Protrusion model

The previously described measurements have been performed on lipids in aqueous solutions, but lipid bilayers also swell in some other solvents (12) and the results of such measurements compare quite well with the aqueous case. In addition, hydration (solvation) forces act between DNA polyelectrolytes (13) and polysaccharides (14). These facts make the interpretation of the forces even more complicated and it is no wonder that different approaches to explain the nature of this solvation force exist. So far no truly ab initio theory has been proposed. The existing theories include models based on the electrostatic approach, the free energy approach, and an approach based on the entropic or protrusion model. 

Protrusion Model for the Hydration Force. Recently Is-raelachvili and Wennerstrom (IW) proposed that the origin of the hydration force is due to the head-group protrusion of the phospholipid molecules into the solvent region (27), and, therefore, the force is more akin to a steric force acting between polymer-covered surfaces. Because such an explanation of the nature of the hydration force does not involve electrostatic concepts, we will not present the IW theory here. A detailed description of a protrusion model is available in a recent review by Israelachvili and Wennerstrom (28), and a critique of IW theory of protrusions can be found in Parsegian and Rand (29). 

Figure 4. The Brownian ratchet model of lamellar protrusion (Peskin et al., 1993). According to this hypothesis, the distance between the plasma membrane (PM) and the filament end fluctuates randomly. At a point in time when the PM is most distant from the filament end, a new monomer is able to add on. Consequently, the PM is no longer able to return to its former position since the filament is now longer. The filament cannot be pushed backwards by the returning PM as it is locked into the mass of the cell cortex by actin binding proteins. In this way, the PM is permitted to diffuse only in an outward direction. The maximum force which a single filament can exert (the stalling force) is related to the thermal energy of the actin monomer by kinetic theory according to the following equation ...

Low resolution models (20-30 A) based on diffraction analysis of membrane crystals of Na,K-ATPase [34,35,39] and Ca-ATPase [40,41] show that the cytoplasmic protrusions of the proteins are remarkably similar. A notable difference is a 10-20 A... 

Figure4.4 c(2 x 2)A structure. Left panel structural model. Right top panel corresponding simulated STM image (VB = + 1.30V, / = 0.04nA). The protrusions correspond to oxygen couples, whereas the depressions are the hollow sites surrounded by O—H complexes. Right bottom panel simulated current profiles along [00 1] at decreasing (light blue to red) tip-surface distances. (Reprinted with permission from Ref. [18].)...

On the submicron scale, the current distribution is determined by the diffusive transport of metal ion and additives under the influence of local conditions at the interface. Transport of additives in solution may be non-locally controlled if they are consumed at a mass-transfer limited rate at the deposit surface. The diffusion of additives in solution must then be solved simultaneously with the flux of reactive ion. Diffusive transport of inhibitors forms the basis for leveling [144-147] where a diffusion-limited inhibitor reduces the current density on protrusions. West has treated the theory of filling based on leveling alone [148], In his model, the controlling dimensionless groups are equivalent to and D divided by the trench aspect ratio. They determine the ranges of concentration within which filling can be achieved. 

All of the above considerations have sometimes led to a too rigid picture of the membrane structure. Of course, the mentioned types of fluctuations (protrusions, fluctuations in area per molecule, chain interdigitations) do exist and will turn out to be important. Without these, the membrane would lack any mechanism to, for example, adjust to the environmental conditions or to accommodate additives. Here we come to the central theme of this review. In order to come to predictive models for permeation in, and transport through bilayers, it is necessary to go beyond the surfactant parameter approach and the fluid mosaic model. 

Because of the protrusion of portions of the hydrocarbon chains into the Stern layer, the core acquires a rough surface. This model seems like a reasonable snapshot of what we have already described as a rapidly changing surface region. 

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