Slow Folding of a Helical Protein: Large Barriers, Strong Internal Friction, or a Shallow, Bumpy Landscape?

Abstract

The rate at which a protein molecule folds is determined by opposing energetic and entropic contributions to the free energy that shape the folding landscape. Delineating the extent to which they impact the diffusional barrier-crossing events, including the magnitude of internal friction and barrier height, has largely been a challenging task. In this work, we extract the underlying thermodynamic and dynamic contributions to the folding rate of an unusually slow-folding helical DNA-binding domain, PurR, which shares the characteristics of ultrafast downhill-folding proteins but nonetheless appears to exhibit an apparent two-state equilibrium. We combine equilibrium spectroscopy, temperature-viscosity-dependent kinetics, statistical mechanical modeling, and coarse-grained simulations to show that the conformational behavior of PurR is highly heterogeneous characterized by a large spread in melting temperatures, marginal thermodynamic barriers, and populated partially structured states. PurR appears to be at the threshold of disorder arising from frustrated electrostatics and weak packing that in turn slows down folding due to a shallow, bumpy landscape and not due to large thermodynamic barriers or strong internal friction. Our work highlights how a strong temperature dependence on the pre-exponential could signal a shallow landscape and not necessarily a slow-folding diffusion coefficient, thus determining the folding timescales of even millisecond folding proteins and hints at possible structural origins for the shallow landscape.

Conflicting Interfacial Electrostatic Interactions as a Design Principle to Modulate Long-Range Interdomain Communication

“…Assuming that the folding dynamics can be described as a diffusion process on a one-dimensional free energy profile, the rate of folding k can be written as k = D eff e –Δ G ‡ / RT , where D eff is the folding diffusion coefficient or the pre-exponential factor ( k 0 , in inverse time units). D eff is a measure of landscape roughness as it lumps together dihedral angle rotation barriers, internal friction, and solvent effects. − To probe whether the higher thermodynamic barrier contributes to slower folding in the mutant, we measured the folding relaxation kinetics as a function of urea employing a stopped flow setup (Methods section; Figure B,C). The folding relaxation rates of both the WT and the mutant exhibit chevron-like behavior with similar slopes in the unfolding limb (Figure D).…”

The Wako-Saitô-Muñoz-Eaton Model for Predicting Protein Folding and Dynamics

“…Such rigorous contact evaluations based on physical chemistry allow the calculation of contact energies for all residue pairs, rather than selecting residue–residue contacts according to an inter-residue distance cutoff. These approaches may require the determination of additional parameters, such as scaling constants, in order for predictions to agree with experimental results, including the temperature-dependent denaturation curves monitored by circular dichroism or NMR spectroscopy [ 43 , 53 , 68 , 69 ], the temperature dependence of specific heat capacity [ 40 , 41 , 63 , 65 , 69 , 70 , 71 , 72 , 73 ], and the denaturant dependence of folding/unfolding rate constants (called a chevron plot) [ 38 , 74 ].…”

“…For example, the predicted folding rates of the 35-residue subdomain from the villin headpiece, which has three short α-helices ( Figure 4 D) and exhibits ultrafast folding, are consistent with those measured experimentally [ 38 , 39 , 40 , 41 ]. Thus, the WSME model is a powerful tool for studying subtle differences in folding rates [ 38 , 73 , 74 , 75 , 106 ]. Because virtual amino-acid substitutions can be introduced by perturbing specific contact energies, the WSME model with such perturbations can be used to calculate the theoretical Φ-values along the folding pathway [ 13 , 26 , 78 , 105 , 107 , 108 , 109 , 110 ].…”

Rouse model with fluctuating internal friction

“…The presence of an additional mode of dissipation in polymer molecules arising from intramolecular interactions, denoted as internal friction or internal viscosity [1][2][3][4][5][6][7] , has been invoked to reconcile the high values of dissipated work observed in force spectroscopic measurements on single molecules [8][9][10][11] , the steepness of the probability distribution of polymer extensions in coil-stretch transitions observed in turbulent flow 12 , and the dampened reconfiguration kinetics of biopolymers [13][14][15][16][17][18][19][20][21][22][23][24][25] . The discontinuous jump in the stress in polymer solutions upon the inception or cessation of flow 26,27 has also been attributed to internal friction.…”