Membrane Curvature Sensing by Amphipathic Helices: Insights from Implicit Membrane Modeling

Sensing and generation of lipid membrane curvature, mediated by the binding of specific proteins onto the membrane surface, play crucial roles in cell biology. A number of mechanisms have been proposed, but the molecular understanding of these processes is incomplete. All-atom molecular dynamics simulations have offered valuable insights but are extremely demanding computationally. Implicit membrane simulations could provide a viable alternative, but current models apply only to planar membranes. In this work, the implicit membrane model 1 is extended to spherical and tubular membranes. The geometric change from planar to curved shapes is straightforward but insufficient for capturing the full curvature effect, which includes changes in lipid packing. Here, these packing effects are taken into account via the lateral pressure profile. The extended implicit membrane model 1 is tested on the wild-types and mutants of the antimicrobial peptide magainin, the ALPS motif of arfgap1, α-synuclein, and an ENTH domain. In these systems, the model is in qualitative agreement with experiments. We confirm that favorable electrostatic interactions tend to weaken curvature sensitivity in the presence of strong hydrophobic interactions but may actually have a positive effect when those are weak. We also find that binding to vesicles is more favorable than binding to tubes of the same diameter and that the long helix of α-synuclein tends to orient along the axis of tubes, whereas shorter helices tend to orient perpendicular to it. Adoption of a specific orientation could provide a mechanism for coupling protein oligomerization to tubule formation.     

Synergism of Antimicrobial Frog Peptides Couples to Membrane Intrinsic Curvature Strain

Mixtures of the frog peptides magainin 2 and PGLa are well-known for their pronounced synergistic killing of Gram-negative bacteria. We aimed to gain insight into the underlying biophysical mechanism by interrogating the permeabilizing efficacies of the peptides as a function of stored membrane curvature strain. For Gram-negative bacterial-inner-membrane mimics, synergism was only observed when the anionic bilayers exhibited significant negative intrinsic curvatures imposed by monounsaturated phosphatidylethanolamine. In contrast, the peptides and their mixtures did not exhibit significant activities in charge-neutral mammalian mimics, including those with negative curvature, which is consistent with the requirement of charge-mediated peptide binding to the membrane. Our experimental findings are supported by computer simulations showing a significant decrease of the peptide-insertion free energy in membranes upon shifting intrinsic curvatures toward more positive values. The physiological relevance of our model studies is corroborated by a remarkable agreement with the peptide’s synergistic activity in Escherichia coli. We propose that synergism is related to a lowering of a membrane-curvature-strain-mediated free-energy barrier by PGLa that assists membrane insertion of magainin 2, and not by strict pairwise interactions of the two peptides as suggested previously.     

Gaussian Curvature Directs Stress Fiber Orientation and Cell Migration

We show that substrates with nonzero Gaussian curvature influence the organization of stress fibers and direct the migration of cells. To study the role of Gaussian curvature, we developed a sphere-with-skirt surface in which a positive Gaussian curvature spherical cap is seamlessly surrounded by a negative Gaussian curvature draping skirt, both with principal radii similar to cell-length scales. We find significant reconfiguration of two subpopulations of stress fibers when fibroblasts are exposed to these curvatures. Apical stress fibers in cells on skirts align in the radial direction and avoid bending by forming chords across the concave gap, whereas basal stress fibers bend along the convex direction. Cell migration is also strongly influenced by the Gaussian curvature. Real-time imaging shows that cells migrating on skirts repolarize to establish a leading edge in the azimuthal direction. Thereafter, they migrate in that direction. This behavior is notably different from migration on planar surfaces, in which cells typically migrate in the same direction as the apical stress fiber orientation. Thus, this platform reveals that nonzero Gaussian curvature not only affects the positioning of cells and alignment of stress fiber subpopulations but also directs migration in a manner fundamentally distinct from that of migration on planar surfaces.     

The Interplay of Structural and Cellular Biophysics Controls Clustering of Multivalent Molecules

Dynamic molecular clusters are assembled through weak multivalent interactions and are platforms for cellular functions, especially receptor-mediated signaling. Clustering is also a prerequisite for liquid-liquid phase separation. It is not well understood, however, how molecular structure and cellular organization control clustering. Using coarse-grained kinetic Langevin dynamics, we performed computational experiments on a prototypical ternary system modeled after membrane-bound nephrin, the adaptor Nck1, and the actin nucleation promoting factor NWASP. Steady-state cluster size distributions favored stoichiometries that optimized binding (stoichiometry matching) but still were quite broad. At high concentrations, the system can be driven beyond the saturation boundary such that cluster size is limited only by the number of available molecules. This behavior would be predictive of phase separation. Domains close to binding sites sterically inhibited clustering much less than terminal domains because the latter effectively restrict access to the cluster interior. Increased flexibility of interacting molecules diminished clustering by shielding binding sites within compact conformations. Membrane association of nephrin increased the cluster size distribution in a density-dependent manner. These properties provide insights into how molecular ensembles function to localize and amplify cell signaling.     

Bilayer Thickness and Curvature Influence Binding and Insertion of a pHLIP Peptide

The physical properties of lipid bilayers, such as curvature and fluidity, can affect the interactions of polypeptides with membranes, influencing biological events. Additionally, given the growing interest in peptide-based therapeutics, understanding the influence of membrane properties on membrane-associated peptides has potential utility. pH low insertion peptides (pHLIPs) are a family of water-soluble peptides that can insert across cell membranes in a pH-dependent manner, enabling the use of pH to follow peptide-lipid interactions. Here we study pHLIP interactions with liposomes varying in size and composition, to determine the influence of several key membrane physical properties. We find that pHLIP binding to bilayer surfaces at neutral pH is governed by the ease of access to the membrane’s hydrophobic core, which can be facilitated by membrane curvature, thickness, and the cholesterol content of the membrane. After surface binding, if the pH is lowered, the kinetics of pHLIP folding to form a helix and subsequent insertion across the membrane depends on the fluidity and energetic dynamics of the membrane. We showed that pHLIP is capable of forming a helix across lipid bilayers of different thicknesses at low pH. However, the kinetics of the slow phase of insertion corresponding to the translocation of C-terminal end of the peptide across lipid bilayer, vary approximately twofold, and correlate with bilayer thickness and fluidity. Although these influences are not large, local curvature variations in membranes of different fluidity could selectively influence surface binding in mixed cell populations.     

Lipid-Protein Interplay in Dimerization of Juxtamembrane Domains of Epidermal Growth Factor Receptor

Transmembrane (TM) helix and juxtamembrane (JM) domains (TM-JM) bridge the extracellular and intracellular domains of single-pass membrane proteins, including epidermal growth factor receptor (EGFR). TM-JM dimerization plays a crucial role in regulation of EGFR kinase activity at the cytoplasmic side. Although the interaction of JM with membrane lipids is thought to be important to turn on EGF signaling, and phosphorylation of Thr654 on JM leads to desensitization, the underlying kinetic mechanisms remain unclear. In particular, how Thr654 phosphorylation regulates EGFR activity is largely unknown. Here, combining single-pair FRET imaging and nanodisc techniques, we showed that phosphatidylinositol 4,5-bis phosphate (PIP₂) facilitated JM dimerization effectively. We also found that Thr654 phosphorylation dissociated JM dimers in the membranes containing acidic lipids, suggesting that Thr654 phosphorylation electrostatically prevented the interaction with basic residues in JM and acidic lipids. Based on the single-molecule experiment, we clarified the kinetic pathways of the monomer (inactive state)-to-dimer (active state) transition of JM domains and alteration in the pathways depending on the membrane lipid species and Thr654 phosphorylation.     

Role of Salt Valency in the Switch of H-NS Proteins between DNA-Bridging and DNA-Stiffening Modes

This work investigates the interactions of H-NS proteins and bacterial genomic DNA through computer simulations performed with a coarse-grained model. The model was developed specifically to study the switch of H-NS proteins from the DNA-stiffening to the DNA-bridging mode, which has been observed repeatedly upon addition of multivalent cations to the buffer but is still not understood. Unraveling the corresponding mechanism is all the more crucial, as the regulation properties of H-NS proteins, as well as other nucleoid proteins, are linked to their DNA-binding properties. The simulations reported here support a mechanism, according to which the primary role of multivalent cations consists in decreasing the strength of H-NS/DNA interactions compared to H-NS/H-NS interactions, with the latter ones becoming energetically favored with respect to the former ones above a certain threshold of the effective valency of the cations of the buffer. Below the threshold, H-NS dimers form filaments, which stretch along the DNA molecule but are quite inefficient in bridging genomically distant DNA sites (DNA-stiffening mode). In contrast, just above the threshold, H-NS dimers form three-dimensional clusters, which are able to connect DNA sites that are distant from the genomic point of view (DNA-bridging mode). The model provides clear rationales for the experimental observations that the switch between the two modes is a threshold effect and that the ability of H-NS dimers to form higher order oligomers is crucial for their bridging capabilities.     

A Cholesterol Analog Induces an Oligomeric Reorganization of VDAC

The oligomeric organization of the voltage-dependent anion-selective channel (VDAC) and its interactions with hexokinase play integral roles in mitochondrially mediated apoptotic signaling. Various small to large assemblies of VDAC are observed in mitochondrial outer membranes, but they do not predominate in detergent-solubilized VDAC samples. In this study, a cholesterol analog, cholesteryl-hemisuccinate (CHS), was shown to induce the formation of detergent-soluble VDAC multimers. The various oligomeric states of VDAC induced by the addition of CHS were deciphered through an integrated biophysics approach using microscale thermophoresis, analytical ultracentrifugation, and size-exclusion chromatography small angle x-ray scattering. Furthermore, CHS stabilizes the interaction between VDAC and hexokinase (K_d of 27 ± 6 μM), confirming the biological relevance of oligomers generated. Thus, sterols such as cholesterol in higher eukaryotes or ergosterol in fungi may regulate the VDAC oligomeric state and may provide a potential target for the modulation of apoptotic signaling by effecting VDAC-VDAC and VDAC-hexokinase interactions. In addition, the integrated biophysical approach described provides a powerful platform for the study of membrane protein complexes in solution.     

Protein Partitioning into Ordered Membrane Domains: Insights from Simulations

Cellular membranes are laterally organized into domains of distinct structures and compositions by the differential interaction affinities between various membrane lipids and proteins. A prominent example of such structures are lipid rafts, which are ordered, tightly packed domains that have been widely implicated in cellular processes. The functionality of raft domains is driven by their selective recruitment of specific membrane proteins to regulate their interactions and functions; however, there have been few general insights into the factors that determine the partitioning of membrane proteins between coexisting liquid domains. In this work, we used extensive coarse-grained and atomistic molecular dynamics simulations, potential of mean force calculations, and conceptual models to describe the partitioning dynamics and energetics of a model transmembrane domain from the linker of activation of T cells. We find that partitioning between domains is determined by an interplay between protein-lipid interactions and differential lipid packing between raft and nonraft domains. Specifically, we show that partitioning into ordered domains is promoted by preferential interactions between peptides and ordered lipids, mediated in large part by modification of the peptides by saturated fatty acids (i.e., palmitoylation). Ordered phase affinity is also promoted by elastic effects, specifically hydrophobic matching between the membrane and the peptide. Conversely, ordered domain partitioning is disfavored by the tight molecular packing of the lipids therein. The balance of these dominant drivers determines partitioning. In the case of the wild-type linker of activation of T cells transmembrane domain, these factors combine to yield enrichment of the peptide at L_o/L_d interfaces. These results define some of the general principles governing protein partitioning between coexisting membrane domains and potentially explain previous disparities among experiments and simulations across model systems.     

Modeling the Effect of Curvature on the Collective Behavior of Cells Growing New Tissue

The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue’s evolution. Understanding the cellular basis of this control is highly significant for bioscaffold tissue engineering, the evolution of bone microarchitecture, wound healing, and tumor growth. Although previous models have proposed geometrical relationships between tissue growth and curvature, the role of cell density and cell vigor remains poorly understood. We propose a cell-based mathematical model of tissue growth to investigate the systematic influence of curvature on the collective crowding or spreading of tissue-synthesizing cells induced by changes in local tissue surface area during the motion of the interface. Depending on the strength of diffusive damping, the model exhibits complex growth patterns such as undulating motion, efficient smoothing of irregularities, and the generation of cusps. We compare this model with in vitro experiments of tissue deposition in bioscaffolds of different geometries. By including the depletion of active cells, the model is able to capture both smoothing of initial substrate geometry and tissue deposition slowdown as observed experimentally.     

Cytoskeleton Remodeling Induces Membrane Stiffness and Stability Changes of Maturing Reticulocytes

Reticulocytes, the precursors of erythrocytes, undergo drastic alterations in cell size, shape, and deformability during maturation. Experimental evidence suggests that young reticulocytes are stiffer and less stable than their mature counterparts; however, the underlying mechanism is yet to be fully understood. Here, we develop a coarse-grained molecular-dynamics reticulocyte membrane model to elucidate how the membrane structure of reticulocytes contributes to their particular biomechanical properties and pathogenesis in blood diseases. First, we show that the extended cytoskeleton in the reticulocyte membrane is responsible for its increased shear modulus. Subsequently, we quantify the effect of weakened cytoskeleton on the stiffness and stability of reticulocytes, via which we demonstrate that the extended cytoskeleton along with reduced cytoskeleton connectivity leads to the seeming paradox that reticulocytes are stiffer and less stable than the mature erythrocytes. Our simulation results also suggest that membrane budding and the consequent vesiculation of reticulocytes can occur independently of the endocytosis-exocytosis pathway, and thus, it may serve as an additional means of removing unwanted membrane proteins from reticulocytes. Finally, we find that membrane budding is exacerbated when the cohesion between the lipid bilayer and the cytoskeleton is compromised, which is in accord with the clinical observations that erythrocytes start shedding membrane surface at the reticulocyte stage in hereditary spherocytosis. Taken together, our results quantify the stiffness and stability change of reticulocytes during their maturation and provide, to our knowledge, new insights into the pathogenesis of hereditary spherocytosis and malaria.     

Visualization of Dynamic Sub-microsecond Changes in Membrane Potential

Direct observation of rapid membrane potential changes is critical to understand how complex neurological systems function. This knowledge is especially important when stimulation is achieved through an external stimulus meant to mimic a naturally occurring process. To enable exploration of this dynamic space, we developed an all-optical method for observing rapid changes in membrane potential at temporal resolutions of ～25 ns. By applying a single 600-ns electric pulse, we observed sub-microsecond, continuous membrane charging and discharging dynamics. Close agreement between the acquired results and an analytical membrane-charging model validates the utility of this technique. This tool will deepen our understanding of the role of membrane potential dynamics in the regulation of many biological and chemical processes within living systems.     

A New Computational Method for Membrane Compressibility: Bilayer Mechanical Thickness Revisited

Because lipid bilayers can bend and stretch in ways similar to thin elastic sheets, physical models of bilayer deformation have utilized mechanical constants such as the moduli for bending rigidity $\left({\kappa }_C\right)$ and area compressibility (K_A). However, the use of these models to quantify the energetics of membrane deformation associated with protein-membrane interactions, and the membrane response to stress is often hampered by the shortage of experimental data suitable for the estimation of the mechanical constants of various lipid mixtures. Although computational tools such as molecular dynamics simulations can provide alternative means to estimate K_A values, current approaches suffer significant technical limitations. Here, we present a novel, to our knowledge, computational framework that allows for a direct estimation of K_A values for individual bilayer leaflets. The theory is based on the concept of elasticity and derives K_A from real-space analysis of local thickness fluctuations sampled in molecular dynamics simulations. We explore and validate the model on a large set of single and multicomponent bilayers of different lipid compositions and sizes, simulated at different temperatures. The calculated bilayer compressibility moduli agree with values estimated previously from experiments and those obtained from a standard computational method based on a series of constrained tension simulations. We further validate our framework in a comparison with an existing polymer brush model and confirm the polymer brush model’s predicted linear relationship with proportionality coefficient of 24, using elastic parameters calculated from the simulation trajectories. The robustness of the results that emerge from the method allows us to revisit the origins of the bilayer mechanical (compressible) thickness and in particular its dependence on acyl-chain unsaturation and the presence of cholesterol.