Excluded volume interactions, conformational

The DNA-nucleosome interaction parameters are not known at present. In most of the theoretical work it is deemed negligible compared to the DNA-DNA and nucleosome-nucleosome interaction, except for a hard-core excluded volume interaction. Nevertheless, recent work on the mechanism of nucleosome repositioning [67] assumes that the DNA can dynamically detach from the nucleosome surface and reattach in different conformations, such that it is conceivable that distant DNA segments may also transiently bind to open regions of the DNA-binding surface of the nucleosome. 

The above calculations assume that the gross chain conformations are those of a random walk, which is the case in the melt. However, for an isolated polymer molecule in a dilute solution, the average conformation is affected by excluded-volume interactions between one part of the chain and another. Because the chain must avoid self-intersection, the conformation of the chain will be that of a self-avoiding walk, rather than a random walk, if the solution is athermal—that is, if all interactions are negligible except excluded volume. Self-avoiding walks lead, on average, to more expanded coil dimensions, since expanded configurations are less likely than contracted ones to lead to self-intersection of the chain. Thus, in an athermal solution, the mean-square end-to-end dimension of a polymer molecule scales as... 

In this section, we will consider the excluded volume interaction follow-ing a similar scaling approach, rhe main idea is that of a thermal length scale (the thermal blob). On length scales smaller than the thermal blob size the excluded volume interactions are weaker than the thermal energy kT and the conformations of these small sections of the chain are nearly ideal. The thermal blob contains gr monomers in a random walk conformation ... 

This parameter describes the excluded volume interactions of an A molecule with itself, mediated by the melt of B molecules. This excluded volume is small for polymer melts because each chain has difficulty distinguishing contacts with itself from contacts with surrounding chains. This very important result was first pointed out by Flory melts of long polymers have v 0 and adopt nearly ideal chain conformations. 

The effect of this interaction on the conformations of an A chain can be analysed using the scaling approach described in detail in Chapter 3. On small length scales (smaller than the thermal blob size < 7), the excluded olume interactions barely affect the Gaussian statistics of the chain where gj- is the number of monomers in a thermal blob. The thermal blob is defined as the section of the chain with excluded volume interactions of order of the thermal energy ... 

On length scales larger than the correlation length, the excluded volume interactions are screened by the overlapping chains. The semidilute solution on these length scales behaves as a melt of chains made of correlation blobs and the polymer conformation is a random walk of correlation blobs ... 

A similar presentation of the polyelectrolyte macromolecule as an extended sequence of blobs is valid also in the case of good solvent, when the interaction between neutral monomers has a repulsive character, and the polymer chain within the electrostatic blob has a conformation of the coil with the excluded volume interaction [15]. 

The second interaction can be considered as follows, for two monomer units separated by a large number of monomers, the probability of an overlap between the two is non-zero. If the balance of the interactions, monomer-solvent and monomer-monomer leads to a repulsive interaction, as happens in a good solvent, these two distant monomer units repel each other. This excluded volume interaction increases the volume occupied by the macromolecule compared to that of an ideal chain the chain is swollen in a good solvent. A new statistical description of tlie chain conformation is needed, but the key point is that the scaling law still applies and we have R=N, but with v = 0.588 instead of 0.5. The normalised scattering intensity in the asymptotic range becomes ... 

Figure 2 shows an example of this 2D shape descriptor. Here, we compare two conformations of a linear polymer model. The polymer chain is an off-lattice random walk with constant bond length and excluded volume interaction between monomers (i.e., a self-avoiding walk). The constant bond length of / = 1.54 A is used to mimic poly methylene. [For a discussion and implementation of this model, see Ref. 56.]... 

The left-hand structure in Figure 2 is a compact conformation generated with a very small excluded volume interaction. In this case, no nonbonded nuclei were allowed to be closer than 0.01 A. This conformation may represent a polymer in a poor solvent. The right-hand structure represents a confer-... 

Figure 2 Characterization of molecular chain conformations by integer matrices derived from interatomic distances. The molecular chain is a 10-atom random walk with excluded volume interaction. The matrix is a 2D descriptor defined by the distances and one external parameter, the number of levels k into which the range of distances is divided. Note that the swollen, strand-like conformation is characterized by a matrix with constant diagonal bands.

Orientation in crosslinked elastomers primarily reflects the configurational entropy and intramolecular conformational energy of the chains. However, as first shown by deuterium NMR experiments on silicone rubber (Deloche and Samulski, 1981 Sotta et al., 1987), unattached probe molecules and chains become oriented by virtue of their presence in a deformed network. This nematic coupling effect is brought about intermolecular interactions (excluded volume interactions and anisotropic forces) which can cause nematic coupling (Zemel and Roland, 1992a Tassin et al., 1990). The orientation is only locally effective, so it makes a negligible conttibution to the stress (Doi and Watanabe, 1991), and the chains retain their isotropic dimensions (Sotta et al., 1987). 

We must know Yl u) and Y u) to convert QeC-t Oi o) into Q L,u,X). In the primary chain, excluded-volume interactions can act between infinitesimally close points on the chain, since the chain is allowed to take on conformations which contain infinitesimally small loops. Owing to this property, unless vo is zero, Qb diverges to infinity as e —> 0, as will be illustrated below. However, no such singularity appears in a coarse-grained chain with cut-off length A because intrachain interactions in it do not act between contour points separated by less than A. Therefore, Q(L, u, A) should remain finite in the limit e 0 if A 0. The renormalization constants Yl and can be determined from this physical requirement, as exemplified below. Because of this operation, renormalization is sometimes misunderstood as a mere mathematical maneuver of removing singular behavior of the primary chain in the limit of e —> 0. 

In dilute solutions of good solvent, the size of a polymer is much larger than that at the 0 condition due to the excluded volume interaction. How does the potymer size behave in the concentrated srdution To answer this question let us suppose that added to the concentrated polymer solution is a test polymer of the same chemical structure and the same molecular weight. If the conformation of the test polymer is R , the... 

In order to proceed, I have to make some assumptions about the chain statistics and about the form of the crystal. The latter should be given again by the model sketched in (Fig. 2.2). In particular, all stems should have the same length. To start with a tractable model, I wU] further ignore excluded volume interactions between the segments of the amorphous fraction as well as the conformational constraints due to the impenetrable crystalline surface. Furthermore, I treat the chain statistics as Gaussian and ignore effects of finite flexibility of the chain. These relaxed conditions overestimate the entropy of the amorphous fraction. 1 will reconsider these approximations in the context of the exact solution for the idealized model. 

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