations, which facilitate uptake and lead to corresponding changes in the phase diagrams.

2018

1. Clathrin-adaptor ratio and membrane tension regulate the flat-to-curved transition of the clathrin coat during endocytosis

   Delia Bucher* ,  Felix Frey* ,  Kem A. Sochacki ,  Susann Kummer , and 7 more authors

   Nat. Commun., Dec 2018

   *contributed equally

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   Although essential for many cellular processes, the sequence of structural and molecular events during clathrin-mediated endocytosis remains elusive. While it was long believed that clathrin-coated pits grow with a constant curvature, it was recently suggested that clathrin first assembles to form flat structures that then bend while maintaining a constant surface area. Here, we combine correlative electron and light microscopy and mathematical growth laws to study the ultrastructural rearrangements of the clathrin coat during endocytosis in BSC-1 mammalian cells. We confirm that clathrin coats initially grow flat and demonstrate that curvature begins when around 70% of the final clathrin content is acquired. We find that this transition is marked by a change in the clathrin to clathrin-adaptor protein AP2 ratio and that membrane tension suppresses this transition. Our results support the notion that BSC-1 mammalian cells dynamically regulate the flat-to-curved transition in clathrin-mediated endocytosis by both biochemical and mechanical factors.

2016

1. Multiscale modeling of virus replication and spread

   Peter Kumberger ,  Felix Frey ,  Ulrich S. Schwarz ,  and  Frederik Graw

   FEBS Lett., Jul 2016

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   Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps.