Chain conformational entropy

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

Disulfides. The introduction of disulfide bonds can have various effects on protein stability. In T4 lyso2yme, for example, the incorporation of some disulfides increases thermal stability others reduce stability (47—49). Stabili2ation is thought to result from reduction of the conformational entropy of the unfolded state, whereas in most cases the cause of destabili2ation is the introduction of dihedral angle stress. In natural proteins, placement of a disulfide bond at most positions within the polypeptide chain would result in unacceptable constraint of the a-carbon chain. 

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. 

At low concentrations, adsorption is a single-chain phenomenon. The adsorption takes place when the enthalpy gain by the monomer-surface contact with respect to the monomer-solvent contact surpasses the loss of the conformational entropy. In a good solvent the adsorption is not likely unless there is a specific interaction between monomers and the surface. At high concentrations, however, interactions between monomers dominate the free energy of the solution. The adsorption takes place when the enthalpy gain by the mono-... 

Entropy is a measure of disorder in materials. Relaxed polymer chains with a random conformation (shape in space), like cooked spaghetti or a box of fishing worms, have a high degree of entropy, which is favored by Mother Nature. If the chains are stretched out (stressed), the number of conformations the chains can have in space is limited, and the entropy is reduced (see Figure B). The ratio of final length to initial length is denoted a. 

Ad layering (Fig. 16a). On the other hand, additional conformational entropy related to the sequenced hydrocarbon-perfluorinated chain prevents the crystallization of the aromatic parts of the molecules in the smectic layers as occurs for hydrocarbon analogues of the same tail length [4]. The stability of Cd phase in polyphilics is more delicate in nature and will be discussed below. 

If peptide residues are converted to peptoid residues, the conformational heterogeneity of the polymer backbone is likely to increase due to cis/trans isomerization at amide bonds. This will lead to an enhanced loss of conformational entropy upon peptoid/protein association, which could adversely affect binding thermodynamics. A potential solution is the judicious placement of bulky peptoid side chains that constrain backbone dihedral angles. 

Other than an effect on backbone solvation, side chains could potentially modulate PPII helix-forming propensities in a number of ways. These include contributions due to side chain conformational entropy and, as discussed previously, side chain-to-backbone hydrogen bonds. Given the extended nature of the PPII conformation, one might expect the side chains to possess significant conformational entropy compared to more compact conformations. The side chain conformational entropy, Y.S ppn (T = 298°K), available to each of the residues simulated in the Ac-Ala-Xaa-Ala-NMe peptides above was estimated using methods outlined in Creamer (2000). In essence, conformational entropy Scan be derived from the distribution of side chain conformations using Boltzmann s equation... 

This expression accounts for the configurational entropy of an ideal binary mixture with identical molecular sizes, but not for that of a polymer solution, since polymer chains are large and flexible. For that case, more contributions arise from the chain conformational entropy, first considered by Meyer [19] and then derived by Huggins [20] and Flory [21]. In analogy with a nonreversing random walk on a lattice, the conformational contribution of polymer chains to the partition function is given by... 

Flexible, coily-structured polymers in solution possess a high conformational entropy resulting from the many rotational possibilities of the single bonds in the polymer chain. 

The influence of adsorption on the structure of a -chymotrypsin is shown in Fig. 10, where the circular dichroism (CD) spectrum of the protein in solution is compared with that of the protein adsorbed on Teflon and silica. Because of absorbance in the far UV by the aromatic styrene, it is impossible to obtain reliable CD spectra of proteins adsorbed on PS and PS- (EO)8. The CD spectrum of a protein reflects its composition of secondary structural elements (a -helices, / -sheets). The spectrum of dissolved a-chymotrypsin is indicative of a low content of or-helices and a high content of //-sheets. After adsorption at the silica surface, the CD spectrum is shifted, but the shift is much more pronounced when the protein was adsorbed at the Teflon surface. The shifts are in opposite directions for the hydrophobic and hydrophilic surfaces, respectively. The spectrum of the protein on the hydrophilic surface of silica indicates a decrease in ordered secondary structure, i.e., the polypeptide chain in the protein has an increased random structure and, hence, a larger conformational entropy. Adsorption on the hydrophobic Teflon surface induces the formation of ordered structural elements, notably an increase in the content of O -helices (cfi, the discussion in Sect. 3.1.4). 

An important property of chain molecules is that a major contribution to the standard entropy is conformational in nature, i.e. is due to hindered internal rotations around single bonds. This property is most relevant to cyclisation phenomena, since a significant change of conformational entropy is expected to take place upon cyclisation. Pitzer (1940) has estimated that the entropy contribution on one C—C internal rotor amounts to 4.43 e.u, A slightly different estimate, namely, 4.52 e.u. has been reported by Person and Pimentel (1953). Thus, it appears that nearly one-half of the constant CH2 increment of 9.3 e.u. arises from the conformational contribution of the additional C—C internal rotor. 

The last column in Table 19 lists the entropy losses due to reduction of freedom of internal rotations around the single bonds upon cyclisation. It is of interest to note, for example, that the conformational entropy lost upon cyclisation of an 8-rotor chain amounts to f of the corresponding quantity related to cyclisation of a 100-rotor chain. 

Equation 2.16 contains contributions from the translational entropy of the mobile species, the conformational entropy of polymer chains, the free energy associated with the different chemical equilibria in the system, the polymer-polymer and polymer-surface van der Waals (vdW) interaction energies, the electrostatic interaction energies and the repulsive interactions between all the different molecular species. The expressions for each of these terms are shown in Table 2.2, while the definition of the symbols is given in Appendix. Note that in Table 2.2, the densities. 

The dynamics of a generic linear, ideal Gaussian chain - as described in the Rouse model [38] - is the starting point and standard description for the Brownian dynamics in polymer melts. In this model the conformational entropy of a chain acts as a resource for restoring forces for chain conformations deviating from thermal equilibrium. First, we attempt to exemphfy the mathematical treatment of chain dynamics problems. Therefore, we have detailed the description such that it may be followed in all steps. In the discussion of further models we have given references to the relevant literature. 

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