Revealing the Effects of Nanoscale Membrane Curvature on Lipid Mobility

Diffusion Analyses along Mean and Gaussian-Curved Membranes with CurD

Curved cellular membranes are both abundant and functionally relevant. While novel tomography approaches reveal the structural details of curved membranes, their dynamics pose an experimental challenge. Curvature especially affects the diffusion of lipids and macromolecules, yet neither experiments nor continuum models distinguish geometric effects from those caused by curvature-induced changes in membrane properties. Molecular simulations could excel here, yet despite community interest toward curved membranes, tools for their analysis are still lacking. Here, we satisfy this demand by introducing CurD, our novel and openly available implementation of the Vertex-oriented Triangle Propagation algorithm to the study of lipid diffusion along membranes with mean and/or Gaussian curvature. This approach, aided by our highly optimized implementation, computes geodetic distances significantly faster than conventional implementations of path-finding algorithms. Our tool, applied to coarse-grained simulations, allows for the first time the analysis of curvature effects on diffusion at size scales relevant to physiological processes such as endocytosis. Our analyses with different membrane geometries reveal that Gaussian curvature plays a surprisingly small role on lipid motion, whereas mean curvature; i.e., the packing of lipid headgroups largely dictates their mobility.

Analysis of Phase Heterogeneity in Lipid Membranes Using Single-Molecule Tracking in Live Cells

In live cells, the plasma membrane is composed of lipid domains separated by hundreds of nanometers in dynamic equilibrium. Lipid phase separation regulates the trafficking and spatiotemporal organization of membrane molecules that promote signal transduction. However, visualizing domains with adequate spatiotemporal accuracy remains challenging because of their subdiffraction limit size and highly dynamic properties. Here, we present a single lipid-molecular motion analysis pipeline (lipid-MAP) for analyzing the phase heterogeneity of lipid membranes by detecting the instantaneous velocity change of a single lipid molecule using the excellent optical properties of nanoparticles, high spatial localization accuracy of single-molecule localization microscopy, and separation capability of the diffusion state of the hidden Markov model algorithm. Using lipid-MAP, individual lipid molecules were found to be in dynamic equilibrium between two statistically distinguishable phases, leading to the formation of small (∼170 nm), viscous (2.5× more viscous than surrounding areas), and transient domains in live cells. Moreover, our findings provide an understanding of how membrane compositional changes, i.e., cholesterol and phospholipids, affect domain formation. This imaging method can contribute to an improved understanding of spatiotemporal-controlled membrane dynamics at the molecular level.

Four-color fluorescence cross-correlation spectroscopy with one laser and one camera

The diffusion and reorganization of phospholipids and membrane-associated proteins are fundamental for cellular function. Fluorescence cross-correlation spectroscopy (FCCS) measures diffusion and molecular interactions at nanomolar concentration in biological systems. We have developed an economical method to simultaneously monitor diffusion and complexation with the use of super-continuum laser and spectral deconvolution from a single detector. Customizable excitation wavelengths were chosen from the wide-band source and spectral fitting of the emitted light revealed the interactions for up to four chromatically overlapping fluorophores simultaneously. This method was applied to perform four-color FCCS that we demonstrated with polystyrene nanoparticles, lipid vesicles, and membrane-bound molecules. Up to four individually customizable excitation channels were selected from the broad-spectrum fiber laser to excite the diffusers within a diffraction-limited spot. The fluorescence emission passed through a cleanup filter and a dispersive prism prior to being collected by a sCMOS or EMCCD camera with up to 1.8 kHz frame rates. The emission intensity versus time of each fluorophore was extracted through a linear least-square fitting of each camera frame and temporally correlated via custom software. Auto- and cross-correlation functions enabled the measurement of the diffusion rates and binding partners. We have measured the induced aggregation of nanobeads and lipid vesicles in solution upon increasing the buffer salinity. Because of the adaptability of investigating four fluorophores simultaneously with a cost-effective method, this technique will have wide application for examining macromolecular complex formation in model and living systems.

Four-color fluorescence cross-correlation spectroscopy with one laser and one camera

The diffusion and reorganization of phospholipids and membrane-associated proteins are fundamental for cellular function. Fluorescence cross-correlation spectroscopy (FCCS) measures the diffusion and molecular interactions at nanomolar concentration in biological systems. We have developed a novel, economical method to simultaneously monitor diffusion and oligomerization with the use of super-continuum laser and spectral deconvolution from a single detector. Customizable excitation wavelengths were chosen from the wide-band source and spectral fitting of the emitted light revealed the interactions for up to four spectrally overlapping fluorophores simultaneously. This method was applied to perform four-color FCCS, as demonstrated with polystyrene nanoparticles, lipid vesicles, and membrane-bound molecules. Up to four individually customizable excitation channels were selected from the broad-spectrum fiber laser to excite the diffusers within a diffraction-limited spot. The fluorescence emission passed through a cleanup filter and a dispersive prism prior to being collected by a sCMOS or EMCCD camera with up to 10 kHz frame rates. The emission intensity versus time of each fluorophore was extracted through a linear least-square fitting of each camera frame and temporally correlated via custom software. Auto- and cross-correlation functions enabled the measurement of the diffusion rates and binding partners. We have measured the induced aggregation of nanobeads and lipid vesicles in solution upon increasing the buffer salinity. Because of the adaptability of investigating four fluorophores simultaneously with a cost-effective method, this technique will have wide application for examining complex homo- and heterooligomerization in model and living systems.

Nanoscale membrane curvature sorts lipid phases and alters lipid diffusion

The precise spatiotemporal control of nanoscale membrane shape and composition is the result of a complex interplay of individual and collective molecular behaviors. Here, we employed single-molecule localization microscopy and computational simulations to observe single-lipid diffusion and sorting in model membranes with varying compositions, phases, temperatures, and curvatures. Supported lipid bilayers were created over 50-nm-radius nanoparticles to mimic the size of naturally occurring membrane buds, such as endocytic pits and the formation of viral envelopes. The curved membranes recruited liquid-disordered lipid phases while altering the diffusion and sorting of tracer lipids. Disorder-preferring fluorescent lipids sorted to and experienced faster diffusion on the nanoscale curvature only when embedded in a membrane capable of sustaining lipid phase separation at low temperatures. The curvature-induced sorting and faster diffusion even occurred when the sample temperature was above the miscibility temperature of the planar membrane, implying that the nanoscale curvature could induce phase separation in otherwise homogeneous membranes. Further confirmation and understanding of these results are provided by continuum and coarse-grained molecular dynamics simulations with explicit and spontaneous curvature-phase coupling, respectively. The curvature-induced membrane compositional heterogeneity and altered dynamics were achieved only with a coupling of the curvature with a lipid phase separation. These cross-validating results demonstrate the complex interplay of lipid phases, molecular diffusion, and nanoscale membrane curvature that are critical for membrane functionality.

Phosphatidic Acid Accumulates at Areas of Curvature in Tubulated Lipid Bilayers and Liposomes

Phosphatidic acid (PA) is a signaling lipid that is produced enzymatically from phosphatidylcholine (PC), lysophosphatidic acid, or diacylglycerol. Compared to PC, PA lacks a choline moiety on the headgroup, making the headgroup smaller than that of PC and PA, and PA has a net negative charge. Unlike the cylindrical geometry of PC, PA, with its small headgroup relative to the two fatty acid tails, is proposed to support negatively curved membranes. Thus, PA is thought to play a role in a variety of biological processes that involve bending membranes, such as the formation of intraluminal vesicles in multivesicular bodies and membrane fusion. Using supported tubulated lipid bilayers (STuBs), the extent to which PA localizes to curved membranes was determined. STuBs were created via liposome deposition with varying concentrations of NaCl (500 mM to 1 M) on glass to form supported bilayers with connected tubules. The location of fluorescently labeled lipids relative to tubules was determined by imaging with total internal reflection or confocal fluorescence microscopy. The accumulation of various forms of PA (with acyl chains of 16:0-6:0, 16:0-12:0, 18:1-12:0) were compared to PC and the headgroup labeled phosphatidylethanolamine (PE), a lipid that has been shown to accumulate at regions of curvature. PA and PE accumulated more at tubules and led to the formation of more tubules than PC. Using large unilamellar liposomes in a dye-quenching assay, the location of the headgroup labeled PE was determined to be mostly on the outer, positively curved leaflet, whereas the tail labeled PA was located more on the inner, negatively curved leaflet. This study demonstrates that PA localizes to regions of negative curvature in liposomes and supports the formation of curved, tubulated membranes. This is one way that PA could be involved with curvature formation during a variety of cell processes.

Lipid flip-flop and desorption from supported lipid bilayers is independent of curvature

Flip-flop of lipids of the lipid bilayer (LBL) constituting the plasma membrane (PM) plays a crucial role in a myriad of events ranging from cellular signaling and regulation of cell shapes to cell homeostasis, membrane asymmetry, phagocytosis, and cell apoptosis. While extensive research has been conducted to probe the lipid flip flop of planar lipid bilayers (LBLs), less is known regarding lipid flip-flop for highly curved, nanoscopic LBL systems despite the vast importance of membrane curvature in defining the morphology of cells and organelles and in maintaining a variety of cellular functions, enabling trafficking, and recruiting and localizing shape-responsive proteins. In this paper, we conduct molecular dynamics (MD) simulations to study the energetics, structure, and configuration of a lipid molecule undergoing flip-flop and desorption in a highly curved LBL, represented as a nanoparticle-supported lipid bilayer (NPSLBL) system. We compare our findings against those of a planar substrate supported lipid bilayer (PSSLBL). Our MD simulation results reveal that despite the vast differences in the curvature and other curvature-dictated properties (e.g., lipid packing fraction, difference in the number of lipids between inner and outer leaflets, etc.) between the NPSLBL and the PSSLBL, the energetics of lipid flip-flop and lipid desorption as well as the configuration of the lipid molecule undergoing lipid flip-flop are very similar for the NPSLBL and the PSSLBL. In other words, our results establish that the curvature of the LBL plays an insignificant role in lipid flip-flop and desorption.

Single-lipid dynamics in phase-separated supported lipid bilayers

Phase separation is a fundamental organizing mechanism on cellular membranes. Lipid phases have complex dependencies on the membrane composition, curvature, tension, and temperature. Lipid diffusion rates vary by up to ten-fold between liquid-disordered (L_d) and liquid-ordered (L_o) phases depending on the membrane composition, measurement technique, and the surrounding environment. This manuscript reports the lipid diffusion on phase-separated supported lipid bilayers (SLBs) with varying temperature, composition, and lipid phase. Lipid diffusion is measured by single-particle tracking (SPT) and fluorescence correlation spectroscopy (FCS) via custom data acquisition and analysis protocols that apply to diverse membranes systems. Traditionally, SPT is sensitive to diffuser aggregation, whereas the diffusion rates reported by FCS are unaffected by the presence of immobile aggregates. Within this manuscript, we report (1) improved single-particle tracking analysis of lipid diffusion, (2) comparison and consistency between diffusion measurement methods for non-Brownian diffusers, and (3) the application of these methods to measure the phase, temperature, and composition dependencies in lipid diffusion. We demonstrate improved SPT analysis methods that yield consistent FCS and SPT diffusion results even when most fluorescent lipids are frequently confined within aggregates within the membrane. With varying membrane composition and temperature, we demonstrate differences in diffusion between the L_d and L_o phases of SLBs.

Variations in Plasma Membrane Topography Can Explain Heterogenous Diffusion Coefficients Obtained by Fluorescence Correlation Spectroscopy

Fluorescence correlation spectroscopy (FCS) is frequently used to study diffusion in cell membranes, primarily the plasma membrane. The diffusion coefficients reported in the plasma membrane of the same cell type and even within single cells typically display a large spread. We have investigated whether this spread can be explained by variations in membrane topography throughout the cell surface, that changes the amount of membrane in the FCS focal volume at different locations. Using FCS, we found that diffusion of the membrane dye DiI in the apical plasma membrane was consistently faster above the nucleus than above the cytoplasm. Using live cell scanning ion conductance microscopy (SICM) to obtain a topography map of the cell surface, we demonstrate that cell surface roughness is unevenly distributed with the plasma membrane above the nucleus being the smoothest, suggesting that the difference in diffusion observed in FCS is related to membrane topography. FCS modeled on simulated diffusion in cell surfaces obtained by SICM was consistent with the FCS data from live cells and demonstrated that topography variations can cause the appearance of anomalous diffusion in FCS measurements. Furthermore, we found that variations in the amount of the membrane marker DiD, a proxy for the membrane, but not the transmembrane protein TCRζ or the lipid-anchored protein Lck, in the FCS focal volume were related to variations in diffusion times at different positions in the plasma membrane. This relationship was seen at different positions both at the apical cell and basal cell sides. We conclude that it is crucial to consider variations in topography in the interpretation of FCS results from membranes.

Structural Dynamics of Lipid Bilayer Membranes Explored by Magnetic Field Effect Based Fluorescence Microscopy

Lipid bilayer membranes are known to exist as heterogeneous and dynamic structures where the molecules are always moving and fluctuating under physiological conditions. Magnetic field effects (MFEs) studied herein are phenomena in which the exciplex emission from an electron donor-acceptor dyad increases or decreases by applying an external magnetic field. The characteristic dependence of MFEs on the viscosity and polarity of the surrounding medium has been applied to investigate the local environments around the probe molecule. In this study, a novel MFE-based fluorescence microscopy technique was developed to explore the structural dynamics of lipid bilayer membranes. The vesicle formation during the membrane deformation was selectively visualized through the MFEs, thus allowing the extraction of information on the cellular dynamics at high temporal and spatial resolutions. This highly versatile and powerful technique is applicable to a wide range of areas, such as biology and material science.

Single-Molecule Detection with Lightguiding Nanowires: Determination of Protein Concentration and Diffusivity in Supported Lipid Bilayers

Determining the surface concentration and diffusivity of cell-membrane-bound molecules is central to the understanding of numerous important biochemical processes taking place at cell membranes. Here we use the high aspect ratio and lightguiding properties of semiconductor nanowires (NWs) to detect the presence of single freely diffusing proteins bound to a lipid bilayer covering the NW surface. Simultaneous observation of light-emission dynamics of hundreds of individual NWs occurring on the time scale of only a few seconds is interpreted using analytical models and employed to determine both surface concentration and diffusivity of cholera toxin subunit B (CTxB) bound to GM1 gangliosides in supported lipid bilayer (SLB) at surface concentrations down to below one CTxB per μm². In particular, a decrease in diffusivity was observed with increasing GM1 content in the SLB, suggesting increasing multivalent binding of CTxB to GM1. The lightguiding capability of the NWs makes the method compatible with conventional epifluorescence microscopy, and it is shown to work well for both photostable and photosensitive dyes. These features make the concept an interesting complement to existing techniques for studying the diffusivity of low-abundance cell-membrane-bound molecules, expanding the rapidly growing use of semiconductor NWs in various bioanalytical sensor applications and live cell studies.

Single-lipid tracking on nanoscale membrane buds: The effects of curvature on lipid diffusion and sorting

Nanoscale membrane curvature in cells is critical for endocytosis/exocytosis and membrane trafficking. However, the biophysical ramifications of nanoscale membrane curvature on the behavior of lipids remain poorly understood. Here, we created an experimental model system of membrane curvature at a physiologically-relevant scale and obtained nanoscopic information on single-lipid distributions and dynamics. Supported lipid bilayers were created over 50 and 70 nm radius nanoparticles to create membrane buds. Single-molecule localization microscopy was performed with diverse mixtures of fluorescent and non-fluorescent lipids. Variations in lipid acyl tales length, saturation, head-group, and fluorescent labeling strategy were tested while maintaining a single fluid lipid phase throughout the membrane. Monte Carlo simulations were used to fit our experimental results and quantify the effects of curvature on the lipid diffusion and sorting. Whereas varying the composition of the non-fluorescent lipids yielded minimal changes to the curvature effects, the labeling strategy of the fluorescent lipids yielded highly varying effects of curvature. Most conditions yield single-population Brownian diffusion throughout the membrane; however, curvature-induced lipid sorting, slowing, and aggregation were observed in some conditions. Head-group labeled lipids such as DPPE-Texas Red and POPE-Rhodamine diffused >2.4× slower on the curved vs. the planar membranes; tail-labeled lipids such as NBD-PPC, TopFluor-PPC, and TopFluor-PIP2, as well as DiIC₁₂ and DiIC₁₈ displayed no significant changes in diffusion due to the membrane curvature. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.

Nanoscale Membrane Budding Induced by CTxB and Detected via Polarized Localization Microscopy

For endocytosis and exocytosis, membranes transition among planar, budding, and vesicular topographies through nanoscale reorganization of lipids, proteins, and carbohydrates. However, prior attempts to understand the initial stages of nanoscale bending have been limited by experimental resolution. Through the implementation of polarized localization microscopy, this article reports the inherent membrane bending capability of cholera toxin subunit B (CTxB) in quasi-one-component-supported lipid bilayers. Membrane buds were first detected with <50 nm radius, grew to >200 nm radius, and extended into longer tubules with dependence on the membrane tension and CTxB concentration. Compared to the concentration of the planar-supported lipid bilayers, CTxB was (12 ± 4)× more concentrated on the positive curvature top and (26 ± 11)× more concentrated on the negative Gaussian curvature neck of the nanoscale membrane buds. CTxB is frequently used as a marker for liquid-ordered lipid phases; however, the coupling between CTxB and membrane bending provides an alternate understanding of CTxB-induced membrane reorganization. These findings allow for the reinterpretation of prior observations by correlating CTxB clustering and diffusion to CTxB-induced membrane bending. Single-particle tracking was performed on single lipids and CTxB to reveal the correlations among single-molecule diffusion, CTxB accumulation, and membrane topography. Slowed lipid and CTxB diffusion was observed at the nanoscale bud locations, suggesting a local increase in the effective membrane viscosity or molecular crowding upon membrane bending. These results suggest inherent CTxB-induced membrane bending as a mechanism for initiating CTxB internalization in cells that could be independent of clathrin, caveolin, actin, and lipid phase separation.