# WILBERT

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• 1
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 357-367
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: The partition function of paper II for short polypetide chains is incorporated here into one for a simple model for side-chain hydrogen bonds between helices. It is thus possible to calculate the fraction of amide hydrogen bonds, the fraction of side-chain hydrogen bonds, and the number of bound protons as a function of temperature and pH. Illustrative data are presented for the probabilities of occurrence of intermediate structures and for the influence of the overall conformation on the observed pK's of ionizable groups.
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• 2
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 335-355
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: The method of sequence-generating functions is applied to long polypeptide chains to describe various types of hydrophobic bonding in the random coil. These results are then combined with a similar treatment of the α-helix in order to discuss the helix-coil transition in single helices and in molecules whose helical segments interact by side-chain hydrophobic bonding. Numerical calculations, based on the equations derived in this and preceding papers, are presented to show the relative probabilities of occurrence in the random coil of neighbor-neighbor hydrophobic bonds and pockets of hydrophobic bonding, and the relative probabilities of occurrence of the various states in a system of interacting helices. A discussion is also presented of the dependence of the helix-coil nucleation and growth parameters on solvent and side chain.
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• 3
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 369-377
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: It is shown how the technique of fluorescence may be used to assess conclusions about conformation which are based on a statistical mechanical treatment of simple protein models. Specifically, the state of bonding and distance between two chromophores in a molecule depend on the overall conformation, which can be computed for model systems. On the assumption that the intensity and polarization of fluorescence are affected by exciton transfer between the chromophores, it is possible to compute the effect of conformation on fluorescence. It is demonstrated that the conformational changes computed in the preceding paper will give rise to marked changes in the intensity and polarization of fluorescence.
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• 4
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 379-399
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: The effect of covalently crosslinked loops on the entropy of polypeptide chains is discussed. Since the available theory applies to single, independent loops, this theory has been extended to cases where the chains are multiply crosslinked and, therefore, dependent. Multiply crosslinked loops are present in many proteins, e.g., ribonuclease. It is shown that, whereas in general there is a significant difference between the entropy computed with the present treatment of dependent chains and that incorrectly computed by applying the theory of independent chains to multiply crosslinked loops, the difference in the two procedures is not very great for ribonuclease (and well within the uncertainty of our knowledge of the residue conformational entropy) because the chains of ribonuclease are only slightly dependent even though they are multiply crosslinked. Specifically, estimates of the entropy losses per residue are: -0.45 e.u. for chains in a single, independent loop, -0.58 to -0.66 e.u. for dependent chains in multiply crosslinked loops, and -0.51 e.u. for a simplified model of ribonuclease. With this information, a treatment is given of a helix-coil transition in two chains, assumed to be polyglycine, connected at each end by disulfide bonds. The results of a previous theory for short chains are combined here with the results for the entropy loss on loop formation. It is seen that the presence of the loop stabilizes the helical forms (because of the lowering of the entropy of the random state) and broadens the transition (because of the increased importance of intermediate states).
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• 5
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 421-437
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: Intrinsic viscosity-temperature studies for isoelectric gelatin in KCl and KSCN aqueous solutions and equilibrium degree of swelling, ν-1, measurements for amorphous crosslinked rat tail tendons in the same solutions were carried out. On increasing salt concentration Cs, both [η] and ν-1 increase, go through a maximum, and then decrease at high Cs, KCl being more effective than KSCN in bringing about this decrease. The trend observed is similar to the variation of solubility of polypeptides and soluble proteins with Cs. By regarding a water-salt solution of a given Cs as a single diluent interacting with the protein modified by solvation and binding of ions, usual polymer solution theories were applied to the experimental results. Thus, quantities related to the entropy and enthalpy components of the excess chemical potential of the diluents were obtained. The data indicate that the initial increase of [η] and ν-1 with Cs results from the balance of an enthalpy component which, on increasing Cs, becomes less favorable to dilution and an entropy component which, conversely, becomes more favorable. The subsequent decrease of [η] and ν-1 with Cs is due to the prevailing of the enthalpy component. The maximum is reached at higher Cs for KSCN than for KCl, primarily because of the large increase in the entropy component operated by the former salt. The increase of the entropy parameter with Cs is associated to a breaking down of the coordinated water structure and to an alteration of the conformation of the macro molecules due to ion-dipole interaction and to ion absorption. The decrease in exothermicity of dilution with Cs indicates a reduced thermodynamic affinity of the diluent toward the polymer which probably results from alteration of the nature of both polymer and diluent.
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• 6
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 401-419
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: The two-state theory of protein denaturation, in which it is assumed that a protein exists as two species, native and denatured, is examined by three approaches in this paper. First, the point is made that denaturation of an isolated molecule involves a continuous shift in the probabilities of occurrence of many states generated by the partition function for the protein. It is argued that the maximum term approximation does not lead to a two-state mechanism of denaturation, and that the extent of cooperation implied by the two-state theory should give very much sharper transitions than are actually found in proteins. Second, the two-state theory is applied to the various model systems treated in this series of papers, and is found to be inadequate. Since the detailed behaviour of the models is known, it is possible to deduce the effect of the incorrect application of the two-state theory to a system that “denatures” by gradual unwinding. This exercise is useful when, thirdly, we examine experimental data that seem to depart radically from a two-state interpretation. We conclude that a mechanism of gradual unwinding is the most generally valid assumption, and that the two-state theory has no theoretical or experimental support.
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• 7
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 439-459
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: A study of the elastic properties of collagen tendons while in the crystalline state while undergoing shrinkage, and while in the amorphous state was carried out. An additional analysis of x-ray diffraction patterns and birefringence was also performed. Our main observations are the following. The lattice spacings of a quinone-crosslinked collagen tendon are not altered when the tendon is in equilibrium with KCl or KSCN solutions of different salt concentrations or with acid solutions having different pH. This occurs in spite of large alterations of the modulus of the crystalline tendon in salt and acid solutions. These results indicate that, within the highly ordered framework of the tendon, the salt or acid solution is able to perform a selective disordering action which may involve a considerable fraction of the material before shrinkage takes place. At temperatures and salt concentrations considerably larger than those corresponding to the shrinkage, the tendon exists in a mesomorphic state where residual ordered regions are constrained by the crosslinks in a tactoidal arrangement. The reversibility of length, volume, and birefringence observed within the mesomorphic state attest that it is indeed an equilibrium property of the tendon. Two types of reversible contractile systems can be obtained using the collagen tendon. If full shrinkage is attained, only a fraction of the original length can be recovered on reducing the temperature or salt concentration below the one causing shrinkage. A contraction-extension cycle will then involve the fully denatured and the partly renatured tendon. In order to obtain a reversible contractile system involving recovery of the original length, it is necessary to maintain a more complex “memory” of the original organization than that assured by merely crosslinking in the oriented state and by the occurrence of the mesomorphic phase. This can be done by a selective melting as operated, for instance, by acid solutions. The occurrence of a glasslike state characterized by a high value of the modulus was revealed for the fully amorphous tendon in solutions of salts causing large deswelling. The unperturbed dimensions of collagen molecules are not greatly affected by alteration of salt or salt concentration in the case of KCl and KSCN. The mean-square end-to-end distance \documentclass{article}\pagestyle{empty}\begin{document}$\overline {r_0^2 }$\end{document} decreases with increasing temperature, i.e., d ln \documentclass{article}\pagestyle{empty}\begin{document}${{\overline {r_0^2 } } \mathord{\left/ {\vphantom {{\overline {r_0^2 } } {dT}}} \right. \kern-\nulldelimiterspace} {dT}}{\rm } = {\rm } - 0.6{\rm } \times {\rm 10}^{ - 3} {\rm deg}{\rm .}^{ - 1}$\end{document}. Elastic properties of quinone-crosslinked tendons in the amorphous state are similar to those exhibited by other polymer systems crosslinked in the oriented state. Networks formed by chromium salts are, however, peculiar, since they exhibit negative stress-temperature coefficients. The relevance of some of the above results on the aging of connective tissue and on the theories of muscle contraction is pointed out.
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• 8
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 481-489
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: Three types of band-forming centerpieces useful in band centrifugation in the analytical ultracentrifuge are described. The mode of filling and the advantages and disadvantages of each type are discussed.
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• 9
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 491-496
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: Calorimetric measurements of the heat of the addition of the second strand of poly U to poly (A + 2U) to form the three-stranded poly (A + 2U) complex in 0.1M and 0.5M NaCl at 24 and 37°C. are reported. A value of ΔH = -3800 cal./mole of poly (A + 2U) formed was found to be fairly insensitive to the experimental conditions employed. The heat of the addition of the third strand to the preformed poly (A + U) helix is considerably less exothermic than the heat of reaction between poly A and poly U to form poly (A + U). The insensitivity of the heat of addition of the third strand (poly U) to changes in salt concentration and temperature lends qualitative support to the earlier hypothesis that the major portion of the variation of the ΔH of the poly A and poly U reaction with experimental conditions arises from differences in the conformation of poly A. Combining the information obtained in this study for the ΔH of the reaction forming poly (A + 2U) with data for the ΔH of the formation of poly (A + U) indicates that the conversion of poly (A + U) to poly (A + 2U) is opposed by an enthalpy change which increases with temperature. Extrapolation of these values to 52°C. where poly (A + U) is transformed to poly (A + 2U) in 0.5M NaCl leads to a value of ΔH = +3800 cal./mole (A + 2U) formed and ΔS = 11.5 cal./mole of (A + 2U) formed. It is concluded from the calorimetric data that the driving force for the poly (A + U) to poly (A + 2U) conversion reaction is the favorable entropy change.
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• 10
Electronic Resource
New York : Wiley-Blackwell
Biopolymers 3 (1965), S. 461-480
ISSN: 0006-3525
Keywords: Chemistry ; Polymer and Materials Science
Source: Wiley InterScience Backfile Collection 1832-2000
Topics: Chemistry and Pharmacology
Notes: The effect of salt type and concentration on the transformation of an oriented crystalline collagen tendon into a crosslinked network under conditions of equilibrium swelling was investigated. Our main observations are the following. The degree of swelling of crystalline tendons increases at low salt concentration Cs, and decreases at higher Cs for a wide variety of salts. The observation is not reconcilable with swelling taking place in interfibrillar spaces or structural voids. Within the tropocollagen units and at their ends, regions of reduced organization are postulated (as suggested by Bear and by Schmitt) which are able to interact with the diluent in the amorphous-like manner. At least four different factors should be considered in assessing the role of salt and salt concentration on the shrinkage temperature Ts under isoelectric conditions. They are: (1) specific effects, (2) diluent effects, (3) crosslinking effects, and (4) nonequilibrium effects. The diluent effects are correlated with the salting-in-salting-out power of the ions which was characterized in Part I of this series. Smaller amounts of diluents are generally available to the tendon when the salt has a higher salting-out power, and this corresponds to higher shrinkage temperatures, other conditions being the same. The crosslinking effect raises Ts due to a reduction of the diluent content and, probably for p-benzoquinone and formaldehyde, also to a reduction of the conformational entropy in the molten state. Nonequilibrium effects arise from the fact that shrinkage and recrystallization are kinetically hindered when the tendon is highly deswollen in strong salting-out solutions, or when the salt has a crosslinking power. The specific effect is the only effect which is not related to the amount of diluent present in the tendon. Its origin is less clear. For anions such as Cl- and SCN-, it is possibly related to an ability of the ion to prevent intersegmental hydrogen bonding and water carbonyl bridges. The competition of several of the above effects for a given salt solution makes possible various types of dependence of Ts upon Cs: Ts may either continuously decrease or continuously increase with increasing Cs, or it may go through a minimum. In absence of salt, the cooperative character of the transition at the pH at which maximum swelling occurs appears extremely reduced. The large swelling maintains the tendon in the elongated state and this simulates a continuous decrease of Ts on lowering pH. In presence of small quantities of salt, which reduce swelling, the transition is sharp and Ts is decreased with pH up to pH 2, when maximum swelling occurs, and then reincreases on further lowering of the pH. The dependence of Ts upon Cs is more complex than under isoelectric conditions. There is generally an increase of Ts with Cs which is equivalent to an increase of the denaturation temperature with Cs for helical polyelectrolytes in solution. At higher salt concentrations, however, Ts may decrease again, and possibly increase again at still higher salt concentrations, depending upon the effect of the salt solution in the isoelectric zone.