Chemistry and biological function of α‐lactalbumin

Shukla, Triveni P.; Ebner, Kurt E.

doi:10.1080/10408397309527142

Cited by 19 publications

(17 citation statements)

References 169 publications

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“…This then warrants the inclusion of the next set of anharmonic contributions of O… ¶ 4 † in the calculation of MSD. As has been pointed out earlier in the free-energy calculations Cowley 1985, Shukla andShanes 1985) for the nearest-neighbou r model of the fcc LJ solid and for other potentials, the exact calculation of many of these diagrams is di cult and none of the diagrams in the set seems to be more important than the other. To avoid double counting, we especially refer to these as remaining contributions because some O… ¶ 4 † contributions to MSD are already included in the GF method.…”

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confidence: 96%

“…It is given by hu 2 i QHˆa T , where the coe cient a depends on V and thus implicitly on T . However, this term was found to be negligible in the MD calculations of Li and Rb by Shukla and Mountain (1982) from the pseudopotential theory, but it seems that now with accurate Mo È ssbauer measurements the Q 4 -dependent T 3 term in the DWF can be detected experimentally (Martin andO' Conner 1977, Shepard et al 1998). However, McDonald (1967), while analysing his measured DWF data on Al in the temperature range 300± 860 K, found that hu 2 iˆaT ‡ bT 2 ‡ cT 3 ® tted the data quite well and concluded that the average deviation from the measured curve of the best ® t is 0.2% compared with 1% for a quadratic ® t. If the simulation results for hu 2 i, from the Monte Carlo (MC) method or molecular dynamics (MD), are ® tted by a similar power series in T , the coe cient of the T 3 term is not so small (Heiser et al 1986).…”

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confidence: 99%

“…In a recent publication (Shukla et al 1996 ) the results for hu 2 i, from the MC and GF methods, have been compared for a fcc Lennard-Jones (LJ) solid in the reduced temperature (T *) range 0.125 4 T * 4 0:5. Here, T * is expressed in units of°=k B where°is the well depth of the LJ potential and k B is the Boltzmann constant.…”

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confidence: 99%

“…The straightforward way of evaluating hu 2 i is to substitute equation ( Shukla and Cowley (1971). q j and e…q j † are the frequencies and eigenvectors respectively for the mode q j, r`is the direct lattice vector and A q j is the sum of creation and annihilation operators for the mode q j.…”

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confidence: 99%

“…q j and e…q j † are the frequencies and eigenvectors respectively for the mode q j, r`is the direct lattice vector and A q j is the sum of creation and annihilation operators for the mode q j. For example, diagrams 1a, 1b, 2a, 2e in ® gures 1 and 2 of Shukla and Cowley (1971) give single contributions to hu 2 i. Therefore, if we introduce an extra vertex 8 for hu 2 i in the phonon lines in all possible ways in the free-energy diagrams, all contributions to hu 2 i of O… ¶ 2 † and O… ¶ 4 † can be obtained from the free-energy diagrams.…”

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Higher-order anharmonic contributions to the Debye-Waller factor

Shukla

2000

Philosophical Magazine B

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We have presented a detailed analysis of the higher-order anharmonic contributions to the average square atomic displacement hu 2 i or Debye± Waller factor by the diagrammatic method and the Zubarev type Green's function method. The Hamiltonian employed in the detailed analysis contains the anharmonic terms up to O… ¶ 4 †, that is the cubic, quartic, quintic and sextic terms which arise from the Taylor expansion of the potential energy. Thus the various contributions to hu 2 i of O… ¶ 2 † and O… ¶ 4 †, presented in the diagrammatic language, arise from the ® rst-, second-, third-and the fourth-order perturbation theory. This analysis establishing interrelationships between the Helmholtz free energy (F), selfenergy and hu 2 i reveals that a total of 16 diagrams contribute to hu 2 i for a Bravais lattice or a lattice with a basis where every atom is at a site of inversion symmetry. A simple prescription is given for the derivation of hu 2 i diagrams from the F diagrams. Out of 16 diagrams, two are of O… ¶ 2 † and 14 of O… ¶ 4 †; where ¶ is a perturbation expansion parameter. It is also shown that at least up to O… ¶ 4 † the contributions to hu 2 i from nine out of 16 diagrams are included in the Green's function iterative solution if the latter is generated from the anharmonic Hamiltonian containing the cubic and quartic terms. Exact and approximate numerical magnitudes for all the diagrams are obtained for a nearest-neighbour 6± 12 Lennard-Jones fcc solid by extrapolating the Brillouin zone (BZ) sums to the q ! 0 limit. A disproportionate contribution to the BZ sums comes from this region of q space in the calculation of hu 2 i. In the context of hu 2 i the importance of the various self-energy diagrams involving the same type of anharmonic vertices is established. It is shown that there exists a heavy cancellation among these 14 diagrams ; nevertheless their total contribution to hu 2 i is su cient to bring it in almost exact agreement with the classical Monte Carlo results, which are also obtained for the same model.

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Higher-order anharmonic contributions to the Debye-Waller factor

Shukla

2000

Philosophical Magazine B

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Nomenklatur und einige Eigenschaften der Molkenproteine. 2. Mitt. α‐Lactalbumin, Immunoglobuline, Proteose‐Peptone, Minorproteine und Enzyme

Sienkiewicz

1981

Nahrung

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Nomenklatur und einige Eigenschaften der Molkenproteine. 2. Mitt. a-Lactalbumin, Immunoglobuline, Proteose-Peptone, Minorproteine und Enzyme' T. SIENKIEWICZ Die Struktur und Funktion von r-Lactalbumin und von anderen Molkenproteinen werden diskutiert und einige Aspekte der thermischen Proteindenaturierung beschrieben. a-Lactaibamia AIIgemeines und Primarstruktur(ca. 1.3 g/l) ist das a-Lactalbumin (a-La) das nveitwichtigste Molkenprotein der Kuhmilch. Unter den Molkenproteinen der Humanmilch ist das a-La dem Gehalt nach (4,6 g/l) das bedeutendste Protein. Zur Reindarstellung von a-La konnen Fallungsverfahren [S. 841 oder physikalische Trennmethoden [45, 1091 eingesetzt werden. Fur einige Verwendungszwecke reicht es aus, ,,robes" I-La-Praparat durch Ammoniumsulfatdllung zu gewinnen und von Blutserumalbumin durch die Gelfiltration an Sephadex G-75 oder G-100 abzutrennen. Besonders reines Praparat (ohne Minorkomponenten) ist durch anschlieknde Ionenaustauschchromatographie an DEAE-Cellulose (bzw. DEAE-Sephadex) zu gewinnen 1591. Die Bezeichnung a-La wurde im Jahre 1930 von S J~R E N und SVEDBERG eingefuhrt fur das erste (a) in der Ultrazentrifuge sedimentierendes Protein aus der durch Auskristallisieren aus lMolke gewomnen Albuminfraktion. Das a-La ist durch die Sgttigung der Molke mit Magnesiumsulfat nicht Gllbar. Die vollstandige Aminosiiuresequenz von a-La wurde von BREW u. a. [25] aufgeklgrt. Das in der Kuhmilch auftretende monomere Protein mit einer relativen Molekiilmasse von 14 176 besteht aus 123 Aminosiiuren und besitzt vier Cystin-und keine Cysteinreste. Weitere charakteristische Merkmale sind: Gesamtstickstoffgehalt von 15.86 %, der hochste Tryptophangehalt von allen bekannten natiirlichen Proteinen (6,9 g/100 g Protein) und ein hohes Verhaltnis von polaren zu nichtpolaren Aminosauren. Der Gehalt von essentiellen Aminosauren ist hoch. der prozentuelle Absorbtionskoeffizient A: : ': bei 280 nm Wellenlange des UV-Lichtes 20.1 bzw. 20,6 [70, IOO]. Gegenwartig ist r-La bei 13 Tierarten gefunden, isoliert und charakterisiert worden [MI. Von Rinder-a-La 1261, Human-a-La [44] und Meerschweinchen-@-La [23j sind die vollstandigen Aminosiiuresequenzen bekannt. Teilsequenzen wurden von vier weiteren a-La ermittelt 1641. z-La kommt in allen Milcharten, die Lactose enthalten, vor. Am Beispiel von 6 Tierarten zeigten LEY u. a. [75], daD zwischen a h -und Lactosegehalt eine positive Korrelation besteht. Dies ist nicht iiberraschend, seitdem bekannt ist, daO das a-La das ,,B"-Protein eines Enzyms ist, niimlich der Lactose-Synthetase [40], Mit einem Gehalt bis zu 25 I. Mitt. Nahrung, 25, 329 (1981).

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