Membrane tension

The combination of the first and second laws of thermodynamics exactly defines the equilibrium of a system. Of course, many biological systems are 

For obvious reasons, we need to introduce surface contributions in the thermodynamic framework. Typically, in interface thermodynamics, the area in the system, e.g. the area of an air-water interface, is a state variable that can be adjusted by the observer while keeping the intensive variables (such as the temperature, pressure and chemical potentials) fixed. The unique feature in selfassembling systems is that the observer cannot adjust the area of a membrane in the same way, unless the membrane is put in a frame. Systems that have self-assembly characteristics are conveniently handled in a setting of thermodynamics of small systems, developed by Hill [12], and applied to surfactant self-assembly by Hall and Pethica [13]. In this approach, it is not necessary to make assumptions about the structure of the aggregates in order to define exactly the equilibrium conditions. However, for the present purpose, it is convenient to take the bilayer as an example. 

Let us consider, for example, a flat symmetrical bilayer of which the area is large, so that end-effects can be ignored. Finite size effects are important, and will be discussed in the following section. The membrane is freely floating in solution, i.e. it is not supported by a frame. Combination of the first and second laws of thermodynamics gives for the difference of internal energy dl/of a bulk system with membranes with area A  

It is often more convenient to control the temperature than to control the entropy, and therefore it is more convenient to switch to the Helmholtz energy F=U TS, for which we can write  

It will be clear that the membrane is free to adjust its area. Let the system be closed, i.e. let the number , of molecules in it be fixed. Let the temperature 

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The attachment of S-layers results in a decreased membrane tension [144]... 

It follows from Eqs. (73) and (74) that the only stabilizing force for a-modes at long X is the membrane tension, and critical voltage vanishes as cr 0. In experiments with black lipid membranes the surface tension a arises from the contact of the bilayer with the bulk phase contained in the surrounding rim and is typically < 0.002 N/m. Then choosing... 

This leads to the equilibrium condition that the membrane tension is zero. For stability reasons it is necessary that d2F/dA2 > 0, or equivalently that Sy/SA > 0. 

There is a discussion in the literature about the effect of undulation entropy on the equilibrium membrane tension [14,15], Formally, undulations are included in the surface tension, and thus we need not worry about this. However, if in some model the two are artificially decoupled, one may allow for a very small (positive) surface tension as the equilibrium structure. In other words, the entropy (per unit area) from undulations should compensate for the tension (excess free energy per unit area). 

The lateral compressibility, i.e. the relative area change upon an imposed membrane tension, decreases slightly more than linearly with the chain length. This means that it is more difficult to expand the membrane surface area of a long-chained lipid than a shorter one. In Figure 20 dimensionless units are used, which means that the surface tension is given in units kT/as. 

Sukharev, S. (1999). Mechanosensitive channels in bacteria as membrane tension reporters, FASEB J., 13 (Suppl.), S55-S61. 

Raucher D, Sheetz MP (1999) Characteristics of a membrane reservoir buffering membrane tension. Biophys. J. 77 1992-2002. 

Until recently there was only limited knowledge on the mechanical properties of animal cells. Micromanipulation has allowed some progress in this area. Figure 11 shows typical force-sampling time data for a hybridoma, with a bursting force of a few micro-Newtons. From such data the intrinsic mechanical properties of cell diameter, membrane tension at bursting and elastic area compressibility modulus can be... 

Mechanosensitive channels respond to changes in membrane tension. A prokaryotic large-conductance mechanosensitive channel, MscL, opens in response to osmotic stress to form a water filled channel between 3 and 4 nm across [18]. The change in pressure on the bilayer imparts a small movement in a transmembrane helix that is then followed by a dramatic rearrangement of the transmembrane domain to a fully open state. 

The consequences of applied membrane tension to an intrinsically mechanosensitive channel can be readily evaluated for a simple two-state system where the channel can exist in either closed (C) or open (O) conformations ... 

The steepness of the response of the channel to applied tension is determined by the magnitude of the change in cross-sectional area for example, in terms of units typically employed in these calculations, if AA= 100 A2, then an increase of 1 dyn cm 1 in membrane tension corresponds to a free energy change of —0.602 kj/mol, and AG will scale proportionally to changes in A A. Consequently, for a channel with A G° = 40 kj/mol and crj/2 = 10 dyn cm-1 (typical for mechanosensitive channels such as MscL), AA 660 A2. 

Consequently, larger spheres require a smaller pressure differential to maintain a given membrane tension than smaller spheres, and vice versa. The magnitudes of the pressure differential required to generate specific levels of membrane tension can be estimated from the following considerations. For a membrane with a radius of curvature = 3 pm (typical of the dimensions in a patch clamp experiment), application of 0.1 atm pressure (where 1 atm = 760 mm Hg = 1.013 x 106 dyn cm-2) corresponds to a = 15 dyn cm-1. The maximum applied pressure depends on the limit at which the patches break ( 20-30 dyn cm-1) and the curvature of the membrane, but is typically 0.2 atm. 

The initial characterizations of the dependence of channel conductance on membrane tension for MscL were interpreted in terms of a two-state model analogous to Eq. (1) (Sukharev etal., 1997). In a more detailed analysis, Sukharev, Sachs, and co-workers (Sukharev etal., 1999c) established the energetic parameters for the gating transition in the E. coli MscL (Ec MscL) and obtained evidence for three subconductance states (S2, S3, and S4) between the fully closed (Cl) and fully open (05) states ... 

Tubular membrane tension/mucosal DNA thermal melting point midpoint of thermal denaturation curve Transmembrane Trimethylamine oxide Transmembrane domain Trimethylsilyl thimersol Tobacco mosaic virus Treose nucleic acid 5-thio-2-nitrobenzoate... 

In their natural environment, bacterial cells need to adapt to a wide range of osmotic conditions. Escherichia coli cells exposed to hypo-osmotic shock respond by a rapid release of cellular osmolytes such as proline, potassium glutamate, trehalose, and ATP. This ability prevents the cells from lysis by decreasing the turgor pressure on the challenge of a sudden shift in osmolarity. Bacterial MS channels, MscL and MscS (Fig. la and b), are major components of adaptation mechanisms to hypo-osmotic shock. Being located in the cytoplasmic membrane, MscL and MscS are activated by an increase of membrane tension... 

Blood is a non-Newtonian suspension showing a shear-dependent viscosity. At low rates of shear, erythrocytes form cylindrical aggregates (rouleaux), which break up when the rate of shear is increased. Calculations show that the shear rate (D) associated with blood flow in large vessels such as the aorta is about 100 s b but for flow in capillaries it rises to about 1000 s b The flow characteristics of blood are similar to those of emulsions except that, while shear deformation of oil globules can occur with a consequent change in surface tension, no change in membrane tension... 

The typical decay hme for the relaxahon of nonporated vesicles, t, is of the order of 100 ps. It is set by the relaxahon of the membrane tension achieved at the end of the pulse. The membrane tension, acquired during the pulse, also referred to as electric tension, arises from the transmembrane potenhal, ( , built across the membrane during the pulse. Lipid membranes are impermeable to ions and, in the presence of an electric field, charges accumulate on both sides of the bilayer, which gives rise to this transmembrane potential [91] ... 

As menhoned above, the decay time for the relaxation of nonporated vesicles, Ti, is defined by the total membrane tension at the end of the pulse. The tension relaxation requires relative displacement of the lipid molecules in the bilayer. 

Above some electroporation threshold, the transmembrane potential cannot be further increased, and can even decrease due to transport of ions across the membrane [91, 95]. The phenomenon of membrane electroporation can also be understood in terms of tension. If the total membrane tension exceeds the lysis tension c ys, the vesicle ruptures. This corresponds to building up a certain critical transmembrane potential, = Pc- According to Eqs. (7.3) and (7.4), this porahon potenhal Pc depends on the inihal membrane tension Co as previously reported [59, 89, 90, 96, 97]. The crihcal hansmembrane potenhal for cell membranes is about IV (e.g., [98, 99]). 

The formation of the spherocylindrical shapes is not well understood. They are observed not only on lipid vesicles but also on polymersomes (vesicles made of diblock copolymers [123, 124]) [107]. Therefore, lipid-specific effects, for example partial head group charge and membrane thickness, as a possible cause for the observed cylindrical deformations are to be excluded. One possible explanation could be that ions flatten the equatorial zone of the deformed vesicle. During the pulse there is an inhomogeneity in the membrane tension due to the fact that the... 

Needham, D. and Hochmuth, R.M. (1989) Electro-mechanical permeabilization of lipid vesicles-role of membrane tension and compressibility. Biophysical Journal, 55 (5), 1001-1009. 

Kakehata S, Santos-Sacchi J. 1995. Membrane tension directly shifts voltage dependence of outer hair cell motility and associated gating charge. Biophys J 68 2190-2197. 

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