Effect of Viscosity on the Kinetics of α-Helix and β-Hairpin Formation

Nanosecond laser temperature jumps and fluorescence detection were used to measure the effect of viscosity on the kinetics of α-helix and β-hairpin formation in peptides containing 21 and 16 amino acids, respectively. The solvent viscosity was changed by adding glucose and sucrose at concentrations that do not significantly alter the equilibrium unfolding curves. Analysis of the temperature dependence at fixed solvent compositions shows that the activation energies are also unaffected, indicating that the slowing of the relaxation rates upon addition of the sugars results entirely from their dynamical effect of increasing the solvent viscosity ( η ). The rate of β-hairpin formation was found to vary nearly as 1/ η, as predicted by Kramers theory in the high friction limit. In contrast, the rate of α-helix formation exhibited a fractional viscosity dependence ( k = η -α ) with an exponent α ≈ 0.6. The intrinsic activation energy for the elementary kinetic step of rotating a pair of backbone dihedral angles, obtained using a simple statistical mechanical model, is near zero for the β-hairpin but is ∼5 kcal/mol for the α-helix. If a higher barrier frequency can be associated with the larger activation energy, the fractional viscosity dependence for the α-helix may result from the fact that motion across the barrier top is faster than the solvent relaxation time.