Membranes fluctuations

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-... 

The 13C nuclear resonance studies in my report provide some informations on lipid membrane fluctuations in binary mixtures. Totally unsolved problems include an appropriate two-dimensional Debye-Huckel theory for membranes, and theoretical treatments of boundary free energies (between proteins and lipids, and between solid and fluid phase lipids). 

Nallet, F. (1991). Membrane fluctuations in dilute lamellar phases. Langmuir 1, 1861-1863. 

Mittelman, L., Levin, S., Verschueren, H., de Baetselier, P. and Korenstein, R. (1994). Direct correlation between cell membrane fluctuations, cell filterability and the metastatic potential of lymphoid cell lines. Biochem. Biophys. Res. Commun. 203, 899-906. 

This potential force occurs in microstructured fluids like microemulsions, in cubic phases, in vesicle suspensions and in lamellar phases, anywhere where an elastic or fluid boundary exists. Real spontaneous fluctuations in curvature exist, and in liposomes they can be visualised in video-enhtuiced microscopy [59]. Such membrane fluctuations have been invoked as a mechanism to account for the existence of oil- or water-swollen lamellar phases. Depending on the natural mean curvature of the monolayers boimding an oil region - set by a mixture of surfactant and alcohol at zero -these swollen periodic phases can have oil regions up to 5000A thick With large fluctuations the monolayers are supposed to be stabilised by steric hindrance. Such fluctuations and consequent steric hindrance play some role in these systems and in a complete theory of microemulsion formation. 

Gracia, R.S., Bezlyepkina, N., Knorr, R.L., Lipowsky, R., and Dimova, R. (2010) Effect of cholesterol on the rigidity of saturated and unsaturated membranes fluctuation and electrodeformation analysis of giant vesicles. Soft Matter, 6 (7), 1472-1482. 

Within this continuum description, the membrane is conceived as a thin elastic sheet. If one assumes that the membrane fluctuations are small, its surface can be parameterized within a Monge representation via a height function, h(y,z), describing its position over some reference plane. Then, the Helfrich-Hamiltonian takes the form... 

Expanding h(y,z) in Fourier space and using the equipartition theorem allows to calculate the power spectrum of membrane fluctuations [40,48] ... 

Indeed, all ingredients for a complete thermodynamic characterization of the system are available in molecular dynamics simulations atomic resolution, protein flexibility, membrane fluctuations, explicit solvent, and ionic motion. Because the free energy profile controls ion conduction, along with nonequilibrium parameters like the diffusion coefficient, one can expect to fully understand the permeation (and selectivity) processes from it. Furthermore, because one can explore the energetics of molecular configurations in response to external stimuli, free energy calculations can in principle supply information about gating mechanisms or, at least, could be used to confirm hypotheses derived from indirect experimental observations. 

Davies et al. smdied phase transitions with H-NMR quadmple sphttings spectra. The longer peptides L24 in DPPC membrane in peptide to hpid molar ratio of 100 1 caused 30 % increase of order in hpids acyl chains, while in molar ratio of 43 1 there was ordy 5 % order increase [11]. In Pan et al. X-ray experiments and MD simulations [51] of alamedthin it has been shown that this peptide decreases thickness of diC22 1-PC membrane and increases its own length in a peptide to hpid molar ratio of 1 10. However, in a DOPC membrane this peptide tilts in approx. -15°. In both cases the peptide decreased of membrane fluctuations (bending modulus K ), but the diC22 l-PC is more stabilized (factor 10) than DOPC (oidy 2). 

Figure 11.2 The liposome shown in Figure 11.1 submitted to a magnetic field H (direction given by the arrow). The deformation is prolate and the membrane fluctuations vanish. Note the high ionic strength (Q = 85 mM). Length of the bar is 20 pm.

There are several methods for the experimental measurement of. One of these, [1] consists of determination of the effective stretching modulus of a membrane fluctuating at very low tensions. The principles of the method are shown on Figure 14.1. 

Figure 30 Surface forces due to configurational confinement of thermally excited modes into a narrow region between two approaching interfaces, (a) Fluctuating protrusion of adsorbed amphiphilic molecules gives rise to the protrusion surface force (b) bending mode of membrane fluctuations gives rise to the undulation force and (c) squeezing (peristaltic) mode of membrane fluctuations gives rise to the peristaltic force.

Similarly, in erythrocytes, trans-membrane ventilation of C02 and 02 may be enhanced by sub-pressure fluctuations, generated by inwardly oriented pwasons due to ATPase activity of branched actin polymerization on membrane-attached filaments [71]. According to the pwason model, the rate and amplitude of these active membrane fluctuations are anticipated also for other membrane-attached hydrophilic ATPases [72]. Such hydraulic compression of the cell membrane might explain the peculiar observation of a higher internal hydrostatic pressure in an intact cellular state of partial inflation. Intracellular vesicles, bacteria or designed objects can utilize this hydraulic machinery for the actin-based propulsion inside the cell or in a cell-like medium [73]-... 

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