Statistical mechanics of a colloidal suspension in contact with a fluctuating membrane

An efficient approach to study membrane nano-inclusions: from the complex biological world to a simple representation

Membrane nano-inclusions (NIs) are of great interest in biophysics, materials science, nanotechnology, and medicine. We hypothesized that the NIs within a biological membrane bilayer interact via a simple and efficient interaction potential, inspired by previous experimental and theoretical work. This interaction implicitly treats the membrane lipids but takes into account its effect on the NIs micro-arrangement. Thus, the study of the NIs is simplified to a two-dimensional colloidal system with implicit solvent. We calculated the structural properties from Molecular Dynamics simulations (MD), and we developed a Scaling Theory to discuss their behavior. We determined the thermal properties through potential energy per NI and pressure, and we discussed their variation as a function of the NIs number density. We performed a detailed study of the NIs dynamics using two approaches, MD simulations, and Dynamics Theory. We identified two characteristic values of number density, namely a critical number density n c = 3.67 × 10-3 Å-2 corresponded to the apparition of chain-like structures along with the liquid dispersed structure and the gelation number density n g = 8.40 × 10-3 Å-2 corresponded to the jamming state. We showed that the aggregation structure of NIs is of fractal dimension d F < 2. Also, we identified three diffusion regimes of membrane NIs, namely, normal for n < n c, subdiffusive for n c ≤ n < n g, and blocked for n ≥ n g. Thus, this paper proposes a simple and effective approach for studying the physical properties of membrane NIs. In particular, our results identify scaling exponents related to the microstructure and dynamics of membrane NIs.

Membrane curvature generated by asymmetric depletion layers of ions, small molecules, and nanoparticles

Biomimetic and biological membranes consist of molecular bilayers with two leaflets that are typically exposed to different aqueous solutions. We consider solutions of "particles" that experience effectively repulsive interactions with these membranes and form depletion layers in front of the membrane leaflets. The particles considered here are water-soluble, have a size between a few angstrom and a few nanometers as well as a rigid, more or less globular shape, and do neither adsorb onto the membranes nor permeate these membranes. Examples are provided by ions, small sugar molecules, globular proteins, or inorganic nanoparticles with a hydrophilic surface. We first study depletion layers in a hard-core system based on ideal particle solutions as well as hard-wall interactions between these particles and the membrane. For this system, we obtain exact expressions for the coverages and tensions of the two leaflets as well as for the spontaneous curvature of the bilayer membrane. All of these quantities depend linearly on the particle concentrations. The exact results for the hard-core system also show that the spontaneous curvature can be directly deduced from the planar membrane geometry. Our results for the hard-core system apply both to ions and solutes that are small compared to the membrane thickness and to nanoparticles with a size that is comparable to the membrane thickness, provided the particle solutions are sufficiently dilute. We then corroborate the different relationships found for the hard-core system by extensive simulations of a soft-core particle system using dissipative particle dynamics. The simulations confirm the linear relationships obtained for the hard-core system. Both our analytical and our simulation results show that the spontaneous curvature induced by a single particle species can be quite large. When one leaflet of the membrane is exposed, e.g., to a 100 mM solution of glucose, a lipid bilayer can acquire a spontaneous curvature of ±1/(270 nm). Our theoretical results can be scrutinized by systematic experimental studies using a large variety of different types of particles.

The ratio of the lateral correlation length and particle radius determines the density profile of spherical molecules near a fluctuating membrane

Interactions between membranes and molecules are important for many biological processes, e.g., transport of molecules across cell membranes. However, the detailed physical description of the membrane-biomolecule system remains a challenge and simplified schemes allow capturing its main intrinsic features. In this work, by means of Monte Carlo computer simulations, we systematically study the distribution of uncharged spherical molecules in contact with a flexible surface. Our results show that the distribution for finite size particles has the same simple functional form as the one obtained for point-like particles and depends only on the ratio of the lateral correlation length of the membrane and the radius of the molecules.

Unbinding transition from fluid membranes with associated polymers

We consider two neighboring fluid membranes that are associated with long flexible polymers (proteins or other macromolecules). We are interested in two physical systems consisting of i) two adjacent membranes with end-grafted (or adsorbed) polymers (system I), or ii) two membranes confining a polymer solution (system II). In addition to the pure interactions between membranes, the presence of polymers gives rise to new induced mediated interactions, which are repulsive, for system I, and attractive, for system II. In fact, repulsive induced interactions are caused by the excluded-volume forces between grafted polymers, while attractive ones, by entropy loss, due to free motion of polymers between membranes. The main goal is a quantitative study of the unbinding transition thermodynamics that is drastically affected by the associated polymers. For system I, the repulsive polymer-mediated force delays this transition that can happen at low temperature. To investigate the unbinding phenomenon, we first present an exact mathematical analysis of the total potential that is the sum of the primitive and induced potentials. This mathematical study enables us to classify the total interaction potentials, in terms of all parameters of the problem. Second, use is made of the standard variational method to calculate the first moments of the membrane separation. Special attention is paid to the determination of the unbinding temperature. In particular, we discuss its dependence on the extra parameters related to the associated polymers, which are the surface coverage and the polymer layer thickness on each membrane (for system I) or the polymer density and the gyration radius of coils (for system II). Third, we compute the disjoining pressure upon membrane separation. Finally, we emphasize that the presence of polymers may be a mechanism to delay or to accentuate the appearance of the unbinding transition between fluid membranes.

Primitive interactions between inclusions on a fluid membrane: the role of thermal fluctuations

Consider a fluid membrane decorated by moving hard or soft inclusions. The aim of this work is a quantitative study of the influence of thermal fluctuations on the three-dimensional primitive forces between these inclusions. Integrating over all membrane fluctuations, we obtain a general form giving the modified primitive interactions upon the transverse distance. The established formalism enables us to obtain the modified expression of some standard interaction potentials. In particular, for power-like potentials, we found a modified expression featuring the Whittaker function. The present formalism may be extended to other primitive interaction potentials. Finally, the main conclusion is that, decorated fluid membranes may be regarded as effective two-dimensional colloidal solutions where inclusions interact via the computed effective interactions.

Confined diffusion of hydrophilic probes inserted in lyotropic lamellar phases

The dynamic behaviour of three hydrophilic probes (two dyes and one fluorescently-labelled protein) inserted in the water layers of lyotropic lamellar phases has been studied by confocal fluorescence recovery experiments. Two different, ionic (AOT/NaCl/ H(2)O and non-ionic ( C(12)E(5) /hexanol/ H(2)O host systems were studied. The confinement effect has been carefully monitored using the swelling properties of the lamellar phases. In all cases, we measure the evolution of the probe diffusion coefficient in the layer plane D ( perpendicular) versus the separation between the membranes d(w). Depending on the composition of the lamellar phase, this distance can be continuously adjusted from 500A to about 20A. For all systems, we observe a first regime, called dilute regime, where the diffusion coefficient decreases almost linearly with 1/d (w) . In this regime, the Faxén theory for the friction coefficient of a spherical particle symmetrically dragged between two rigid walls can largely explain our results. More unexpectedly, when the membranes are non-ionic, and also quite flexible ( C(12)E(5) /hexanol in water), we observe the existence of a second, concentrated (or confined) regime, where the diffusion coefficient is nearly constant and different from zero for membrane separations smaller than the particle size. This new regime can be heuristically explained by simple arguments taking into account the membrane fluidity.