Transition from curvature sensing to generation in a vesicle driven by protein binding strength and membrane tension

OrganL: Dynamic triangulation of biomembranes using curved elements

We describe a method for simulating biomembranes of arbitrary shape. In contrast to other dynamically triangulated surface (DTS) algorithms, our method provides a rich, quasi-tangent-continuous, yet local description of the surface. We use curved Nagata triangles, which we generalize to cubic order to achieve the requisite flexibility. The resulting interpolation can be constructed locally without iterations, at the cost of having only approximate tangent continuity away from the vertices. This allows us to provide a parallelized and fine-tuned Monte Carlo implementation. As a first example of the potential benefits of the enhanced description, our method supports inhomogeneous lipid distributions as well as lipid mixing. It also supports restraints and constraints of various types and is constructed to be as easily extensible as possible. We validate the approach by testing its numerical accuracy, followed by reproducing the known Helfrich solutions for shapes with rotational symmetry. Finally, we present some example applications, including curvature-driven demixing and stylized effects of proteins. Input files for these examples, as well as the implementation itself, are freely available for researchers under the name OrganL (https://zenodo.org/doi/10.5281/zenodo.11204709).

Membrane curvature as a signal to ensure robustness of diverse cellular processes

An increasing corpus of research has demonstrated that membrane shape, generated either by the external environment of the cell or by intrinsic mechanisms such as cytokinesis and vesicle or organelle formation, is an important parameter in the control of diverse cellular processes. In this review we discuss recent findings that demonstrate how membrane curvature (from nanometer to micron length-scales) alters protein function. We describe an expanding toolkit for experimentally modulating membrane curvature to reveal effects on protein function, and discuss how membrane curvature - far from being a passive consequence of the physical environment and the internal protein activity of a cell - is an important signal that controls protein affinity and enzymatic activity to ensure robust forward progression of key processes within the cell.

Insights into Membrane Curvature Sensing and Membrane Remodeling by Intrinsically Disordered Proteins and Protein Regions

Cellular membranes are highly dynamic in shape. They can rapidly and precisely regulate their shape to perform various cellular functions. The protein’s ability to sense membrane curvature is essential in various biological events such as cell signaling and membrane trafficking. As they are bound, these curvature-sensing proteins may also change the local membrane shape by one or more curvature driving mechanisms. Established curvature-sensing/driving mechanisms rely on proteins with specific structural features such as amphipathic helices and intrinsically curved shapes. However, the recent discovery and characterization of many proteins have shattered the protein structure–function paradigm, believing that the protein functions require a unique structural feature. Typically, such structure-independent functions are carried either entirely by intrinsically disordered proteins or hybrid proteins containing disordered regions and structured domains. It is becoming more apparent that disordered proteins and regions can be potent sensors/inducers of membrane curvatures. In this article, we outline the basic features of disordered proteins and regions, the motifs in such proteins that encode the function, membrane remodeling by disordered proteins and regions, and assays that may be employed to investigate curvature sensing and generation by ordered/disordered proteins.

Vesicle budding induced by binding of curvature-inducing proteins

Vesicle budding induced by protein binding that generates an isotropic spontaneous curvature is studied using a mean-field theory. Many spherical buds are formed via protein binding. As the binding chemical potential increases, the proteins first bind to the buds and then to the remainder of the vesicle. For a high spontaneous curvature and/or high bending rigidity of the bound membrane, it is found that a first-order transition occurs between a small number of large buds and a large number of small buds. These two states coexist around the transition point. The proposed scheme is simple and easily applicable to many interaction types, so we investigate the effects of interprotein interactions, the protein-insertion-induced changes in area, the variation of the saddle-splay modulus, and the area-difference-elasticity energy. The differences in the preferred curvatures for curvature sensing and generation are also clarified.

Recent developments in membrane curvature sensing and induction by proteins

BACKGROUND

Membrane-bound intracellular organelles have characteristic shapes attributed to different local membrane curvatures, and these attributes are conserved across species. Over the past decade, it has been confirmed that specific proteins control the large curvatures of the membrane, whereas many others due to their specific structural features can sense the curvatures and bind to the specific geometrical cues. Elucidating the interplay between sensing and induction is indispensable to understand the mechanisms behind various biological processes such as vesicular trafficking and budding.

SCOPE OF REVIEW

We provide an overview of major classes of membrane proteins and the mechanisms of curvature sensing and induction. We then discuss the importance of membrane elastic characteristics to induce the membrane shapes similar to intracellular organelles. Finally, we survey recently available assays developed for studying the curvature sensing and induction by many proteins.

MAJOR CONCLUSIONS

Recent theoretical/computational modeling along with experimental studies have uncovered fascinating connections between lipid membrane and protein interactions. However, the phenomena of protein localization and synchronization to generate spatiotemporal dynamics in membrane morphology are yet to be fully understood.

GENERAL SIGNIFICANCE

The understanding of protein-membrane interactions is essential to shed light on various biological processes. This further enables the technological applications of many natural proteins/peptides in therapeutic treatments. The studies of membrane dynamic shapes help to understand the fundamental functions of membranes, while the medicinal roles of various macromolecules (such as proteins, peptides, etc.) are being increasingly investigated.

Binding of thermalized and active membrane curvature-inducing proteins

The phase behavior of a membrane induced by the binding of curvature-inducing proteins is studied by a combination of analytical and numerical approaches. In thermal equilibrium under the detailed balance between binding and unbinding, the membrane exhibits three phases: an unbound uniform flat phase (U), a bound uniform flat phase (B), and a separated/corrugated phase (SC). In the SC phase, the bound proteins form hexagonally-ordered bowl-shaped domains. The transitions between the U and SC phases and between the B and SC phases are second order and first order, respectively. At a small spontaneous curvature of the protein or high surface tension, the transition between B and SC phases becomes continuous. Moreover, a first-order transition between the U and B phases is found at zero spontaneous curvature driven by the Casimir-like interactions between rigid proteins. Furthermore, nonequilibrium dynamics is investigated by the addition of active binding and unbinding at a constant rate. The active binding and unbinding processes alter the stability of the SC phase.

Temperature- and Composition-Induced Multiarchitectural Transitions in the Catanionic System of a Conventional Surfactant and a Surface-Active Ionic Liquid

The mixture of the cationic surfactant, cetyltrimethylammonium bromide (CTAB), and anionic surface-active ionic liquid, 1-butyl-3-methylimidazoliumdodecyl sulfate (bmimDS), has been studied as a function of the mole fraction of CTAB, X _CTAB, with the total surfactant concentration fixed at 50 mM using turbidity measurements, rheology, dynamic light scattering, differential scanning calorimetry, small-angle neutron scattering, and small-angle X-ray scattering techniques. The catanionic mixture has been found to exhibit phase transitions from vesicles to micelles as a function of temperature, with some mole fractions of CTAB showing dual transitions. Solutions of X _CTAB = 0.2 to 0.5 exhibited a single transition from vesicles to cylindrical micelles at 45 °C. With an increase in the mole fraction of CTAB from 0.55 to 0.65, dual structural transitions at 30 and 45 °C were observed. The microstructural transition at 30 °C is ascribed to the vesicle aggregation process with smaller vesicles fusing into bigger ones, whereas the transition at 45 °C was evaluated to be the vesicle-to-cylindrical micelle transition. However, at higher mole fractions of CTAB, X _CTAB from 0.65 to 0.90, a single transition from vesicles to small cylindrical/spherical micelles was observed in the solutions, at a lower temperature of 30 °C. To the best of our knowledge, such a microstructural transitions as a function of temperature in a single mixture of cationic and anionic surfactants without any additive has not been reported so far.

Binding, unbinding and aggregation of crescent-shaped nanoparticles on nanoscale tubular membranes

Using molecular dynamics simulations of a coarse-grained implicit solvent model, we investigate the binding of crescent-shaped nanoparticles (NPs) on tubular lipid membranes. The NPs adhere to the membrane through their concave side. We found that the binding/unbinding transition is first-order, with the threshold binding energy being higher than the unbinding threshold, and the energy barrier between the bound and unbound states at the transition that increases with increasing the NP's arclength L_np or curvature mismatch μ = R_c/R_np, where R_c and R_np are the radii of curvature of the tubular membrane and the NP, respectively. Furthermore, we found that the threshold binding energy increases with increasing either L_np or μ. NPs with curvature larger than that of the tubule (μ > 1) lie perpendicularly to the tubule's axis. However, for μ smaller than a specific arclength-dependent mismatch μ*, the NPs are tilted with respect to the tubule's axis, with the tilt angle that increases with decreasing μ. We also investigated the self-assembly of the NPs on the tubule at relatively weak adhesion strength and found that for μ > 1 and high values of L_np, the NPs self-assemble into linear chains, and lie side-by-side. For μ < μ* and high L_np, the NPs also self-assemble into chains, while being tilted with respect to the tubule's axis.

Diffuso-kinetic membrane budding dynamics

A wide range of proteins are known to create shape transformations of biological membranes, where the remodelling is a coupling between the energetic costs from deforming the membrane, the recruitment of proteins that induce a local spontaneous curvature C₀ and the diffusion of proteins along the membrane. We propose a minimal mathematical model that accounts for these processes to describe the diffuso-kinetic dynamics of membrane budding processes. By deploying numerical simulations we map out the membrane shapes, the time for vesicle formation and the vesicle size as a function of the dimensionless kinetic recruitment parameter K₁ and the proteins sensitivity to mean curvature. We derive a time for scission that follows a power law ∼K₁^-2/3, a consequence of the interplay between the spreading of proteins by diffusion and the kinetic-limited increase of the protein density on the membrane. We also find a scaling law for the vesicle size ∼1/([small sigma, Greek, macron]_avC₀), with [small sigma, Greek, macron]_av the average protein density in the vesicle, which is confirmed in the numerical simulations. Rescaling all the membrane profiles at the time of vesicle formation highlights that the membrane adopts a self-similar shape.

A Novel Aβ40 Assembly at Physiological Concentration

Aggregates of amyloid-β (Aβ) are characteristic of Alzheimer's disease, but there is no consensus as to either the nature of the toxic molecular complex or the mechanism by which toxic aggregates are produced. We report on a novel feature of amyloid-lipid interactions where discontinuities in the lipid continuum can serve as catalytic centers for a previously unseen microscale aggregation phenomenon. We show that specific lipid membrane conditions rapidly produce long contours of lipid-bound peptide, even at sub-physiological concentrations of Aβ. Using single molecule fluorescence, time-lapse TIRF microscopy and AFM imaging we characterize this phenomenon and identify some exceptional properties of the aggregation pathway which make it a likely contributor to early oligomer and fibril formation, and thus a potential critical mechanism in the etiology of AD. We infer that these amyloidogenic events occur only at areas of high membrane curvature, which suggests a range of possible mechanisms by which accumulated physiological changes may lead to their inception. The speed of the formation is in hours to days, even at 1 nM peptide concentrations. Lipid features of this type may act like an assembly line for monomeric and small oligomeric subunits of Aβ to increase their aggregation states. We conclude that under lipid environmental conditions, where catalytic centers of the observed type are common, key pathological features of AD may arise on a very short timescale under physiological concentration.

Fluctuations and conformational stability of a membrane patch with curvature inducing inclusions

Membranes with curvature inducing inclusions display a range of cooperative phenomena, which can be linked to biomembrane function, e.g. membrane tubulation, vesiculation, softening and spontaneous tension. We investigate how these phenomena are related for a fluctuating, framed membrane through analysis of a descretized membrane model by Monte Carlo simulation techniques. The membrane model is based on a dynamically triangulated surface equipped with non-interacting, up-down symmetry breaking inclusions where only terms coupled linearly to mean-curvature are maintained. We show that the lateral configurational entropy plays a key role for the mechanical properties of the semi-flexible membrane, e.g. a pronounced softening at intermediate inclusion coverages of the membrane and generation of membrane tension. Tensionless framed membranes will remain quasi-flat up to some threshold coverage, where a shape instability occurs with formation of pearling or tubular membranes, which below full coverage is associated with segregation of inclusions between the curved and flat membrane geometries. For inclusions with preference for highly curved membranes the instability appears at dilute inclusion coverages and is accompanied by strong configurational fluctuations.

Structured and intrinsically disordered domains within Amphiphysin1 work together to sense and drive membrane curvature

Cellular membranes undergo remodeling during many cellular processes including endocytosis, cytoskeletal protrusion, and organelle biogenesis. During these events, specialized proteins sense and amplify fluctuations in membrane curvature to create stably curved architectures. Amphiphysin1 is a multi-domain protein containing an N-terminal crescent-shaped BAR (Bin/Amphiphysin/Rvs) domain and a C-terminal domain that is largely disordered. When studied in isolation, the BAR domain of Amphiphysin1 senses membrane curvature and generates membrane tubules. However, the disordered domain has been largely overlooked in these studies. Interestingly, our recent work has demonstrated that the disordered domain is capable of substantially amplifying the membrane remodeling ability of the BAR domain. However, the physical mechanisms responsible for these effects are presently unclear. Here we elucidated the functional role of the disordered domain by gradually truncating it, creating a family of mutant proteins, each of which contained the BAR domain and a fraction of the disordered domain. Using quantitative fluorescence and electron microscopy, our results indicate that the disordered domain contributes to membrane remodeling by making it more difficult for the protein to bind to and assemble on flat membrane surfaces. Specifically, we found that the disordered domain began to significantly impact membrane remodeling when its projected area exceeded that of the BAR domain. Once this threshold was crossed, steric interactions with the membrane surface and with neighboring disordered domains gave rise to increased curvature sensing and membrane vesiculation, respectively. These findings provide insight into the synergy between structured and disordered domains, each of which play important biophysical roles in membrane remodeling.