Simple two‐state protein folding kinetics requires near‐levinthal thermodynamic cooperativity

Abstract

Simple two-state folding kinetics of many small single-domain proteins are characterized by chevron plots with linear folding and unfolding arms consistent with an apparent two-state description of equilibrium thermodynamics. This phenomenon is hereby recognized as a nontrivial heteropolymer property capable of providing fundamental insight into protein energetics. Many current protein chain models, including common lattice and continuum Gō models with explicit native biases, fail to reproduce this generic protein property. Here we show that simple two-state kinetics is obtainable from models with a cooperative interplay between core burial and local conformational propensities or an extra strongly favorable energy for the native structure. These predictions suggest that intramolecular recognition in real two-state proteins is more specific than that envisioned by common Gō-like constructs with pairwise additive energies. The many-body interactions in the present kinetically two-state models lead to high thermodynamic cooperativity as measured by their van't Hoff to calorimetric enthalpy ratios, implying that the native and denatured conformational populations are well separated in enthalpy by a high free energy barrier. It has been observed experimentally that deviations from Arrhenius behavior are often more severe for folding than for unfolding. This asymmetry may be rationalized by one of the present modeling scenarios if the effective many-body cooperative interactions stablizing the native structure against unfolding is less dependent on temperature than the interactions that drive the folding kinetics.2

Theoretical and experimental demonstration of the importance of specific nonnative interactions in protein folding

“…Experimental differences in mutational (28) and temperature (42) effects on folding and unfolding rates suggest strongly that the driving forces for folding and unfolding kinetics can be significantly different (43). Evidently, folding kinetics is more influenced by ''classical'' hydrophobic effects, as characterized typically by solubility measurement of nonpolar compounds (which is the basis for the pairwise HP potential), whereas unfolding kinetics is rate-limited by the disruption of tight native packing (28,43). For these reasons, the pairwise hydrophobic interactions in our model should provide predictive information about the kinetic process leading up to the folding transition state, i.e., before tight packing becomes overwhelmingly important.…”

Multicanonical study of coarse-grained off-lattice models for folding heteropolymers

“…The values quoted throughout the paper were obtained by comparing the lowest-energy conformation found with both reference conformations and quoting the value indicating better coincidence (i.e., lower rmsd and higher overlap). This obvious ambiguity can be circumvented by adding a symmetry-breaking term to the models that disfavors, e.g., left-handed helicity [15].…”

“…There is also growing interest in modeling the folding behavior of single-domain proteins with simplified models as many of them show up a simple twostate kinetics [13] without intermediary states that would slow down the folding dynamics ("traps"). It seems, however, that native-centric models such as those of Gō type require modifications for a qualitatively correct description of this sharp folding transition [14,15].…”

First-order coil-globule transition driven by vibrational entropy

“…Although the special (non-random) heteropolymeric features of proteins have a crucial role in protein thermodynamics 13 , it must be noted that no simple protein model with designed sequence exhibits full-fledged coexistence at the transition. It becomes thus necessary to understand how the continuous transition predicted by de Gennes 7,8 can be turned into a discontinuous one as shown by proteins 6,14 , and whether it is possible to do so. Two paths have been previously proposed to that goal.…”