Membrane-Protein Interactions Are Key to Understanding Amyloid Formation

Co-registration of MALDI-MSI and histology demonstrates gangliosides co-localize with amyloid beta plaques in Alzheimer's disease

Alzheimer's disease (AD) is a progressive neurological condition characterized by impaired cognitive function and behavioral alterations. While AD research historically centered around mis-folded proteins, advances in mass spectrometry techniques have triggered increased exploration of the AD lipidome with lipid dysregulation emerging as a critical player in AD pathogenesis. Gangliosides are a class of glycosphingolipids enriched within the central nervous system. Previous work has suggested a shift in a-series gangliosides from complex (GM1) to simple (GM2 and GM3) species may be related to the development of neurodegenerative disease. In addition, complex gangliosides with 20 carbon sphingosine chains have been shown to increase in the aging brain. In this study, we utilized matrix-assisted laser desorption ionization mass spectrometry imaging (MALDI-MSI) to interrogate the in situ relationship of a-series gangliosides with either 18 or 20 carbon sphingosine chains (d18:1 or d20:1, respectively) in the post-mortem human AD brain. Here, we expanded upon previous literature and demonstrated a significant decrease in the GM1 d20:1 to GM1 d18:1 ratio in regions of the dentate gyrus and entorhinal cortex in AD relative to control brain tissue. Then, we demonstrated that the MALDI-MSI profile of GM3 co-localizes with histologically confirmed amyloid beta (Aβ) plaques and found a significant increase in both GM1 and GM3 in proximity to Aβ plaques. Collectively, this study demonstrates a perturbation of the ganglioside profile in AD, and validates a pipeline for MALDI-MSI and classic histological staining in the same tissue sections. This demonstrates feasibility for integrating untargeted mass spectrometry imaging approaches into a digital pathology framework.

Cholesterol as a key player in amyloid β-mediated toxicity in Alzheimer’s disease

Alzheimer’s disease (AD) is a neurodegenerative disorder that is one of the most devastating and widespread diseases worldwide, mainly affecting the aging population. One of the key factors contributing to AD-related neurotoxicity is the production and aggregation of amyloid β (Aβ). Many studies have shown the ability of Aβ to bind to the cell membrane and disrupt its structure, leading to cell death. Because amyloid damage affects different parts of the brain differently, it seems likely that not only Aβ but also the nature of the membrane interface with which the amyloid interacts, helps determine the final neurotoxic effect. Because cholesterol is the dominant component of the plasma membrane, it plays an important role in Aβ-induced toxicity. Elevated cholesterol levels and their regulation by statins have been shown to be important factors influencing the progression of neurodegeneration. However, data from many studies have shown that cholesterol has both neuroprotective and aggravating effects in relation to the development of AD. In this review, we attempt to summarize recent findings on the role of cholesterol in Aβ toxicity mediated by membrane binding in the pathogenesis of AD and to consider it in the broader context of the lipid composition of cell membranes.

The role of membranes in function and dysfunction of intrinsically disordered amyloidogenic proteins

Membrane-protein interactions play a major role in human physiology as well as in diseases pathology. Interaction of a protein with the membrane was previously thought to be dependent on well-defined three-dimensional structure of the protein. In recent decades, however, it has become evident that a large fraction of the proteome, particularly in eukaryotes, stays disordered in solution and these proteins are termed as intrinsically disordered proteins (IDPs). Also, a vast majority of human proteomes have been reported to contain substantially long disordered regions, called intrinsically disordered regions (IDRs), in addition to the structurally ordered regions. IDPs exist in an ensemble of conformations and the conformational flexibility enables IDPs to achieve functional diversity. IDPs (and IDRs) are found to be important players in cell signaling, where biological membranes act as anchors for signaling cascades. Therefore, IDPs modulate the membrane architectures, at the same time membrane composition also affects the binding of IDPs. Because of intrinsic disorders, misfolding of IDPs often leads to formation of oligomers, protofibrils and mature fibrils through progressive self-association. Accumulation of amyloid-like aggregates of some of the IDPs is a known causative agent for numerous diseases. In this chapter we highlight recent advances in understanding membrane interactions of some of the intrinsically disordered proteins involved in the pathogenesis of human diseases.

Binding Mechanisms of Amyloid-like Peptides to Lipid Bilayers and Effects of Divalent Cations

In several neurodegenerative diseases, cell toxicity can emerge from damage produced by amyloid aggregates to lipid membranes. The details accounting for this damage are poorly understood including how individual amyloid peptides interact with phospholipid membranes before aggregation. Here, we use all-atom molecular dynamics simulations to investigate the molecular mechanisms accounting for amyloid-membrane interactions and the role played by calcium ions in this interaction. Model peptides known to self-assemble into amyloid fibrils and bilayer made from zwitterionic and anionic lipids are used in this study. We find that both electrostatic and hydrophobic interactions contribute to peptide-bilayer binding. In particular, the attraction of peptides to lipid bilayers is dominated by electrostatic interactions between positive residues and negative phosphate moieties of lipid head groups. This attraction is stronger for anionic bilayers than for zwitterionic ones. Hydrophobicity drives the burial of nonpolar residues into the interior of the bilayer producing strong binding in our simulations. Moreover, we observe that the attraction of peptides to the bilayer is significantly reduced in the presence of calcium ions. This is due to the binding of calcium ions to negative phosphate moieties of lipid head groups, which leaves phospholipid bilayers with a net positive charge. Strong binding of the peptide to the membrane occurs less frequently in the presence of calcium ions and involves the formation of a "Ca²⁺ bridge".

The interplay between lipid and Aβ amyloid homeostasis in Alzheimer's Disease: risk factors and therapeutic opportunities

Alzheimer's Diseases (AD) is characterized by the accumulation of amyloid deposits of Aβ peptide in the brain. Besides genetic background, the presence of other diseases and an unhealthy lifestyle are known risk factors for AD development. Albeit accumulating clinical evidence suggests that an impaired lipid metabolism is related to Aβ deposition, mechanistic insights on the link between amyloid fibril formation/clearance and aberrant lipid interactions are still unavailable. Recently, many studies have described the key role played by membrane bound Aβ assemblies in neurotoxicity. Moreover, it has been suggested that a derangement of the ubiquitin proteasome pathway and autophagy is significantly correlated with toxic Aβ aggregation and dysregulation of lipid levels. Thus, studies focusing on the role played by lipids in Aβ aggregation and proteostasis could represent a promising area of investigation for the design of valuable treatments. In this review we examine current knowledge concerning the effects of lipids in Aβ aggregation and degradation processes, focusing on the therapeutic opportunities that a comprehensive understanding of all biophysical, biochemical, and biological processes involved may disclose.

Computer simulations of protein-membrane systems

The interactions between proteins and membranes play critical roles in signal transduction, cell motility, and transport, and they are involved in many types of diseases. Molecular dynamics (MD) simulations have greatly contributed to our understanding of protein-membrane interactions, promoted by a dramatic development of MD-related software, increasingly accurate force fields, and available computer power. In this chapter, we present available methods for studying protein-membrane systems with MD simulations, including an overview about the various all-atom and coarse-grained force fields for lipids, and useful software for membrane simulation setup and analysis. A large set of case studies is discussed.

Lipids and Alzheimer's Disease

Lipids, as the basic component of cell membranes, play an important role in human health as well as brain function. The brain is highly enriched in lipids, and disruption of lipid homeostasis is related to neurologic disorders as well as neurodegenerative diseases such as Alzheimer’s disease (AD). Aging is associated with changes in lipid composition. Alterations of fatty acids at the level of lipid rafts and cerebral lipid peroxidation were found in the early stage of AD. Genetic and environmental factors such as apolipoprotein and lipid transporter carrying status and dietary lipid content are associated with AD. Insight into the connection between lipids and AD is crucial to unraveling the metabolic aspects of this puzzling disease. Recent advances in lipid analytical methodology have led us to gain an in-depth understanding on lipids. As a result, lipidomics have becoming a hot topic of investigation in AD, in order to find biomarkers for disease prediction, diagnosis, and prevention, with the ultimate goal of discovering novel therapeutics.

Acetylation of Aβ40 Alters Aggregation in the Presence and Absence of Lipid Membranes

A hallmark of Alzheimer's disease (AD) is the formation of senile plaques comprised of the β-amyloid (Aβ) peptide. Aβ fibrillization is a complex nucleation-dependent process involving a variety of metastable intermediate aggregates and features the formation of inter- and intramolecular salt bridges involving lysine residues, K16 and K28. Cationic lysine residues also mediate protein-lipid interactions via association with anionic lipid headgroups. As several toxic mechanisms attributed to Aβ involve membrane interactions, the impact of acetylation on Aβ₄₀ aggregation in the presence and absence of membranes was determined. Using chemical acetylation, varying mixtures of acetylated and nonacetylated Aβ₄₀ were produced. With increasing acetylation, fibril and oligomer formation decreased, eventually completely arresting fibrillization. In the presence of total brain lipid extract (TBLE) vesicles, acetylation reduced the interaction of Aβ₄₀ with membranes; however, fibrils still formed at near complete levels of acetylation. Additionally, the combination of TBLE and acetylated Aβ promoted annular aggregates. Finally, toxicity associated with Aβ₄₀ was reduced with increasing acetylation in a cell culture assay. These results suggest that in the absence of membranes that the cationic character of lysine plays a major role in fibril formation. However, acetylation promotes unique aggregation pathways in the presence of lipid membranes.

Folding and Misfolding of Human Membrane Proteins in Health and Disease: From Single Molecules to Cellular Proteostasis

Advances over the past 25 years have revealed much about how the structural properties of membranes and associated proteins are linked to the thermodynamics and kinetics of membrane protein (MP) folding. At the same time biochemical progress has outlined how cellular proteostasis networks mediate MP folding and manage misfolding in the cell. When combined with results from genomic sequencing, these studies have established paradigms for how MP folding and misfolding are linked to the molecular etiologies of a variety of diseases. This emerging framework has paved the way for the development of a new class of small molecule "pharmacological chaperones" that bind to and stabilize misfolded MP variants, some of which are now in clinical use. In this review, we comprehensively outline current perspectives on the folding and misfolding of integral MPs as well as the mechanisms of cellular MP quality control. Based on these perspectives, we highlight new opportunities for innovations that bridge our molecular understanding of the energetics of MP folding with the nuanced complexity of biological systems. Given the many linkages between MP misfolding and human disease, we also examine some of the exciting opportunities to leverage these advances to address emerging challenges in the development of therapeutics and precision medicine.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Conformational Change of Amyloid-β 40 in Association with Binding to GM1-Glycan Cluster

Aggregates of amyloid-β (Aβ) peptide are well known to be the causative substance of Alzheimer's disease (AD). Recent studies showed that monosialotetrahexosylganglioside (GM1) clusters induce the pathological aggregation of Aβ peptide responsible for the onset and development of AD. However, the effect of GM1-glycan cluster on Aβ conformations has yet to be clarified. Interactions between Aβ peptide and GM1-glycan cluster is important for the earliest stage of the toxic aggregation on GM1 cluster. Here, we performed all-atom molecular dynamics (MD) simulations of Aβ40 on a recently developed artificial GM1-glycan cluster. The artificial GM1-glycan cluster facilitates the characterization of interactions between Aβ40 and multiple GM1-glycans. We succeeded in observing the binding of Aβ40 to the GM1-glycan cluster in all of our MD simulations. Results obtained from these MD simulations indicate the importance of HHQ (13-15) segment of Aβ40 for the GM1-glycan cluster recognition. This result is consistent with previous experimental studies regarding the glycan recognition of Aβ peptide. The recognition mechanism of HHQ (13-15) segment is mainly explained by non-specific stacking interactions between side-chains of histidine and rings of sugar residues, in which the HHQ regime forms coil and bend structures. Moreover, we found that Aβ40 exhibits helix structures at C-terminal side on the GM1-glycan cluster. The helix formation is the initial stage of the pathological aggregation at ceramide moieties of GM1 cluster. The binding of Lys28 to Neu triggers the helix formation at C-terminus side because the formation of a salt bridge between Lys28 and Neu leads to change of intrachain interactions of Aβ40. Our findings suggest that the pathological helix formation of Aβ40 is initiated at GM1-glycan moieties rather than lipid ceramide moieties.

Direct observation of alpha-lactalbumin, adsorption and incorporation into lipid membrane and formation of lipid/protein hybrid structures

The interaction between proteins and membranes is of great interest in biomedical and biotechnological research for its implication in many functional and dysfunctional processes. We present an experimental study on the interaction between model membranes and alpha-lactalbumin (α-La). α-La is widely studied for both its biological function and its anti-tumoral properties. We use advanced fluorescence microscopy and spectroscopy techniques to characterize α-La-membrane mechanisms of interaction and α-La-induced modifications of membranes when insertion of partially disordered regions of protein chains in the lipid bilayer is favored. Moreover, using fluorescence lifetime imaging, we are able to distinguish between protein adsorption and insertion in the membranes. Our results indicate that, upon addition of α-La to giant vesicles samples, protein is inserted into the lipid bilayer with rates that are concentration-dependent. The formation of heterogeneous hybrid protein-lipid co-aggregates, paralleled with protein conformational and structural changes, alters the membrane structure and morphology, leading to an increase in membrane fluidity.

Interactions between amyloid β peptide and lipid membranes

The presence of amyloid plaques in the brain is a typical characteristic of Alzheimer's disease (AD). Amyloid plaques are formed from the deposits of aggregated amyloid β peptide (Aβ). The toxicity induced by Aβ aggregates is correlated with Aβ-membrane interactions. The mutual influences between aggregation and membranes are complicated and unclear. In recent years advanced experiments and findings are emerging to give us more detailed information on Aβ-membrane interactions. In this review, we mainly focus on the Aβ-membrane interactions and membrane-induced Aβ structures. The mechanism of Aβ-membrane interactions is also summarized, which provides insights into the prevention and treatment of AD.

Structural Modulation of Human Amylin Protofilaments by Naturally Occurring Mutations

Human islet amyloid polypeptide (hIAPP), also known as amylin, is a 37-amino-acid peptide, co-secreted with insulin, and widely found in fibril form in type-2 diabetes patients. By using all-atom molecular dynamics simulations, we study hIAPP fibril segments (i.e., fibrillar oligomers) formed with sequences of naturally occurring variants from cat, rat, and pig, presenting different aggregation propensities. We characterize the effect of mutations on the structural dynamics of solution-formed hIAPP fibril models built from solid-state NMR data. Results from this study are in agreement with experimental observations regarding their respective relative aggregation propensities. We analyze in detail the specific structural characteristics and infer mechanisms that modulate the conformational stability of amylin fibrils. Results provide a platform for further studies and the design of new drugs that could interfere with amylin aggregation and its cytotoxicity. One particular mutation, N31K, has fibril-destabilizing properties, and could potentially improve the solubility of therapeutic amylin analogs.

Alzheimer's Disease Risk Genes and Lipid Regulators

Brain lipid homeostasis plays an important role in Alzheimer's disease (AD) and other neurodegenerative disorders. Aggregation of amyloid-β peptide is one of the major events in AD. The complex interplay between lipids and amyloid-β accumulation has been intensively investigated. The proportions of lipid components including phospholipids, sphingolipids, and cholesterol are roughly similar across different brain regions under physiological conditions. However, disruption of brain lipid homeostasis has been described in AD and implicated in disease pathogenesis. Moreover, studies suggest that analysis of lipid composition in plasma and cerebrospinal fluid could improve our understanding of the disease development and progression, which could potentially serve as disease biomarkers and prognostic indicators for AD therapies. Here, we summarize the functional roles of AD risk genes and lipid regulators that modulate brain lipid homeostasis including different lipid species, lipid complexes, and lipid transporters, particularly their effects on amyloid processing, clearance, and aggregation, as well as neuro-toxicities that contribute to AD pathogenesis.

Tipping the Scale from Disorder to Alpha-helix: Folding of Amphiphilic Peptides in the Presence of Macroscopic and Molecular Interfaces

Secondary amphiphilicity is inherent to the secondary structural elements of proteins. By forming energetically favorable contacts with each other these amphiphilic building blocks give rise to the formation of a tertiary structure. Small proteins and peptides, on the other hand, are usually too short to form multiple structural elements and cannot stabilize them internally. Therefore, these molecules are often found to be structurally ambiguous up to the point of a large degree of intrinsic disorder in solution. Consequently, their conformational preference is particularly susceptible to environmental conditions such as pH, salts, or presence of interfaces. In this study we use molecular dynamics simulations to analyze the conformational behavior of two synthetic peptides, LKKLLKLLKKLLKL (LK) and EAALAEALAEALAE (EALA), with built-in secondary amphiphilicity upon forming an alpha-helix. We use these model peptides to systematically study their aggregation and the influence of macroscopic and molecular interfaces on their conformational preferences. We show that the peptides are neither random coils in bulk water nor fully formed alpha helices, but adopt multiple conformations and secondary structure elements with short lifetimes. These provide a basis for conformation-selection and population-shift upon environmental changes. Differences in these peptides' response to macroscopic and molecular interfaces (presented by an aggregation partner) can be linked to their inherent alpha-helical tendencies in bulk water. We find that the peptides' aggregation behavior is also strongly affected by presence or absence of an interface, and rather subtly depends on their surface charge and hydrophobicity.

Exploring the role of hydration and confinement in the aggregation of amyloidogenic peptides Aβ(16-22) and Sup35(7-13) in AOT reverse micelles

Knowledge of how intermolecular interactions of amyloid-forming proteins cause protein aggregation and how those interactions are affected by sequence and solution conditions is essential to our understanding of the onset of many degenerative diseases. Of particular interest is the aggregation of the amyloid-β (Aβ) peptide, linked to Alzheimer's disease, and the aggregation of the Sup35 yeast prion peptide, which resembles the mammalian prion protein linked to spongiform encephalopathies. To facilitate the study of these important peptides, experimentalists have identified small peptide congeners of the full-length proteins that exhibit amyloidogenic behavior, including the KLVFFAE sub-sequence, Aβ16-22, and the GNNQQNY subsequence, Sup357-13. In this study, molecular dynamics simulations were used to examine these peptide fragments encapsulated in reverse micelles (RMs) in order to identify the fundamental principles that govern how sequence and solution environment influence peptide aggregation. Aβ16-22 and Sup357-13 are observed to organize into anti-parallel and parallel β-sheet arrangements. Confinement in the sodium bis(2-ethylhexyl) sulfosuccinate (AOT) reverse micelles is shown to stabilize extended peptide conformations and enhance peptide aggregation. Substantial fluctuations in the reverse micelle shape are observed, in agreement with earlier studies. Shape fluctuations are found to facilitate peptide solvation through interactions between the peptide and AOT surfactant, including direct interaction between non-polar peptide residues and the aliphatic surfactant tails. Computed amide I IR spectra are compared with experimental spectra and found to reflect changes in the peptide structures induced by confinement in the RM environment. Furthermore, examination of the rotational anisotropy decay of water in the RM demonstrates that the water dynamics are sensitive to the presence of peptide as well as the peptide sequence. Overall, our results demonstrate that the RM is a complex confining environment where substantial direct interaction between the surfactant and peptides plays an important role in determining the resulting ensemble of peptide conformations. By extension the results suggest that similarly complex sequence-dependent interactions may determine conformational ensembles of amyloid-forming peptides in a cellular environment.

Modulation of Alzheimer's Aβ protofilament-membrane interactions by lipid headgroups

The molecular pathogenesis of Alzheimer's disease (AD) is complex and sparsely understood. The relationship between AD's amyloid β (Aβ) peptides and neuronal membranes is central to Aβ's cytotoxicity and is directly modulated by the composition of the lipid headgroups. Molecular studies of the insertion of model Aβ40 protofilaments in lipid bilayers revealed strong interactions that affect the structural integrity of both the membranes and the ordered amyloid aggregates. In particular, electrostatics plays a crucial role in the interaction between Aβ protofilaments and palmytoil-oleoyl-phosphatidylethanolamine (POPE) lipids, a common component of neuronal plasma membranes. Here, we use all-atom molecular dynamics and steered molecular dynamics simulations to systematically compare the effects that POPE and palmytoil-oleoyl-phosphatidylcholine (POPC) headgroups have on the Aβ-lipid interactions. We find that Aβ protofilaments exhibit weaker electrostatic interactions with POPC headgroups and establish significantly shorter-lived contacts with the POPC bilayer. This illustrates the crucial yet complex role of electrostatic and hydrogen bonding interactions in modulating the anchoring and insertion of Aβ peptides into lipid bilayers. Our study reveals the atomistic details behind the barrier created by the lipid headgroup region in impeding solution-aggregated fibrillar oligomers to spontaneously insert into POPC bilayers, in contrast to the POPE case. While the biological reality is notoriously more complex (e.g., including other factors such as cholesterol), our results evidence a simple experimentally and computationally testable case for probing the factors that control the insertion of Aβ oligomeric aggregates in neuronal cell membranes--a process central to their neurotoxicity.

Lipids in Amyloid-β Processing, Aggregation, and Toxicity

Aggregation of amyloid-beta (Aβ) peptide is the major event underlying neuronal damage in Alzheimer's disease (AD). Specific lipids and their homeostasis play important roles in this and other neurodegenerative disorders. The complex interplay between the lipids and the generation, clearance or deposition of Aβ has been intensively investigated and is reviewed in this chapter. Membrane lipids can have an important influence on the biogenesis of Aβ from its precursor protein. In particular, increased cholesterol in the plasma membrane augments Aβ generation and shows a strong positive correlation with AD progression. Furthermore, apolipoprotein E, which transports cholesterol in the cerebrospinal fluid and is known to interact with Aβ or compete with it for the lipoprotein receptor binding, significantly influences Aβ clearance in an isoform-specific manner and is the major genetic risk factor for AD. Aβ is an amphiphilic peptide that interacts with various lipids, proteins and their assemblies, which can lead to variation in Aβ aggregation in vitro and in vivo. Upon interaction with the lipid raft components, such as cholesterol, gangliosides and phospholipids, Aβ can aggregate on the cell membrane and thereby disrupt it, perhaps by forming channel-like pores. This leads to perturbed cellular calcium homeostasis, suggesting that Aβ-lipid interactions at the cell membrane probably trigger the neurotoxic cascade in AD. Here, we overview the roles of specific lipids, lipid assemblies and apolipoprotein E in Aβ processing, clearance and aggregation, and discuss the contribution of these factors to the neurotoxicity in AD.

Protein/lipid coaggregates are formed during α-synuclein-induced disruption of lipid bilayers

Amyloid formation is associated with neurodegenerative diseases such as Parkinson's disease (PD). Significant α-synuclein (αSN) deposition in lipid-rich Lewy bodies is a hallmark of PD. Nonetheless, an unraveling of the connection between neurodegeneration and amyloid fibrils, including the molecular mechanisms behind potential amyloid-mediated toxic effects, is still missing. Interaction between amyloid aggregates and the lipid cell membrane is expected to play a key role in the disease progress. Here, we present experimental data based on hybrid analysis of two-photon-microscopy, solution small-angle X-ray scattering and circular dichroism data. Data show in real time changes in liposome morphology and stability upon protein addition and reveal that membrane disruption mediated by amyloidogenic αSN is associated with dehydration of anionic lipid membranes and stimulation of protein secondary structure. As a result of membrane fragmentation, soluble αSN:-lipid coaggregates are formed, hence, suggesting a novel molecular mechanism behind PD amyloid cytotoxicity.

A coarse-grained model for peptide aggregation on a membrane surface

The aggregation of peptides on a lipid bilayer is studied using coarse-grained molecular dynamics in implicit solvent. Peptides bind to and self-assemble on the membrane surface into β-rich fibrillar aggregates, even under conditions where only disordered oligomers form in bulk solution. Relative to a solid surface, the membrane surface facilitates peptide mobility and a more complex network of morphology transitions as aggregation proceeds. Additionally, final aggregate structures realized on the membrane surface are distinct from those observed on a comparable solid surface. The aggregated fibrils alter the local structure and material properties of the lipid bilayer in their immediate vicinity but have only a modest effect on the overall bending rigidity of the bilayer.