Comparison of thermal unfolding curves and
kinetics for modified single sequence and complete models.
(a) Fractional population of the hydrophobic cluster as
a function of temperature. Derived from a two-state analysis of
fluorescence equilibrium curves (large dots). Fit to the data with the
modified single sequence model (Eqs. 3 and 4),
producing the parameters ΔSconf = −2.74
cal mol−1 K−1,
ΔHhb = −0.96 kcal mol−1,
ΔGsc = −1.94 kcal mol−1
(dashed line). Calculated with the complete model using these
parameters (continuous line). Fraction of native hydrogen bonds
calculated using the model with modified single sequence approximation
(dotted line). (b) Simulations of progress curves for
the complete model (continuous line) and the model using the modified
single sequence approximation (dotted line). The fractional population
of the hydrophobic cluster vs. time is plotted following a temperature
jump from 283 to 298 K. The dashed lines are single exponential fits to
the simulated progress curves at times >10 ns, the resolution of the
T-jump instrument. The fits of the modified single sequence model to
the kinetic data were performed using the lsoda routine
(36), which incorporates algorithms for solving both stiff and nonstiff
systems of equations. The resulting parameters were
k0 = 8.0 × 108
s−1 and E0 = 0 (equilibrium
parameters same as in a. The equilibrium and kinetic
parameters are slightly different from those
reported by Muñoz et al. (27) for two reasons. One is
that in the previous work the viscosity dependence was not included in
the preexponential factor, and the second is that in the present work
the kinetic and equilibrium data were fit simultaneously, whereas in
the previous analysis (27), the equilibrium data were fit
independently. (c) Arrhenius plot of relaxation times
following 15 degree temperature jumps. The points are the experimental
relaxation rates, whereas the dashed curve through the points is
obtained from the fit to the data using the modified single sequence
model. The continuous curve is obtained from single exponential fits to
the kinetic progress curves generated by the complete
215-state model using the kinetic parameters from the
modified single sequence model.