Chains, conformations

Prior to a discussion of the theory of rubber elasticity, it is important to review how isolated polymer chains behave as this will provide a picture of the size and shape of a polymer. Clearly a polymer chain in a vacuum will collapse into a dense unit, but when in a solution the molecule will take on a conformation which is a function of the interaction with the surrounding molecules and the balance between the entropically driven tendency to maximise the spatial configuration and the connectivity of the monomer units. This is the case whether the chain is surrounded by small molecules (solvent) or other macromolecules that may or may not act like a solvent. 

It has already been pointed out that the rotation about the chemical bonds linking the building blocks of the chains allows many possible conformations. The simplest model of a polymer chain is that of a 3-D 

Rotation about a carbon atom means that the following bond sweeps out a cone with an included angle of 28. The hydrogen atoms are white and the oxygen atoms are grey 

C b2 is the effective bond length , b. For the case of the bond angle restriction on the random walk  

As we have the free energy of mixing, we may now estimate the osmotic pressure of our dilute polymer solution  

The structure and morphology of fibers and films can be described at various levels of structural dimensions, depending on the resolution of the diffraction equipment and of the microscopes used in the investigation. First the chain conformation in the solid state is discussed then the packing modes of the chains in the crystallites determined by X-ray diffraction are reviewed next the structural characteristics of the fibrils observed by X-ray and electron diffraction are examined and finally the morphological features as seen by electron and optical microscopy are dealt with. After this survey of the structure and morphology, the formation of the fiber and film by coagulation from a lyotropic solution is discussed. 

Fibers are identified here by their chemical names. In this respect it is useful to know that T war on and Kevlar are the trade names for PpPTA fibers, and that PRD-49 is a fiber made from PpBA. The para-aromatic polyamide fibers PpPTA, PpBAT and PpBA are often called aramid fibers. 

The relative importance of the various factors determining the persistence length in solution and the conformation in the solid state of aromatic polyamides are well illustrated by the differences between the para and the meta forms of poly(phenylene terephthalamide). Both chains consist of the same planar elements, viz. the phenyl and amide groups. The latter group adopts only the trans conformation in these polymers, wherein the chance of a transition to the cis conformation is extremely small owing to a barrier of about 60-80 kJ mol Although in both para- and meta-linked chains the same intermolecular interactions exist between phenyl 

The conformational energy calculations for the PBO chain by Welsh et al resulted in a planar molecule, which appears to be consistent with experimental results.  

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Miller, KE. Rich, D.H. Molecular Mechanics Calculations of Cyclosporin A Analogues. Effect of Chirality and Degree of Substitution on the Side-Chain Conformations of (2s, 3r, 4r, 6e)-3-Hydroxy-4-methyl-2-(methylamino)-6-octenoic Acid and Related Derivatives. 

Unlike other synthetic polymers, PVDF has a wealth of polymorphs at least four chain conformations are known and a fifth has been suggested (119). The four known distinct forms or phases are alpha (II), beta (I), gamma (III), and delta (IV). The most common a-phase is the trans-gauche (tgtg ) chain conformation placing hydrogen and fluorine atoms alternately on each side of the chain (120,121). It forms during polymerization and crystallizes from the melt at all temperatures (122,123). The other forms have also been well characterized (124—128). The density of the a polymorph crystals is 1.92 g/cm and that of the P polymorph crystals 1.97 g/cm (129) the density of amorphous PVDF is 1.68 g/cm (130). 

Fig. 2. (a) Chain conformation of isotactic polypropylene, and (b) model of a polypropylene spheruHte. 

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

Vasquez [121] reviewed and commented on various approaches to side chain modeling. The importance of two effects on side chain conformation was emphasized. The first effect was the coupling between the main chain and side chains, and the second effect was the continuous nature of the distributions of side chain dihedral angles for example. 

A recent survey analyzed the accuracy of tliree different side chain prediction methods [134]. These methods were tested by predicting side chain conformations on nearnative protein backbones with <4 A RMSD to the native structures. The tliree methods included the packing of backbone-dependent rotamers [129], the self-consistent mean-field approach to positioning rotamers based on their van der Waals interactions [145],... 

M Vasquez. Modeling side-chain conformation. Curr Opm Stiaict Biol 6 217-221, 1996. JM Thornton. Disulphide bridges m globular proteins. J Mol Biol 151 261-287, 1981. 

FI Schrauber, F Eisenhaber, P Argos. Rotamers To be or not to be An analysis of ammo acid side-chain conformations m globular proteins. J Mol Biol 230 592-612, 1993. 

RL Dunbrack, M Karplus. Pi ediction of protein side-chain conformations from a backbone conformation dependent rotamer library. J Mol Biol 230 543-571, 1993. 

MJ McGregor, SA Islam, MJE Sternberg. Analysis of the relationship between side-chain conformation and secondary structure m globular proteins. J Mol Biol 198 295-310, 1987. 

C Wilson, LM Gregoret, DA Agard. Modeling side-chain conformation for homologous proteins using an energy-based rotamer search. J Mol Biol 229 996-1006, 1993. 

P Koehl, M Delarue. Application of a self-consistent mean field theory to predict protein side-chains conformation and estimate their conformational entropy. J Mol Biol 239 249-275, 1994. 

LM Gregoret, FE Cohen. Effect of packing density on chain conformation. J Mol Biol 219 109-122, 1991. 

Analysis and prediction of side-chain conformation have long been predicated on statistical analysis of data from protein structures. Early rotamer libraries [91-93] ignored backbone conformation and instead gave the proportions of side-chain rotamers for each of the 18 amino acids with side-chain dihedral degrees of freedom. In recent years, it has become possible to take account of the effect of the backbone conformation on the distribution of side-chain rotamers [28,94-96]. McGregor et al. [94] and Schrauber et al. [97] produced rotamer libraries based on secondary structure. Dunbrack and Karplus [95] instead examined the variation in rotamer distributions as a function of the backbone dihedrals ( ) and V /, later providing conformational analysis to justify this choice [96]. Dunbrack and Cohen [28] extended the analysis of protein side-chain conformation by using Bayesian statistics to derive the full backbone-dependent rotamer libraries at all... 

E Benedetti, G Morelh, G Nemethy, HA Scheraga. Statistical and energetic analysis of side-chain conformations m oligopeptides. Int J Peptide Pi otem Res 22 1-15, 1983. 

A second example is that of an Ala-to-Cys mutation, which causes the fonnation of a rare SH S hydrogen bond between the cysteine and a redox site sulfur and a 50 mV decrease in redox potential (and vice versa) in the bacterial ferredoxins [73]. Here, the side chain contribution of the cysteine is significant however, a backbone shift can also contribute depending on whether the nearby residues allow it to happen. Site-specific mutants have confirmed the redox potential shift [76,77] and the side chain conformation of cysteine but not the backbone shift in the case with crystal structures of both the native and mutant species [78] the latter can be attributed to the specific sequence of the ferre-doxin studied [73]. 

Figure 14a. Although our values are not in quantitative agreement with the experimental values (see Ref. 50 for a discussion), they faithfully reproduce the well-known observation that the disorder increases from the tops of the chains toward the middle of the bilayer, with a more pronounced increase in the last few carbons of the chain. The. S cd represent different types of disorder, including chain conformational defects and whole molecule wobbling [67].

Certain side-chain conformations are energetically favorable... 

Certain side-chain conformations are energetically mote favorable than others. Computer programs used to model protein structures contain rotamer libraries of such favored conformations. 

The loop region between the two a helices binds the calcium atom. Carboxyl side chains from Asp and Glu, main-chain C =0 and H2O form the ligands to the metal atom (see Figure 2.13b). Thus both the specific main-chain conformation of the loop and specific side chains are required to provide the function of this motif. The helix-loop-helix motif provides a scaffold that holds the calcium ligands in the proper position to bind and release calcium. 

Blake, C.C.F., et al. Structure of human plasma prealbumin at 2.5 A resolution. A preliminary report on the polypeptide chain conformation, quaternary structure and thyroxine binding. J. Mol. Biol. 88 1-12, 1974. 

In order to examine whether this sequence gave a fold similar to the template, the corresponding peptide was synthesized and its structure experimentally determined by NMR methods. The result is shown in Figure 17.15 and compared to the design target whose main chain conformation is identical to that of the Zif 268 template. The folds are remarkably similar even though there are some differences in the loop region between the two p strands. The core of the molecule, which comprises seven hydrophobic side chains, is well-ordered whereas the termini are disordered. The root mean square deviation of the main chain atoms are 2.0 A for residues 3 to 26 and 1.0 A for residues 8 to 26. 

Figure 17.15 Schematic diagrams of the main-chain conformations of the second zinc finger domain of Zif 268 (red) and the designed peptide FSD-1 (blue). The zinc finger domain is stabilized by a zinc atom whereas FSD-1 is stabilized by hydrophobic interactions between the p strands and the a helix. (Adapted from B.I. Dahiyat and S.L. Mayo, Science 278 82-87, 1997.)...

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