Fluctuations of membranes

Further progress in understanding membrane instability and nonlocality requires development of microscopic theory and modeling. Analysis of membrane thickness fluctuations derived from molecular dynamics simulations can serve such a purpose. A possible difficulty with such analysis must be mentioned. In a natural environment isolated membranes assume a stressless state. However, MD modeling requires imposition of special boundary conditions corresponding to a stressed state of the membrane (see Refs. 84,87,112). This stress can interfere with the fluctuations of membrane shape and thickness, an effect that must be accounted for in analyzing data extracted from computer experiments. 

Kramer L (1971) Theory of light scattering fiom fluctuations of membranes and monolayers. J Chem Phys 55 2097-2105... 

Two different bending elastic moduli exist A f, when the exchange of lipid molecules between the monolayers of the bilayer is free, and when it is blocked. When the exchange is forbidden, the number of the molecules in each monolayer of the bilayer is constant. At free flip-flop, the bending elasticity energy is lower because it has been minimized with respect to the difference between the number of molecules in each monolayer and, consequently, k < kf. For all phenomena related to the out-of-plane fluctuations of membranes, the relevant quantity is k [6-8]. These phenomena include the thermal fluctuations of quasispherical vesicles [9,10], as well as vesicle suction in micropipettes at very low suction pressures [1]. 

Biomembranes are complex structures composed of various lipids and proteins. Different membrane compositions affect viscoelastic and hydrodynamic properties of membranes, which are critical to their functions. Cholesterol-rich vesicles are similar to cell membranes in structure and component. Therefore, cholesterol-rich vesicles can represent a typical model for studying membrane dynamics and functions. Nuclear magnetic relaxation dispersion was used to investigate the detailed molecular dynamics of membrane differences between vesicles and cholesterol vesicles in the temperature range of 278-298 K. Vesicles of two different sizes were prepared. The effect of cholesterol mainly affected the order fluctuation of membranes and the diffusional motion of lipid molecules. ... 

The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

Olle Edholm, Oliver Berger, and Fritz Jahnig. Structure and fluctuations of bacteriorhodopsin in the purple membrane. J. Mol. Biol., 250 94 111, 1995. 

Baumgartner and coworkers [145,146] study lipid-protein interactions in lipid bilayers. The lipids are modeled as chains of hard spheres with heads tethered to two virtual surfaces, representing the two sides of the bilayer. Within this model, Baumgartner [145] has investigated the influence of membrane curvature on the conformations of a long embedded chain (a protein ). He predicts that the protein spontaneously localizes on the inner side of the membrane, due to the larger fluctuations of lipid density there. Sintes and Baumgartner [146] have calculated the lipid-mediated interactions between cylindrical inclusions ( proteins ). Apart from the... 

Since Ca is transferred from one side of the membrane to the other side in association with the Ca -ATPase, thermal fluctuation of critical regions of the Ca -ATPase influenced in specific ways through the phosphorylation of the enzyme by ATP may play a role in Ca translocation. Similar ideas have been proposed some time ago by Huxley [419] in relationship to crossbridge movements during muscle contraction and by Welch and others on the role of protein fluctuations in enzyme action [420-430]. 

An alternative description of membrane stability has been based on hydrodynamic models, originally developed for liquid films in various environments [54-56]. Rupture of the film was rationalized by the instability of symmetrical squeezing modes (SQM) related to the thickness fluctuations. In the simplest form it can be described by a condition [54] d Vdis/dh < where is the interaction contribution related to the dis-... 

Other possible direct probes are optical experiments similar to studies [113] of vesicles but expanded towards shorter A (20-30 A). Alternatively neutron spin-echo studies of stacked bilayer arrays, which can probe the 10-30 A range [114], might possibly be applicable here. Finally, the x-ray grazing-incidence technique has been shown to be a powerful tool for studying short wavelength fluctuations at fluid interfaces [100]. The application of this technique to the investigation of membrane surface fluctuations can reasonably be expected in the near future [115,116]. 

H. Noguchi and G. Gompper, Dynamics of fluid vesicles in shear flow effect of membrane viscosity and thermal fluctuations, Phys. Rev. E 72, 011901 (2005). 

Using liposomes made from phospholipids as models of membrane barriers, Chakrabarti and Deamer [417] characterized the permeabilities of several amino acids and simple ions. Phosphate, sodium and potassium ions displayed effective permeabilities 0.1-1.0 x 10 12 cm/s. Hydrophilic amino acids permeated membranes with coefficients 5.1-5.7 x 10 12 cm/s. More lipophilic amino acids indicated values of 250 -10 x 10-12 cm/s. The investigators proposed that the extremely low permeability rates observed for the polar molecules must be controlled by bilayer fluctuations and transient defects, rather than normal partitioning behavior and Born energy barriers. More recently, similar magnitude values of permeabilities were measured for a series of enkephalin peptides [418]. 

TABLE 2 Estimated fluctuation changes in the transmembrane and cytoplasmic a-helices for a variety of membrane proteins and their complexes (Hz)°... 

It is emphasized that revealing the dynamics as well as the structure (or conformation) based on several types of spin-relaxation times is undoubtedly a unique and indispensable means, only available from NMR techniques at ambient temperature of physiological significance. Usually, the structure data themselves are available also from X-ray diffraction studies in a more refined manner. Indeed, better structural data can be obtained at lower temperature by preventing the unnecessary molecular fluctuations, which are major subjects in this chapter, since structural data can be seriously deteriorated for domains where dynamics are predominant even in the 2D or 3D crystalline state or proteoliposome at ambient temperature. It should be also taken into account that the solubilization of membrane proteins in detergents is an alternative means to study structure in solution NMR. However, it is not always able faithfully to mimick the biomembrane environment, because the interface structure is not always the same between the bilayer and detergent system. This typically occurs in the case of PLC-81(1-140) described in Section 4.2.4 and other types of peptide systems. 

The assumption of membrane softness is supported by a theoretical argument of Nelson et al., who showed that a flexible membrane cannot have crystalline order in thermal equilibrium at nonzero temperature, because thermal fluctuations induce dislocations, which destroy this order on long length scales.188 189 The assumption is also supported by two types of experimental evidence for diacetylenic lipid tubules. First, Treanor and Pace found a distinct fluid character in NMR and electron spin resonance experiments on lipid tubules.190 Second, Brandow et al. found that tubule membranes can flow to seal up cuts from an atomic force microscope tip, suggesting that the membrane has no shear modulus on experimental time scales.191 However, conflicting evidence comes from X-ray and electron diffraction experiments on diacetylenic lipid tubules. These experiments found sharp diffraction peaks, which indicate crystalline order in tubule membranes, at least over the length scales probed by the diffraction techniques.123,192 193... 

With the Monte Carlo technique, a very large number of membrane problems have been worked on. We have insufficient space to review all the data available. However, the formation of pores is of relevance for permeation. The formation of perforations in a polymeric bilayer has been studied by Muller by using Monte Carlo simulation [67] within the bond fluctuation model. In this particular MC technique, realistic moves are incorporated, such that the number of MC steps can be linked to a simulated time. 

Action potential a fluctuation in membrane potential caused hy opening and closing of voltage-gated ion channels. 

The membrane composition of Quantro II has been under continuous research for 19 months. Early samples were put on test in order to establish a long-term data base for this chemistry. While that early composition has been modified to achieve higher flux and rejection, its durability can be judged from Table I. Table I plots data obtained daily over the time period indicated. Curves on all tables have been smoothed to avoid daily fluctuations. It should be understood that fluctuations of as much as 0.2% rejection and 0.2 gfd in flux are routinely experienced and are not shown. 

The energetic coupling between environment and enzymes is more general. It must occur also in membranes and free aqueous solutions as well. In view of the overall occurrence of the translational thermal coupling and the experimentally proved fluctuations of proteins, our model must be valid in case of any enzymes. 

As just mentioned, there are a large number of unsolved problems in membrane biophysics, including the questions of local anisotropic diffusion, hysteresis, protein-lipid phase separations, the role of fluctuations in membrane fusion, and the mathematical problems of diffusion in two dimensions Stokes paradox). 

We have not yet said much about the second major constituent of eukaryotic membrane lipids, cholesterol. Cholesterol broadens the melting transition of the phospholipid bilayer (see fig. 17.20). Below the Tm, cholesterol disorders the membrane because it is too bulky to fit well into the neatly packed arrangement of the fatty acid chains that is favored at low temperatures. Above the Tm, cholesterol restricts further disordering because it is too large and inflexible to join in the rapid fluctuations of the chains. If the amount of cholesterol in a phospholipid bilayer is increased to about 30%, roughly the amount in the plasma membranes of typical animal cells, the melting transition becomes so broad as to be almost undetectable. 

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