Trafficking and sorting of membrane-anchored Ras GTPases are regulated by partitioning between distinct membrane domains. Here, in vitro experiments and microscopic molecular theory reveal membrane curvature as a new modulator of N-Ras lipid anchor and palmitoyl chain partitioning. Membrane curvature was essential for enrichment in raft-like liquid-ordered phases; enrichment was driven by relief of lateral pressure upon anchor insertion and most likely affects the localization of lipidated proteins in general.
For the superheated Lennard-Jones liquid, the free energy of forming a bubble with a given particle number and volume is calculated using density-functional theory. As conjectured, a consequence of known properties of the critical cavity [S. N. Punnathanam and D. S. Corti, J. Chem. Phys. 119, 10 224 (2003), the free energy surface terminates at a locus of instability. These stability limits reside, however, unexpectedly close to the saddle point. A new picture of homogeneous bubble nucleation and growth emerges from our study, being more appropriately described as an "activated instability."
There is clear evidence of an interleaflet coupling in model lipid/cholesterol membranes exhibiting liquid-liquid phase separation. The strength of this coupling is quantified by the mismatch free energy, γ. We calculate it using a molecular mean-field model of a phase-separated lipid/cholesterol bilayer and obtain values that increase as the concentration of saturated lipids in the coexisting phases is increased. These values lie in the range 0.01-0.03 k(B)T/nm(2). We clarify the relationship between the interleaflet coupling and the extent of interleaflet alignment of liquid domains by analyzing a statistical mechanical model of coupled fluctuating domain interfaces. The model is solved exactly using the correspondence between statistical mechanics and quantum mechanics, yielding an expression for the characteristic size of fluctuations out of domain registry. This length scale depends only weakly on the strength of the interleaflet coupling and inevitably is only of the order of nanometers, which explains the experimental result that fluctuations out of domain registry have not been observed by optical microscopy.
Given the proposed importance of membrane tension in regulating cellular functions, we explore the effects of a finite surface tension on phase equilibrium using a molecular theory that captures the quantitative structure of the phase diagram of the tensionless DPPC/DOPC/Cholesterol lipid bilayer. We find that an increase in the surface tension decreases the temperature of the transition from liquid to gel in a pure DPPC system by ∼1.0 K/(mN/m), and decreases the liquid-disordered to liquid-ordered transition at constant chemical potentials by approximately the same amount. Our results quantitatively isolate the role of tension in comparison to other thermodynamic factors, such as pressure, in determining the phase behavior of lipid bilayers.
Proteins anchored to membranes through covalently linked fatty acids and/or isoprenoid groups play crucial roles in all forms of life. Sorting and trafficking of lipidated proteins has traditionally been discussed in the context of partitioning to membrane domains of different lipid composition. We recently showed that membrane shape/curvature can in itself mediate the recruitment of lipidated proteins. However, exactly how membrane curvature and composition synergize remains largely unexplored. Here we investigated how three critical structural parameters of lipids, namely acyl chain saturation, headgroup size, and acyl chain length, modulate the capacity of membrane curvature to recruit lipidated proteins. As a model system we used the lipidated minimal membrane anchor of the GTPase, N-Ras (tN-Ras). Our data revealed complex synergistic effects, whereby tN-Ras binding was higher on planar DOPC than POPC membranes, but inversely higher on curved POPC than DOPC membranes. This variation in the binding to both planar and curved membranes leads to a net increase in the recruitment by membrane curvature of tN-Ras when reducing the acyl chain saturation state. Additionally, we found increased recruitment by membrane curvature of tN-Ras when substituting PC for PE, and when decreasing acyl chain length from 14 to 12 carbons (DMPC versus DLPC). However, these variations in recruitment ability had different origins, with the headgroup size primarily influencing tN-Ras binding to planar membranes whereas the change in acyl chain length primarily affected binding to curved membranes. Molecular field theory calculations recapitulated these findings and revealed lateral pressure as an underlying biophysical mechanism dictating how curvature and composition synergize to modulate recruitment of lipidated proteins. Our findings suggest that the different compositions of cellular compartments could modulate the potency of membrane curvature to recruit lipidated proteins and thereby synergistically regulate the trafficking and sorting of lipidated proteins.
We consider various ensemble averages within the molecular dynamics (MD) ensemble, corresponding to those states sampled during a MD simulation in which the application of periodic boundary conditions imposes a constraint on the momentum of the center of mass. As noted by Shirts et al. [J. Chem. Phys. 125, 164102 (2006)] for an isolated system, we find that the principle of equipartition is not satisfied within such simulations, i.e., the total kinetic energy of the system is not shared equally among all the translational degrees of freedom. Nevertheless, we derive two different versions of Tolman's generalized equipartition theorem, one appropriate for the canonical ensemble and the other relevant to the microcanonical ensemble. In both cases, the breakdown of the principle of equipartition immediately follows from Tolman's result. The translational degrees of freedom are, however, still equivalent, being coupled to the same bulk property in an identical manner. We also show that the temperature of an isolated system is not directly proportional to the average of the total kinetic energy (in contrast to the direct proportionality that arises between the temperature of the external bath and the kinetic energy within the canonical ensemble). Consequently, the system temperature does not appear within Tolman's generalized equipartition theorem for the microcanonical ensemble (unlike the immediate appearance of the temperature of the external bath within the canonical ensemble). Both of these results serve to highlight the flaws in the argument put forth by Hertz [Ann. Phys. 33, 225 (1910); 33, 537 (1910)] for defining the entropy of an isolated system via the integral of the phase space volume. Only the Boltzmann-Planck entropy definition, which connects entropy to the integral of the phase space density, leads to the correct description of the properties of a finite, isolated system. We demonstrate that the use of the integral of the phase space volume leads to unphysical results, indicating that the property of adiabatic invariance has little to do with the behavior of small systems.
We calculate partition coefficients of various chain anchors in liquid-ordered and liquid-disordered phases utilizing a theoretical model of a bilayer membrane containing cholesterol, dipalmitoyl phosphatidylcholine, and dioleoylphosphatidylcholine. The partition coefficients are calculated as a function of chain length, degree of saturation, and temperature. Partitioning depends on the difference between the lipid environments of the coexisting phases in which the anchors are embedded. Consequently, the partition coefficient depends on the nature of the anchor, and on the relative compositions of the coexisting phases. We find that saturated anchors prefer the denser liquid-ordered phase, and that the fraction of anchors in the liquid-ordered phase increases with increasing degree of saturation of the anchors. The partition coefficient also depends upon the location of the double bonds. Anchors with double bonds closer to the middle of the chain have a greater effect on partitioning than those near the end. Doubling the number of saturated chains increases the partitioning into the liquid-ordered phase for tails that are nearly as long or longer than those comprising the bilayer. Partitioning of such chains increases with decreasing temperature, indicating that energy considerations dominate entropic ones. In contrast, partitioning of shorter chains increases with increasing temperature, indicating that entropic considerations dominate.
BackgroundDeposits of aggregated amyloid-β protein (Aβ) are a pathological hallmark of Alzheimer’s disease (AD). Thus, one therapeutic strategy is to eliminate these deposits by halting Aβ aggregation. While a variety of possible aggregation inhibitors have been explored, only nanoparticles (NPs) exhibit promise at low substoichiometric ratios. With tunable size, shape, and surface properties, NPs present an ideal platform for rationally designed Aβ aggregation inhibitors. In this study, we characterized the inhibitory capabilities of gold nanospheres exhibiting different surface coatings and diameters.ResultsBoth NP diameter and surface chemistry were found to modulate the extent of aggregation, while NP electric charge influenced aggregate morphology. Notably, 8 nm and 18 nm poly(acrylic acid)-coated NPs abrogated Aβ aggregation at a substoichiometric ratio of 1:2,000,000. Theoretical calculations suggest that this low stoichiometry could arise from altered solution conditions near the NP surface. Specifically, local solution pH and charge density are congruent with conditions that influence aggregation.ConclusionsThese findings demonstrate the potential of surface-coated gold nanospheres to serve as tunable therapeutic agents for the inhibition of Aβ aggregation. Insights gained into the physiochemical properties of effective NP inhibitors will inform future rational design of effective NP-based therapeutics for AD.Electronic supplementary materialThe online version of this article (doi:10.1186/s13036-017-0047-6) contains supplementary material, which is available to authorized users.
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