Calculation of resonance energy transfer in crowded biological membranes.

Analytical and numerical models were developed to describe fluorescence resonance energy transfer (RET) in crowded biological membranes. It was assumed that fluorescent donors were linked to membrane proteins and that acceptors were linked to membrane lipids. No restrictions were placed on the location of the donor within the protein or the partitioning of acceptors between the two leaflets of the bilayer; however, acceptors were excluded from the area occupied by proteins. Analytical equations were derived that give the average quantum yield of a donor at low protein concentrations. Monte Carlo simulations were used to generate protein and lipid distributions that were linked numerically with RET equations to determine the average quantum yield and the distribution of donor fluorescence lifetimes at high protein concentrations, up to 50% area fraction. The Monte Carlo results show such crowding always reduces the quantum yield, probably because crowding increases acceptor concentrations near donor-bearing proteins; the magnitude of the reduction increases monotonically with protein concentration. The Monte Carlo results also show that the distribution of fluorescence lifetimes can differ markedly, even for systems possessing the same average lifetime. The dependence of energy transfer on acceptor concentration, protein radius, donor position within the protein, and the fraction of acceptors in each leaflet was also examined. The model and results are directly applicable to the analysis of RET data obtained from biological membranes; their application should result in a more complete and accurate determination of the structures of membrane components.     

Transmembrane helices can induce domain formation in crowded model membranes

We studied compositionally heterogeneous multi-component model membranes comprised of saturated lipids, unsaturated lipids, cholesterol, and α-helical TM protein models using coarse-grained molecular dynamics simulations. Reducing the mismatch between the length of the saturated and unsaturated lipid tails reduced the driving force for segregation into liquid-ordered (l(o)) and liquid-disordered (l(d)) lipid domains. Cholesterol depletion had a similar effect, and binary lipid mixtures without cholesterol did not undergo large-scale phase separation under the simulation conditions. The phase-separating ternary dipalmitoyl-phosphatidylcholine (DPPC)/dilinoleoyl-PC (DLiPC)/cholesterol bilayer was found to segregate into l(o) and l(d) domains also in the presence of a high concentration of ΤΜ helices. The l(d) domain was highly crowded with TM helices (protein-to-lipid ratio ~1:5), slowing down lateral diffusion by a factor of 5-10 as compared to the dilute case, with anomalous (sub)-diffusion on the μs time scale. The membrane with the less strongly unsaturated palmitoyl-linoleoyl-PC instead of DLiPC, which in the absence of TM α-helices less strongly deviated from ideal mixing, could be brought closer to a miscibility critical point by introducing a high concentration of TM helices. Finally, the 7-TM protein bacteriorhodopsin was found to partition into the l(d) domains irrespective of hydrophobic matching. These results show that it is possible to directly study the lateral reorganization of lipids and proteins in compositionally heterogeneous and crowded model biomembranes with coarse-grained molecular dynamics simulations, a step toward simulations of realistic, compositionally complex cellular membranes. This article is part of a Special Issue entitled: Protein Folding in Membranes.     

Asymmetrical membranes and surface tension

The (31)P-nuclear magnetic resonance chemical shift of phosphatidic acid in a membrane is sensitive to the lipid head group packing and can report qualitatively on membrane lateral compression near the aqueous interface. We have used high-resolution (31)P-nuclear magnetic resonance to evaluate the lateral compression on each side of asymmetrical lipid vesicles. When monooleoylphosphatidylcholine was added to the external monolayer of sonicated vesicles containing dioleoylphosphatidylcholine and dioleoylphosphatidic acid, the variation of (31)P chemical shift of phosphatidic acid indicated a lateral compression in the external monolayer. Simultaneously, a slight dilation was observed in the inner monolayer. In large unilamellar vesicles on the other hand the lateral pressure increased in both monolayers after asymmetrical insertion of monooleoylphosphatidylcholine. This can be explained by assuming that when monooleoylphosphatidylcholine is added to large unilamellar vesicles, the membrane bends until the strain is the same in both monolayers. In the case of sonicated vesicles, a change of curvature is not possible, and therefore differential packing in the two layers remains. We infer that a variation of lipid asymmetry by generating a lateral strain in the membrane can be a physiological way of modulating the conformation of membrane proteins.     

"Entropic traps" in the kinetics of phase separation in multicomponent membranes stabilize nanodomains

We quantitatively describe the creation and evolution of phase-separated domains in a multicomponent lipid bilayer membrane. The early stages, termed the nucleation stage and the independent growth stage, are extremely rapid (characteristic times are submillisecond and millisecond, respectively) and the system consists of nanodomains of average radius approximately 5-50 nm. Next, mobility of domains becomes consequential; domain merger and fission become the dominant mechanisms of matter exchange, and line tension gamma is the main determinant of the domain size distribution at any point in time. For sufficiently small gamma, the decrease in the entropy term that results from domain merger is larger than the decrease in boundary energy, and only nanodomains are present. For large gamma, the decrease in boundary energy dominates the unfavorable entropy of merger, and merger leads to rapid enlargement of nanodomains to radii of micrometer scale. At intermediate line tensions and within finite times, nanodomains can remain dispersed and coexist with a new global phase. The theoretical critical value of line tension needed to rapidly form large rafts is in accord with the experimental estimate from the curvatures of budding domains in giant unilamellar vesicles.     

Interaction between bending and tension forces in bilayer membranes.

A theoretical analysis is presented of the bending mechanics of a membrane consisting of two tightly-coupled leaflets, each of which shears and bends readily but strongly resists area changes. Structures of this type have been proposed to model biological membranes such as red blood cell membrane. It is shown that when such a membrane is bent, anisotropic components of resultant membrane tension (shear stresses) are induced, even when the tension in each leaflet is isotropic. The induced shear stresses increase as the square of the membrane curvature, and become significant for moderate curvatures (when the radius of curvature is much larger than the distance between the leaflets). This effect has implications for the analysis of shape and deformation of freely suspended and flowing red blood cells.     

Protein aggregation in crowded environments

The generic tendency of proteins to aggregate into non-functional, and sometimes cytotoxic, structures poses a universal problem for all types of cell. This tendency is greatly exacerbated by the high total concentration of macromolecules found within most intracellular compartments, a phenomenon referred to as macromolecular crowding. This review discusses the quantitative effects of crowding on protein aggregation and the role of molecular chaperones in combating this problem.     

Coupling between line tension and domain contact angle in heterogeneous membranes

The compositional differences between domains in phase-separated membranes are associated with differences in bilayer thickness and moduli. The resulting packing deformation at the phase boundary gives rise to a line tension, the one dimensional equivalent of surface tension. In this paper we calculate the line tension between a large membrane domain and a continuous phase as a function of the thickness mismatch and the contact angle between the phases. We find that the packing-induced line tension is sensitive to the contact angle, reaching a minimum at a specific value. The difference in the line tension between a flat domain (that is within the plane of the continuous phase) and a domain at the optimal contact angle may be of order 40%. This could explain why previous calculations of the thickness mismatch based line tension tend to yield values that are higher than those measured experimentally.     

Mechanism of pore formation in stearoyl-oleoyl-phosphatidylcholine membranes subjected to lateral tension

Theoretical model of a through pore formation in lipid bilayer membrane under applied lateral tension was developed. In the framework of elastic theory of liquid crystals adapted to lipid membranes, we calculated a continuous trajectory from intact bilayer through a hydrophobic defect to a through pore. It was shown that the major energetic characteristic of membrane stability with respect to the pore formation, i. e., line tension, depends both on the pore radius and on the value of the applied lateral tension. This leads to a non-monotonous dependence of the average waiting time of the pore formation on the lateral tension: at low tensions the waiting time was large, then there was a local minimum, after which the average waiting time was increasing again. For membranes formed from stearoyl oleoyl phosphatidylcholine, the local minimum corresponded to the lateral tension of 7 mN/m; the calculated value of the edge line tension of a large pore was 16.5 pN. These results are consistent with available experimental data.     

Surface tension induced by sphingomyelin to ceramide conversion in lipid membranes

We have investigated the effect of sphingomyelin (SM) to ceramide enzymatic conversion on lipid bilayers using Giant Unilamellar Vesicles (GUVs). Sphingomyelinase was added externally to GUVs containing various proportions of SM. In situ asymmetrical SM conversion to ceramide reduced the area of one leaflet. In the absence of equilibration of all the lipids between the two leaflets, a mismatch between the two monolayers was generated. The tension generated by this mismatch was sufficient to trigger the formation of membrane defects and total vesicle collapse at relatively low percentage of SM (≈ 5% mol). The formation of nanometric size defects was visualised by AFM in supported bilayers. Vesicle rupture was prevented in two circumstances: (a) in GUVs containing a mixture of l_d and l_o domains and (b) in GUVs containing 5% lyso-phosphatidylcholine. In both cases, the accumulation of enough ceramide (at initial SM concentration of 10%) allowed the formation of ceramide-rich domains. The coupling between the two asymmetrical monolayers and the condensing effect produced by the newly formed ceramide generated a tension that could underlie the mechanism through which ceramide formation induces membrane modifications observed during the late stages of apoptosis.     

Surface tension induced by sphingomyelin to ceramide conversion in lipid membranes

We have investigated the effect of sphingomyelin (SM) to ceramide enzymatic conversion on lipid bilayers using Giant Unilamellar Vesicles (GUVs). Sphingomyelinase was added externally to GUVs containing various proportions of SM. In situ asymmetrical SM conversion to ceramide reduced the area of one leaflet. In the absence of equilibration of all the lipids between the two leaflets, a mismatch between the two monolayers was generated. The tension generated by this mismatch was sufficient to trigger the formation of membrane defects and total vesicle collapse at relatively low percentage of SM ( approximately 5% mol). The formation of nanometric size defects was visualised by AFM in supported bilayers. Vesicle rupture was prevented in two circumstances: (a) in GUVs containing a mixture of l(d) and l(o) domains and (b) in GUVs containing 5% lyso-phosphatidylcholine. In both cases, the accumulation of enough ceramide (at initial SM concentration of 10%) allowed the formation of ceramide-rich domains. The coupling between the two asymmetrical monolayers and the condensing effect produced by the newly formed ceramide generated a tension that could underlie the mechanism through which ceramide formation induces membrane modifications observed during the late stages of apoptosis.     

Internal forces, tension and energy density in tethered cellular membranes

We analyze tethered cellular membranes by considering the membrane resultants, tension and densities of two modes of energy, bending and adhesion. These characteristics are determined based on a computational (finite-difference) analysis of membrane shape. We analyze the relative contribution and distribution of the membrane characteristics in four typical zones of the membrane surface. Using an axisymmetric model, we found that the meridional and circumferential components of the resultant are different near the tether body and they converge to the value of membrane tension farther from the tether. At the beginning of the area of membrane detachment from the cytoskeleton, the density of bending energy is on the same order of magnitude as membrane tension (resultant). Away from the tether, the bending energy density quickly decreases and becomes of the same order as that of the adhesion energy in the membrane-cytoskeleton attachment area. In that area, both modes of energy are significantly smaller than the membrane tension. We also consider the effect of the membrane bending modulus on the distribution of the membrane characteristics. An increase in the bending modulus results in changing the length and position on the membrane surface of zone 1 characterized by significant evolution of the resultant components. It also results in shortening zone 2 that covers the rest of the area of membrane detachment. The obtained results can help in a better interpretation of the measurements of membrane mechanical properties as well as in analyses of proteins and channels in curved membranes.     

Coupling between line tension and domain contact angle in heterogeneous membranes

The compositional differences between domains in phase-separated membranes are associated with differences in bilayer thickness and moduli. The resulting packing deformation at the phase boundary gives rise to a line tension, the one dimensional equivalent of surface tension. In this paper we calculate the line tension between a large membrane domain and a continuous phase as a function of the thickness mismatch and the contact angle between the phases. We find that the packing-induced line tension is sensitive to the contact angle, reaching a minimum at a specific value. The difference in the line tension between a flat domain (that is within the plane of the continuous phase) and a domain at the optimal contact angle may be of order 40%. This could explain why previous calculations of the thickness mismatch based line tension tend to yield values that are higher than those measured experimentally.     

Entropic particle transport in periodic channels

The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two-dimensional periodic channels, exhibiting periodically varying cross-sections. The particles in addition are subjected to an external force acting alongside the direction of the longitudinal channel axis. For a fixed channel geometry, the dynamics of the two-dimensional problem is characterized by a single dimensionless parameter which is proportional to the ratio of the applied force and the temperature of the particle environment. In such structures entropic effects may play a dominant role. Under certain conditions the two-dimensional dynamics can be approximated by an effective one-dimensional motion of the particle in the longitudinal direction. The Langevin equation describing this reduced, one-dimensional process is of the type of the Fick-Jacobs equation. It contains an entropic potential determined by the varying extension of the eliminated channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. Different forms of this correction term have been suggested before, which we here compare for a particular class of models. We analyze the regime of validity of the Fick-Jacobs equation, both by means of analytical estimates and the comparisons with numerical results for the full two-dimensional stochastic dynamics. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility and the effective diffusion constant.     

Mechanosensitivity of gramicidin A channels in bulged bilayer membranes at constant tension

Mechanoelectrical transduction in gramicidin A channels was studied in macroscopic planar lipid bilayer membranes bulged at constant tension. We found a supralinear increase in the single channel activity that was proportional to the square of membrane radius, but could not be accounted for by the increase in membrane surface area, or by recruitment of new channels. Extrapolated to biological membranes, these observations may suggest that the permeability of ion channels can be influenced simply by changing shape of the membrane, with or without stretching. Published in Russian in Biofizika, 2006, Vol. 51, No. 6, pp. 1014–1018. The text was submitted by the authors in English.     

Renormalization of the tension and area expansion modulus in fluid membranes.

Renormalization of the membrane tension and elastic area expansion modulus by thermally induced bending fluctuations is treated in terms of the formalism of Brochard, De Gennes, and Pfeuty (J. de Phys. (France). 37:1099-1104, 1976). The dependence of the renormalized tension on the bare membrane tension parallels the dependence on the fractional area extension of giant vesicles found experimentally by Evans and Rawicz (Physiol. Rev. Lett. 64:2094-2097, 1990), and suggests conditions for molecular dynamics simulations with membrane patches of limited size that might best represent the properties of macroscopic vesicles.     

Ganglioside GM1 increases line tension at raft boundary in model membranes

Gangliosides are significant participants in suppression of immune system during tumor processes. It was shown that they can induce apoptosis of T-lymphocytes in a raft-dependent manner. Fluorescence confocal microscopy was used to study distribution and influence of ganglioside GM1 on raft properties in giant unilamellar vesicles. Both raft and non-raft phase markers were utilized. No visible phase separation was observed without GM1 unless lateral tension was applied to the membrane. At 2 mol % of GM1 large domains appeared indicating macroscopic phase separation. Increase of GM1 content to 5 mol % resulted in shape transformation of the domains consistent with growth of line tension at the domain boundary. At 10 mol % of GM1 almost all domains were pinched out from vesicles, forming their own homogeneous liposomes. Estimations showed that the change of the GM1 content from 2 to 5–10 mol % resulted in a several-fold increase of line tension. This finding provides a possible mechanism of apoptosis induction by GM1. Incorporation of GM1 into a membrane leads to an increase of the line tension. This results in a growth of the average size of rafts due to coalescence or merger of small domains. Thus, necessary proteins can find themselves in one common raft and start the corresponding cascade of reactions. The article is published in the original.     

Mechanosensitivity of gramicidin A channels in semispherical bilayer membranes at constant tension

Mechanoelectrical transduction in gramicidin A channels was studied in macroscopic planar lipid bilayer membranes bulged at constant tension. We found a supralinear increase in the single channel activity, which was proportional to the square of membrane radius but could not be accounted for by the increase in membrane surface area or by recruitment of new channels. When being extrapolated to biological membranes, these observations may suggest that the activity of permeability of ion channels can be influenced simply by changing the shape of the membrane, with or without stretching.     

Protein diffusion in crowded electrolyte solutions

We report on a combined cold neutron backscattering and spin-echo study of the short-range and long-range nanosecond diffusion of the model globular protein bovine serum albumin (BSA) in aqueous solution as a function of protein concentration and NaCl salt concentration. Complementary small angle X-ray scattering data are used to obtain information on the correlations of the proteins in solution. Particular emphasis is put on the effect of crowding, i.e. conditions under which the proteins cannot be considered as objects independent of each other. We thus address the question at which concentration this crowding starts to influence the static and in particular also the dynamical behaviour. We also briefly discuss qualitatively which charge effects, i.e. effects due to the interplay of charged molecules in an electrolyte solution, may be anticipated. Both the issue of crowding as well as that of charge effects are particularly relevant for proteins and their function under physiological conditions, where the protein volume fraction can be up to approximately 40% and salt ions are ubiquitous. The interpretation of the data is put in the context of existing studies on related systems and of existing theoretical models.