The helix, s Applequist, 1963) in which the Zimm-Bragg parameters u and s are defined respectively as the cooperativity factor for helix initiation, and the equi- librium constant for converting a coil residue to a helical ~~~~

Conformational parameters for amino acids in helical, beta-sheet, and random coil regions calculated from proteins.

Publisher Summary In the proper environment, a polypeptide chain can fold spontaneously to the three-dimensional structure of a native protein, and despite the possible presence of barriers in conformational space, the chain can find its way around these barriers to reach the structure of lowest free energy. This chapter describes the spontaneous folding of proteins; in vitro complementation of protein fragments; flexibility of proteins in solution: effect of cross-links and ligands, synthetic analogs of proteins; experimental approaches to the study of conformation; and energetic factors determining protein folding. The interatomic interactions within the chain and between the chain and the solvent dictate the folding and the range of the forces involved, is such that near-neighbor interactions are dominant. Folding is envisaged as taking place by the formation of nucleation sites in various parts of the chain, in response to near-neighbor interactions; the various nucleation sites become stabilized, when they are brought into proximity, so that long-range interactions can become operative. However, the development of conformational energy calculation procedures will enable the three-dimensional structure of a native protein to be predicted from the knowledge of its amino acid sequence and its interactions with the solvent in which it is dissolved.

Experimental and theoretical aspects of protein folding.

Four alanine-based peptides were designed, synthesized, and tested by circular dichroism for alpha-helix formation in H2O. Each peptide has three glutamic/lysine residue pairs, is 16 or 17 amino acids long, and has blocked alpha-NH2 and alpha-COOH groups. In one set of peptides ("i+4"), the glutamic and lysine residues are spaced 4 residues or 1 residue apart. In the other set ("i+3"), the spacing is 3 or 2 residues. Within each of these sets, a pair of peptides was made in which the positions of the glutamic and lysine residues are reversed [Glu, Lys (E,K) vs. Lys, Glu (K,E)] in order to assess the interaction of the charged side chains with the helix dipole. Since the amino acid compositions of these peptides differ at most by a single alanine residue, differences in helicity are caused chiefly by the spacing and positions of the charged residues. The basic aim of this study was to test for helix stabilization by (Glu-, Lys+) ion pairs or salt bridges (H-bonded ion pairs). The results are as follows. (i) All four peptides show significant helix formation, and the stability of the alpha-helix does not depend on peptide concentration in the range studied. The best helix-former is (i+4)E,K, which shows approximately 80% helicity in 0.01 M NaCl at pH 7 and 0 degree C. (ii) The two i+4 peptides show more helix formation than the i+3 peptides. pH titration gives no evidence for helix stabilization by i+3 ion pairs. (iii) Surprisingly, the i+4 peptides form more stable helices than the i+3 peptides at extremes of pH (pH 2 and pH 12) as well as at pH 7. These results may be explained by helix stabilization through Glu-...Lys+ salt bridges at pH 7 and singly charged H bonds at pH 2 (Glu0...Lys+) and pH 12 (Glu-...Lys0). The reason why these links stabilize the alpha-helix more effectively in the i+4 than in the i+3 peptides is not known. (iv) Reversal of the positions of glutamic and lysine residues usually affects helix stability in the manner expected for interaction of these charged groups with the helix dipole. (v) alpha-Helix formation in these alanine-based peptides is enthalpy-driven, as is helix formation by the C-peptide of ribonuclease A.

https://www.pnas.org/content/pnas/84/24/8898.full.pdf

Helix stabilization by Glu-...Lys+ salt bridges in short peptides of de novo design

A general strategy is described for the de novo design of proteins. In this strategy the sequence locations of hydrophobic and hydrophilic residues were specified explicitly, but the precise identities of the side chains were not constrained and varied extensively. This strategy was tested by constructing a large collection of synthetic genes whose protein products were designed to fold into four-helix bundle proteins. Each gene encoded a different amino acid sequence, but all sequences shared the same pattern of polar and nonpolar residues. Characterization of the expressed proteins indicated that most of the designed sequences folded into compact alpha-helical structures. Thus, a simple binary code of polar and nonpolar residues arranged in the appropriate order can drive polypeptide chains to collapse into globular alpha-helical folds.

https://science.sciencemag.org/content/sci/262/5140/1680.full.pdf

Protein design by binary patterning of polar and nonpolar amino acids

Experimental studies of protein folding and unfolding

Helix-Coil Stability Constants for the Naturally Occurring Amino Acids in Water. VI. Leucine Parameters from Random Poly(hydroxypropylglutamine-co-L-leucine) and Poly(hydroxybutylglutamine-co-L-leucine)

The synthesis and characterization of water-soluble random copolymers containing L-glutamic acid with N5-(4-hydroxybutyl)-L-glutamine and the thermally induced helix-coil transitions of these copolymers in water and in 0.1 N KCl are described. The incorporation of L-glutamic acid was found to increase the helix content of the polymer at low pH and to decrease it at high pH even though the presence of 0.1 N KCl effectively eliminated the difference between the electrostatic free energies of the helix and the coil. The Zimm-Bragg parameters sigma and s for the helix-coil transition in poly(L-glutamic acid) in water and in 0.1 N KCl were deduced from an analysis of the melting curves of the copolymers in the manner described in earlier papers. The synthesis of N-acetyl-N'-methylglutamic acid amide and its titration, as well as that of the copolymers and poly(L-glutamic acid), in 0.1 N KCl are described.

Helix-coil stability constants for the naturally occurring amino acids in water. IX. Glutamic acid parameters from random poly(hydroxybutylglutamine-co-L-glutamic acid).

Helix-Coil Stability for the Naturally Occurring Amino Acids in Water. VIII. Valine Parameters from Random Poly(hydroxypropylglutamine-co-L-valine) and Poly(hydroxybutylglutamine-co-L-valine)

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Helix-Coil Stability Constants for the Naturally Occurring Amino Acids in Water. VI. Leucine Parameters from Random Poly(hydroxypropylglutamine-co-L-leucine) and Poly(hydroxybutylglutamine-co-L-leucine)

Helix-coil stability constants for the naturally occurring amino acids in water. IX. Glutamic acid parameters from random poly(hydroxybutylglutamine-co-L-glutamic acid).

Helix-Coil Stability for the Naturally Occurring Amino Acids in Water. VIII. Valine Parameters from Random Poly(hydroxypropylglutamine-co-L-valine) and Poly(hydroxybutylglutamine-co-L-valine)