Persistence length membrane

The finite size of the box has several important consequences. One of them is that the area of the membrane piece is only of the order of 100 nm2. It is expected that the membrane is, on this length scale, roughly flat, i.e. the area is small as compared with the persistence length for the bilayer. Interestingly, however, in recent simulations the first signs of fluctuations away from the flat bilayer structure (undulations) have reportedly been found by MD simulations [33],... 

The IKS model is more natural for the low water content, with backbones not plasticized by excess water, whereas in water-saturated membranes the quasicrystallinity may not be the dominating motif at all. The main assumption of the quasicrystalline model is that the persistence length of the bundles of the backbone chains is at least several times greater than the distance between neighboring micelles. This condition may break down with the increase of water content. The IKS model helps to understand the birth of conductivity and its evolution with increasing water content, but a more complete theory of this evolution should invoke the... 

FIG. 16 Sketch of an integral membrane protein complexed by amphiphilic short polymers (amphipols). Protein and polymers are drawn to scale. The polymer/protein mass ratio corresponds to a typical experimental value of 1. The persistence length of the amphipol has been taken equal to about 3 nm. The number of contacts among the partners is largely speculative. (Reprinted from Ref. 3. Copyright 1996 National Academy of Sciences, U.S.A.)... 

Probability of an open site or bond in Chapter 4 Hydrostatic pressure (mmHg) in Chapters 5 and 6 Persistence length on polymer chain (cm) in Chapter 4 Membrane permeability (cm/s) in Chapter 5 Probability density function Critical probability Peclet number... 

The normal-normal correlation function can be used to define the persistence length of the membrane as the distance over which the normal becomes decorrelated via the thermal undulations the distance r at which gnir) is of order unity. The persistence length, is defined as... 

Find the tangent-tangent correlation function and persistence length for a polymeric chain with curvature elasticity — i.e., a one-dimensional membrane embedded in a three-dimensional space. This is applicable to the physics of a flexible rod undergoing thermal fluctuations. Contrast the results with those of a two-dimensional membrane. 

At low water content the quasi-crystalline motif in the distribution of inverted micelles is strong the size of the micelle is smaller than the persistence length of the bundles of backbone-chains forming the membrane skeleton. A legitimate question arises then how can one build a quasicrystalline structure of inverted micelles (aqueous droplets supported by hydrated sidechains), if the sidechains are attached to the backbones In an attempt to answer this question, a more detailed morphological model of Nafion-type ionomers was suggested [31] a quasi-crystalline arrangement of units cells as depicted in Fig. 1. 

There is one more essential difference between the flexibility of 2-dimensional membranes and that of giant 1-dimensional micelles. In the present case, the moduli K, K have dimensions of energy. There is therefore no equivalent for the idea of persistence length defined in the 1-dimensional case. Once again, this can be related to common experience. The effort required to curve a square plate through a given angle does not depend on its size, provided the thickness remains the same, of course. 

There is one final major difference with the 1-dimensional case. Membrane curvature elasticity does not a priori define any persistence length. It displays... 

We are now in a position to understand under what conditions thermal fluctuations should be important. DeGennes and Taupin introduced the notion of a persistence length fp for a membrane defined as the characteristic length scale. of tne surface normal-normal correlation function - e (n(x) is the unit vector normal to the... 

Where a is a microscopic lower distance cutoff = 5k, Thus, one expects that if kc/kfiT 1, which is what is found in most single lipid or surfactant membranes, (e.g. ke/kfiT ranges between 20 and 50), the membrane is flat on macroscopic length scales and fluctuations are not important. These are the class of rigid membranes. On the other hand, when kc/kgT = 1 we expect that the membranes will be flexible and layer undulations will be important. We now consider the effect that, thermal fluctuations have on the interlayer interactions for multilayers consisting of flexible membranes. We shall return to the role of the persistence length in understanding the ultimate stability of extremely dilute phases in the next section. 

We now return to the persistence length and its role in understanding the stability of dilute phases. From Eq.(8), we see that the length = (Ap) is a measure of a typical distance required before a correlated section of a membrane experiences a collision with... 

Shape persistence as a basis for controllable function is one of the main features of proteins that serve as mechanical support for cofactors (e.g., chromophores in light harvesting complexes), transmit mechanical force (e.g., in muscles), or function as nanoscopic pumps in active transport of substrates through cell membranes. Transfer of this concept to the realm of functional materials is a rather recent development and the term shape persistence for synthetic macromolecules is often used with the loose meaning of relatively rigid compared to most synthetic polymers. For linear polymers, shape persistence can be quantified by the persistence length Lp if one assumes that residual flexibility conforms to the worm-like chain (WLC) model. This assumption has been rarely tested and for many synthetic polymers Lp is either unknown or known with rather limited precision. 

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