Session T07: The Physics of Cell Membranes II: From Simplified Models to Complex Functionality

Physical limits to membrane curvature sensing by a single protein

Membrane curvature sensing plays an important role during biological processes such as cell division. Recent experiments have revealed that nanometer-sized proteins such as septins can distinguish between micron-sized membrane-coated glass beads of different diameters, despite being orders of magnitude smaller. Membranes are also subject to local curvatures that vary spatiotemporally due to thermal fluctuations, leading to discrepancies between the instantaneously measured curvature and the bead’s curvature. Using continuum models of fluctuating membranes, we investigate whether it is feasible for a protein to sense deviations in bilayer lipid densities as a proxy for local curvature to infer the membrane’s overall shape. With concepts from estimation theory, we quantify how the sensing efficacy of a single protein depends on parameters such as protein size, bilayer thickness, membrane bending modulus, membrane-substrate adhesion strength, and bead size. Proteins can better distinguish between a pair of membrane-adhered beads if the beads are small; however, when the beads are sufficiently different in size, the sensing efficacy is appreciable even for micron-sized beads.   

Lipid Bilayer Fluctuations in silico: Statistical Improvements and Systematic Corrections

The energetics of lipid bilayer deformations can be described by continuum theories in which each type of deformation is weighted by an elastic modulus. In computer simulations, these moduli can be determined by fitting power spectra of fluctuating fields (e.g. surface height) to the predictions of those continuum theories. This data analysis involves numerous choices, such as how to define a membrane surface or how to determine the fitting range, which significantly affect the observables of interest. Here, we examine in detail the systematic trends resulting from these choices, on the basis of atomistic simulation trajectories of 13 different lipid model membranes, as well as coarse-grained MARTINI simulations of much larger systems, both created by Venable et al. We in particular discuss systematic effects connected with: (1) interpolation of height and directional fields; (2) normalization and averaging of lipid directors; (3) determining small-scale cutoffs. Additionally, we discuss statistical aspects such as correcting for time correlations in the power spectra, bootstrapping for uncertainties on the parameters, and simultaneously fitting different spectra. Overall, ever-improving computational abilities have lead to statistical uncertainties in the elastic moduli that are often smaller than systematic shifts arising from equally plausible choices, rendering the latter the more important concern.   

Mechanical Properties of Pseudomonas Aeruginosa Outer Membrane

Pseudomonas aeruginosa is a major pathogen for many infectious diseases such as Pneumonia. The outer membrane of these gram-negative bacteria acts as an external shield against environmental threats, which also makes them resistant to antibiotics. This work aims to develop an accurate in silico model of P. aeruginosa outer membrane using all-atom molecular dynamics and characterize its mechanical properties. The outer leaflet of this asymmetric membrane contains PA14 Lipid A, and the inner leaflet is composed of a mixture of POPE and POPG phospholipids. A major challenge in modeling asymmetric membranes is determining the numbers of distinct lipids in each leaflet, which would affect the mechanical properties of bilayers. The most widely used method matches the equilibrium areas of two leaflets, which are obtained from corresponding symmetric bilayers. However, this method may render non-zero tension within each leaflet, and the bilayer would be subject to differential stress. Recently, a new method has been proposed to construct asymmetric membranes with zero leaflet tension. We compare the mechanical properties of PA14 outer membranes made with two methods to understand the effects of membrane building protocols to provide important guidelines for future simulation studies.   

Formation of buds, pearls, and tubes in membranes

The formation of highly curved structures on the plasma membranes of cells is critical for trafficking. Buds form during endo and exocytosis, tubes and pearled structures also form during trafficking from internal organelles and in yeast endocytosis. In this work, using continuum models, I will elaborate on continuum models that can help us obtain insight into the parameter spaces necessary to obtain these shapes and particularly, how membrane tension can play a critical role in determining the outcome of these shapes. These models are based on the classic Helfrich energy with modifications to address the particular biophysical problem. Using clathrin-mediated endocytosis as an example, I will share results on how tension governs the formation of a vesicle and a tube. The contributions of spontaneous curvature and forces due to cytoskeleton interactions will also be discussed.  Since these shapes are motivated by experimental observations in cells and in vesicles, I will also talk about some of the challenges of using simple continuum models for such processes and room for advances in model development and computational schemes.     

Coupled Evolution of Viral Protein Density and Membrane Shape in Coronavirus Assembly

The assembly of coronaviruses in cells proceeds via the aggregation of membrane associated viral capsid proteins, leading to budding encapsulating the genetic material. For this process, the dynamics are controlled by interactions between proteins and their coupling to membrane curvature. To quantitatively understand the dynamics of this process, we propose a generalized analytical model that accounts for the key physical features. We describe the coupled time evolution of the protein density field and the membrane height (above a reference plane), taking into account the diffusion of proteins across the membrane and the effects their spontaneous curvature has on membrane bending. We performed linear stability analysis to determine the behavior of oscillations about various equilibrium configurations, finding stable/unstable/fastest growing modes based on original conditions. Numerical simulations, using the finite difference method, and Monte Carlo simulations, based on the free energy functional of the system, were then used to validate our results and analyze the evolution of the system both within and outside the domains defined by the linear stability analysis.   

Erythro-PmBs: A Novel Polymyxin B Delivery System Using Antibody-Conjugated Hybrid Erythrocyte Liposomes

As a result of the growing world-wide antibiotic resistance crisis, many currently existing antibiotics have become ineffective due to bacteria developing resistive mechanisms. There are a limited number of potent antibiotics successful at suppressing microbial growth, such as polymyxin B (PmB); however, they are deemed as a last resort due to their toxicity. We present a novel PmB delivery system constructed by conjugating hybrid erythrocyte liposomes with bacterial antibodies to combine a high loading efficiency with guided delivery. PmB encapsulation is enhanced by incorporating negatively charged lipids into the red blood cells' cytoplasmic membrane. Anti-E.coli antibodies are attached to the hybrid erythrocyte liposomes through DSPE-PEG malemeide linkers. We show that these Erythro-PmBs have a loading efficiency of 90%, and are effective in delivering PmB to E. coli, with values for the minimum inhibitory concentration (MIC) comparable to those of free PmB. MIC values for K. aerogenes were significantly increased beyond the resistant breakpoint, indicating that inclusion of the  anti-E.coli antibodies enables the Erythro-PmBs to selectively deliver antibiotics to specific targets. This versatile platform can be used for different types of antibiotics and bacterial targets.   

Sterol conjugated lipids for improved liposomal stability

Liposomal nanoparticles are outstanding candidates for vaccine and drug delivery applications. However, the liposomal stability under physiological conditions is a major challenge, and often results in premature drug release. This has been traditionally addressed by incorporating cholesterol which increases membrane stability through its lipid densification effect. But cholesterol tends to rapidly exchange into cell membranes, which compromises liposomal stability. To mitigate this effect, sterol-modified lipids (SMLs) present attractive substitutes for cholesterol. Our experimental results confirm the anticipated structural and mechanical effects of SMLs on lipid membranes. Small-angle X-ray measurements show that SML inclusion increases the bilayer thickness and decreases the area per lipid, indicating tighter molecular packing. These results agree with differential scanning calorimetry studies and surface pressure-area isotherms. Complementary neutron spin-echo (NSE) spectroscopy measurements confirm that the observed structural changes lead to increased membrane bending rigidity and increased liposomal stability. These findings illustrate the structure-property relations underlying improved liposomal designs required for circumventing a current bottleneck in drug delivery.   

Viral Fusion Peptide Interactions with Lipid Bilayers Studied by Neutron Scattering

The HIV-1 virus infects a target cell through a process that begins with binding to the surface of the cell membrane and then fusing with it. Key to the process is a short sequence at the end of the gp41 capsid protein, which is called the fusion peptide (FP). The isolated FP can also cause vesicles to fuse, a process that involves a conformational transition that depends on peptide concentration and the composition of the membrane.  Here, the dependence of the lipid composition, specifically the acyl chain composition, on the behavior of the FP was studied by neutron spin echo spectroscopy, small-angle neutron scattering and circular dichroism spectroscopy.  The results indicate that the behavior of the FP depends strongly on the unsaturated acyl chain composition of the membrane but suggest that the behavior does not depend on the composition in a linear fashion. The present results provide new insight into how the FP conformational transition drives vesicle fusion.   

Dependence of protein-induced lipid bilayer thickness deformations on protein shape

Structural biology has shown that membrane proteins come in a great variety of shapes, with distinct membrane proteins, and even different conformational states of the same membrane protein, often showing distinct hydrophobic thicknesses deviating from the unperturbed thickness of the surrounding lipid bilayer. The resulting protein-induced bilayer thickness deformations can be captured quantitatively by membrane elasticity theory, and have been found to play an important role in membrane protein regulation. Physical models of protein-induced bilayer thickness deformations usually focus on idealized, cylindrical membrane protein shapes. We describe here a boundary value method for the straightforward calculation of protein-induced bilayer thickness deformations for arbitrary protein shapes. We find that the deviations of protein shape from rotational symmetry suggested by structural biology can have a large effect on the energy of protein-induced bilayer thickness deformations. Intriguingly, our calculations suggest that the elastic coupling of lipid bilayer properties and membrane protein conformational state may provide a generic physical mechanism for temperature sensing through ion channels.   

How pinning influences the dynamics of cell membranes

We simulate a membrane in thermal equilibrium, tethered to a flat surface at discrete random points.  We consider two cases, one where there is no correlation between randomly chosen tethered points and second where the tethered points appear in randomly placed clusters. We find that:

(a) for small frame tension the internal tension  decreases as pinning increases, 

(b) The internal tension and the fluctuating tension are approximately equal,   

(c) how the pinned points are distributed affects the spectrum  at small wavenumbers but has no significant effect on the internal tension.

Assuming small deformation we derive, theoretically, how the change in area varies with change in surface tension for a pinned membrane. This agrees with our simulations.  We use flicker imaging of HeLA cells to probe the same relation experimentally while we turn off the pinning of the cell membrane (partially) to the cytoskeleton by manipulating the protein ezrin.  Results of these experiments agree with both theory and numerical simulations showing that dynamics of the cell membrane is dominated by its pinning to the cytoskeleton.

     

Spontaneous Lipid Nano Tubulation Driven by Automotive Passive Nanoparticles

Lipid nanotubules (LNTs) form an integral part of intracellular and intercellular communication and transport. Recent research interests on these LNTs are owing to their crucial role in the spread of infection from diseased cells and on the other hand its role in the facilitation of drug transport across cells. Hence, it becomes very relevant to investigate the control parameters pertaining to the initiation and inhibition of LNTs. In this study, the role of the membrane phase has been varied to analyze its effect on the properties of LNTs such as tube length, tube stiffness, and growth kinetics such as tubulation and retraction time scale. For the first time, passive nanoparticles have been employed to spontaneously generate dynamically evolving LNT structures encompassing growth and retraction regimes. The results inferred from the controlled model membrane study provides insights about the role of membrane fluidity/rigidity in determining the onset or delay of an infection or drug transfer   

Multiscale geometry and mechanics of lipid monolayer collapse

Langmuir monolayers at gas/liquid interfaces provide a rich framework to investigate the interplay between multi-scale geometry and mechanics. Monolayer collapse is investigated at a topological and geometric level by building a scale space M from experimental imaging data. We present a general lipid monolayer collapse phase diagram, which shows that wrinkling, folding, crumpling, shear banding, and vesiculation are a continuous set of mechanical states that can be approached by either tuning monolayer composition or temperature. The origin of the different mechanical states can be understood by investigating the monolayer geometry at two scales: fluorescent versus atomic force microscopy imaging. We show that an interesting switch in continuity occurs in passing between the two scales, C_AFM ∈M_AFM ≠C_FM ∈M. Studying the difference between monolayers that fold versus shear band, we show that shear banding is correlated to the persistence of a multilength scale microstructure within the monolayer at all surface pressures. A detailed analytical geometric formalism to describe this microstructure is developed using the theory of structured deformations. Lastly, we provide the first finite element simulations of lipid monolayer collapse utilizing a direct mapping from the experimental image space M into a simulation domain P. We show that elastic dissipation in the form of bielasticity is a necessary and sufficient condition to capture loss of in-plane stability and shear banding.