Helix-Coil Transition Theory: from biophysics to biochemistry via probability

~ Lauraine Dalton

• Protein primary, secondary, tertiary structure.

• Alpha helix secondary structure properties.

• Historical development of helix-coil transition theory (HCTT); from chemical physics to empirical biochemistry.

• Helices at work; selected examples.

The peptide bond has partial pi character; its geometry is planar.

C is a member of two planes.

Rotation about Ca sigma bonds:

dihedral angles phi and psi

psiphi

psiphi

(yellow arcs)

Ramachandran plot of allowed dihedral

angles. Steric clashes of side chains limit rotation.

Hydrogen bond network of the alpha helix

Helix-coil transition, a

disruptive view of unraveling

Nucleation involves adjustment of 6 dihedral angles; elongation, 2

Nucleation (difficult) & Propagation (facile)

The equilibrium constant for nucleation (sigma) is typically 1000 times lower than for propagation (s).

(…cccchhhcccc….) s = (…ccccccccccc….)

and the equilibrium constant (statistical weight) for adding another helical segment at the end of a stretch of helical residues is

(….ccchhhhhhhhccc…) s = (….ccchhhhhhhcccc…)

Typical values of and s is approx 0. 001 * s

Residue s RemarksGlycine 1E-5 0.62 Glycineexceptional rangeofφ,ψAlanine 8E-4 1.06 SmallvolumeofsidechainSerine 7.5E-5 0.79 Likealaninebutone-OHLeucine 33E-4 1.14 Flexibl e hydrocarbonsidechain

Helix macro dipole increases stability for long helices (supports elongation s)

Zimm-Bragg and Lifson-Roig concepts of weighting

Sharpness of the transition,

as calculated by Schellman in 1958A = coexistence of

hhh and ccc intermediate states;

B = h or c all or none

C = infinitely long

helix

Chou-Fasman “rules” of biochemistry (probabilities)

Helix initation and termination in proteins

• J & D Richardson focused on Ncap and Ccap in analysis of 215 helical segment in known structures.

• Current view is that Ncap motif consists of four residues S(T)XXE(D) = hydroxyl-XX-carboxylate.

• Carboxylate (-) interacts favorably with helix macro dipole (+)

• Ccap contributors are misfits; P (bulky ring) and G (no side chain; 2 H; very flexible)

Helices at work; stable structures perform mechanical tasks in lipid bilayer

Biotin (+Avidin) measurement tool