Membrane-Mediated Cooperativity of Proteins

Nonadditivity in Many-Body Interactions between Membrane-Deforming Spheres Increases Disorder

Membrane-induced interactions play an important role in organizing membrane proteins. Measurements of the interactions between two and three membrane deforming objects have revealed their nonadditive nature. They are thought to lead to complex many-body effects, however, experimental evidence is lacking. We here present an experimental method to measure many-body effects in membrane-mediated interactions using colloidal spheres placed between a deflated giant unilamellar vesicles and a planar substrate. The confined colloidal particles cause a large deformation of the membrane while not being physicochemically attached to it and interact through it. Two particles attract with a maximum force of 0.2 pN. For three particles, compact equilateral triangles were preferred over linear arrangements. We use numerical energy minimization to establish that the attraction stems from a reduction in the membrane-deformation energy caused by the particles. Confining up to 36 particles, we find a preference for hexagonally close packed clusters. However, with increasing number of particles the order of the confined particles decreases, at the same time, diffusivity of the particles increases. Our experiments show that the nonadditive nature of membrane-mediated interactions affects the interactions and arrangements and ultimately leads to spherical aggregates with liquid-like order of potential importance for cellular processes.

Which Coverages of Arc-Shaped Proteins Are Required for Membrane Tubulation?

Arc-shaped BIN/Amphiphysin/Rvs (BAR) domain proteins generate curvature by binding to membranes and induce membrane tubulation at sufficiently large protein coverages. For the amphiphysin N-BAR domain, Le Roux et al., Nat. Commun. 2021, 12, 6550, measured a threshold coverage of 0.44 ± 0.097 for nanotubules emerging from the supported lipid bilayer. In this article, we systematically investigate membrane tubulation induced by arc-shaped protein-like particles with coarse-grained modeling and simulations and determine the threshold coverages at different particle-particle interaction strengths and membrane spontaneous curvatures. In our simulations, the binding of arc-shaped particles induces a membrane shape transition from spherical vesicles to tubules at a particle threshold coverage of about 0.5, which is rather robust to variations of the direct attractive particle interactions or spontaneous membrane curvature in the coarse-grained model. Our study suggests that threshold coverages of around or slightly below 0.5 are a general requirement for membrane tubulation by arc-shaped BAR domain proteins.

Membrane Tilt Drives Phase Separation of Adhesion Receptors

Cell adhesion receptors are transmembrane proteins that bind cells to their environment. These proteins typically cluster into disk-shaped or linear structures. Here, we show that such clustering patterns spontaneously emerge when the receptor senses the membrane deformation gradient, for example, by reaching a lower-energy conformation when the membrane is tilted relative to the underlying binding substrate. Increasing the strength of the membrane gradient-sensing mechanism first yields isolated disk-shaped clusters and then long linear structures. Our theory is coherent with experimental estimates of the parameters, suggesting that a tilt-induced clustering mechanism is relevant in the context of cell adhesion.

Curvature-induced clustering of cell adhesion proteins

Cell adhesion proteins typically form stable clusters that anchor the cell membrane to its environment. Several works have suggested that cell membrane protein clusters can emerge from a local feedback between the membrane curvature and the density of proteins. Here, we investigate the effect of such a curvature-sensing mechanism in the context of cell adhesion proteins. We show how clustering emerges in an intermediate range of adhesion and curvature-sensing strengths. We identify key differences with the tilt-induced gradient sensing mechanism we previously proposed (Lin et al., arXiv:2307.03670).

Dynamic framework for large-scale modeling of membranes and peripheral proteins

In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.

Lattice-based mesoscale simulations and mean-field theory of cell membrane adhesion

Adhesion of cell membranes involves multi-scale phenomena, ranging from specific molecular binding at Angstrom scale all the way up to membrane deformations and phase separation at micrometer scale. Consequently, theory and simulations of cell membrane adhesion require multi-scale modeling and suitable approximations that capture the essential physics of these phenomena. Here, we present a mesoscale model for membrane adhesion which we have employed in a series of our recent studies. This model quantifies, in particular, how nanoscale lipid clusters physically affect and respond to the intercellular receptor-ligand binding that mediates membrane adhesion. The goal of this Chapter is to present all details and subtleties of the mean-field theory and Monte Carlo simulations of this mesoscale model, which can be used to further explore physical phenomena related to cell membrane adhesion.

T-cell virtuosity in ''knowing thyself"

Major Histocompatibility Complex (MHC) I and II and the αβ T-cell antigen receptor (TCRαβ) govern fundamental traits of adaptive immunity. They form a membrane-borne ligand-receptor system weighing host proteome integrity to detect contamination by nonself proteins. MHC-I and -II exhibit the "MHC-fold", which is able to bind a large assortment of short peptides as proxies for self and nonself proteins. The ensuing varying surfaces are mandatory ligands for Ig-like TCRαβ highly mutable binding sites. Conserved molecular signatures guide TCRαβ ligand binding sites to focus on the MHC-fold (MHC-restriction) while leaving many opportunities for its most hypervariable determinants to contact the peptide. This riveting molecular strategy affords many options for binding energy compatible with specific recognition and signalling aimed to eradicated microbial pathogens and cancer cells. While the molecular foundations of αβ T-cell adaptive immunity are largely understood, uncertainty persists on how peptide-MHC binding induces the TCRαβ signals that instruct cell-fate decisions. Solving this mystery is another milestone for understanding αβ T-cells' self/nonself discrimination. Recent developments revealing the innermost links between TCRαβ structural dynamics and signalling modality should help dissipate this long-sought-after enigma.

Membrane-Mediated Cooperative Interactions of CD47 and SIRPα

The specific binding of the ubiquitous 'marker of self' protein CD47 to the SIRPα protein anchored in the macrophage plasma membrane results in the inhibition of the engulfment of 'self' cells by macrophages and thus constitutes a key checkpoint of our innate immune system. Consequently, the CD47-SIRPα protein complex has been recognized as a potential therapeutic target in cancer and inflammation. Here, we introduce a lattice-based mesoscale model for the biomimetic system studied recently in fluorescence microscopy experiments where GFP-tagged CD47 proteins on giant plasma membrane vesicles bind to SIRPα proteins immobilized on a surface. Computer simulations of the lattice-based mesoscale model allow us to study the biomimetic system on multiple length scales, ranging from single nanometers to several micrometers and simultaneously keep track of single CD47-SIRPα binding and unbinding events. Our simulations not only reproduce data from the fluorescence microscopy experiments but also are consistent with results of several other experiments, which validates our numerical approach. In addition, our simulations yield quantitative predictions on the magnitude and range of effective, membrane-mediated attraction between CD47-SIRPα complexes. Such detailed information on CD47-SIRPα interactions cannot be obtained currently from experiments alone. Our simulation results thus extend the present understanding of cooperative effects in CD47-SIRPα interactions and may have an influence on the advancement of new cancer treatments.

Receptor-Ligand Binding: Effect of Mechanical Factors

Gaining insight into the in situ receptor-ligand binding is pivotal for revealing the molecular mechanisms underlying the physiological and pathological processes and will contribute to drug discovery and biomedical application. An important issue involved is how the receptor-ligand binding responds to mechanical stimuli. This review aims to provide an overview of the current understanding of the effect of several representative mechanical factors, such as tension, shear stress, stretch, compression, and substrate stiffness on receptor-ligand binding, wherein the biomedical implications are focused. In addition, we highlight the importance of synergistic development of experimental and computational methods for fully understanding the in situ receptor-ligand binding, and further studies should focus on the coupling effects of these mechanical factors.

Dependence of protein-induced lipid bilayer deformations on protein shape

Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. While analytic solutions of protein-induced elastic bilayer deformations are most easily developed for proteins with approximately circular cross sections, structural biology has shown that membrane proteins come in a variety of distinct shapes, with often considerable deviations from a circular cross section. We develop here a boundary value method (BVM) that permits the construction of analytic solutions of protein-induced elastic bilayer deformations for protein shapes with arbitrarily large deviations from a circular cross section, for constant as well as variable boundary conditions along the bilayer-protein interface. We apply this BVM to protein-induced lipid bilayer thickness deformations. Our BVM reproduces available analytic solutions for proteins with circular cross section and yields, for proteins with noncircular cross section, excellent agreement with numerical, finite element solutions. On this basis, we formulate a simple analytic approximation of the bilayer thickness deformation energy associated with general protein shapes and show that, for modest deviations from rotational symmetry, this analytic approximation is in good agreement with BVM solutions. Using the BVM, we survey the dependence of protein-induced elastic bilayer thickness deformations on protein shape, and thus explore how the coupling of protein shape and bilayer thickness deformations affects protein oligomerization and transitions in protein conformational state.

Intercellular Receptor-ligand Binding: Effect of Protein-membrane Interaction

Gaining insights into the intercellular receptor-ligand binding is of great importance for understanding numerous physiological and pathological processes, and stimulating new strategies in drug design and discovery. In contrast to the in vitro protein interaction in solution, the anchored receptor and ligand molecules interact with membrane in situ, which affects the intercellular receptor-ligand binding. Here, we review theoretical, simulation and experimental works regarding the regulatory effects of protein-membrane interactions on intercellular receptor-ligand binding mainly from the following aspects: membrane fluctuations, membrane curvature, glycocalyx, and lipid raft. In addition, we discuss biomedical significances and possible research directions to advance the field and highlight the importance of understanding of coupling effects of these factors in pharmaceutical development.

Interplay of receptor-ligand binding and lipid domain formation during cell adhesion

Cell adhesion involved in biological processes such as cell migration, immune responses, and cancer metastasis, is mediated by the specific binding of receptor and ligand proteins. Some of these proteins exhibit affinity for nanoscale lipid clusters in cell membranes. A key question is how these nanoscale lipid clusters influence and react to the receptor-ligand binding during cell adhesion. In this article, we review recent computational studies that shed new light on the interplay of the receptor-ligand binding and the formation of lipid domains in adhering membranes. These studies indicate that the receptor-ligand binding promotes coalescence of lipid clusters into mesoscale domains, which, in turn, enhances both the affinity and cooperativity of the receptor-ligand binding in cell-cell adhesion with mobile ligands. In contrast, in the case of cell-extracellular matrix adhesion with immobile ligands, the receptor-ligand binding and the lipid cluster coalescence can be correlated or anti-correlated, depending strongly on the ligand distribution. These findings deepen our understanding of correlations between cell adhesion and membrane heterogeneities.

Membrane Remodeling Due to a Mixture of Multiple Types of Curvature Proteins

We present an extension of the Monte Carlo based mesoscopic membrane model, where the membrane is represented as a dynamically triangulated surface and the proteins are modeled as anisotropic inclusions formulated as in-plane nematic field variables adhering to the deformable elastic sheet. In the extended model, we have augmented the Hamiltonian to study membrane deformation due to a mixture of multiple types of curvature generating proteins. This feature opens the door for understanding how multiple kinds of curvature-generating proteins may be working in a coordinated manner to induce desired membrane morphologies. For example, among other things, we study membrane deformations and tubulation due to a mixture of positive and negative curvature proteins as mimics of various proteins from BAR domain family. We also study the effect of membrane anisotropy that manifests as differential binding affinity and organization of curvature proteins, leading to insights into the tightly regulated cargo sorting and transport processes. Our simulation results show different morphology of deformed vesicles that depend on membrane tension, the curvatures and number of the participating proteins as well as on protein-protein and membrane-protein interactions.

Insights into intercellular receptor-ligand binding kinetics in cell communication

Cell-cell communication is crucial for cells to sense, respond and adapt to environmental cues and stimuli. The intercellular communication process, which involves multiple length scales, is mediated by the specific binding of membrane-anchored receptors and ligands. Gaining insight into two-dimensional receptor-ligand binding kinetics is of great significance for understanding numerous physiological and pathological processes, and stimulating new strategies in drug design and discovery. To this end, extensive studies have been performed to illuminate the underlying mechanisms that control intercellular receptor-ligand binding kinetics via experiment, theoretical analysis and numerical simulation. It has been well established that the cellular microenvironment where the receptor-ligand interaction occurs plays a vital role. In this review, we focus on the advances regarding the regulatory effects of three factors including 1) protein-membrane interaction, 2) biomechanical force, and 3) bioelectric microenvironment to summarize the relevant experimental observations, underlying mechanisms, as well as their biomedical significances and applications. Meanwhile, we introduce modeling methods together with experiment technologies developed for dealing with issues at different scales. We also outline future directions to advance the field and highlight that building up systematic understandings for the coupling effects of these regulatory factors can greatly help pharmaceutical development.

Investigating the entropic nature of membrane-mediated interactions driving the aggregation of peripheral proteins

Peripheral membrane-associated proteins are known to accumulate on the surface of biomembranes as a result of membrane-mediated interactions. For a pair of rotationally-symmetric curvature-inducing proteins, membrane mechanics at the low-temperature limit predicts pure repulsion. On the other hand, temperature-dependent entropic forces arise between pairs of stiff-binding proteins suppressing membrane fluctuations. These Casimir-like interactions have thus been suggested as candidates for attractive forces leading to aggregation. With dense assemblies of peripheral proteins on the membrane, both these abstractions encounter short-range and multi-body complications. Here, we make use of a particle-based membrane model augmented with flexible peripheral proteins to quantify purely membrane-mediated interactions and investigate their underlying nature. We introduce a continuous reaction coordinate corresponding to the progression of protein aggregation. We obtain free energy and entropy landscapes for different surface concentrations along this reaction coordinate. In parallel, we investigate time-dependent estimates of membrane entropy corresponding to membrane undulations and coarse-grained director field and how they change dynamically with protein aggregation. Congruent outcomes of the two approaches point to the conclusion that for low surface concentrations, interactions with an entropic nature may drive the aggregation. But at high concentrations, enthalpic contributions due to concerted membrane deformation by protein clusters are dominant.

Membrane-Mediated Interactions Between Protein Inclusions

Integral or peripheral membrane proteins, or protein oligomers often get close to each other on cell membranes and carry out biological tasks in a collective manner. In addition to electrostatic and van der Waals interactions, those proteins also experience membrane-mediated interactions, which may be necessary for their functionality. The membrane-mediated interactions originate from perturbation of lipid membranes by the presence of protein inclusions, and have been the subject of intensive research in membrane biophysics. Here we review both theoretical and numerical studies of such interactions for membrane proteins and for nanoparticles bound to lipid membranes.

Stepwise membrane binding of extended synaptotagmins revealed by optical tweezers

Extended synaptotagmins (E-Syts) mediate lipid exchange between the endoplasmic reticulum (ER) and the plasma membrane (PM). Anchored on the ER, E-Syts bind the PM via an array of C2 domains in a Ca²⁺- and lipid-dependent manner, drawing the two membranes close to facilitate lipid exchange. How these C2 domains bind the PM and regulate the ER-PM distance is not well understood. Here, we applied optical tweezers to dissect PM binding by E-Syt1 and E-Syt2. We detected Ca²⁺- and lipid-dependent membrane-binding kinetics of both E-Syts and determined the binding energies and rates of individual C2 domains or pairs. We incorporated these parameters in a theoretical model to recapitulate salient features of E-Syt-mediated membrane contacts observed in vivo, including their equilibrium distances and probabilities. Our methods can be applied to study other proteins containing multiple membrane-binding domains linked by disordered polypeptides.

Curvature-Mediated Pair Interactions of Soft Nanoparticles Adhered to a Cell Membrane

The curvature-mediated interactions by cell membranes are crucial in many biological processes. We systematically studied the curvature-mediated wrapping of soft nanoparticles (NPs) by a tensionless membrane and the underlying pair interactions between NPs in determining it. We found that there are three types of wrapping pathways, namely, independence, cooperation, and tubulation. The particle size, adhesion strength, and softness are found to be strongly related with the wrapping mechanism. Reducing the adhesion strength transforms the wrapping pathway from cooperation to independence, while enhancing the NP softness requires a stronger adhesion to achieve the cooperative wrapping. This transformation of the wrapping pathway is controlled by the curvature-mediated interactions between NPs. For either soft or rigid NPs, the pair interactions are repulsive at short-ranged distances between NPs, while at long-ranged distances, a larger adhesion between NPs and a membrane is needed to generate attraction between NPs. Moreover, an enhancement of NP softness weakens the repulsion between NPs. These distinct behaviors of soft NPs are ascribed to the gentler deformation of the membrane at the face-to-face region between NPs due to the flattening and spreading of soft NPs along the membrane, requiring a reduced energy cost for soft NPs to approach each other. Our results provide a mechanistic understanding in detail about the membrane-mediated interactions between NPs and their interactions with cell membranes, which is helpful to understand the curvature-mediated assemblies of adhesive proteins or NPs on membranes, and offer novel possibilities for designing an effective NP-based vehicle for controlled drug delivery.

Thermodynamics and Kinetics of Aggregation of Flexible Peripheral Membrane Proteins

Biomembrane remodeling is essential for cellular trafficking, with membrane-binding peripheral proteins playing a key role in it. Significant membrane remodeling as in endo- and exocytosis is often due to aggregates of many proteins with direct or membrane-mediated interactions. Understanding this process via computer simulations is extremely challenging: protein-membrane systems involve time and length scales that make atomistic simulations impractical, while most coarse-grained models fall short in resolving dynamics and physical effects of protein and membrane flexibility. Here, we develop a coarse-grained model of the bilayer membrane bestrewed with rotationally symmetric flexible proteins, parametrized to reflect local curvatures and lateral dynamics of proteins. We investigate the kinetics, equilibrium distributions, and the free energy landscape governing the formation and breakup of protein clusters on the surface of the membrane. We demonstrate how the flexibility of the proteins as well as their surface concentration play deciding roles in highly selective macroscopic aggregation behavior.

Cooperative Stabilization of Close-Contact Zones Leads to Sensitivity and Selectivity in T-Cell Recognition

T cells are sensitive to 1 to 10 foreign-peptide-MHC complexes among a vast majority of self-peptide-MHC complexes, and discriminate selectively between peptide-MHC complexes that differ not much in their binding affinity to T-cell receptors (TCRs). Quantitative models that aim to explain this sensitivity and selectivity largely focus on single TCR/peptide-MHC complexes, but T cell adhesion involves a multitude of different complexes. In this article, we demonstrate in a three-dimensional computational model of T-cell adhesion that the cooperative stabilization of close-contact zones is sensitive to one to three foreign-peptide-MHC complexes and occurs at a rather sharp threshold affinity of these complexes, which implies selectivity. In these close-contact zones with lateral extensions of hundred to several hundred nanometers, few TCR/foreign-peptide-MHC complexes and many TCR/self-peptide-MHC complexes are segregated from LFA-1/ICAM-1 complexes that form at larger membrane separations. Previous high-resolution microscopy experiments indicate that the sensitivity and selectivity in the formation of closed-contact zones reported here are relevant for T-cell recognition, because the stabilization of close-contact zones by foreign, agonist peptide-MHC complexes precedes T-cell signaling and activation in the experiments.

Interactions between Phase-Separated Liquids and Membrane Surfaces

Liquid-liquid phase separation has recently emerged as an important fundamental organizational phenomenon in biological settings. Most studies of biological phase separation have focused on droplets that "condense" from solution above a critical concentration, forming so-called "membraneless organelles" suspended in solution. However, membranes are ubiquitous throughout cells, and many biomolecular condensates interact with membrane surfaces. Such membrane-associated phase-separated systems range from clusters of integral or peripheral membrane proteins in the plane of the membrane to free, spherical droplets wetting membrane surfaces to droplets containing small lipid vesicles. In this review, we consider phase-separated liquids that interact with membrane surfaces and we discuss the consequences of those interactions. The physical properties of distinct liquid phases in contact with bilayers can reshape the membrane, and liquid-liquid phase separation can construct membrane-associated protein structures, modulate their function, and organize collections of lipid vesicles dynamically. We summarize the common phenomena that arise in these systems of liquid phases and membranes.

Membrane morphologies induced by mixtures of arc-shaped particles with opposite curvature

Biological membranes are shaped by various proteins that either generate inward or outward membrane curvature. In this article, we investigate the membrane morphologies induced by mixtures of arc-shaped particles with coarse-grained modeling and simulations. The particles bind to the membranes either with their inward, concave side or their outward, convex side and, thus, generate membrane curvature of opposite sign. We find that small fractions of convex-binding particles can stabilize three-way junctions of membrane tubules, as suggested for the protein lunapark in the endoplasmic reticulum of cells. For comparable fractions of concave-binding and convex-binding particles, we observe lines of particles of the same type, and diverse membrane morphologies with grooves and bulges induced by these particle lines. The alignment and segregation of the particles is driven by indirect, membrane-mediated interactions.

Effect of protein steric constraints on the symmetry of membrane protein polyhedra

Experiments have shown that, in an aqueous environment, lipids and membrane proteins can self-assemble into membrane protein polyhedral nanoparticles (MPPNs). MPPNs are closed, spherical vesicles composed of a lipid bilayer membrane and membrane proteins, with a polyhedral arrangement of membrane proteins. The observed symmetry and size of MPPNs can be understood from the interplay of protein-induced lipid bilayer deformations in MPPNs, topological defects in protein packing necessitated by the spherical shape of MPPNs, and thermal fluctuations in MPPN self-assembly. We explore here the effect of protein steric constraints on MPPN shape. The protein steric constraints considered here may arise from a well-defined shape of protein domains outside the membrane, entropic repulsion between membrane proteins with flexible domains outside the membrane, or binding of other molecules to membrane proteins. Calculating MPPN self-assembly diagrams under protein steric constraints we find that protein steric constraints can strongly affect MPPN self-assembly. Depending on the specific scenario considered, protein steric constraints can leave large portions of the MPPN self-assembly diagrams with no clearly defined MPPN symmetry or substantially expand the regions of MPPN self-assembly diagrams dominated by highly symmetric MPPN states, such as MPPNs with icosahedral or snub cube symmetry. Our results suggest that modification of protein steric constraints may allow the directed self-assembly of MPPNs with specified symmetry, size, and protein composition and may thus facilitate the further utilization of MPPNs for membrane protein structural analysis or targeted drug delivery.

Weak carbohydrate-carbohydrate interactions in membrane adhesion are fuzzy and generic

Carbohydrates such as the trisaccharide motif LeX are key constituents of cell surfaces. Despite intense research, the interactions between carbohydrates of apposing cells or membranes are not well understood. In this article, we investigate carbohydrate-carbohydrate interactions in membrane adhesion as well as in solution with extensive atomistic molecular dynamics simulations that exceed the simulation times of previous studies by orders of magnitude. For LeX, we obtain association constants of soluble carbohydrates, adhesion energies of lipid-anchored carbohydrates, and maximally sustained forces of carbohydrate complexes in membrane adhesion that are in good agreement with experimental results in the literature. Our simulations thus appear to provide a realistic, detailed picture of LeX-LeX interactions in solution and during membrane adhesion. In this picture, the LeX-LeX interactions are fuzzy, i.e. LeX pairs interact in a large variety of short-lived, bound conformations. For the synthetic tetrasaccharide Lac 2, which is composed of two lactose units, we observe similarly fuzzy interactions and obtain association constants of both soluble and lipid-anchored variants that are comparable to the corresponding association constants of LeX. The fuzzy, weak carbohydrate-carbohydrate interactions quantified in our simulations thus appear to be a generic feature of small, neutral carbohydrates such as LeX and Lac 2.

Curvature-mediated cooperative wrapping of multiple nanoparticles at the same and opposite membrane sides

Cell membrane interactions with nanoparticles (NPs) are essential to cellular functioning and mostly accompanied by membrane curvature generation and sensing. Multiple NPs inducing curvature from one side of a membrane are believed to be wrapped cooperatively by the membrane through curvature-mediated interactions. However, little is known about another biologically ubiquitous and important case, i.e., NPs binding to opposite membrane sides induce a curved bend of different directions. Combining coarse-grained molecular dynamics and theoretical analysis, here we systematically investigate the cooperative effect in the wrapping of multiple adhesive NPs at the same and opposite membrane sides and demonstrate the importance of the magnitude and direction of the membrane bend in regulating curvature-mediated NP interactions. Effects of the NP size, size difference, initial distance, number, and strength of adhesion with the membrane on the wrapping cooperativity and wrapping states are analyzed. For NPs binding to the same membrane side, rich membrane wrapping and NP aggregation states are observed, and the curvature-mediated interactions could be either attractive or repulsive, depending on the initial NP distance and the competition between the membrane bending, NP binding and membrane protrusion. In sharp contrast, the interaction between two NPs binding to opposite membrane sides is always attractive and the cooperative wrapping of NPs is promoted, as the curved membrane regions induced by the NPs are shared in a manner that the NP-membrane contact is increased and the energy cost of membrane bending is reduced. Owing to the ubiquity and heterogeneity of membrane shaping proteins in biology, our results enrich the cutting-edge knowledge on the curvature-mediated interaction of NPs for better and profound understanding on high-order cooperative assemblies of NPs or proteins in numerous biological processes.

Protein Recruitment through Indirect Mechanochemical Interactions

Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation and is strongly affected by membrane composition.

Shiga Toxin Induces Lipid Compression: A Mechanism for Generating Membrane Curvature

Biomembranes are hard to compress laterally, and membrane area compressibility has not been associated with biological processes. Using X-ray surface scattering, we observed that bacterial Shiga toxin compresses lipid packing in a gel phase monolayer upon binding to its cellular receptor, the glycolipid Gb3. This toxin-induced reorganization of lipid packing reached beyond the immediate membrane patch that the protein was bound to, and linkers separating the Gb3 carbohydrate and ceramide moieties modulated the toxin's capacity to compress the membrane. Within a natural membrane, asymmetric compression of the toxin-bound leaflet could provide a mechanism to initiate narrow membrane bending, as observed upon toxin entry into cells. Such lipid compression and long-range membrane reorganization by glycolipid-binding proteins represent novel concepts in membrane biology that have direct implications for the construction of endocytic pits in clathrin-independent endocytosis.

Vesicle constriction by rings of Janus nanoparticles and aggregates of curved proteins

Membrane constriction and associated scission by proteins and nano structures are crucial to many processes in cellular and synthetic biology. We report mechanical constriction of vesicles by rings of adsorbed Janus nanoparticles that represent synthetic nano structures and mimic contractile proteins, and by aggregates of curved crescents that mimic scaffold proteins. Membrane energetics from Monte Carlo simulations and simulated annealing of the elastic membrane model confirms spontaneous vesicle constriction by aggregates of sufficiently-curved crescents of various lengths and by rings of Janus nanoparticles with a variety of ring lengths, particle sizes, and particle area fractions. We show that shorter rings of smaller particles with higher area fractions reinforce the constriction by increasing the energetic drive towards the constricted vesicle with smaller constriction radius. We demonstrate that vesicle constriction by crescent aggregates strongly depends on the crescent curvature. In contrast to aggregates of sufficiently-curved crescents that are capable of inducing full vesicle constriction, those of near flat crescents with negligible curvature leave the vesicle unconstricted. Our results offer promising perspectives for designing membrane-constricting nano structures such as nanoparticle aggregates and clusters of synthetic curved proteins such as DNA origami scaffolds with applications in synthetic biology. Our findings reveal the significant contribution of highly-curved F-BAR domains to cell division and explain how contractile protein rings such as dynamin GTPase, actomyosin rings, and endosomal sorting complexes required for transport constrict the membrane.

The interactions of an Aβ protofibril with a cholesterol-enriched membrane and involvement of neuroprotective carbazolium-based substances

Recent studies have shown that the aggregation of the amyloid-beta peptide (Aβ) in the brain cell membrane is responsible for the emergence of Alzheimer's disease (AD); the exploration of effective factors involved in the extension of the aggregation process and alternatively the examination of an effective inhibitor via theoretical and experimental tools are among the main research topics in the field of AD treatment. Therefore, in this study, we used all-atom molecular dynamics (MD) simulations to clarify the impact of cell membrane cholesterol on the interaction of Aβ with 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) as a membrane model. Moreover, the effect of the P7C3-S243 molecule on the abovementioned process was investigated. The simulation results disclosed the neuroprotective property of the P7C3-S243 molecule. The MD simulation results indicate that the interaction of cholesterol molecules with the Aβ oligomer is negligible and cannot enhance membrane rupture. However, strong hydrogen bonding between the POPC molecules and the oligomers led to membrane perturbation. According to our modellings, the P7C3-S243 molecular layer can protect the cell membrane by inhibiting the direct interaction between the bilayer and Aβ. In addition, free-energy calculations were conducted to determine the possible penetration of Aβ fibrils into the cholesterol-enriched membrane.

Supramolecular organization of membrane proteins with anisotropic hydrophobic thickness

Experiments have revealed that membrane proteins often self-assemble into locally ordered clusters. Such membrane protein lattices can play key roles in the functional organization of cell membranes. Membrane protein organization can be driven, at least in part, by bilayer-mediated elastic interactions between membrane proteins. For membrane proteins with anisotropic hydrophobic thickness, bilayer-mediated protein interactions are inherently directional. Here we establish general relations between anisotropy in membrane protein hydrophobic thickness and supramolecular membrane protein organization. We show that protein symmetry is distinctively reflected in the energy landscape of bilayer-mediated protein interactions, favoring characteristic lattice architectures of membrane protein clusters. We find that, in the presence of thermal fluctuations, anisotropy in protein hydrophobic thickness can induce membrane proteins to form mesh-like structures dividing the membrane into compartments. Our results help to elucidate the physical principles and mechanisms underlying the functional organization of cell membranes.

Membrane Morphologies Induced by Arc-Shaped Scaffolds Are Determined by Arc Angle and Coverage

The intricate shapes of biological membranes such as tubules and membrane stacks are induced by proteins. In this article, we systematically investigate the membrane shapes induced by arc-shaped scaffolds such as proteins and protein complexes with coarse-grained modeling and simulations. We find that arc-shaped scaffolds induce membrane tubules at membrane coverages larger than a threshold of ∼40%, irrespective of their arc angle. The membrane morphologies at intermediate coverages below this tubulation threshold, in contrast, strongly depend on the arc angle. Scaffolds with arc angles of about 60°, akin to N-BAR domains, do not change the membrane shape at coverages below the tubulation threshold, whereas scaffolds with arc angles larger than about 120° induce double-membrane stacks at intermediate coverages. The scaffolds stabilize the curved membrane edges that connect the membrane stacks, as suggested for complexes of reticulon proteins. Our results provide general insights on the determinants of membrane shaping by arc-shaped scaffolds.

Formation of α-helical and β-sheet structures in membrane-bound human IAPP monomer and the resulting membrane deformation

Upon adsorption on membrane, human IAPP monomer takes conformational changes from coils to α-helices and β-sheets. The helices inserted and β on surface cause different types of membrane deformation, implying two distinct aggregation mechanisms.

Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.