Membrane Biophysics

This article reviews the application of solid-state 2H nuclear magnetic resonance (NMR) spectroscopy for
investigating the deformation of lipid bilayers at the atomistic level. For liquid-crystalline membranes, the
average structure is manifested by the segmental order parameters (SCD) of the lipids. Solid-state 2H NMR yields
observables directly related to the stress field of the lipid bilayer. The extent to which lipid bilayers are deformed
by osmotic pressure is integral to how lipid–protein interactions affect membrane functions. Calculations of the
average area per lipid and related structural properties are pertinent to bilayer remodeling and molecular
dynamics (MD) simulations ofmembranes. To establish structural quantities, such as area per lipid and volumetric
bilayer thickness, amean-torque analysis of 2H NMR order parameters is applied. Osmotic stress is introduced
by adding polymer solutions or by gravimetric dehydration, which are thermodynamically equivalent. Solidstate
NMR studies of lipids under osmotic stress probe membrane interactions involving collective bilayer
undulations, order-director fluctuations, and lipid molecular protrusions. Removal of water yields a reduction
of the mean area per lipid, with a corresponding increase in volumetric bilayer thickness, by up to 20% in the
liquid-crystalline state. Hydrophobic mismatch can shift protein states involving mechanosensation, transport,
and molecular recognition by G-protein-coupled receptors. Measurements of the order parameters versus
osmotic pressure yield the elastic area compressibility modulus and the corresponding bilayer thickness at an
atomistic level. Solid-state 2H NMR thus reveals how membrane deformation can affect protein conformational
changeswithin the stress field of the lipid bilayer. This article is part of a Special Issue entitled:NMR Spectroscopy
for Atomistic Views of Biomembranes and Cell Surfaces.

Membrane budding and wrapping of particles, such as viruses and nano-particles, play a key role in intracellular transport and have been studied for a variety of biological and soft matter systems. We study nano-particle wrapping by numerical minimization of bending, surface tension, and adhesion energies. We calculate deformation and adhesion energies as a function of membrane elastic parameters and adhesion strength to obtain wrapping diagrams. We predict unwrapped, partially wrapped, and completely wrapped states for prolate and oblate ellipsoids with various aspect ratios and particle sizes. In contrast to spherical particles, where partially wrapped states exist only for finite surface tensions, partially wrapped states for ellipsoids occur already for tensionless membranes. In addition, the partially wrapped states are long-lived, because of an increased energy cost for wrapping of the highly curved tips. Our results suggest a lower uptake rate of ellipsoidal particles by cells and thereby a higher virulence of tubular viruses compared with icosahedral viruses, as well as co-operative budding of ellipsoidal particles on membranes.

Intracellular organelles are subject to a steady flux of lipids and proteins through active, energy consuming transport processes. Active fission and fusion are promoted by GTPases, e.g., Arf-Coatamer and the Rab-Snare complexes, which both sense and generate local membrane curvature. Here we investigate, through Dynamical Triangulation Monte Carlo simulations, the role that these active processes play in determining the morphology and composition segregation in closed membranes. We find that the steady state shapes obtained as a result of such active pro- cesses, bear a striking resemblance to the ramified morphologies of organelles in-vivo, pointing to the relevance of nonequilibrium fission-fusion in organelle morphogenesis.

Curvature-sensing and curvature-remodeling proteins, such as Amphiphysin, Epsin, and Exo70, are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing pro- teins can act as curvature sensors; they aggregate to membrane regions matching their intrinsic curvature; as well as induce curvature in cell membranes to stabilize emergent high curvature, non-spherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains incomplete. Here, within a continuum framework and using the machinery of Monte Carlo simulations, we introduce and compare three free-energy methods to delineate the free-energy landscape of curvature-inducing proteins on bilayer membranes. We demonstrate the utility of the Widom test-particle/field insertion methodology in computing the excess chemical potentials associated with curvature-inducing proteins on the membrane—in particular, we use this method to track the onset of morphological transitions in the membrane at elevated protein densities. We validate this approach by comparing the results from the Widom method with those of thermodynamic integration and Bennett acceptance ratio methods. Furthermore, the predictions from the Widom method have been tested against analytical calculations of the excess chemical potential at infinite dilution. Our results are useful in precisely quantifying the free-energy landscape, and also in determining the phase boundaries associated with curvature-induction, curvature-sensing, and morphological transitions. This approach can be extended to studies exploring the role of ther- mal fluctuations and other external (control) variables, such as membrane excess area, in shaping curvature-mediated interactions on bilayer membranes.

A model of vesicle electrodeformation is described which obtains a parametrized vesicle shape by minimizing the sum of the membrane bending energy and the energy due to the electric field. Both the vesicle membrane and the aqueous media inside and outside the vesicle are treated as leaky dielectrics, and the vesicle itself is modelled as a nearly spherical shape enclosed within a thin membrane. It is demonstrated (a) that the model achieves a good quantitative agreement with the experimentally determined prolate-to-oblate transition frequencies in the kHz range, and (b) that the model can explain a phase diagram of shapes of giant phospholipid vesicles with respect to two parameters: the frequency of the applied AC electric field and the ratio of the electrical conductivities of the aqueous media inside and outside the vesicle, explored in a recent paper (S. Aranda et al., Biophys. J. 95:L19--L21, 2008). A possible use of the frequency-dependent shape transitions of phospholipid vesicles in conductometry of microliter samples is discussed.

The putative Plasmodium translocon of exported proteins (PTEX) is essential for transport of malarial effector proteins across a parasite-encasing vacuolar membrane into host erythrocytes, but the mechanism of this process remains unknown. Here we show that PTEX is a bona fide translocon by determining structures of the PTEX core complex at near-atomic resolution using cryo-electron microscopy. We isolated the endogenous PTEX core complex containing EXP2, PTEX150 and HSP101 from Plasmodium falciparum in the 'engaged' and 'resetting' states of endogenous cargo translocation using epitope tags inserted using the CRISPR–Cas9 system. In the structures, EXP2 and PTEX150 interdigitate to form a static, funnel-shaped pseudo-seven-fold-symmetric protein-conducting channel spanning the vacuolar membrane. The spiral-shaped AAA+ HSP101 hexamer is tethered above this funnel, and undergoes pronounced compaction that allows three of six tyrosine-bearing pore loops lining the HSP101 channel to dissociate from the cargo, resetting the translocon for the next threading cycle. Our work reveals the mechanism of P. falciparum effector export, and will inform structure-based design of drugs targeting this unique translocon.

Solute transport across cell membranes is ubiquitous in biology as an essential physiological process. Secondary active transporters couple the unfavorable process of solute transport against its concentration gradient to the energetically favorable transport of one or several ions. The study of such transporters over several decades indicates that their function involves complex allosteric mechanisms that are progressively being revealed in atomistic detail. We focus on two well-characterized sodium-coupled symporters: the bacterial amino acid transporter LeuT, which is the prototype for the " gated pore " mechanism in the mammalian synaptic monoamine transporters, and the archaeal GltPh, which is the prototype for the " elevator " mechanism in the mammalian excitatory amino acid transporters. We present the evidence for the role of allostery in the context of a quantitative formalism that can reconcile biochemical and biophysical data and thereby connects directly to recent insights into the molecular structure and dynamics of these proteins. We demonstrate that, while the structures and mechanisms of these transporters are very different, the available data suggest a common role of specific models of allostery in their functions. We argue that such allosteric mechanisms appear essential not only for sodium-coupled symport in general but also for the function of other types of molecular machines in the membrane. CONTENTS

The recent identification of Vitamin E acetate as one of the causal agents for the e-cigarette, or vaping, product use associated lung injury (EVALI) is a major milestone. In membrane biophysics, Vitamin E is a linactant and a potent modulator of lateral phase separation that effectively reduces the line tension at the two-dimensional phase boundaries and thereby exponentially increases the surface viscosity of the pulmonary surfactant. Disrupted dynamics of respiratory compression-expansion cycling may result in an extensive hypoxemia, leading to an acute respiratory distress entailing the formation of intraalveolar lipid-laden macrophages. Supplemen-tation of pulmonary surfactants which retain moderate level of cholesterol and controlled hypothermia for patients are recommended when the hypothesis that the line-active property of the vitamin derivative drives the pathogenesis of EVALI holds.

The experimental data for the giant squid axon propagated action potential is examined in phase space. Plots of capacitive and ionic currents vs. potential exhibit linear portions providing temperature dependent time rates and maximum conductance constants for sodium and Potassium channels. First order phase transitions of ionic channels are identified. Incorporation of time rates into Avrami equations for fractions of open channels yields for each channel a temperature independent dimensionless constant that is close in value to the fine structure constant. It also reveals temperature independent scaling exponents. Evidence is presented that the action potential traverses a ferroelectric hysteresis loop. This results in a second order phase transition polarization flip at the peak of the action potential, followed by closing of sodium and opening of potassium channels, and finally closing the loop by reversing the polarization flip as the resting potential is reached. The existence...

The experimental data for the giant squid axon propagated action potential is examined in phase space. Plots of capacitive and ionic currents vs. potential exhibit linear portions providing temperature dependent time rates and maximum conductance constants for sodium and Potassium channels. First order phase transitions of ionic channels are identified. Incorporation of time rates into Avrami equations for fractions of open channels yields for each channel a temperature independent dimensionless constant that is close in value to the fine structure constant. It also reveals temperature independent scaling exponents. Evidence is presented that the action potential traverses a ferroelectric hysteresis loop. This results in a second order phase transition polarization flip at the peak of the action potential, followed by closing of sodium and opening of potassium channels, and finally closing the loop by reversing the polarization flip as the resting potential is reached. The existence...

We study here the permeability of the hydrophobic O 2 molecule through a model DPPC bi-layer at 323K and 350K, and of the trace amine p-tyramine through PC bilayers at 310K. The tyramine results are compared to previous experimental work at 298K. Nonequilibrium work methods were used in conjunction to simultaneously obtain both the potential of mean force (PMF) and the position dependent transmembrane diffusion coefficient, D(z), from the simulations. These in turn were used to calculate the permeability coefficient, P, through the inhomogeneous solubility-diffusion model. The results for O 2 are consistent with previous simulations, and agree with experimentally measured P values for PC bilayers. A temperature dependence in the permeability of O 2 through DPPC was obtained, with P decreasing at higher temperatures. Two relevant species of p-tyramine were simulated, from which the PMF and D(z) were calculated. The charged species had a large energetic barrier to crossing the bilayer of * 21 kcal/mol, while the uncharged, deprotonated species had a much lower barrier of * 7 kcal/mol. The effective in silico permeability for p-tyramine was calculated by applying three approximations, all of which gave nearly identical results (presented here as a function of the pK a). As the permeability value calculated from simulation was highly dependent on the pK a of the amine group, a further pK a study was performed that also varied the fraction of the uncharged and zwitterionic p-tyramine species. Using the experimental P value together with the simulated results, we were able to label the phenolic group as responsible for the pK a1 and the amine for the pK a2 , that together represent all of the experimentally measured pK a values for p-tyramine. This agrees with older experimental results, in contrast to more recent work that has suggested there is a strong ambiguity in the pK a values.