Chain statistics conformation

Using the generator-matrix formalism of the chain conformational statistics, the chain conformation partition function E can be expressed as a product of three matrices... 

Finally, we note that Schmidt-Rohr and co-workers have elegantly demonstrated that 2D 13C-13C DQ spectra recorded for static samples can identify the chain conformation statistics for 13C-labeled polymer samples.112 Remembering that the frequency of a given 13C resonance depends on the orientation of the CSA tensor, the method relies on the fact that the adoption of a particular torsional angle along the chain results in DQ peaks for only specific pairs of 13C frequencies. In particular, it was shown that trans and gauche conformations lead to very different 2D DQ powder spectra, and it was thus possible to quantitatively determine the conformation statistics for a sample of amorphous polyethylene terephtha-late) (PET). 

DQ spectra recorded for static samples can identify the chain conformation statistics for C-IabeUed polymer samples [100]. Remembering that the frequency of a given resonance depends on the orientation of the CSA tensor (see Section... 

Plavsic, M., Pajic-Lijakovic, I., Cubric, B., Popovic, R.S., Bugarski, B., Cvetkovic, M., and Lazic, N., Chain conformational statistics and mechanical properties of elastomer composites. Mater. Sci. Forum, 453-454, 485-490, 2004. 

Plavsic, M.B., Pajic-Lijakovic, I., Putanov, P., Chain Conformational Statistics and Mechanical Properties of Elastomer Blends, in New Polymeric Materials, MacKnight, W.J., Martuscelli E., Korugic-Karasz Lj., Eds., American Chemical Society Washington, in press. 

For the description of the chain-melting phase transition of pure lipid bilayer membranes the microscopic model of Pink and collaborators has been adopted. This model takes into account the acyl-chain conformational statistics and the van der Waals interaction between various conformers in a detailed way, while the excluded volume effect is accounted for by assigning each lipid chain to a site in a triangular lattice. The acyl chain conformations are represented by ten single chain states a , each described by a cross-sectional area A , an internal energy Ea and an internal degeneracy Da- The second membrane component is assumed to be a stiff, hydrophobically smooth molecule with no internal degrees of freedom and a cross-sectional area Ac- The model parameters will be chosen so that the mixture display the properties of the DPPC-cholesterol bilayer system for small concentrations of cholesterol [3]. The impurity will hereafter be called cholesterol . 

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. 

Before discussing details of their model and others, it is useful to review the two main techniques used to infer the characteristics of chain conformation in unordered polypeptides. One line of evidence came from hydrodynamic experiments—viscosity and sedimentation—from which a statistical end-to-end distance could be estimated and compared with values derived from calculations on polymer chain models (Flory, 1969). The second is based on spectroscopic experiments, in particular CD spectroscopy, from which information is obtained about the local chain conformation rather than global properties such as those derived from hydrodynamics. It is entirely possible for a polypeptide chain to adopt some particular local structure while retaining characteristics of random coils derived from hydrodynamic measurements this was pointed out by Krimm and Tiffany (1974). In support of their proposal, Tiffany and Krimm noted the following points ... 

The prime objective of this concise review is to provide an illustration of the interaction of these two disciplines using particular examples. In choosing the examples, we seek to demonstrate the potentialities of the conformation-dependent design of the sequences of monomeric units in heteropolymer macromolecules. Under such a design, their chemical structure is controlled not only by the kinetic parameters of a reaction system but also by the conformational statistics of polymer chains. 

In the same year in which Stoll et al. (1934) defined the cyclisation constant C, Kuhn (1934) laid the foundations of the theoretical approaches to the conformational statistics of hydrocarbon chains and considered the cyclisation probability of the chain as a fundamental, chain length dependent phenomenon related to chain shape. He proposed to view the specific rate kintra of an intramolecular reaction between a pair of reactive groups attached to the ends of a chain molecule as the product of the effective concentration Ceff of... 

For a particular conformation c of a molecule, the positions of all (united) atoms in space as well as the chain conformers are known. The potential energy of this conformation is therefore just the sum of the contributions, as given by equation (9) for all the united atoms and a particular energy quantity per gauche bond in the chain. The statistical weight for this conformation is proportional to the Boltzmann factor containing this segment potential ... 

Fattal, D. R. and Ben-Shaul, A. (1994). Mean-field calculations of chain packing and conformational statistics in lipid bilayers comparison with experiments and molecular dynamics studies, Biophys. J., 67, 983-995. 

The consequences of this relative internal freedom of thermal motion for the conformations of a chain containing a large number of bonds are profound. It was realized by several of Staudinger s contemporaries (14) although not by him, that a statistical distribution of possible bond configurations necessarily results in a statistical distribution of overall chain conformations. The average represents a loose coil rather than an extended structure with dimensions increasing as and p at most a small... 

Key words intertwining chains, SARW statistics, conformation, polymer chain, random walks, lattice, thermodynamics, modules of elasticity, forces, work.. 

Thus, to reflect correctly the state of the system at a certain temperature, one needs a simulation technique that generates an ensemble of chain conformations whose statistical properties reflect those of the real chain at thermodynamic equilibrium. The chromatin fiber models that are discussed in the following use one or the other variation of such techniques. 

It is however possible to find conditions, called unperturbed or theta conditions (because for each polymer-solvent pair they correspond to a well-defined temperature called d temperature) in which a tends to 1 and the mean-square distance reduces to Q. In 6 conditions well-separated chain segments experience neither attraction nor repulsion. In other words, there are no long-range interactions and the conformational statistics of the macromolecule may be derived from the energy of interaction between neighboring monomer units. For a high molecular weight chain in unperturbed conditions there is a simple relationship between the mean-square end-to-end distance < > and the mean-... 

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