Timur R. Galimzyanov

Energy of the interaction between membrane lipid domains calculated from splay and tilt deformations

Specific domains, called rafts, are formed in cell membranes. Similar lipid domains can be formed in model membranes as a result of phase separation with raft size may remaining small (∼10–100 nm) for a long time. The characteristic lifetime of a nanoraft ensemble strongly depends on the nature of mutual raft interactions. The interaction energy between the boundaries of two rafts has been calculated under the assumption that the thickness of the raft bilayer is greater than that of the surrounding membrane, and elastic deformations appear in order to smooth the thickness mismatch at the boundary. When rafts approach each other, deformations from their boundaries overlap, making interaction energy profile sophisticated. It has been shown that raft merger occurs in two stages: rafts first merge in one monolayer of the lipid bilayer and then in another monolayer. Each merger stage requires overcoming of an energy barrier of about 0.08–0.12 kBT per 1 nm of boundary length. These results allow us to explain the stability of the ensemble of finite sized rafts.

Pore formation in lipid membrane I: Continuous reversible trajectory from intact bilayer through hydrophobic defect to transversal pore

Lipid membranes serve as effective barriers allowing cells to maintain internal composition differing from that of extracellular medium. Membrane permeation, both natural and artificial, can take place via appearance of transversal pores. The rearrangements of lipids leading to pore formation in the intact membrane are not yet understood in details. We applied continuum elasticity theory to obtain continuous trajectory of pore formation and closure, and analyzed molecular dynamics trajectories of pre-formed pore reseal. We hypothesized that a transversal pore is preceded by a hydrophobic defect: intermediate structure spanning through the membrane, the side walls of which are partially aligned by lipid tails. This prediction was confirmed by our molecular dynamics simulations. Conversion of the hydrophobic defect into the hydrophilic pore required surmounting some energy barrier. A metastable state was found for the hydrophilic pore at the radius of a few nanometers. The dependence of the energy on radius was approximately quadratic for hydrophobic defect and small hydrophilic pore, while for large radii it depended on the radius linearly. The pore energy related to its perimeter, line tension, thus depends of the pore radius. Calculated values of the line tension for large pores were in quantitative agreement with available experimental data.

Pore formation in lipid membrane II: Energy landscape under external stress

Lipid membranes are extremely stable envelopes allowing cells to survive in various environments and to maintain desired internal composition. Membrane permeation through formation of transversal pores requires substantial external stress. Practically, pores are usually formed by application of lateral tension or transmembrane voltage. Using the same approach as was used for obtaining continuous trajectory of pore formation in the stress-less membrane in the previous article, we now consider the process of pore formation under the external stress. The waiting time to pore formation proved a non-monotonous function of the lateral tension, dropping from infinity at zero tension to a minimum at the tension of several millinewtons per meter. Transmembrane voltage, on the contrary, caused the waiting time to decrease monotonously. Analysis of pore formation trajectories for several lipid species with different spontaneous curvatures and elastic moduli under various external conditions provided instrumental insights into the mechanisms underlying some experimentally observed phenomena.

Line Activity of Ganglioside GM1 Regulates the Raft Size Distribution in a Cholesterol-Dependent Manner

Liquid-ordered lipid domains, also called rafts, are assumed to be important players in different cellular processes, mainly signal transduction and membrane trafficking. They are thicker than the disordered part of the membrane and are thought to form to compensate for the hydrophobic mismatch between transmembrane proteins and the lipid environment. Despite the existence of such structures in vivo still being an open question, they are observed in model systems of multicomponent lipid bilayers. Moreover, the predictions obtained from model experiments allow the explanation of different physiological processes possibly involving rafts. Here we present the results of the study of the regulation of raft size distribution by ganglioside GM1. Combining atomic force microscopy with theoretical considerations based on the theory of membrane elasticity, we predict that this glycolipid should change the line tension of raft boundaries in two different ways, mainly depending on the cholesterol content. These results explain the shedding of gangliosides from the surface of tumor cells and the following ganglioside-induced apoptosis of T-lymphocytes in a raft-dependent manner. Moreover, the generality of the model allows the prediction of the line activity of different membrane components based on their molecular geometry.

Influenza virus Matrix Protein M1 preserves its conformation with pH, changing multimerization state at the priming stage due to electrostatics

Influenza A virus matrix protein M1 plays an essential role in the virus lifecycle, but its functional and structural properties are not entirely defined. Here we employed small-angle X-ray scattering, atomic force microscopy and zeta-potential measurements to characterize the overall structure and association behavior of the full-length M1 at different pH conditions. We demonstrate that the protein consists of a globular N-terminal domain and a flexible C-terminal extension. The globular N-terminal domain of M1 monomers appears preserved in the range of pH from 4.0 to 6.8, while the C-terminal domain remains flexible and the tendency to form multimers changes dramatically. We found that the protein multimerization process is reversible, whereby the binding between M1 molecules starts to break around pH 6. A predicted electrostatic model of M1 self-assembly at different pH revealed a good agreement with zeta-potential measurements, allowing one to assess the role of M1 domains in M1-M1 and M1-lipid interactions. Together with the protein sequence analysis, these results provide insights into the mechanism of M1 scaffold formation and the major role of the flexible and disordered C-terminal domain in this process.

Switching between Successful and Dead-End Intermediates in Membrane Fusion

Fusion of cellular membranes during normal biological processes, including proliferation, or synaptic transmission, is mediated and controlled by sophisticated protein machinery ensuring the preservation of the vital barrier function of the membrane throughout the process. Fusion of virus particles with host cell membranes is more sparingly arranged and often mediated by a single fusion protein, and the virus can afford to be less discriminative towards the possible different outcomes of fusion attempts. Formation of leaky intermediates was recently observed in some fusion processes, and an alternative trajectory of the process involving formation of π-shaped structures was suggested. In this study, we apply the methods of elasticity theory and Lagrangian formalism augmented by phenomenological and molecular geometry constraints and boundary conditions to investigate the traits of this trajectory and the drivers behind the choice of one of the possible scenarios depending on the properties of the system. The alternative pathway proved to be a dead end, and, depending on the parameters of the participating membranes and fusion proteins, the system can either reversibly enter the corresponding “leaky” configuration or be trapped in it. A parametric study in the biologically relevant range of variables emphasized the fusion protein properties crucial for the choice of the fusion scenario.

Interaction of amphipathic peptides mediated by elastic membrane deformations

Amphipathic alpha-helical peptides are perspective antimicrobial drugs. These peptides are partially embedded into the membrane to a shallow depth so that the longitudinal axis of the helix is parallel to the plane of the membrane or deviates from it by a small angle. In the framework of theory of elasticity of liquid crystals, adapted to lipid membranes, we calculated the energy of deformations occurring near the peptides partially embedded into the membrane. The energy of deformations is minimal when two peptides are parallel to each other and stay at a distance of about 5 nm. This configuration is stable with respect to small parallel displacements of the peptides and with respect to small variation of the angle between their axes both in the plane of the membrane and in the perpendicular direction. As a result of deformation the average thickness of the membrane decreases. The distribution of the elastic energy density has a maximum in the middle between the peptides. This region is the most likely place for formation of the through pores in the membrane. Since the equilibrium distance between the peptides is relatively large, it is assumed that the originally appearing pore should be purely lipidic.

Reply to Comment to “Elastic membrane deformations governinterleaflet coupling of lipid-ordered domains”

Our recent publication in this journal [1] challenges the concept that domains in opposing membrane leaflets are in register because of interactions at a membrane midplane. Compelled by the lack of direct experimental proof for (i) midplane interaction via an overhang [2] or (ii) LO and LD phases repelling each other [3] we propose that minimization of line tension γ drives registration (R) [1]. We dismiss antiregistration (AR) as an unlikely event because its twofold larger domain area translates into a 2-fold larger boundary length. Moreover, the line tensions at the LD/LD−LD/LO and LO/LO−LD/LO interfaces (Cartoon 1), γDD and γOO, respectively, exceed the line tension at the LD/LD−LO/LO interface, γR rendering the elastic energy WR of the registered state smaller than the elastic energy WAR of the antiregistered state. Consequently, registration is energetically favorable. Also, γR > γDD, γOO because an isolated LD/LO boundary in only one leaflet leads to membrane bending. As readily observed in the Cartoon, for the membrane to remain flat, a substantial torque must be applied or an LD/LO boundary must be created in the upper monolayer to oppose the LD/LO boundary in the lower monolayer. Cartoon 1 Calculated membrane shape at raft boundary for L = 100nm. The transitional LO/LD zone is tilted. A flat membrane is assured in [1] by boundary conditions (Eq. 6), which set the LO/LO and LD/LD bilayers to a flat horizontal (in Cartoon 1 at x→+∞ and x→−∞, respectively). A tilt was only allowed for the transitional L zone to yield minimal W. Accounting for the spontaneous curvatures of LO, and LD, JO = −0.07 nm−1 and JD = −0.1 nm−1, respectively, in a 1:1:1 mixture of dioleoylphosphatdiylcholine:dipalmitoylphatdiylcholine:cholesterol [4] and assuming hD = 1.3 nm (LD-phase) and hO = 1.6 nm (LO-phase) [5] yields the line tensions (in pN) of γDD=1.06, γOO=1.54, and γR=0.52. This is in stark contrast to Williamson’s and Olmsted’s erroneous assumption [6] that γR−AR = γDD = γOO = γ∞/2. There γ∞ was defined as γR(L→∞). For the specific lipid mixture γ∞ is equal to 0.83 pN. Thus, for the physiological relevant case of small LO domains (signaling platforms = rafts) surrounded by a large area of LD lipids, the ratio WR/WAR=γR/(2γDD)=0.5/1.5≈0.34<1, clearly favors registration. This is true for values of lateral tension σ ≤ 6mN/m per monolayer. Higher values of σ result in membrane rupture [7] and may thus be disregarded. Experimental data are available also for a second 1:1:1 mixture of palmitoyloleoylphosphatdiylcholine:sphingomyelin:cholesterol: For JO = −0.2 nm−1 and JD = −0.1 nm−1 [4] we find γDD=1.02, γOO=1.65, γR=0.6, and γ∞= 0.74. For small LO domains within a sea of LD lipids, WR/WAR ≈ 0.41 < 1, indicating that antiregistration does not occur. We conclude that our theory works well for all physiologically relevant cases. Williamson and Olmsted [6] raised the issue of large LO domains occupying an area fraction (1−ϕ) that is comparable to that of LD phases. Although such a configuration precludes the LO phase from functioning as a signaling platform (raft), their analysis may be helpful for a generalization of the theory. For 1/4<ϕ<1/2 we find: WR=γR2ϕπA,WAR=γOO2(1−2ϕ)πA where ϕ×A is the area of the LO domain. The ratio WR/WAR =1 for a critical ϕ value, ϕcrit: ϕcrit=γOO22γOO2+γR2 to yield ϕ = 0.47 for both lipid mixtures. Thus, if only γ causes domain registration, registration might not occur in the interval 0.47<ϕ<0.53. Therefore, our theory should be extended to account for these rare cases. In [1] we ignored the doubling of the area that is stiff if antiregistration occurs. Because stiff LO areas show reduced undulations, antiregistration violates the tendency of the system toward maximum entropy. In contrast, the mutual attraction of stiff membrane regions from both monolayers maximizes the membrane area in which the membrane is free to undulate, thereby providing a gain in free energy [8]. Since energy is required to prevent the membrane from undulating [9], we envision that accounting for it will rule out antiregistration for all ϕ values. A paper in preparation will provide a full quantitative analysis.

Galimzyanovet al.Reply

Our recent publication in this journal [1] challenges the concept that domains in opposing membrane leaflets are in register because of interactions at a membrane midplane. Compelled by the lack of direct experimental proof for (i) midplane interaction via an overhang [2] or (ii) LO and LD phases repelling each other [3] we propose that minimization of line tension γ drives registration (R) [1]. We dismiss antiregistration (AR) as an unlikely event because its twofold larger domain area translates into a 2-fold larger boundary length. Moreover, the line tensions at the LD/LD−LD/LO and LO/LO−LD/LO interfaces (Cartoon 1), γDD and γOO, respectively, exceed the line tension at the LD/LD−LO/LO interface, γR rendering the elastic energy WR of the registered state smaller than the elastic energy WAR of the antiregistered state. Consequently, registration is energetically favorable. Also, γR > γDD, γOO because an isolated LD/LO boundary in only one leaflet leads to membrane bending. As readily observed in the Cartoon, for the membrane to remain flat, a substantial torque must be applied or an LD/LO boundary must be created in the upper monolayer to oppose the LD/LO boundary in the lower monolayer. Cartoon 1 Calculated membrane shape at raft boundary for L = 100nm. The transitional LO/LD zone is tilted. A flat membrane is assured in [1] by boundary conditions (Eq. 6), which set the LO/LO and LD/LD bilayers to a flat horizontal (in Cartoon 1 at x→+∞ and x→−∞, respectively). A tilt was only allowed for the transitional L zone to yield minimal W. Accounting for the spontaneous curvatures of LO, and LD, JO = −0.07 nm−1 and JD = −0.1 nm−1, respectively, in a 1:1:1 mixture of dioleoylphosphatdiylcholine:dipalmitoylphatdiylcholine:cholesterol [4] and assuming hD = 1.3 nm (LD-phase) and hO = 1.6 nm (LO-phase) [5] yields the line tensions (in pN) of γDD=1.06, γOO=1.54, and γR=0.52. This is in stark contrast to Williamson’s and Olmsted’s erroneous assumption [6] that γR−AR = γDD = γOO = γ∞/2. There γ∞ was defined as γR(L→∞). For the specific lipid mixture γ∞ is equal to 0.83 pN. Thus, for the physiological relevant case of small LO domains (signaling platforms = rafts) surrounded by a large area of LD lipids, the ratio WR/WAR=γR/(2γDD)=0.5/1.5≈0.34<1, clearly favors registration. This is true for values of lateral tension σ ≤ 6mN/m per monolayer. Higher values of σ result in membrane rupture [7] and may thus be disregarded. Experimental data are available also for a second 1:1:1 mixture of palmitoyloleoylphosphatdiylcholine:sphingomyelin:cholesterol: For JO = −0.2 nm−1 and JD = −0.1 nm−1 [4] we find γDD=1.02, γOO=1.65, γR=0.6, and γ∞= 0.74. For small LO domains within a sea of LD lipids, WR/WAR ≈ 0.41 < 1, indicating that antiregistration does not occur. We conclude that our theory works well for all physiologically relevant cases. Williamson and Olmsted [6] raised the issue of large LO domains occupying an area fraction (1−ϕ) that is comparable to that of LD phases. Although such a configuration precludes the LO phase from functioning as a signaling platform (raft), their analysis may be helpful for a generalization of the theory. For 1/4<ϕ<1/2 we find: WR=γR2ϕπA,WAR=γOO2(1−2ϕ)πA where ϕ×A is the area of the LO domain. The ratio WR/WAR =1 for a critical ϕ value, ϕcrit: ϕcrit=γOO22γOO2+γR2 to yield ϕ = 0.47 for both lipid mixtures. Thus, if only γ causes domain registration, registration might not occur in the interval 0.47<ϕ<0.53. Therefore, our theory should be extended to account for these rare cases. In [1] we ignored the doubling of the area that is stiff if antiregistration occurs. Because stiff LO areas show reduced undulations, antiregistration violates the tendency of the system toward maximum entropy. In contrast, the mutual attraction of stiff membrane regions from both monolayers maximizes the membrane area in which the membrane is free to undulate, thereby providing a gain in free energy [8]. Since energy is required to prevent the membrane from undulating [9], we envision that accounting for it will rule out antiregistration for all ϕ values. A paper in preparation will provide a full quantitative analysis.

Metabolic Precursor of Cholesterol Causes Formation of Chained Aggregates of Liquid-Ordered Domains.

7-Dehydrocholesterol, an immediate metabolic predecessor of cholesterol, can accumulate in tissues due to some metabolic abnormalities, causing an array of symptoms known as Smith-Lemli-Opitz syndrome. Enrichment of cellular membranes with 7-dehydrocholesterol interferes with normal cell-signaling processes, which involve interaction between rafts and formation of the so-called signaling platforms. In model membranes, cholesterol-based ordered domains usually merge upon contact. According to our experimental data, ordered domains in the model systems where cholesterol is substituted for 7-dehydrocholesterol never merge on the time scale of the experiment, but clusterize into necklace-like aggregates. We attribute such different dynamical behavior to altered properties of the domain boundary. In the framework of thickness mismatch model, we analyzed changes of interaction energy profiles of two approaching domains caused by substitution of cholesterol by 7-dehydrocholesterol. The energy barrier for domain merger is shown to increase notably, with simultaneous appearance of another distinct local energy minimum. Such energy profile is in perfect qualitative agreement with the experimental observations. The observed change of domain dynamics can impair proper interaction between cellular rafts underlying pathologies associated with deviations in cholesterol metabolism.