Elucidating the mechanics of clathrin-mediated endocytosis

Clathrin-mediated endocytosis (CME) is a key metabolic pathway that plays a central role in the delivery of nutrients and drug carriers into cells. In this study, we model the interactions of lipid membranes with different types of protein scaffolds and active forces to provide mechanistic insights into CME. To this end, we develop and employ an extended theoretical framework of lipid membranes that entertains spatial heterogeneity and local anisotropy that could arise from membrane–protein interactions. We show that a departure from homogeneity and isotropy can lead to a variable surface tension field, conventionally assumed to be a constant parameter. We model the impact of resting tension in a cell and discuss its consequences on the minimal protein machinery needed to complete vesicle formation. Based on our quantitative model and findings, we highlight the physical principles that unify CME in apparently distinct yeast and mammalian cells

Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins can preferentially bind or diffuse towards curved regions of the membrane, induce or stabilize membrane curvature and sequester membrane area into protein-rich curved domains. The resulting tight interplay between mechanics and chemistry is thought to control organelle morphogenesis and dynamics, including traffic, membrane mechanotransduction, or membrane area regulation and tension buffering. Despite all these processes are fundamentally dynamical, previous work has largely focused on equilibrium and a self-consistent theoretical treatment of the dynamics of curvature sensing and generation has been lacking. Here, we develop a general theoretical and computational framework based on a nonlinear Onsager’s formalism of irreversible thermodynamics for the dynamics of curved proteins and membranes. We develop variants of the model, one of which accounts for membrane curving by asymmetric crowding of bulky off-membrane protein domains. As illustrated by a selection of test cases, the resulting governing equations and numerical simulations provide a foundation to understand the dynamics of curvature sensing, curvature generation, and more generally membrane curvature mechano-chemistry.Peer ReviewedPostprint (author's final draft

Onsager’s variational principle in soft matter : introduction and application to the dynamics of adsorption of proteins onto fluid membranes

This book is the first collection of lipid-membrane research conducted by leading mechanicians and experts in continuum mechanics. It brings the overall intellectual framework afforded by modern continuum mechanics to bear on a host of challenging problems in lipid membrane physics. These include unique and authoritative treatments of differential geometry, shape elasticity, surface flow and diffusion, interleaf membrane friction, phase transitions, electroelasticity and flexoelectricity, and computational modelling. [Chapter] Lipid bilayers are unique soft materials operating in general in the low Reynolds limit. While their shape is predominantly dominated by curvature elasticity as in a solid shell, their in-plane behavior is that of a largely inextensible viscous fluid. Furthermore, lipid membranes are extremely responsive to chemical stimuli. Because in their biological context they are continuously brought out-of-equilibrium mechanically or chemically, it is important to understand their dynamics. Here, we introduce Onsager’s variational principle as a general and transparent modeling tool for lipid bilayer dynamics. We introduce this principle with elementary examples, and then use it to study the sorption of curved proteins on lipid membranes.Peer ReviewedPostprint (author's final draft

The plasma membrane as a mechanochemical transducer

Cells are constantly submitted to external mechanical stresses, which they must withstand and respond to. By forming a physical boundary between cells and their environment that is also a biochemical platform, the plasma membrane (PM) is a key interface mediating both cellular response to mechanical stimuli, and subsequent biochemical responses. Here, we review the role of the PM as a mechanosensing structure. We first analyse how the PM responds to mechanical stresses, and then discuss how this mechanical response triggers downstream biochemical responses. The molecular players involved in PM mechanochemical transduction include sensors of membrane unfolding, membrane tension, membrane curvature or membrane domain rearrangement. These sensors trigger signalling cascades fundamental both in healthy scenarios and in diseases such as cancer, which cells harness to maintain integrity, keep or restore homeostasis and adapt to their external environment

Caveolin-1 dolines form a distinct and rapid caveolae-independent mechanoadaptation system.

In response to different types and intensities of mechanical force, cells modulate their physical properties and adapt their plasma membrane (PM). Caveolae are PM nano-invaginations that contribute to mechanoadaptation, buffering tension changes. However, whether core caveolar proteins contribute to PM tension accommodation independently from the caveolar assembly is unknown. Here we provide experimental and computational evidence supporting that caveolin-1 confers deformability and mechanoprotection independently from caveolae, through modulation of PM curvature. Freeze-fracture electron microscopy reveals that caveolin-1 stabilizes non-caveolar invaginations-dolines-capable of responding to low-medium mechanical forces, impacting downstream mechanotransduction and conferring mechanoprotection to cells devoid of caveolae. Upon cavin-1/PTRF binding, doline size is restricted and membrane buffering is limited to relatively high forces, capable of flattening caveolae. Thus, caveolae and dolines constitute two distinct albeit complementary components of a buffering system that allows cells to adapt efficiently to a broad range of mechanical stimuli.We thank R. Parton (Institute for Molecular Biosciences, Queensland), P. Pilch (Boston University School of Medicine) and L. Liu (Boston University School of Medicine) for kindly providing PTRFKO cells and reagents, S. Casas Tintó for kindly providing SH-Sy5y cells, P. Bassereau (Curie Institute, Paris) for kindly providing OT setup, V. Labrador Cantarero from CNIC microscopy Unit for helping with ImageJ analysis, O. Otto and M. Herbig for providing help with RTDC experiments, S. Berr and K. Gluth for technical assistance in cell culture, F. Steiniger for support in electron tomography, and A. Norczyk Simón for providing pCMV-FLAG-PTRF construct. This project received funding from the European Union Horizon 2020 Research and Innovation Programme through Marie Sklodowska-Curie grant 641639; grants from the Spanish Ministry of Science and Innovation (MCIN/AEI/10.13039/501100011033): SAF2014-51876-R, SAF2017-83130-R co-funded by ‘ERDF A way of making Europe’, PID2020-118658RB-I00, PDC2021-121572-100 co-funded by ‘European Union NextGenerationEU/PRTR’, CSD2009- 0016 and BFU2016-81912-REDC; and the Asociación Española Contra el Cáncer foundation (PROYE20089DELP) all to M.A.d.P. M.A.d.P. is member of the Tec4Bio consortium (ref. S2018/NMT¬4443; Comunidad Autónoma de Madrid/FEDER, Spain), co-recipient with P.R.-C. of grants from Fundació La Marató de TV3 (674/C/2013 and 201936- 30-31), and coordinator of a Health Research consortium grant from Fundación Obra Social La Caixa (AtheroConvergence, HR20-00075). M.S.-A. is recipient of a Ramón y Cajal research contract from MCIN (RYC2020-029690-I). The CNIC Unit of Microscopy and Dynamic Imaging is supported by FEDER ‘Una manera de hacer Europa’ (ReDIB ICTS infrastructure TRIMA@CNIC, MCIN). We acknowledge the support from Deutsche Forschungsgemeinschaft through grants to M.M.K. (KE685/7-1) and B.Q. (QU116/6-2 and QU116/9-1). Work in D.N. laboratory was supported by grants from the European Union Horizon 2020 Research and Innovation Programme through Marie Sklodowska-Curie grant 812772 and MCIN (DPI2017-83721-P). Work in C.L. laboratory was supported by grants from Curie, INSERM, CNRS, Agence Nationale de la Recherche (ANR-17-CE13-0020-01) and Fondation ARC pour la Recherche (PGA1-RF20170205456). Work in P.R.-C. lab is funded by the MCIN (PID2019-110298GB-I00), the EC (H20 20-FETPROACT-01-2016-731957). Work in X.T. lab is funded by the MICIN (PID2021-128635NB-I00), ERC (Adv-883739) and La Caixa Foundation (LCF/PR/HR20/52400004; co-recipient with P.R.-C.). IBEC is recipient of a Severo Ochoa Award of Excellence from the MINECO. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. The CNIC is supported by the Instituto de Salud Carlos III (ISCIII), the MCIN and the Pro CNIC Foundation, and is a Severo Ochoa Center of Excellence (grant CEX2020-001041-S funded by MICIN/AEI/10.13039/501100011033).S

Mechanics of Cellular Transport

Lipid membranes are versatile structures that interact with various kinds of proteins to maintain the shape and functionality of cells and their organelles. For example, they are actively involved in the transport of various proteins and other nutrients in and out of cells. The transport of macromolecules, which cannot diffuse through these bilayer membranes occur through an extensive remodeling of plasma membrane. This is executed by a designated set of membrane-deforming proteins, which supply the energy and drive membrane remodeling leading to formation of cargo-carrying vesicles. In our study, we focus on the most commonly used transport pathway termed "Clathrin Mediated Endocytosis." We use continuum mechanics to study the equilibrium of lipid bilayers in the presence of three key membrane-deforming proteins, namely, clathrin, BAR and actin filaments.To the end, we generalize the theory of lipid membranes to incorporate the anisotropic curvatures generated by proteins. Our study reveals a protein-induced "Snap-through Instability" that offsets tension in the lipid membrane and drives vesicle growth. It disentangles the individual role of key proteins and provides mechanistic insights into fundamental debates in the field of cellular transport. Since these proteins (actin and BAR proteins) are involved in other interfacial rearrangements in cells, our work could provide new insights into biological processes in cells at-large. Motivated by the observed instability, we derive the generalized stability conditions for heterogeneous lipid membranes. These theories, in the future, can provide physical insights into the observed instability.Mechanical Engineering, Department o

Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins can preferentially bind or diffuse towards curved regions of the membrane, induce or stabilize membrane curvature and sequester membrane area into protein-rich curved domains. The resulting tight interplay between mechanics and chemistry is thought to control organelle morphogenesis and dynamics, including traffic, membrane mechanotransduction, or membrane area regulation and tension buffering. Despite all these processes are fundamentally dynamical, previous work has largely focused on equilibrium and a self-consistent theoretical treatment of the dynamics of curvature sensing and generation has been lacking. Here, we develop a general theoretical and computational framework based on a nonlinear Onsager’s formalism of irreversible thermodynamics for the dynamics of curved proteins and membranes. We develop variants of the model, one of which accounts for membrane curving by asymmetric crowding of bulky off-membrane protein domains. As illustrated by a selection of test cases, the resulting governing equations and numerical simulations provide a foundation to understand the dynamics of curvature sensing, curvature generation, and more generally membrane curvature mechano-chemistry.Peer Reviewe

A theory of ordering of elongated and curved proteins on membranes driven by density and curvature

Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved and elongated, and hence may adopt different states of orientational order, from isotropic to maximize entropy to nematic as a result of crowding or to adapt to the curvature of the underlying membrane. Here, extending the classical work of Onsager for ordering in hard particle systems and that of [E. S. Nascimento et al., Phys. Rev. E, 2017, 96, 022704], we develop a mean-field density functional theory to predict the orientational order and evaluate the free energy of ensembles of elongated and curved objects on curved membranes. This theory depends on the microscopic properties of the particles and explains how a density-dependent isotropic-to-nematic transition is modified by anisotropic curvature. We also examine the coexistence of isotropic and nematic phases. This theory predicts how ordering depends on geometry but we assume here that the geometry is fixed. It also lays the ground to understand the interplay between membrane reshaping by BAR proteins and molecular order, examined by [Le Roux et al., submitted, 2020]. This journal i