Figure 3.

Experimental signatures of downhill folding upon protein stabilization: only the fastest-folding, most stable mutants of lambda repressor fragment have a significant population undergoing prompt reaction (the molecular phase shown in Fig. 2D). (A) The measured molecular phase amplitude increases smoothly when the activated rate k_a increases towards the molecular rate k_m ≈ 1 µs⁻¹ (Yang & Gruebele; ⁵² Liu & Gruebele (1) and (2); ^{52, 168} Ma & Gruebele⁸⁷), as predicted when the free energy barrier approaches RT (downhill folding).¹³⁷ (B) The kinetics of mutants that are relatively unstable can be fitted by slow single-exponential kinetics upon temperature jumps (orange area); their activation barrier is too high to carry a measurable pre-activated population. Mutants that have T_m > 60 °C show an additional fast molecular phase (triangles) because their barrier is low enough so there is a promptly reacting (downhill folding) protein population (C) On the left: The normalized enthalpy of the polypeptide chain generally decreases when the configurational entropy s_c decreases: as favorable contacts are made, the polypeptide chain moves less freely. Folding is ‘downhill’ in enthalpy (folding is an exothermic reaction), resulting in an ‘enthalpy funnel,’ but this is not what is meant by downhill folding. On the right: The free energy G can be computed from the enthalpy and entropy as a function of an arbitrarily chosen reaction coordinate x by evaluating H and S at x and averaging over all other orthogonal coordinates. ‘x’ could be the radius of gyration, distance between two FRET labels, etc., and is normalized from -1 (unfolded) to 1 (native) here. Of course, a carefully chosen set of coordinates x,y,^… provides a more complete description of a reaction as complicated as folding than just a single coordinate x. The free energy has a barrier (orange) when the enthalpy does not funnel the protein towards the native state efficiently enough to offset the decreasing entropy (orange funnel on the left). The free energy is downhill (green) when the exothermicity of the reaction is sufficient to offset the loss of entropy everywhere along the reaction coordinate (green funnel on the left). The protein then folds with the molecular rate k_m instead of the slower rate k_a (black circle in (B)). In intermediate cases both rates can be measured simultaneously (triangles+circles in (B) connected by a dot, or T<T_m trace in Fig. 2D), allowing an absolute determination of the free energy barrier height.^{49, 52, 85, 87, 100, 168}