Membrane remodeling and mechanics: Experiments and simulations of α-Synuclein

    Membrane remodeling and mechanics: Experiments and simulations of α-Synuclein A. West, B.E. Brummel, A.R. Braun, E. Rhoades, J.N. Sachs PII: DOI: Reference:

S0005-2736(16)30098-0 doi: 10.1016/j.bbamem.2016.03.012 BBAMEM 82176

To appear in:

BBA - Biomembranes

Received date: Revised date: Accepted date:

18 November 2015 5 March 2016 7 March 2016

Please cite this article as: A. West, B.E. Brummel, A.R. Braun, E. Rhoades, J.N. Sachs, Membrane remodeling and mechanics: Experiments and simulations of α-Synuclein, BBA - Biomembranes (2016), doi: 10.1016/j.bbamem.2016.03.012

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Graphical Abstract (for review)

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-Syn-induced tubulation was detected in electron microscopy (EM) experiments (from Varkey et al. J Biol Chem, 2010). Complementary simulations provided critical insights into the physical determinants driving tubulation (from Braun et al. JACS, 2014)

ACCEPTED MANUSCRIPT Membrane remodeling and mechanics: Experiments and simulations of Synuclein 1

West A., 1Brummel B. E., 2Braun A. R., 3Rhoades, E. and 1Sachs, J. N. Department of Biomedical Engineering, University of Minnesota, Twin Cities, MN, USA 2 Department of Neuroscience, University of Minnesota, Twin Cities, MN, USA 3 Department of Chemistry, University of Pennsylvania, Philadelphia, PA, USA.

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Abstract: We review experimental and simulation approaches that have been used to determine curvature generation and remodeling of lipid bilayers by membrane-bending proteins. Particular emphasis is placed on the complementary approaches used to study α-Synuclein (Syn), a major protein involved in Parkinson’s disease (PD). Recent cellular and biophysical experiments have shown that the protein 1) deforms the native structure of mitochondrial and model membranes; and 2) inhibits vesicular fusion. Today’s advanced experimental and computational technology has made it possible to quantify these protein-induced changes in membrane shape and material properties. Collectively, experiments, theory and multi-scale simulation techniques have established the key physical determinants of membrane remodeling and rigidity: protein binding energy, protein partition depth, protein density, and membrane tension. Despite the exciting and significant progress made in recent years in these areas, challenges remain in connecting biophysical insights to the cellular processes that lead to disease.

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KEYWORDS:

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-synuclein, Parkinson Disease, synaptic vesicles, membrane curvature, tubulation, bilayer rigidity, coarse-grain molecular dynamics (CGMD)

Corresponding author: Dr. Jonathan Sachs, Department of Biomedical Engineering, University of Minnesota, Nils Hasselmo Hall, 312 Church Street S.E. Minneapolis, MN 55455. Phone: 612-624-7158; Email: [email protected]

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ACCEPTED MANUSCRIPT 1. INTRODUCTION

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As part of their natural function, cellular membranes take on complicated three-dimensional shapes of varying curvatures. Proteins that associate with cellular membranes play an important role in controlling membrane curvature. Recent studies have established a connection between aberrant curvature generation and the onset of disease [1, 2]. For example, mutations in the curvature-generating regions of CIP4 have been linked to Huntington disease and cancer cell metastasis [2]. This protein contains an F-BAR domain, and is a member of the BAR family of membrane curvature-inducing proteins. In addition to the BAR family proteins [3, 4], proteins with amphipathic -helices (AH) [5-8], such as Amphipathic Lipid Packing Sensors (ALPS) motifs and -Synuclein (Syn) control curvature by reversibly adhering to the peripheral regions of lipid bilayers [9, 10]. Mutations in ArfGAP1, a protein with an ALPS motif, have been found in colorectal cancer tumors [11], and Syn dysfunction has been implicated as the cause of Parkinson’s disease (PD) [12]. Each membrane-curving protein that binds to a membrane induces a small change in the local bilayer curvature. Simultaneous binding of multiple proteins can globally reconfigure flat bilayers into new three-dimensional shapes, such as tubules or small vesicles. Membrane-curving proteins also bind to small, highly curved vesicles (e.g. synaptic vesicles), and how the proteins impact the physical and/or dynamic properties of such vesicles is poorly understood.

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In this article, we review the intersection between experimental and computational biophysics tools that have provided a mechanistic connection between local membrane curvature, global remodeling and bilayer material properties. We discuss a number of curvature-generating proteins, but give special emphasis to recent work on Syn. Interactions between overexpressed Syn (associated with gene duplication and triplication in the PD) and cellular membranes (both mitochondrial and synaptic vesicles) have emerged recently as a potential mechanism for the onset or progression of PD [13-19]. In the context of mitochondria, cellular studies of Syn have implicated the protein in membrane fragmentation [1, 20], and fusion [20, 21]. Mitochondrial membranes are large and flat, and resemble giant unilamellar vesicles (GUVs). Biophysical research on GUVs, large multilamellar structures, and large unilamellar vesicles (LUVs) has shown that at high surface density Syn causes them to rearrange into cylindrical tubes and spherical vesicles [7, 22, 23]. In the context of synaptic vesicles, which are far smaller and more highly curved than mitochondrial membranes or GUVs, several studies have shown that Syn can stall proper vesicle trafficking [24-31]. Syn is found in the neuronal synapse at elevated levels, and is associated with impaired synaptic trafficking of vesicles in Parkinsonism [12, 13, 18, 29-33]. Biophysical studies have shown that high levels of the protein inhibit fusion of small unilamellar vesicles (SUVs) [20, 21, 34]. These studies have suggested that when bound to small vesicles the protein may alter the material properties of the lipid membrane. Together these findings suggest that the curvature-inducing mechanisms of Syn are responsible for two very different effects: global remodeling of flat bilayers (e.g. mitochondria) and fusion inhibition in small vesicles. The bilayer bending rigidity, a parameter that varies with lipid composition, is at the heart of both types of transformations. The energy needed to change a flat bilayer into a tube structure is dependent on the bending rigidity, and as such the bilayer mechanical properties correlate with observed remodeling. As we will discuss in section 3.1.4, simulations found that bound proteins also modify the bending rigidity of small vesicles. In addition to imparting vesicle fusion inhibition effects, in vitro studies suggest that Syn can transform small unilammellar vesicles (SUVs) into tubules [7, 35]. Ultimately, determining the biophysical underpinnings for how the effects of Syn on different lipid constructs are connected will most likely require a creative interplay between experiment and computation. Following a brief overview of the field, our review is organized into two main sections. In section 2, we describe how molecular simulations have been used to complement experimental observations of membrane proteins that generate local curvature and induce global tubulation of flat membranes. In

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section 3, we focus on proteins that alter the mechanical properties of both flat and vesicular membranes. First, we highlight EPR spectroscopy and NMR relaxometry as techniques that have been used, specifically in the context of Syn, to determine the protein’s insertion depth in the bilayer [36-38]. Complimentary continuum theory and molecular simulation approaches are introduced next. We describe how these approaches have been useful in refining the experimental data and in establishing partition depth as one of the key parameters in dictating the extent of protein-induced bilayer curvature. We then discuss global membrane remodeling (tubulation of GUVs and MLVs), which has been observed with both electron microscopy (EM) and light scattering (vesicle clearance assays) [7, 22, 23]. Computational modeling has advanced our understanding of such large-scale membrane deformations. Recent theoretical developments, coupled to both mesoscopic simulations [39], and more recently, coarse-grained molecular dynamics simulations (CGMD) [23], have revealed the importance of binding energy (affinity) in dictating tubulation propensity. Binding affinity measurements using fluorescence correlation spectroscopy (FCS) are thus discussed in that context [23, 40-42].

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Second, we explore recent methodological developments for determining the mechanical properties of bilayers. We distinguish between approaches in flat (on the scale of the protein) geometries (e.g. GUVs) and highly curved small vesicles. In the case of flat membranes, we discuss the use of diffuse xray scattering [43-49], pipette aspiration and tether pulling [50-58], and fluctuations analysis [50, 51, 59, 60]. In the more challenging case of small vesicles, we explore neutron spin echo (NSE) [61-63], and atomic force microscopy (AFM) experiments [64-69]. Finally, we describe the most recent efforts, including our own, to accurately capture bending rigidity from simulations of fluctuating membranes, both in flat bilayers and small vesicles [70-74].

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1.1. Mechanisms of protein-induced membrane remodeling

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Commonly used models to explain protein-induced membrane curvature include protein scaffolding [75], wedging or protein insertion [76, 77], and protein-protein crowding [35, 78-80]. In this review we primarily focus on two of these models, namely protein scaffolding and wedging. Schematized illustrations of these two mechanisms are given in Figure 1. In the scaffolding mechanism, the rigid and curved structure of the protein forces the bilayer to adopt the protein’s shape, overcoming the bilayer’s own energetically preferred (intrinsic) curvature. This puts a local strain on the underlying bilayer, relaxation of which may explain the drive towards global remodeling. This mechanism is only thermodynamically favorable if the binding energy is greater than the energetic cost of curving the bilayer [81]. In section 2.2, we will highlight recent theoretical and computational advances that have emphasized the importance of binding energy, and experiments that have borne out these predictions. The BAR family is the most commonly studied group of proteins that act via the scaffolding mechanism. Binding of the bilayer by BAR/N-BAR domains induces substantial positive curvature in membranes [81-83]. FBAR proteins sculpt lower positive curvature surfaces [84, 85], and I-BAR domains have the opposite effect on bilayers by introducing negative curvature [58, 86]. A recent review article on the BAR protein family provides an excellent overview of the physical parameters that determine the subsequent curvature-mediated membrane remodeling in that context [87].

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Figure 1. Cartoon representations to differentiate between the two conceptual models typically used to explain

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protein-imparted curvatures: (A) In the scaffolding mechanism, several rigid protein domains (coiled-coil structural motifs) adhere to and bend the bilayer. The Amphiphysin N-Bar domain, which induces positive curvature is shown on the left, and the I-BAR (inverse BAR) domain, which induces negative curvature, is shown on the right (for additional examples see also http://www.endocytosis.org/BARdomains/BARs.html). (B) In the ‘wedging’ or the ‘protein insertion’ mechanism, a single rigid -helix lodges itself inside the bilayer at an interfacial location referred to as the protein’s partition depth, causing the bilayer to bend away from the protein. We illustrate this method by showingSyn embedded in a lipid bilayer. The partition depth is determined by the chemical nature of the amino acids and the physicochemical properties of the bilayer. 

There are many examples of proteins with amphipathic -helices that insert into the bilayer headgroup region and then generate curvature via the wedging mechanism. The epsin ENTH domain was the first amphipathic helix (AH) discovered to impart curvature via this mechanism [88]. Another notable and highly studied example is the ALPS motif of ArfGap1 protein [10, 89]. Here we will focus on Syn, a 140 amino-acid, intrinsically disordered protein whose N-terminal residues (1-93) fold into an amphipathic -helix upon binding to a bilayer.In the case of Syn, an electrostatic attraction between a series of basic residues positions Syn at the lipid-water interface of negatively charged bilayers. In addition to the enthalpic interactions with the lipid headgroups and acyl chains, the binding of the protein is also driven by the energy of helical folding [90]. The protein wedges into the bilayer by splitting the lipid headgroups apart. The protein’s equilibrium partition depth (at the glycerol backbone level) is dictated by a balance between the hydrophobic face of the protein interacting with the underlying hydrocarbon core of the bilayer, and the charged residues interacting with the polar surroundings. As a result, the protein inserts itself shallowly in the bilayer. At this level, Syn disrupts the intrinsic balance of forces between the lipids that, absent a perturbing insertion, dictate the flat state of the bilayer. The result is induction of positive curvature, which minimizes the overall energy in this perturbed state

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ACCEPTED MANUSCRIPT (Figure 2A). The insertion mechanism drives curvature through the induction of area per lipid asymmetry between the two lipid monolayers. As we will discuss below, we have shown that monolayer area mismatch is not the sole driving force for Syn-induced global membrane remodeling.

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Figure 2.

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Syn-imparted curvatures in POPC-POPS bilayers from coarse-grained molecular dynamics (CGMD) simulations. (A) is the maximum principle curvature from which the diameter D is calculated (D =2/). (B) Both positive and negative Gaussian curvatures () resulted, consistent with Helfrich’s hat model [91]. (C) Representative height surfaces, h(x,y) = z for the outer leaflet of a POPC-POPS bilayer with multiple Syn monomers show that the effect in (A) remains when the protein density is increased. Color map units are nanometers. In all panels, the white star indicates the N-terminus of Syn. (All images are from Braun et al. (2012) [74], reproduced with the author’s permission).

In addition to wedging, Syn-generated remodeling has been explained using protein crowding. In protein crowding, the energy necessary to induce membrane curvature is provided by an enrichment of colliding proteins associated with only one bilayer leaflet [79]. Unlike other curvature-generating mechanisms, crowded proteins can induce curvature without being strongly bound to the bilayer, and Syn tubulates zwitterionic unilamellar POPC vesicles through weak interactions. The protein associated near the choline headgroups, rather than the glycerol backbone, and did not adopt a secondary structure. In

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ACCEPTED MANUSCRIPT their studies, while not excluding other mechanisms, protein crowding was suggested as the mechanism for tubulation [35].

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The Langen group used EM imaging and light scattering to investigate how Syn remodels vesicles, both by increasing Syn concentration and varying the lipid composition. Their EPR’s studies (described below) demonstrate wedging of -helical Syn into anionic membranes. They show that increasing the protein density on the membrane provides additional bending energy, and increases the membrane curvature of the resulting remodeled structures [7, 22]. The detected remodeling consisted of cylindrical micelles, different-size bilayer tubes, spherical vesicles, and other small non-spherical shapes, such as discoid particles. The chemical composition of the lipid bilayer was shown to correlate with tube morphology. For example, unsaturation in lipid tails and longer fatty-acid chains produced widerdiameter bilayer tubes. While Syn added to saturated lipid DMPG [1,2-dimyristoyl-sn-glycero-3phospho-1'-rac-glycerol] generated cylindrical micelles, Syn incubated with anionic lipids having longer chains and double bonds, such as DAPG [1,2-diarachidonoyl-sn-glycero-3-phospho-rac-1-glycerol] produced mostly bilayer tubes [22]. The kinks in DAPG lipid tails, due to cis-double bonds, are believed to prevent its packing into cylindrical micelles.

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In the Langen study, at the lowest protein density investigated (1:40 protein-to-lipid concentration), Syn remodels large non-extruded vesicles (MLVs) into tubular structures approximately 40 nm in diameter, which closely correlates with the size of synaptic vesicle [7]. Interestingly, FCS binding affinity experiments by the Rhoades group have shown that Syn binds to small vesicles of approximately this same size with an order of magnitude higher affinity than it does to larger vesicles [92]. Thus, based on these experimental findings and in conjunction with our simulations, we have proposed that Syn has its own intrinsic curvature, which is matched by the curvature it both induces (tubule formation) and senses (preferential binding to small vesicles). The observations of tubule induction in biophysical experiments can easily be connected to the pathological effect of Syn on mitochondria. The effect of the protein binding to small vesicles—whose high curvature prevents global remodeling (tubulation)—is less clear. A longstanding hypothesis has been that the Syn may alter the lipid packing and surface tension in a small vesicle, and that this perturbation may influence the fusogenicity of the vesicles. In section 3, we discuss recent developments that connect protein-vesicle interactions to reduced vesicle stiffness, and suggest that this may explain both cellular and biophysical experiments that show that Syn reduces vesicle fusion. 1.2. Conceptual framework for characterizing membrane curvature & rigidity All mechanisms of curvature induction rely on the intrinsic elasticity of the phospholipid bilayer. The connection between curvature and bending energy is typically made by the Canham-Helfrich continuum elasticity theory [93, 94]. Recent developments also take into consideration the tilting of the lipid tails [95-97]. Using a notation introduced in the context of promoting curvature evaluation in computational studies [98], the Hamiltonian Hc that describes the curvature free energy is defined as:

Equation (1) includes a combination of geometric parameters and material constants as follows: Hc is the Hamiltonian that describes the curvature free energy; dA is the bilayer surface over which the bending deformations are integrated; kc is the bending rigidity (the material constant that describes the ease to depart from an intrinsic curvature); 1/r1 = k1 and 1/r2=k2 are the two principle radii of curvature; co is the spontaneous mean curvature (the intrinsic tendency of a bilayer to curve); and kg is the Gaussian curvature

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ACCEPTED MANUSCRIPT modulus (the bilayer’s resistance to deform into a surface shaped like a saddle). For an excellent and deeper review of additional curvature related concepts such as energy required to generate specific shapes from flat bilayers see Koslov’s work [75, 81]. In addition, Simunovic and co-workers recently reviewed these important elasticity theory concepts in the context of membrane remodeling by BAR proteins [87].

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Fusion and fission events require the evolution of both mean and Gaussian curvatures, which facilitates connection between the source bilayer and fusion/fission intermediates [91]. The Gaussian curvature energy is an important aspect of fusion and fission [99-101]. A shift towards a positive Gaussian modulus reflects the tendency of a membrane to fuse and a shift towards a negative Gaussian modulus relates to bilayer fission and fusion suppression [101]. Our simulations have shown that Syn imparts both negative and positive Gaussian curvature (the so-called Helfrich hat model) (Figure 2B) [91]. How these Syn-generated curvatures precisely relate to fusion and fission events remains an ongoing area of research.

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2.1. Curvature induction and partition depth

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2. PROTEIN-INDUCED MEMBRANE REMODELING

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The ability of an amphipathic helix to induce local bilayer curvature and global remodeling (tubulation) is highly sensitive to its partition depth, which is determined relative to the bilayer’s overall hydrocarbon thickness. Sylvio May’s foundational lipid chain packing theory for bilayers with adsorbed amphipathic helices suggests that subtle variations (±2 Å) in protein’s partition depth lead to surprisingly large changes in both spontaneous curvature (co) and bending rigidity (kc) [102]. In fact, as the protein insertion goes from peripheral to deeply embedded, the theory predicts that the induced curvature inverts from positive to negative (Figure 3A). Additionally, as discussed in more depth in section 2.1.2, a significant increase in bilayer rigidity is observed when an AH is positioned near the bilayer surface. As the position of an AH in a bilayer becomes deeper, the bilayer rigidity decreases and eventually plateaus. Thus, May’s theory promotes the inextricable energetic link between curvature generation and alterations in membrane mechanical properties (Equation 1). Therefore, accurately measuring the protein insertion depth to a resolution of 1-2 Å is necessary to establish the biophysics of membrane remodeling. The combination of low-resolution experimental techniques with atomic-scale molecular simulations has been used to precisely determine partition depth. 2.1.1. Experimental approaches to determine the partition depth of Syn Partition depths vary with both protein amino acid sequence and lipid bilayer properties [23]. Probebased experiments are typically used to measure the protein’s partition depth. These methods include continuous-wave electron paramagnetic resonance (EPR) [36, 37, 103], and more recently, neutron reflectometry (NR) [104-106], site-specific Trp measurements [105, 106], NMR paramagnetic relaxation (PREs) [107], and 1H Overhauser dynamic nuclear polarization (ODNP), an NMR relaxometry method [38]. Figure 3B shows the partition depth of Syn in POPC:POPS (7:3) bilayers as detected via ODNP, a method that provides enhanced resolution inside the complicated lipid headgroup-water interface. Signals associated with Syn either bound to the membrane or in solution are shown. The center of the Syn helix was measured at 1-3 Å below the lipid headgroup phosphates (Figure 3C). Earlier EPR studies agreed well with this finding, presenting a slightly broader range (1-4 Å) [36, 37].

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Figure 3. Syn’s partition depth from theory, simulations, and experiments:

(A) Spontaneous curvature and bending rigidity vary with partition depth. Left: Spontaneous curvature (co) vs. protein partition depth (p). Right: Bending rigidity constant (kc, units of kbT) vs. the protein’s partition depth (p). The lines in both panels correspond to three non-equilibrium hydrophobic bilayer thicknesses: 26 Å, 24 Å, and 22 Å. The arrow indicates the system with intermediate thickness and the dashed line belongs to the thinnest bilayer. The curve marked with open circles represents the equilibrium bilayer thickness. (Figure by Zemel et al. (2008) [102] reproduced with permission from the author). (B) NMR relaxometry data, specifically Overhauser dynamic nuclear polarization (ODNP) shows retardation factor (t) vs. distance (xi) for Syn residues with respect to the phosphate group of POPC-POPS bilayer. (C) A composite figure compares this ODNP data (red ribbon) with prior (EPR) data (gray ribbon) [36, 37]. The black dashed line shows the center of the helix. (The original figures, (B) and (C), were published by Cheng et al. (2013) [38] and are included here with permission from the author). (D) VMD snapshot shows Syn’s partition depth in a DOPS bilayer from an atomistic molecular dynamics (MD) simulation. (Image by Perlmutter et al. (2009) [108], published here with permission from the author). (E) Potential of mean force profile (PMF) obtained using coarse-grained molecular dynamics (CGMD) simulations reveals Syn’s partition depth in a POPC-POPS bilayer. (The PMF was originally published by Braun et al. (2012) in the supplemental information of reference [74] and included here with permission from the author). (F) Comparison between Syn variants adsorbed to neutral POPC, or anionic POPG, lipid bilayers shows how the excess area in the bilayer changes with partition depth. The bilayers differ in lipid head-group charge and hydrophobic thicknesses (2DC). The ‘mod1’ and ‘mod2’ refer to Syn variants changed to make the peptide more hydrophobic or more hydrophilic, respectively. For a description of how the amino-acids were changed, see the supplement of Braun et al. (2014) [23]. (The figure is reproduced from this study

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2.1.2. Simulations to determine the partition depth of Syn

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From Syn simulations, we found the protein’s partition depth in three ways. In our first study, we used the GROMOS united atom force-field to simulate the protein in an SDS-micelle and a POPS bilayer [108]. We used the equilibrated depth from the SDS simulation to seed a starting configuration in a bilayer composed of all negatively charged phosphatidylserine lipids. In this case, we used the NMR structure of the protein (a helix-turn-helix horseshoe) that has subsequently been shown to be less important on a bilayer surface (where the protein is known to be a single, extended helix) [36, 108]. We found that the protein was inserted more deeply (~5Å) beneath the phosphates than the early EPR studies described above (Figure 3D). We suspect that the different lipid compositions in the two studies are likely the root of this subtle variation. Because these early simulations were of small bilayers, no curvature analysis was possible. More recently, we have used MARTINI coarse-grained simulations of larger bilayers to calculate both local and global curvature induction [74]. In this study, we explored the relationship between insertion depth and the extent of curvature generation. Figure 3E shows a potential of mean force (PMF) free energy simulation in which we calculated the equilibrium partition depth in a different bilayer that more closely matched the EPR and ODNP studies (3:1 PC:PS). The calculation was consistent with a brute-force simulation (in which we started the protein in solution and allowed it to bind and equilibrate on its own). In each case, the partition depth of the protein was found between phosphate and carbonyl-glycerol region, ~3.5Å below the phosphates, more consistent with the experiments. We also simulated model variants of Syn, in which we computationally modified the hydrophobicity of the protein (by manipulating the force-field) [23]. Our results, which are collected in Figure 3F, show the sensitivity of the curvature induction to partition depth (relative to the bilayer’s hydrocarbon thickness), which is itself sensitive to the lipid constituency of the bilayer. 2.2. Binding affinity correlates with vesicle tubulation In a recent theoretical study, Lipowsky showed that the adhesion energy of an adsorbed protein is directly coupled to the induction of spontaneous membrane curvature [109, 110]. The study includes the N-BAR protein as a model for curvature induction. As described in section 1.1 in the context of the scaffolding mechanism of curvature generation, when a protein binds a membrane with sufficient energy, the membrane deforms (e.g. buckles) to adopt the intrinsic curvature of the protein itself. In a landmark study, electron micrographs of BAR domain protein-induced tubulation of lipid vesicles from the Unger group were reproduced from simulations of the same event from the Voth group (Figure 4A) [39]. The study used mesocopic modeling—a technique based on a discrete representation of the Helfrich equation—to explore bilayer remodeling as a function of bilayer binding strength, bending modulus (kc), spontaneous curvature (co), and protein density. Collectively, these studies have clarified that the binding energy (which is directly related to experimentally measured binding affinity) is the central parameter that dictates the protein’s capacity to globally remodel membranes. In the context of Syn, Langen was the first to show that the protein also causes tubulation of GUVs and other multilamellar and unilamellar vesicles larger than 100 nm [7, 22]. Figure 4B displays results obtained for large non-extruded vesicles. Despite the fact that AHs are thought to act through the wedge-mechanism (in contrast to F-BAR which acts through the scaffolding mechanism) [85], we have shown that this same binding energy argument generalizes to amphipathic helices (e.g. Syn). The results of this study are discussed in the following section.

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Protein-induced tubulation from experiments and simulations: (A) Remodeling by Amphiphysin N-BAR protein is shown using a mesoscale simulation in the two images on the left, and with an electron microscopy (EM) micrograph on the right. These images show strikingly similar tube diameters and void shapes. (For a detailed description of the colors in the two simulation images, see Atyon et al. (2009) [39], from which we reproduced these images with the author’s permission) (B) Wild-type (wt) Syn’s ability to impress tubulation is shown using EM. The arrows show smaller tubes extending out of larger tubes. The black scale bar is 100 nm. The lipid composition is POPG:POPC (1:4 molar ratio) and 1:10 protein to lipid ratio. (This image was produced by Varkey et al. (2010) [7] and it is included here with permission from the author) (C) The protein’s binding affinity was determined from fluorescence correlation spectroscopy (FCS) curves of large unilamellar vesicles (LUVs) made of either pure POPG, 100% POPG+wt-Syn, or (1:1 ratio) POPG:POPC+wt-Syn. A greater shift to the right indicates a larger fraction of αSyn bound to vesicles. (D) A vesicle clearance assay captures significant tubulation in 100% POPG with added wt-Syn (inset). The resulting tubulation capacity is displayed as a bar graph. (E) Another vesicle clearance assay show that the NAC-null variant reduces tubulation capacity in a 100% POPG system relative to wt-Syn. (F) and (G) show curvature fields from CGMD simulations of anionic POPG bilayers with wt-Syn and the NAC-null variant, respectively. The images display the evolution in bilayer height () under high density protein coverage (400:1 lipid to protein ratio). (H) CGMD simulation results compare the (%) excess area per protein in low protein density bilayers (1600:1, blue) conditions to the excess area under in higher protein density bilayers (400:1, green) for both wt-αSyn and the NAC-null variant. The tubulation measured in experiment (D) correlates with the (%) excess area values shown here. (Panels (C) through (H) were all originally published in the main body or in the supporting information of Braun et al. (2014) [23] and are included here with permission from the author.)

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2.2.1. Syn binding energy (affinity) and tubulation: Experiments

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Utilizing fluorescence correlation spectroscopy (FCS), the Rhoades group has provided critical insight into the biophysical determinants of Syn binding [92]. FCS is a rapid (10’s of seconds), quantitative method to measure binding of αSyn to LUVs over three orders of magnitude of lipid concentration [111]. In FCS, the temporal autocorrelation of spontaneous fluctuations in fluorescence intensity in a solution of diffusing molecules can be fit with a variety of models to yield quantitative parameters associated with concentration, diffusion, and chemical or photophysical kinetics of the observed species. In the case of protein binding to vesicles, FCS is used to analyze diffusion behavior, which is dependent upon the size of the diffusing species and the viscosity of its environment. Binding of a labeled protein to an unlabeled partner (in the case here, a freely diffusing vesicle – these are not measurements of diffusion of αSyn on the vesicles) can be seen unequivocally by a shift to longer timescales of the autocorrelation curve of the labeled species. Fitting the calculated autocorrelation curve allows for extraction of parameters corresponding to the diffusion time, and concentration of each species present – in this case, freely diffusing αSyn and αSyn bound to freely diffusing vesicles. The Rhoades group used a fixed protein concentration with a series of lipid concentrations to construct binding curves, which were fit to determine the binding affinity of αSyn for vesicles of a particular lipid composition or size.

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Using FCS, we showed that the binding affinity of Syn to 1:1 charged (PG):neutral (PC) lipid mixtures is sixty-times higher than to a completely neutral bilayer (Figure 4C). Surprisingly, when the headgroup of the lipid was PA, the binding affinity was substantially stronger than PG or PS (by >60 fold) [92]. Relatedly, cardiolipin (CL) (found in the inner-mitochondrial membrane) has two doubly negatively charged PA groups connected to the glycerol backbone at physiological pH. In vitro studies showed that Syn binds CL-containing bilayers [112]. Western blots of isolated rat and human brain mitochondria incubated with Syn showed that the protein prefers to associate with the inner mitochondrial membrane [113, 114]. Because CL contains two PA moieties, Syn binding to mitochondrial membranes is likely very strong, possibly explaining the observed effects (tubulation/vesiculation) of these membranes and associated dysfunction (fusion and fission) observed in PD [1]. Sensitive quantitative analysis of the extent of remodeling is important for understanding the extent of remodeling. Two experimental techniques are used to observe tubulation of vesicles of varying size (including large and small). First, images of proteins bound to curved membranes have been produced via electron microscopy (EM) methods. These techniques have been used to detect and quantify various sized tubes and spherical vesicles generated by both scaffolding domains and AHs [6, 35, 39, 115-119], and can provide information even if tubulation is incomplete (or a statistically rare event). For example, the Lee group used EM imaging of neutral lipid (POPC) vesicles prepared by sonication (average diameter ~100 nm) to monitor tubule formation. They quantified their images and found that at most ~40% of the vesicle area was remodeled, indicating incomplete tubulation (vesicles are intact with protruding tubes) [120]. This is in contrast to fully charged bilayers which appear to undergo complete tubulation (i.e. few if any vesicles remain) [7] [120]. In addition to EM imaging, a second experiment that has been used to measure bulk remodeling of vesicles is a light scattering (vesicle clearance) assay. The clearance assay detects the transition from large, high-scattering vesicles to low-scattering tubes and smaller vesicles. Following Langen [7, 22], we used a vesicle clearance assay and showed a correlation between FCS-derived binding affinity (Figure 4C) and tubulation capacity (Figure 4D). At equal density of adsorbed protein (1:10 protein:lipid ratio), we showed that Syn added to anionic POPG bilayers leads to significant bilayer tubulation compared to no quantifiable tubulation in the case of 1:1 POPG:POPC lipid vesicles. While

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the vesicle clearance assay has a lower detection threshold for tubulation than EM, it is convenient because it does not require burdensome image processing. On the other hand, there is a risk of missing incomplete tubulation events. If no changes in turbidity upon protein incubation are detected via scattering due to incomplete tubulation (e.g. Figure 4D), EM may be important because it can resolve incomplete or statistically rare tubulation events that are otherwise undetectable by light scattering (e.g. Figure 4B).

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In an effort to further isolate the contribution of binding energy to tubulation (for example, from the effect of partition depth), we engineered a variant of αSyn that lacks the hydrophobic NAC domain. The AH of Syn has seven repeats with consensus sequence XKTKEGVXXXX (X = any residue). The variant, which we called NAC-null, replaces the core of the NAC domain (the sixth heptad) with a replicate of the fifth heptad (GAVVTGVTAVA → EKTKEQVTNVG). Using CGMD simulations we showed that the alteration had little effect on the partition depth (Figure 3F). FCS binding data showed that the NAC-null variant has a 6-fold lower binding affinity than the native sequence. Clearance assays showed that the tubulation capacity of the variant was also reduced (Figure 4E), further confirming binding strength as a critical determinant in tubulation remodeling.

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To study the role of binding energy in the process of Syn-induced curvature, we have used CGMD simulations (MARTINI) [121, 122]. We have studied the impact of the protein on flat bilayers at both low protein density, (protein:lipid ratio of 1:1600) (Figure 2A-C) and at high protein density (protein:lipid ratio of 1:400) (Figures 4F-H). We note that even at the high densities we simulated, direct proteinprotein contacts were not frequently observed and did not contribute to the overall curvature effects we reported. It is important to note that in these simulations we removed lipids from the protein-containing monolayer so as to avoid a monolayer area mismatch between the leaflets. Thus, the induced curvature fields are not trivially explained by the bilayer-couple mechanism. The fact that the curvature fields extend well beyond a given protein in the high-density systems reflects what we termed “curvature-field reinforcement”. The position and size of the height maps suggest intermediate-ranged protein−protein alignments (not direct interactions) that stabilize the curvature fields between proteins. We have postulated that the reinforcement of these fields is due to reduced protein mobility on the surface of the membrane, and that the magnitude of the mobility correlates with the binding affinity. Our assertion is that higher binding affinity results in larger and more stable complexes between the negatively charged lipids and the protein. These complexes should have reduced diffusion rates (we did not calculate this) that would stabilize (both spatially and temporally) the induced curvature fields. We speculated that this might in turn lead to stabilized networks of proteins on the membrane surface, though we have not observed such a phenomena on the timescale of our simulations. We do note that such a phenomena has been observed by Voth and co-workers, whose work is detailed later in this section [123]. Continuing with our curvature field analysis, we quantified the extent of Syn-induced curvature induction from the height maps in Figure 4F and 4G by computing the percent excess area over a flat bilayer, (1-Ah(x,y)/ Axy) x 100%. The results are given in Figure 4H and reflect the idea that reduced affinity, which correlates with reduced tubulation (Figure 4D,E), is reflected in a loss of curvature-field reinforcement. For example, comparing the native Syn sequence to the NAC-null variant, we showed that at low density there is negligible difference in the induced curvature field (from one protein). In the case of the native sequence, the per-protein curvature was the same at high density. Quite to the contrary, in the case of the NAC-null variant (reduced affinity and tubulation, same partition depth) the per-protein curvature was significantly reduced at high density. In the case of a lower lipid headgroup charge density (3:1 PC:PG), we showed a severely reduced curvature induction even at the low-density (Figure 4H).

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We have also directly simulated the process of a budding (tubulating) GUV, approximating the local protein environment with a large, flat bilayer (approximately 85,000 lipids) (Figure 5A). We artificially constructed a starting configuration in which we aligned and constrained Syn monomers in a spoke-like arrangement. Again, we removed the appropriate number of lipids in the protein-containing monolayer to test whether tubulation requires global area mismatch (it does not). From these large-scale simulations we observed a reduction in lipid acyl chain order parameter asymmetry (Sz) as the budding tubule formed. This led us to postulate that alleviating asymmetric lipid ordering is a driving force for tubulation. Figure 5B shows the time evolution of this asymmetry. As the tubule grows from the flat bilayer the asymmetry is weakened and is totally lost within 300 ns. We also noted that accompanying the change in the order asymmetry is an increase in the contacts between lipid chains in the protein spoke (Figure 5C). The increased contacts result in increased coupling across the bilayer and may contribute to stabilization of the highly curved state. Thus there is both an entropic (lipid order) and enthalpic (interdigitation) component driving the tubulation. These two observations highlight the utility of coarse-grained or atomistic MD simulations, which allow detailed views of the ensemble behavior of the lipids.

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Figure 5. wt-Syn‘s ability to initiate tubulation determined from coarse-grain molecular dynamics (CGMD) simulations. (A) The figure shows a VMD representation of the evolved tubule at 300 ns. This system consists of ~85,000 POPG lipids and 48 Syn proteins adsorbed unto the bilayer in the extended-helix conformation. The height to the top of the mound from the flat region at the base is ~25 nm. (B) Lipid tail ordering asymmetry Sz determined as the difference of mean order parameter of each monolayer is shown across the 850ns CGMD trajectory. (C) The total number of inter-leaflet contacts found near the protein is compared to the number of contacts in the bulk bilayer region. The inset shows the contacts found within the first shell. (All figures were reproduced from Braun et al. (2014) [23], with the author’s permission)

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Because of limitations in sampling, we were forced to start the tubulation simulations with a predefined, non-random protein configuration. We tested three distinct starting structures, in which the proteins were concentrated at the center of the large bilayer. In addition to the spoke-like configuration (in which the proteins were aligned and constrained in a side-by-side, circumferential pattern), we also aligned the proteins end-to-end in concentric rings, and end-to-end in a carpet-like pattern (See our Supporting Information in [23]). Regardless of the initial configuration, the bilayers all formed a budding tube (as in Figure 5A). This approach left open the question of how and why proteins organize in advance of tubulation. A 2015 simulation study of N-BAR domains by the Voth group has shed important light on this issue [124]. Their simulations explored protein dynamics and protein self-interactions on bilayers under tension. The importance of tension to tubulation has been made clear with recent experiments from the Baumgart group that showed that high membrane tension inhibits the initial stages of membrane remodeling [125]. In particular, membrane shape transitions are initiated only under lower tension regimes. In the Voth group simulations, applied tension was shown to affect protein aggregate size, patterns of protein diffusion, dynamics of protein-protein self-interaction, and the orientations adopted by monomers relative to one another. The study showed that tension can dictate the probability of end-to-end association of proteins as opposed to side-by-side dimerization. Low-tension regions potentially represent recruitment sites for proteins to initiate remodeling. These findings collectively inspire the need to design experiments that are capable of tracking the protein-protein organization at the neck of a budding tube. This is a far-from-trivial experimental challenge that will likely require going beyond advanced microscopy and single-molecule techniques (for example, cyro-electron microscopy may be able to trap nucleating protein structures). These findings also connect global membrane remodeling to bilayer material properties, which we will now discuss.

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3. PROTEIN-INDUCED ALTERATIONS IN MEMBRANE MATERIAL PROPERTIES Multiple in vivo studies have shown that αSyn, which associates with synaptic vesicles (SVs) [126], can disrupt SV trafficking [12]. A series of studies by the Beyer group investigated the biophysical basis for the influence of αSyn on model vesicles and mitochondria. The first in this series of studies showed that αSyn has a preference for packing defects in synthetic, gel-phase SUVs [127]. The research used a combination of isothermal titration calorimetry (ITC) and differential scanning calorimetry. The ITC results showed that the titration of αSyn into synthetic SUVs below their phase transition temperature is highly exothermic, whereas titration into LUVs is not. The exothermic reaction is a result of protein folding and membrane binding. A direct follow-up to this study used electron spin resonance spectroscopy and fluorescence spectroscopy to investigate the effects of αSyn on gel-phase SUVs [21]. Their results suggest that bound αSyn relieves the curvature stress induced by the small diameter of these vesicles. This led them to hypothesize that αSyn functions to prevent premature SV fusion. A third and more recent study from the same groups firmly established that αSyn inhibits small vesicle fusion [20]. In a related study, Dewitt and Rhoades showed that αSyn inhibits SNARE-mediated vesicle fusion using a lipid mixing fluorescence assay [34]. Critically, in order to determine whether the mechanism of fusion inhibition involves binding to the SNARE complexes, they used fluorescence correlation spectroscopy on soluble SNAREs. In this assay, they removed the membrane-binding region of the vesicle- and target-SNAREs, labeled only the vesicle-SNAREs, and monitored diffusion time after mixing. As the SNARE complexes formed, the diffusion time increased linearly. They conducted this assay with and without αSyn in solution. Their results show no difference in SNARE complex formation with the addition of αSyn. Additionally, they assessed the binding of αSyn to lipid vesicles with and

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without v- and t-SNAREs using an NBD fluorescence assay. They found that αSyn binds more strongly to pure lipid vesicles than vesicles containing SNAREs. This indicated that αSyn does not bind directly with membrane-bound SNAREs. Because αSyn does not bind soluble SNAREs and had a decreased affinity for SNARE-containing vesicles, the study concluded that αSyn causes fusion inhibition by directly interacting with the lipid vesicles [34]. While others have focused on αSyn’s interaction with the fusion protein machinery [126], the Beyer and Rhoades studies suggest that αSyn-induced alterations in lipid properties (e.g. small vesicle mechanics) may at least in part underlie the protein’s inhibition of vesicle fusion. 3.1. Bilayer rigidity

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Theory suggests that curvature induction due to absorption of AHs is dependent on the bilayer thickness [77]. Additionally, bilayer bending rigidity (kc) typically increases linearly with bilayer thickness [128]. Thus, determining how an AH changes bilayer structure (e.g. thickness) is a first and critical step in understanding its potential effect on bilayer mechanics. To show the effect of αSyn on the structure of a bilayer, we combined x-ray scattering with CGMD simulations. Our LAXS scattering experiments on oriented bilayer stacks revealed changes in POPC/POPS (3:1 ratio) bilayer thickness introduced by Syn association [23]. Figure 6A shows the resulting form factor. Other experiments have determined bilayer structure with added protein using this approach [43, 129]. In our study, the scattering density profile (SDP) model from the Nagle group was used in conjunction with the experimental data [130, 131]. A low Syn:lipid ratio was used (1:200) in order to avoid tubulation (which would render the x-ray experiment un-interpretable) as well as to avoid complications due to protein-protein interactions. The results of the SDP modeling showed a modest, but detectable global bilayer thinning (~1 Å) (Figure 6A, inset).

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Figure. 6: Experiment and simulation strategies to study pure and the protein-added bilayer structures. (A) The

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image displays the form factor from Low-Angle X-ray Scattering (LAXS) experiment of POPC-POPS bilayer stacks with added protein (200:1). Comparing the red line (added protein) to the black (pure bilayer) shows that Syn thins the bilayer (q shift to higher values). The inset shows the resulting electron density profile (EDP). (B) Detected changes in bilayer thickness (DPP) from coarse-grained molecular dynamics (CGMD) Martini simulations due to bound Syn are shown. DPP was evaluated using methodology derived by our group to eliminate the thermal undulations effects [132]. (The figure is from Braun et al. (2012) [74], reproduced here with the author’s permission.)

Our CGMD simulations recapitulated the finding of a small thinning of the bilayer (Figure 6B). Relatedly, Baumgart studied structural changes in αSyn-induced tubulation of GUVs [133]. Reversible, yet extensive lipid bilayer area expansion and bilayer thinning preceded tubulation. This thinning effect was significantly more pronounced in a bilayer with a complex lipid composition. Likewise, the Brown group recently used the mean-torque model [134] and solid-state NMR to show that the protein causes a substantially greater thinning (~6 Å) when bound to a lipid raft mixture, presumably reflecting a proteininduced homogenization of the ordered and disordered phases [135]. Matching bending rigidities from simulations and experiments is a more challenging task than matching structural and thickness changes. This is especially true in the case of a small vesicular geometry, where experimental tools are more limited. Furthermore, experimentally reported bending rigidities vary based on the methods employed [136]. The three main experiments to determine bending rigidities for pure lipid bilayers are diffuse x-ray scattering of flat bilayers [43-49], force-based methods to deform a membrane such as the pipette aspiration technique and pulling membrane nanotubes [50-58, 137-144], and fluctuating shape analysis of GUVs [51, 59, 60, 145-156]. To measure the rigidity of SUVs and purified synaptic vesicles [64], neutron spin echo (NSE) [61-63], and atomic force-microscopy (AFM) experiments have been used [65-69]. There are no experimental reports on the influence of adsorbed αSyn on bending rigidity.

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3.1.1. Material properties: Experimental methods in a flat bilayer geometry

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Diffuse x-ray scattering was pioneered by the Nagle group to measure the bilayer bending rigidity from stacks of flat, undulating bilayers [48, 49]. Over the past several years, the group has made important discoveries regarding the impact of membrane-bound proteins on bilayer mechanics [43-47, 157]. In particular, several studies looked at the role played by membrane-binding proteins in modulating the fusion between the HIV-1 virus membrane and the T-cell membrane. From this work a hypothesis emerged that explains how protein-binding events impact the fusion of locally flat bilayers. Proteins partitioned inside membranes were found to thin the bilayers, disrupt lipid tails configurations, induce spontaneous curvatures, and significantly reduce the bending rigidity constant (kc) of membranes [43-46]. In one such study kc decreased exponentially with increasing fusion peptide concentration, an effect that is believed to lower the activation free energy barrier for fusion of two approaching (flat) bilayers [46]. One of their recent studies used an eleven amino acid, cell-penetrating peptide extracted from the HIV-1 TAT protein [43]. A representative LAXS profile is given in Figure 7A. kc is determined from the diffuse scattering, which is extracted from the white lobes in the qr direction. This is in contrast to the bilayer form factor that is used to determine structure (Figure 6C), which is obtained from the scattering in the qz direction. Figure 7B shows the influence of protein concentration on kc in membranes of varying lipid constituency [43]. The most dramatic change in bilayer rigidity is detected in experiments where HIV-1 TAT is added to a complex multicomponent lipid system. These data, like the Brown NMR data on lipid rafts underscores the importance of developing computationally efficient strategies to study the material properties of complex mixtures [135]. While LAXS and small-angle neutron scattering (SANS) have been used to extract structural parameters from vesicles as small as 50 nm diameter [158], the current use of diffuse scattering to extract kc relies on lamellar stacking of the bilayers. Interpretation of diffuse scatter may be complicated when a curvature-inducing protein, like Syn, is included in the sample. This is because the length scale of the protein-induced static curvature is convolved with the bilayer undulations in a critical region of the scattering spectrum. Further research is needed to resolve this potential problem if we are to use diffuse x-ray scattering to ascertain kc in the presence of Syn.

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Figure 7:

Bilayer rigidity in experiments and computational models: (A) Diffuse x-ray scattering intensities for a DOPC-DOPE (1:1) bilayer at a fraction x = 0.034 HIV-1 Tat protein (B) Bending rigidity constants (kc) obtained from diffuse scattering profiles are shown with changing protein concentration and lipid composition (P: protein concentration, L: lipid concentration). In all instances, increasing the protein concentration softens the bilayers. The nuclear membrane mimic shows a more pronounced drop in rigidity with increasing the HIV-1 Tat concentration (◆symbol, turquoise color), than the other compositions. (Image (A) and (B) are from Akabori et al. (2014) [43] and are displayed here with the author’s permission). (C) Undulation spectra (Su(q)) and number density structure factors (S(q)) of pure bilayers determined from molecular dynamics (MD) simulations. Two different force field representations were employed, the united atom (UA) and the coarse grain (CG). The resulting kc values differ by a factor of ~2 (kc = 7.5 x 10-20 J from UA and kc = 15 x 10-20 J from CG). (The image was originally published by Brandt et al. (2011) [72]). (D) Variations in bending modulus (left axis) and imparted spontaneous curvatures (right axis) with increasing the protein surface coverage at three bilayer heights. The computational technique used in this study is the continuum elastic modeling (CEM) [77]. (Image by Sodt and Pastor (2014) [159], reproduced with permission from the author).

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The second category of experiments used to determine the bending rigidity of GUVs with added protein includes force-based methods [50-57, 137-141]. Like the multi-lamellar stacks used in x-ray, GUVs are considered flat on the length-scale of single, curvature-inducing proteins, such as Syn. The two main techniques are 1) pipette aspiration developed by Evans [142, 143], which has since been modified [144]; and 2) force measurements made by pulling membrane nanotubes by various approaches such as optical and magnetic traps [160-163]. The micropipette aspiration technique typically consists of trapping a GUV vesicle in a micropipette to regulate the vesicle absorbing pressure. In this manner, the bilayer tension is controlled and the resulting changes in bilayer lateral area are tracked. The bending modulus, kc, is then calculated using an established relationship between excess area, membrane tension and kc [142, 143]. Micropipette aspiration was also used to determine the change in rigidity due to the fusion peptide, the same protein that was studied via x-ray diffuse scattering by the Nagle group in the context of T-cell membrane and HIV-1 membrane fusion [51]. In addition, both dynamin [55], a protein that converts membranes into tubules and induces membrane fission, and BAR proteins [53, 56] have been studied with force-based approaches.

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Finally, the bending rigidity in the vesicle geometry has been measured using fluctuation or flicker spectroscopy of GUVs [145-154]. Several studies used this technique to report rigidities of vesicle with added proteins [51, 59, 156]. In these studies, kc is extracted from thermal fluctuations in the vesicle contours. In one noteworthy example, Loftus and co-workers recently reported bending rigidity of a POPC bilayer with changing Sar1 protein concentration from a modified fluctuation spectroscopy technique called selective plane illumination microscopy (SPIM) [60]. Sar1 is a membrane-bending protein implicated in COPII vesicle fission [164]. The protein contains an AH domain that inserts and bends the membrane, and the experiments showed that adding Sar1 softens the bilayers. The experimentally determined rigidity constants closely matched those from tether-pulling experiments [50]. While each of these experimental methods is able to show that adding protein affects bilayer rigidity, they are unable to explain the molecular origin of these effects. To do so, complimentary computational approaches have the potential to provide invaluable biophysical insight. 3.1.2. Material properties: Computational methods in a flat bilayer geometry Due to the increase in computational power over the past fifteen years, simulations of large undulating bilayers are now possible. As such, there has been an extensive effort, including our own, to develop algorithms to extract kc from these simulations. Different approaches have been used, including spectral analysis [71, 72, 165], lipid tilt modulus [166], and simulated buckling [167]. Spectral analysis evaluates kc from power spectrum data [71, 72, 165]. This approach rests on the Helfrich continuum model to extract kc by fitting to the small-q regime. These calculated bending rigidities vary significantly with force field. Pure DMPC bending rigidities obtained in the united atom (UA) representation and in coarse-grained (CG) Martini simulation differ by a factor of ~2 (Figure 7C). The UA-derived bending rigidity (kc = 7.5x10-20 J) is closer than the CG result (15x10-20 J) to what has been measured in experiments (kc = 6.9x10-20 J) [72, 168]. Because the underlying theory, which treats the membrane as a homogeneous continuum, breaks down when an inhomogeneity is included, kc cannot be extracted from simulations of membranes with bound proteins using this method. The co≠ 0 spontaneous curvature introduced by the protein significantly complicates the (kc) analysis [70, 132, 169]. Additional computational methodologies that either deconvolve the contribution of undulations and static curvature in the linear regime or include the spectral contribution of a characterized protein induced spontaneous curvature are needed to overcome this limitation. One possible approach would include the addition of temporal analysis to the undulation spectrum, following the work of Lindahl and Edholm 2000 [165]. Here, temporal analysis on the low-q undulation modes were performed to extract a correlation time for each mode. If a similar approach is applied to systems where static curvature is present, the undulation

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There are two recent examples where simulations of smaller systems have been used to investigate changes in bilayer rigidity. First, Brown developed a formalism to calculate kc for smaller, single-species bilayers (~ 400 lipids) [170]. Second, Sodt and Pastor adapted the continuum elastic modeling (CEM) approach of Kozlov to specifically explore differences and similarities in protein-induced curvature with atomistic simulations [159]. In the process, they reported on the influence of protein insertion on bending rigidity. The AHs considered were segments (<25 amino-acids long) of ArfGAP1 protein, an ALPS motif that associates to positively curved lysosomes, and a section of DivIVA, a peptide that prefers surfaces with negative curvature. The calculations captured the expected relationship between bending rigidity and partition depth. The resulting spontaneous curvatures and rigidity with changes in protein coverage for three different partition depths are shown in Figure 7D. This figure shows that as the protein density increases, the bilayer softens and the spontaneous curvature increases. Overall, the CEM model predicts a softening of the bilayer near the protein, a result that we qualitatively recapitulate in the case of Syn bound to a small vesicle (see section 3.1.4). The Pastor group also calculated kc using all-atom simulations of antimicrobial peptides in bilayers [171]. In this case, in order to extract kc the authors relied upon a polymer brush model developed by Evans [143]. This approach relies upon time-averaged bilayer lateral area fluctuations to approximate the bending modulus with the area expansion modulus.

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Experiments on small vesicles are exceedingly challenging and the biophysical literature is limited. Nonetheless, there are several experimental studies that have shed light on the mechanics of small vesicles (SUVs and purified synaptic vesicles). Two such examples are neutron spin echo (NSE) and atomic force microscopy (AFM), though only the latter has been made on complex vesicles. In neither case have there been systematic studies of the effect of adsorbed proteins on the material properties. A recent study evaluated bending rigidity constants from vesicles extruded with ~40-50 nm radii, however dynamic light scattering (DLS) experiments indicated that some of the radii quickly grew to 70-80 nm [62], rendering these vesicles substantially larger than an average synaptic vesicle (~40 nm) [172]. NSE measurements were fit based on the Helfrich-like treatment of a bilayer as a thin, homogenous sheet by Zilman and Granek [61] and bending rigidities were determined via the undulation relaxation rates. The authors were able to observe bilayer softening as a result of adding a second lipid type to the vesicles. The Brown group has further extended this Zilman/Granek formalism to include internal dissipation within the bilayer [173]. The authors of the NSE study on vesicle mechanics do not discuss the applicability of their approach in the case of adsorbed proteins, though invariably the interpretation of the data using a simplified bending model will complicate such efforts in the future. Another technique used to determine the bending rigidity of small vesicles is atomic force microscopy (AFM) [67]. This technique has been used to characterize a variety of lipid systems ranging from synthetic liposomes (Figure 8A) to synaptic vesicles [64-68, 174-176]. AFM is capable of extracting material properties of extremely small vesicles, but like other approaches requires modeling of the force curves (Figure 8B) in order to obtain material properties such as stiffness (Figure 8C) or kc. Early AFM experiments on lipid vesicle mechanics relied on the spherical Hertz contact model to calculate the Young’s modulus [64-66]. While the Hertz model is still routinely employed to calculate elastic properties, it assumes adhesion- and friction-free contact between two solid spherical bodies with a curvature radius much larger than the radius of their circular contact area. Additionally, the model assumes deformation within the elastic limit [177]. Because the composition of a lipid vesicle is non-

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homogeneous and cannot be considered a solid sphere, this model leads to underestimation of elastic properties [67, 178]. The Hansma group applied the Hertz model to obtain the Young’s modulus of cholinergic synaptic vesicles in different buffer solutions [64]. More recent studies have abandoned the Hertz model in favor of empirically derived formulas that consider lipid vesicles to be thin spherical shells rather than solid spheres. The Schaap group applied finite element modeling (FEM) to accurately model the interface between cantilever and liposome and calculate Young’s modulus [67]. Using this approach, the AFM-derived kc for a simple DMPC vesicle compared well to values from micropipette aspiration experiments on DMPC giant vesicles (1.8x10-20 J vs. 5.6x10-20 J) [143]. Here too, as in many techniques we’ve discussed above, the FEM model assumes the membrane is a homogeneous elastic sheet, considerably complicating the ongoing question of how to interpret data in the presence of adsorbed proteins.

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Rigidity of lipid vesicles from experiments and simulations. (A) An AFM topography image of a DMPC vesicle obtained using pulsed-force mode imaging. (B) Representative force curve highlighting stiffness data. The stiffness is obtained by fitting the slope of the curve during indentation (grey highlight). (C) Stiffness image of the DMPC vesicle shown in (A). The stiffness was obtained through the method shown in (B). Dark colors represent lower stiffness values than light colors. (D) A 9 µs snapshot from a coarse-grained molecular dynamics simulation of viral capsid indentation with an AFM probe tip. The tip is orange, the substrate is grey and the capsid proteins are green, red, blue, and yellow (Used with permission from Arkhipov et al. (2009) [179]). (E) Snapshot from a coarse-grained molecular dynamics (CGMD ) simulation of a DPPC vesicle coated with αSyn monomers. (F) Lateral pressure profiles of pure DPPC(-) and DPPC+ Syn (--) vesicles that indicate a softening due to the added protein. The arrows point to the significant pressure profile changes introduced by Syn. (G) Fluctuation spectra <|alm|2> for DPPC and DPPC+Syn vesicles in CGMD simulations. The higher fluctuations in the DPPC+Syn case (red symbols), describe a softer vesicle. (Panels (E), (F), and (G) were originally published by Braun and Sachs (2015) [70], and are reproduced here with permission from the author).

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In order to investigate AFM on the molecular scale, the Schulten group used shape-based coarsegrained molecular dynamics to simulate an AFM probe tip indenting a viral capsid (Figure 8D) [179]. From these simulations, the authors were able to determine the indentation depth required for irreversible (plastic) deformation, and the underlying cause. They showed that the positions of capsid proteins changed very little upon indentation and that plastic deformation results from local changes in protein geometry. The calculated force curves matched experimental curves remarkably well given the coarseness of their model.

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Using another computational approach, we have recently developed algorithmic tools for calculating an undulations spectrum from molecular dynamics simulations of vesicles (Figure 8E) [132]. We have done so for CGMD (MARTINI) vesicles, but the algorithms apply to atomistic representations as well (although such simulations are still unlikely due to the number of atoms required). These methods build on our approach to handling undulations in flat-patch systems [71, 72]. In that case, we calculate an undulating reference surface (URS) that approximates the bilayer as a single surface at its mid-plane. The undulations can then be easily transformed into Fourier space (yielding the undulations spectrum), which as described in section 3.1.2, can be fit to give kc. In the vesicle geometry, we establish a local reference frame by defining a radial URS. A truncated series of spherical harmonics is then used to determine the long-wavelength fluctuations. The power spectrum of spherical harmonic coefficients is then fit to a Helfrich continuum model in spherical geometry to extract bending rigidity. Using this method, we determined kc for both DMPC and DMPC+Cholesterol vesicles, and showed that the calculated values are consistent, though not perfectly overlapping with values from simulations of flat systems. While we were able to show the expected increase in bilayer rigidity with cholesterol, the source of small discrepancies in kc values obtained from flat-patch simulations and (more importantly) from experiments remains an area of ongoing investigation and algorithm development. 3.1.5. Simulations of Syn bound to a small vesicle suggest the protein softens the bilayer Ultimately, we would like to be able to simulate small vesicles with a complex lipid constituency in order to understand the role of curvature-inducing lipids (e.g. those containing PE headgroups), polyunsaturated lipids, and understudied lipids that are prevalent in synaptic vesicles (e.g. plasmalogens). The light scattering study described earlier showed that Syn inhibits fusion of highly fusogenic vesicles made of complex mixtures (DOPC/DOPE/SM/Chol) [20]. Designing initial configurations for MD simulations of vesicles, even single-component ones, is challenging because of the unknown water density distribution between the outside and inside of the vesicle, and because of the asymmetry in number of lipids in each leaflet of a small vesicle. This is made more challenging when there are multiple lipid species, as would be the case in a model of synaptic vesicles, because of the unknown compositional asymmetry between leaflets [172]. Marrink developed a method of equilibration to handle this complication, which involves opening pores during equilibration that allows water (by transport) and lipids (by flipping) to equilibrate [73, 180]. Despite the efficacy of this approach, the process of equilibration can be slow and uncertainties remain as to whether the vesicles are fully equilibrated. Nevertheless, one can still monitor alterations in the material behavior of simulated vesicles, as we have recently done with an ~35nm vesicle with Syn bound at high density (1:200 protein:lipid) [132]. Our simulations showed that Syn: 1) considerably reduced the surface tension of the vesicle (Figure 8F); and 2) markedly increased the magnitude of the low-frequency undulations (Figure 8G). The proteininduced changes in the lateral pressure profile are consistent with the results from Sodt and Pastor discussed earlier [181]. The data shows that the protein reduces the negative pressure in the lipid

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headgroup region of the outer (protein-containing) leaflet. The data also shows an increase in the positive pressure in the hydrocarbon core. The result is an overall reduction in the surface tension. This reduced tension then correlates with increased undulatory dynamics. Collectively, these simulated findings suggest that Syn softens a vesicular bilayer. Whether and how protein-induced softening of small vesicles influences their fusogenicity with flat, target membranes remains uncertain. Softening is expected to enhance fusion of flat bilayers by lowering barriers to formation of highly curved fusion intermediates. A small vesicle is already highly curved, and so softening/reduced surface tension may reduce fusion by lowering the driving force of lipids in the vesicle to join the flat membrane.

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Thus, while we now have compelling computational evidence that Syn alters the material properties of a small vesicle, we are left with several tasks: 1) Experimentally verify this computational observation; 2) Expand the understanding of how/if these alterations directly relate to a vesicle’s propensity to fuse with a flat membrane; and 3) Understand the interplay between the impact of Syn on the material properties and complex lipid constituency (and highly dense protein mileu) found in synaptic vesicles ; 4) Connect the effects of Syn on small vesicles to the experimental observations of mitochondrial fragmentation.

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The role of membrane curvature and disruption in Parkinson’s disease is still unclear. The majority of clinically oriented αSyn research in PD has not focused on the membrane. Instead, the focus has been on oligomerization and fibrillization into Lewy bodies. However, while αSyn is the predominant protein found in Lewy bodies, lipids are also present [182, 183]. In fact, it was shown that lipids and αSyn colocalize to the periphery of isolated Lewy bodies. Thus, it is quite possible that the formation of Lewy bodies is closely related to the behavior of αSyn on membranes. It has been speculated that the process of oligomerization starts on the surface of the membrane [184-186], and it has now been shown that membranes can facililtate/accelerate fiber formation [185]. Certainly, from the perspective of a diffusionlimited reaction (oligomerization), reducing the diffusion space from three-dimensions (in solution) to two-dimension (on the surface of the membrane) suggests that the membrane may be a central player. It is also possible that the process of tubulation and vesiculation of membranes goes hand-in-hand with fibrillization, and that this accounts for the lipids in the Lewy bodies (the proteins may bring the lipids along for the ride). Relatedly, much recent work in the PD field has focused on the intercellular transport of so-called toxic αSyn oligomers [187-191]. The process involves oligomeric αSyn association with lipid exosomes, which are (interestingly) typically 60-100 nm in size. It was found that cellular uptake and resulting toxicity of oligomeric αSyn is greater when associated with exosomes than when free in solution [187]. Thus, the field is becoming increasingly aware of the membrane as a critical part of the story of PD onset and progression. Developing novel interventions (therapies) may therefore be aimed at 1) preventing mitochondrial membrane disruption; 2) re-normalizing dysfunctional synaptic transmission; and 3) halting the cell-to-cell transmission of oligomeric αSyn. We have presented here a deepened understanding of αSyn as a curvature-generating and membrane-softening protein. The intimate combination of experimental, theoretical and computational biophysics has positioned the community to further our mechanistic insight into αSyn/membrane interactions and dysfunction, and perhaps to take advantage of these insights in developing new therapeutic strategies.

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ACCEPTED MANUSCRIPT Highlights: Syn-membrane interactions have been implicated in Parkinson’s Disease.

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Syn generates curvatures and remodels membranes into new 3-D shapes.

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Syn binding energy, partition depth, and bilayer tension determine remodeling.

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Syn modifies lipid membrane material properties such as bilayer rigidity.

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We review simulations and experiments used to study remodeling and mechanics.

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