Number of monomers crossing the

Another interesting characteristic of the reptation model is that the number of monomers crossing the interface as determined by the integral of the concentration profile behaves as > ... 

The type of motion considered here is shown in Fig. 3. We follow one labeled chain in the layer. The chain reptates on the self-similar grid. It is subdivided into subunits (i) with a spatial size Zi equal to the distance to the wall, and a number of monomers gi - gizi) Instead of computing directly the diffusion constant Du, we use as an intermediate the mobility p = D /kT of the chain (where kT is the thermal energy). When the chain reptates, the subunit (i) has a certain curvilinear velocity Ud It is important to realize that Ud is different for different subunits what is conserved is the tube current J , i.e., the number of monomers, crossing one given point on the tube, per second. 

We shall call this rate the nucleation rate for the polymer translocation process. Once the barrier in Figure 10.9a is crossed, the translocation process is generally a downhill process. The role of the entropic barrier in controlling the translocation is captured by Equation 10.33. It is in the familiar Arrhenius form or equivalently the Kramers-type form. The nucleation time is the average time taken by the polymer chain to put sufficient number of monomers on the receiver side, after crossing the nucleation barrier, for further progress of the translocation event. We define the nucleation time as the reciprocal of the nucleation rate,... 

A second model was proposed by Benkoski et al. [16] based on the idea that chain friction and pull-out, rather than chain scission are the important molecular scale failure processes. It is assumed that the chain failure force is given by fc = N/mono, where N is the number of monomers in a loop that crosses the interface, and that... 

The mole fraction of the monomer units that are cross-linked in the polymer is X,., and nt is Ihe number-average number of atoms in the polymer backbone between cross-links. The temperature should be expressed in absolute degrees in this equation. The constant K is predicted to be between 1.0 and 1.2 it is a function of the ratio of segmental mobilities of cross-linked to uncross-linked polymer units and the relative cohesive energy densities of cross-linked and uncross-linked polymer (88). The theoretical equation is probably fairly good, but accurate tests of it are difficult because of the uncertainty in making the correction for the copolymer effect and because of errors in determining nf. 

Fig. 8 Proposed model for gramicidin S in a membrane according to the orientational constraints obtained from and N-NMR. The upright backbone alignment (r 80°) and slant of the /3-sheets (p -45°) are compatible with the formation of an oligomeric /3-barrel that is stabilized by hydrogen bonds (dotted lines). A The oligomer is depicted sideways from within the lipid bilayer interior (showing only backbone atoms for clarity, but with hydrophobic side chains added to one of the monomers). Atomic coordinates of GS were taken from a monomeric structure [4], and the two DMPC lipid molecules are drawn to scale (from a molecular dynamics simulation coordinate file). The bilayer cross-section is coloured yellow in its hydrophobic core, red in the amphiphilic regions, and light blue near the aqueous surface. B Illustrates a top view of the putative pore, although the number of monomers remains speculative...

Fig. 7. Geometry of a helical structure (A) and the form of its diffraction pattern (B). In (A), the pitch (P) of the helix is like the wavelength of a sine wave. The radius (r) of the helix is like the amplitude of the sinewave. The subunit axial translation (h) is the rise along the helix axis from one monomer to the next. If there is not a whole number of monomers in one turn of the helix (said to be a non-integral helix), then there may be a longer repeat (C). In the case illustrated C = 2P. Dimensions in the helix in (A) have their counterparts in the diffraction pattern illustrated in (B), but dimensions in (B) are reciprocal to those in (A). Meridional reflections occur at positions m/h from the equator, where m is an integer. Each of these positions is the center of a so-called helix cross consisting of layer lines, which are n/P up or down from the meridional peaks, where n is another integer. All of the resulting layers of intensity can be related to orders of 1/C, where C is the repeat of the helix and l is the layer line number.

The copolymers of styrene and DVB discussed so far were made via free radical polymerization, which is known to produce crosslinked polymer with a very broad distribution of X in the polystyrene segments between cross-link junctions. On the other hand anionic polymerization of styrene monomer [140] to give the corresponding living dicarbanion n-mer1 followed by addition of DVB monomer gives a crosslinked network with a very narrow range of X (i.e. twice the number of monomer units) between nodules of (DVB)y. 

If a fraction q of all monomer units in the sample forms parts of cross-links and these cross-links are randomly placed, then an additional q y — 1) monomer units in our original y-mer are also cross-linked, on the average. That is to say, the probability that an arbitrarily selected cross-link is attached to a primary chain which contains y monomer units is Wy, and it is expected that q y - ) of these y monomer units are also cross-linked. Thus, the initial, randomly chosen crosslink leads through the primary molecules and other cross-links to Wyqiy — 1) additional primary molecules. Since y can have any positive nonzero value, the expected number of additional cross-links e in a molecule that already contains one arbitrarily chosen cross-link is... 

Table 7 Fraction of free counterions, fc (normalized to the number of chemically quater-nized monomers), the effective charge density, / (normalized to the total number of monomers), the effective charge density per main chain monomer fma the cross sectional radius of gyration RgjC) the mean concentration of counterions cc and the mean inverse Debye screening length Xb l within the volume of a cylindrical brush molecule due to condensed counterions...

Figure 3 The linkage between the position of the conjugation sites and the effect introduced by the conjugation. The glycosylation (a) and ubiquitination (b) sites are characterized by the number of native contacts the modification site is involved in. Both glycosylation and ubiquitination will show destabilization if the modification is made at a more structured position. Experimentally, it was shown that cross-linked dimers will be destabilized compared to the isolated monomers if the cross-linking is made through a structured residue (b, triangles).

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