Free energy landscape for protein folding kinetics: Intermediates, traps, and multiple pathways in theory and lattice model simulations

Abstract

The implications of thermodynamics of heteropolymers for their folding kinetics are formulated and discussed. The predictions are tested by Monte Carlo simulation of folding of a lattice model 36-monomer proteins at different temperatures. Using a simulated annealing procedure in sequence space, a number of sequences are designed which have sufficiently low energy in a given target conformation. This conformation plays a role of the native structure for the model proteins. The folding transition is found to be cooperative, and the nature of the free energy barrier is studied. At high temperature the barrier is entropic, and at low temperature it is mainly energetic. This can be explained by transformation of the early partly folded intermediate from the disordered state (belonging to the quasicontinuous part of the energy spectrum) at high temperature to the non-native low-energy frozen conformation at low temperature. The latter plays a role of an off-pathway trap. A parallel folding process has been detected at low temperature where direct folding competes with relaxation of the intermediate. The frozen intermediate must unfold to make it possible to form a folding nucleus, which is the prerequisite of subsequent fast descent to the native state.

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

“…7,8,25 In fact, extensive testing for ten values of ǫ/k B T between −2.22 and −2.78 covering the quasi-linear regime and beyond indicates that they are consistent with single exponential relaxation. Unfolding kinetics is essentially single-exponential as well (detailed data not shown).…”

Reconstruction of the src-SH3 Protein Domain Transition State Ensemble using Multiscale Molecular Dynamics Simulations

“…This barrier arises from the incomplete cancellation of the entropic and enthalpic contributions to folding. [3][4][5][6] Folding can proceed through a multiplicity of routes, and the transition state consists of an ensemble of structures rather than of a single conformation. Despite decades of effort, the identification of this transition state ensemble (TSE) still poses serious challenges, both experimentally and computationally.…”

Criterion that Determines the Foldability of Proteins

“…We also demonstrated that there is "no useful correlation between folding times and the energy gap between the native conformation and the first excited state" [1]. In response to these results Karplus and Shakhnovich (KS) [2] try to argue (i) that the folding criterion used by KT is "essentially the same as one introduced earlier [3,4]" and (ii) that the energy gap used by KT is not "appropriate". We take up these two issues separately.…”

“…There is no plot of folding time versus T f in [3], an article that was submitted after [5] was accepted for publication. It was shown in [5] (cited in [4]) that folding times correlate with σ. We showed using numerical results and theoretical arguments that "there appears to be useful correlation between folding time τ r and σ = 1 −T f /T θ : the smaller the value of σ the smaller the value of τ r " [5].…”

“…The criterion used by KT was already established in 1993 in [5] which was published before [4] was even received for review. There is no plot of folding time versus T f in [3], an article that was submitted after [5] was accepted for publication.…”