Cycling and spiral-wave modes in an active cyclic Potts model.

We studied the nonequilibrium dynamics of a cycling three-state Potts model using simulations and theory. This model can be tuned from thermal-equilibrium to far-from-equilibrium conditions. At low cycling energy, the homogeneous dominant state cycles via nucleation and growth, while spiral waves are formed at high energy. For large systems, a discontinuous transition occurs from these cyclic homogeneous phases to spiral waves, while the opposite transition is absent. Conversely, these two modes can coexist for small systems. The waves can be reproduced by a continuum theory, and the transition can be understood from the competition between nucleation and growth.

Field-mediated interactions of passive and conformation-active particles: multibody and retardation effects.

Particles in soft matter interact through the deformation field they create, as in the "cheerios" effect or the curvature-mediated interactions of membrane proteins. Using a simple model for field-mediated interactions between passive particles, or active particles that switch conformation randomly or synchronously, we derive generic results concerning multibody interactions, activity driven patterns, and retardation effects.

Binding of thermalized and active membrane curvature-inducing proteins.

The phase behavior of a membrane induced by the binding of curvature-inducing proteins is studied by a combination of analytical and numerical approaches. In thermal equilibrium under the detailed balance between binding and unbinding, the membrane exhibits three phases: an unbound uniform flat phase (U), a bound uniform flat phase (B), and a separated/corrugated phase (SC). In the SC phase, the bound proteins form hexagonally-ordered bowl-shaped domains. The transitions between the U and SC phases and between the B and SC phases are second order and first order, respectively. At a small spontaneous curvature of the protein or high surface tension, the transition between B and SC phases becomes continuous. Moreover, a first-order transition between the U and B phases is found at zero spontaneous curvature driven by the Casimir-like interactions between rigid proteins. Furthermore, nonequilibrium dynamics is investigated by the addition of active binding and unbinding at a constant rate. The active binding and unbinding processes alter the stability of the SC phase.

Interaction and structuration of membrane-binding and membrane-excluding colloidal particles in lamellar phases.

Within the framework of a discrete Gaussian model, we present analytical results for the interaction induced by a lamellar phase between small embedded colloidal particles. We consider the two limits of particles strongly adherent to the adjacent membranes and of particles impenetrable to the membranes. Our approach takes into account the finite size of the colloidal particles, the discrete nature of the layers, and includes the Casimir-like effect of fluctuations, which is very important for dilute phases. Monte Carlo simulations of the statistical behavior of the membrane-interacting colloidal particles account semi-quantitatively, without any adjustable parameters, for the experimental data measured on silica nanospheres inserted within lyotropic smectics. We predict the existence of finite-size and densely packed particle aggregates originating from the competition between attractive interactions between colloidal particles in the same layer and repulsion between colloidal particles one layer apart.

Saffman-Delbrück and beyond: A pointlike approach.

We show that a very good analytical approximation of Saffman-Delbrück's (SD) law (mobility of a bio-membrane inclusion) can be obtained easily from the velocity field produced by a pointlike force in a 2D fluid embedded in a solvent, by using a small wavelength cutoff of the order of the particle's radius a . With this method, we obtain analytical generalizations of the SD law that take into account the bilayer nature of the membrane and the intermonolayer friction b . We also derive, in a calculation that consistently couples the quasi-planar two-dimensional (2D) membrane flow with the 3D solvent flow, the correction to the SD law arising when the inclusion creates a local spontaneous curvature. For an inclusion spanning a flat bilayer, the SD law is found to hold simply upon replacing the 2D viscosity [Formula: see text] of the membrane by the sum of the monolayer viscosities, without influence of b as long as b is above a threshold in practice well below known experimental values. For an inclusion located in only one of the two monolayers (or adhering to one monolayer), the SD law is influenced by b when b < [Formula: see text]/(4a2) . In this case, the mobility can be increased by up to a factor of two, as the opposite monolayer is not fully dragged by the inclusion. For an inclusion creating a local spontaneous curvature, we show that the total friction is the sum of the SD friction and that due to the pull-back created by the membrane deformation, a point that was assumed without demonstration in the literature.

Field-Embedded Particles Driven by Active Flips.

Systems of independent active particles embedded into a fluctuating environment are relevant to many areas of soft-matter science. We use a minimal model of noninteracting spin-carrying Brownian particles in a Gaussian field and show that activity-driven spin dynamics leads to patterned order. We find that the competition between mediated interactions and active noise alone can yield such diverse behaviors as phase transitions and microphase separation, from lamellar up to hexagonal ordering of clusters of opposite magnetization. These rest on complex multibody interactions. We find regimes of stationary patterns, but also dynamical regimes of relentless birth and growth of lumps of magnetization opposite of the surrounding one. Our approach combines Monte Carlo simulations with analytical methods based on dynamical density functional approaches.

Coupling between Inclusions and Membranes at the Nanoscale.

The activity of cell membrane inclusions (such as ion channels) is influenced by the host lipid membrane, to which they are elastically coupled. This coupling concerns the hydrophobic thickness of the bilayer (imposed by the length of the channel, as per the hydrophobic matching principle) but also its slope at the boundary of the inclusion. However, this parameter has never been measured so far. We combine small-angle x-ray scattering data and a complete elastic model to measure the slope for the model gramicidin channel and show that it is surprisingly steep in two membrane systems with very different elastic properties. This conclusion is confirmed and generalized by the comparison with recent results in the simulation literature and with conductivity measurements.

Membrane structure formation induced by two types of banana-shaped proteins.

The assembly of banana-shaped rodlike proteins on membranes and the associated membrane shape transformations are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two banana-shaped inclusions are derived theoretically using a point-like formalism based on fixed anisotropic curvatures, both for zero surface tension and for finite surface tension. On a larger scale, the interactions between the assemblies of such rodlike inclusions are determined analytically. Meshless membrane simulations are performed in the presence of a large number of inclusions of two types, corresponding to the curved rods of opposite curvatures, both for flat membranes and vesicles. Rods of the same type aggregate into linear assemblies perpendicular to the rod axis, leading to membrane tubulation. However, rods of the other type, those of opposite curvature, are attracted to the lateral sides of these assemblies, and stabilize a straight bump structure that prevents tubulation. When the two types of rods have almost opposite curvatures, the bumps attract one another, forming a striped structure. Positive surface tension is found to stabilize stripe formation. The simulation results agree well with the theoretical predictions provided the point-like curvatures of the model are scaled-down to account for the effective flexibility of the simulated rods.

Hydrodynamics of bilayer membranes with diffusing transmembrane proteins.

We consider the hydrodynamics of lipid bilayers containing transmembrane proteins of arbitrary shape. This biologically-motivated problem is relevant to the cell membrane, whose fluctuating dynamics play a key role in phenomena ranging from cell migration, intercellular transport, and cell communication. Using Onsager's variational principle, we derive the equations that govern the relaxation dynamics of the membrane shape, of the mass densities of the bilayer leaflets, and of the diffusing proteins' concentration. With our generic formalism, we obtain several results on membrane dynamics. We find that proteins that span the bilayer increase the intermonolayer friction coefficient. The renormalization, which can be significant, is in inverse proportion to the protein's mobility. Second, we find that asymmetric proteins couple to the membrane curvature and to the difference in monolayer densities. For practically all accessible membrane tensions (σ > 10(-8) N m(-1)) we show that the protein density is the slowest relaxing variable. Furthermore, its relaxation rate decreases at small wavelengths due to the coupling to curvature. We apply our formalism to the large-scale diffusion of a concentrated protein patch. We find that the diffusion profile is not self-similar, owing to the wavevector dependence of the effective diffusion coefficient.

Monte Carlo study of the frame, fluctuation and internal tensions of fluctuating membranes with fixed area.

Three types of surface tensions can be defined for lipid membranes: the internal tension, σ, conjugated to the real membrane area in the Hamiltonian, the mechanical frame tension, τ, conjugated to the projected area, and the "fluctuation tension", r, obtained from the fluctuation spectrum of the membrane height. We investigate these surface tensions by means of a Monge gauge lattice Monte Carlo simulation involving the exact, nonlinear, Helfrich Hamiltonian and a measure correction for the excess entropy of the Monge gauge. Our results for the relation between σ and τ agrees well with the theoretical prediction of [J.-B. Fournier and C. Barbetta, Phys. Rev. Lett., 2008, 100, 078103] based on a Gaussian approximation. This provides a valuable knowledge of τ in the standard Gaussian models where the tension is controlled by σ. However, contrary to the conjecture in the above paper, we find that r exhibits no significant difference from τ over more than five decades of tension. Our results appear to be valid in the thermodynamic limit and are robust to changing the ensemble in which the membrane area is controlled.

Relaxation dynamics of two-component fluid bilayer membranes.

We theoretically investigate the relaxation dynamics of a nearly flat binary lipid bilayer membrane by taking into account the membrane tension, hydrodynamics of the surrounding fluid, inter-monolayer friction and mutual diffusion. Mutual diffusion is the collective irreversible process that leads to homogenization of the density difference between the two lipid species. We find that two relaxation modes associated with the mutual diffusion appear in addition to the three previously discussed relaxation modes reflecting the bending and compression of the membrane. Because of the symmetry, only one of the two diffusive modes is coupled to the bending mode. The two diffusive modes are much slower than the bending and compression modes in the entire realistic wave number range. This means that the long time relaxation behavior is dominated by the mutual diffusion in binary membranes. The two diffusive modes become even slower in the vicinity of the unstable region towards phase separation, while the other modes are almost unchanged. In short time scales, on the other hand, the lipid composition heterogeneity induces in-plane compression and bending of the bilayer.

High-order power series expansion of the elastic interaction between conical membrane inclusions.

We revisit the problem of the long-range interaction between two conical proteins inserted into a lipid membrane and interacting via the induced deformation of the membrane, first considered by Goulian et al. (M. Goulian, R. Bruinsma, P. Pincus, Europhys. Lett. 22, 145 (1993); Europhys. Lett. 23, 155 (1993)). By means of a complex variables formulation and an iterative solution, we determine analytically an arbitrary high-order expansion of the interaction energy in powers of the inverse distance between two inclusions of different sizes. At leading order and for inclusions of equal sizes, we recover the result obtained by Goulian et al.. We generalize the development to inclusions of different sizes and give explicit formulas that increase the precision by ten orders in the inverse distance.

Interplay of packing and flip-flop in local bilayer deformation. How phosphatidylglycerol could rescue mitochondrial function in a cardiolipin-deficient yeast mutant.

In a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant unilamellar vesicles, leads to the formation of tubules that retract after the dissipation of this gradient. These tubules have morphologies similar to mitochondrial cristae. The tubulation effect is attributable to direct phospholipid packing modification in the outer leaflet, that is promoted by protonation of cardiolipin headgroups. In this study, we compare the case of cardiolipin-containing giant unilamellar vesicles with that of giant unilamellar vesicles that contain phosphatidylglycerol (PG). Local acidification also promotes formation of tubules in the latter. However, compared with cardiolipin-containing giant unilamellar vesicles the tubules are longer, exhibit a visible pearling, and have a much longer lifetime after acid micro-injection is stopped. We attribute these differences to an additional mechanism that increases monolayer surface imbalance, namely inward PG flip-flop promoted by the local transmembrane pH gradient. Simulations using a fully nonlinear membrane model as well as geometrical calculations are in agreement with this hypothesis. Interestingly, among yeast mutants deficient in cardiolipin biosynthesis, only the crd1-null mutant, which accumulates phosphatidylglycerol, displays significant mitochondrial activity. Our work provides a possible explanation of such a property and further emphasizes the salient role of specific lipids in mitochondrial function.

Membrane properties revealed by spatiotemporal response to a local inhomogeneity.

We study theoretically the spatiotemporal response of a lipid membrane submitted to a local chemical change of its environment, taking into account the time-dependent profile of the reagent concentration due to diffusion in the solution above the membrane. We show that the effect of the evolution of the reagent concentration profile becomes negligible after some time. It then becomes possible to extract interesting properties of the membrane response to the chemical modification. We find that a local density asymmetry between the two monolayers relaxes by spreading diffusively in the whole membrane. This behavior is driven by intermonolayer friction. Moreover, we show how the ratio of the spontaneous curvature change to the equilibrium density change induced by the chemical modification can be extracted from the dynamics of the local membrane deformation. Such information cannot be obtained by analyzing the equilibrium vesicle shapes that exist in different membrane environments in light of the area-difference elasticity model.

The Vanadium Iodoperoxidase from the marine flavobacteriaceae species Zobellia galactanivorans reveals novel molecular and evolutionary features of halide specificity in the vanadium haloperoxidase enzyme family.

Vanadium haloperoxidases (VHPO) are key enzymes that oxidize halides and are involved in the biosynthesis of organo-halogens. Until now, only chloroperoxidases (VCPO) and bromoperoxidases (VBPO) have been characterized structurally, mainly from eukaryotic species. Three putative VHPO genes were predicted in the genome of the flavobacterium Zobellia galactanivorans, a marine bacterium associated with macroalgae. In a phylogenetic analysis, these putative bacterial VHPO were closely related to other VHPO from diverse bacterial phyla but clustered independently from eukaryotic algal VBPO and fungal VCPO. Two of these bacterial VHPO, heterogeneously produced in Escherichia coli, were found to be strictly specific for iodide oxidation. The crystal structure of one of these vanadium-dependent iodoperoxidases, Zg-VIPO1, was solved by multiwavelength anomalous diffraction at 1.8 Å, revealing a monomeric structure mainly folded into α-helices. This three-dimensional structure is relatively similar to those of VCPO of the fungus Curvularia inaequalis and of Streptomyces sp. and is superimposable onto the dimeric structure of algal VBPO. Surprisingly, the vanadate binding site of Zg-VIPO1 is strictly conserved with the fungal VCPO active site. Using site-directed mutagenesis, we showed that specific amino acids and the associated hydrogen bonding network around the vanadate center are essential for the catalytic properties and also the iodide specificity of Zg-VIPO1. Altogether, phylogeny and structure-function data support the finding that iodoperoxidase activities evolved independently in bacterial and algal lineages, and this sheds light on the evolution of the VHPO enzyme family.

Dynamics of the force exchanged between membrane inclusions.

We study the dynamical response of a fluid membrane to the sudden conformation change of active inclusions linearly coupled to the membrane curvature. The mutual force between two inclusions triggered simultaneously is shown to exhibit a transient maximum much larger than the equilibrium force. Even in the presence of tension, this dynamical interaction is long range over distances much larger than the correlation length. We derive the scaling laws describing these phenomena analytically, and we stress the importance of the damping due to intermonolayer friction.

Capillary force acting on a colloidal particle floating on a deformed interface.

We analytically determine the lateral capillary force acting on a spherical colloid trapped at an interface of arbitrary shape. Our calculations, which are valid for colloids that are small with respect to the capillary length, take into account surface tension, pressure and gravity. We relate the force acting on the colloid to the shape of the liquid interface prior to colloid deposition. Our approach is a generalization of a previous study of ours [Ch. Blanc et al., Phys. Rev. Lett., 2013, 111, 058302] to the case in which gravity is present. Our findings are in agreement with the so-called Nicolson superposition approximation [D. Y. C. Chan, J. D. J. Henry and L. R. White, J. Colloid Interface Sci., 1981, 79, 410] and with the curvature-dependent capillary force predicted by Würger [A. Würger, Phys. Rev. E, 2006, 74, 041402], and extend these results by including higher-order terms in the ratio between the size of the colloid and the capillary length. We thoroughly validate our theoretical expressions by means of an exact nonlinear numerical calculation.

Capillary force on a micrometric sphere trapped at a fluid interface exhibiting arbitrary curvature gradients.

We report theoretical predictions and measurements of the capillary force acting on a spherical colloid smaller than the capillary length that is placed on a curved fluid interface of arbitrary shape. By coupling direct imaging and interferometry, we are able to measure the in situ colloid contact angle and to correlate its position with respect to the interface curvature. Extremely tiny capillary forces down to femtonewtons can be measured with this method. Measurements agree well with a theory relating the capillary force to the gradient of Gaussian curvature and to the mean curvature of the interface prior to colloidal deposition. Numerical calculations corroborate these results.

Lipid packing variations induced by pH in cardiolipin-containing bilayers: the driving force for the cristae-like shape instability.

Cardiolipin is a four-tailed acidic lipid found predominantly within the inner membrane of mitochondria, and is thought to be a key component in determining inner membrane properties and potential. Thus, cardiolipin may be involved in the dynamics of the inner membrane characteristic invaginations (named cristae) that protrude into the matrix space. In previous studies, we showed the possibility to induce, by localized proton flow, a macroscopic cristae-like shape remodeling of an only-lipid model membrane mimicking the inner mitochondrial membrane. In addition, we reported a theoretical model describing the dynamics of a chemically driven membrane shape instability caused by a modification of the plane-shape equilibrium density of the lipids in the membrane. In the present work, we focus on the lipid-packing modifications observed in a model cardiolipin-containing lipid membrane submitted to pH decrease because this is the driving force of the instability. Laurdan fluorescence and ζ-potential measurements show that under pH decrease, membrane surface charge decreases, but that significant modification of the lipid packing is observed only for CL-containing membranes. Our giant unilamellar vesicle experiments also indicate that cristae-like morphologies are only observed for CL-containing lipid membranes. Taken together, these results highlight the fact that only a strong modulation of the lipid packing of the exposed monolayer leads to membrane shape instability and suggest that mitochondrial lipids, in particular the cardiolipin, play a specific role under pH modulation in inner mitochondrial membrane morphology and dynamics.

Mass spectrometry - based imaging techniques for iodine-127 and iodine-129 detection and localization in the brown alga Laminaria digitata.

129I is one of the main radioisotopes of iodine derived from the nuclear fuel cycle that can be found sustainably in the environment due to its long half-life. In coastal marine environment, brown macroalgae, such laminariales (or kelps), are known to naturally feature highest rates of iodine accumulation, and to be an important source of biogenic volatile iodinated compounds released to the atmosphere. These seaweeds are therefore likely to be significantly marked by but also potential vectors of radioactive iodine. In order to better understand the chemical and isotopic speciation of iodine in brown algal tissues, we combined mass spectrometry-based imaging approaches in natural samples of Laminaria digitata young sporophytes, collected at two different locations along the south coast of the English Channel (Roscoff and Goury). Laser desorption ionization (LDI) and desorption electrospray-ionization techniques (DESI), coupled with mass spectrometry, confirmed the predominance of inorganic I- species on the surface of fresh algae, and a peripheral iodine localization when applied on micro-sections. Moreover, radioactive isotope 129I was not detected on plantlet surface or in stipe sections of algal samples collected near Roscoff but was detected in L. digitata samples collected at Goury, near La Hague, where controlled liquid radioactive discharges from the ORANO La Hague reprocessing plant occur. At the subcellular scale, cryo-fixed micro-sections of algal blade samples from both sites were further analyzed by secondary ion mass spectrometry (nano-SIMS), leading to similar results. Even if the signal detected for 129I was much weaker than for 127I in samples from Goury, the chemical imaging revealed some differences in extracellular distribution between radioactive and stable iodine isotopes. Altogether LDI and nano-SIMS are complementary and powerful techniques for the detection and localization of iodine isotopes in algal samples, and for a better understanding of radioactive and stable iodine uptake mechanisms in the marine environment.