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For the nonnatural amino acids norvaline and alloisoleucine, six possible rotamers (-and t for χ1; -, +, and t for χ2) were tested. Notation: -, -60°; +, +60°; t, 180°.
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36
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3643137044
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note
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0) of the initial backbone coordinates was set to 2 centiradians per amino acid and then explored in both the positive and negative directions until the potential minimum with respect to superhelix frequency had been located. Third, single-site enumerations (for example, with alanine at positions a and d and a variable residue at position h) were performed initially to identify good symmetrical single-level packing rotamers. The values of the a-position orientation angles (φ) were required to lie between -3° and 32° for these calculations (for an undecatad repeat, one full asymmetric unit in φ covers 360/11 = 32.7°; larger changes in φ produce symmetry-related structures that differ only in the assignment of the undecatad repeat). The 11 single-level packings with the largest calculated stabilities at each position (a, d, and h) were then combined in all possible combinations to construct undecatad packings. Each of the six amino acids under consideration was represented at least once at each core position.
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2) (25). Second, free energies of permutation in vacuo were approximated as CHARMM19 (26) potential differences between the lowest energy packings of the native coiled coils and the lowest energy packings of the permuted coiled coils. All bonded potentials, the Lennard-Jones potential (switched off between 6.0 and 6.5 Å), and the explicit hydrogen-bond potential in the polar EF2 configuration [ L. Nilsson and M. Karplus, J. Comput. Chem. 7, 591 (1986)] were used. Finally, transfer free energies of the permuted coiled-coil sequences from vacuum to water were estimated from the accessible hydrophobic surface areas of their lowest energy conformations. Our approximation of relative stability derives from the assumptions that (i) translational, rotational, and electronic contributions to the classical partition function roughly cancel in the difference, (ii) the lowest potential energy-packing conformations dominate the partition sums, and (iii) the entropic contributions from the vibrational properties of the lowest potential energy-packing conformations roughly cancel in the difference.
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2) (25). Second, free energies of permutation in vacuo were approximated as CHARMM19 (26) potential differences between the lowest energy packings of the native coiled coils and the lowest energy packings of the permuted coiled coils. All bonded potentials, the Lennard-Jones potential (switched off between 6.0 and 6.5 Å), and the explicit hydrogen-bond potential in the polar EF2 configuration [ L. Nilsson and M. Karplus, J. Comput. Chem. 7, 591 (1986)] were used. Finally, transfer free energies of the permuted coiled-coil sequences from vacuum to water were estimated from the accessible hydrophobic surface areas of their lowest energy conformations. Our approximation of relative stability derives from the assumptions that (i) translational, rotational, and electronic contributions to the classical partition function roughly cancel in the difference, (ii) the lowest potential energy-packing conformations dominate the partition sums, and (iii) the entropic contributions from the vibrational properties of the lowest potential energy-packing conformations roughly cancel in the difference.
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Analytical ultracentrifugation measurements were carried out as described in (27). All experiments were performed in 50 mM sodium phosphate (pH 7.0) and 150 mM NaCl at 4°C. Data for RH3 and RH4 were collected at peptide concentrations of 20, 70, and 200 μM, and snowed no systematic dependence of molecular weight on concentration. At concentrations below 100 μM, the molecular weight of the RH2 peptide varied systematically between monomer and dimer values. The data reported here for RH2 were therefore collected at 200 μM, 700 μM, and 2 mM peptide concentrations and show no systematic dependence of molecular weight on concentration. The molecular weights derived from the complete data sets (followed by expected molecular weight) and [the rotor speeds in thousand revolutions per minute at which data were collected] are as follows: RH2 - 8623 (7792) [30, 35]; RH3 - 13,087 (11,637) [32]; RH4 - 15,833 (15,516) [27, 32].
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49
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0000236570
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7, respectively, relative to poly D,L-alanine. Although these protection factors are quite large by comparison with protection factors for most naturally occurring proteins, it is likely that they are smaller than would be predicted by a global unfolding mechanism. It is possible that for coiled coils in the extremely slow exchange regime, a local exchange mechanism dominates [see S. W. Englander, T. R. Sosnick, J. J. Englander, L. Mayne, Curr. Opin. Struct. Biol. 6, 18 (1996) and references therein for a discussion of exchange mechanisms].
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7, respectively, relative to poly D,L-alanine. Although these protection factors are quite large by comparison with protection factors for most naturally occurring proteins, it is likely that they are smaller than would be predicted by a global unfolding mechanism. It is possible that for coiled coils in the extremely slow exchange regime, a local exchange mechanism dominates [see S. W. Englander, T. R. Sosnick, J. J. Englander, L. Mayne, Curr. Opin. Struct. Biol. 6, 18 (1996) and references therein for a discussion of exchange mechanisms].
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Englander, S.W.1
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0029911695
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and references therein for a discussion of exchange mechanisms
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7, respectively, relative to poly D,L-alanine. Although these protection factors are quite large by comparison with protection factors for most naturally occurring proteins, it is likely that they are smaller than would be predicted by a global unfolding mechanism. It is possible that for coiled coils in the extremely slow exchange regime, a local exchange mechanism dominates [see S. W. Englander, T. R. Sosnick, J. J. Englander, L. Mayne, Curr. Opin. Struct. Biol. 6, 18 (1996) and references therein for a discussion of exchange mechanisms].
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(1996)
Curr. Opin. Struct. Biol.
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Englander, S.W.1
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Mayne, L.4
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52
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0023140814
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24 do not have clear side-chain density and are modeled as alanine), 8 water molecules, and 3 isopropanol molecules, exhibits root mean square deviations from ideal bond lengths and bond angles of 0.009 Å and 1.97°, respectively. All main-chain torsional angles fall within the helical region of a Ramachandran plot The coordinates have been deposited in the Brookhaven Protein Data Bank (accession code #1RH4).
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(1987)
Science
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, pp. 458
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Brünger, A.T.1
Kuriyan, J.2
Karplus, M.3
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53
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84889120137
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24 do not have clear side-chain density and are modeled as alanine), 8 water molecules, and 3 isopropanol molecules, exhibits root mean square deviations from ideal bond lengths and bond angles of 0.009 Å and 1.97°, respectively. All main-chain torsional angles fall within the helical region of a Ramachandran plot The coordinates have been deposited in the Brookhaven Protein Data Bank (accession code #1RH4).
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(1991)
Acta Crystallogr.
, vol.A47
, pp. 110
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Jones, T.A.1
Zou, J.Y.2
Cowan, S.W.3
Kjeldgaard, M.4
-
54
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-
0026597444
-
-
24 do not have clear side-chain density and are modeled as alanine), 8 water molecules, and 3 isopropanol molecules, exhibits root mean square deviations from ideal bond lengths and bond angles of 0.009 Å and 1.97°, respectively. All main-chain torsional angles fall within the helical region of a Ramachandran plot The coordinates have been deposited in the Brookhaven Protein Data Bank (accession code #1RH4).
-
(1992)
Nature
, vol.355
, pp. 472
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Brünger, A.T.1
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59
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0027756896
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P. B. Harbury, T. Zhang, P. S. Kim, T. Alber, Science 262, 1401 (1993).
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(1993)
Science
, vol.262
, pp. 1401
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Harbury, P.B.1
Zhang, T.2
Kim, P.S.3
Alber, T.4
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60
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3643089213
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-
note
-
Abbreviations for the amino acid residues are A, Ala; E, Glu; I, Ile; K, Lys; L, Leu; Q, Gln; Y, Tyr; nV, nor-Val; al, allo-Ile.
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61
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3643086044
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note
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We gratefully acknowledge M. Burgess for peptide synthesis, C. Lockshin, L. Stern, and A. Rich for use of their rotating anode and image-plate detector, J. Harris for assistance with the preparation of figures, A. Keating and R. Varadarajan for comments on the manuscript, and Z. Y. Peng, D. J. Lockhart, and members of the Kim laboratory for insightful discussions and criticism throughout the course of this work. This research was supported by NIH grants (GM55758 to B.T., GM48598 to T.A., and GM44162 to P.S.K.).
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