Dynamic heterogeneity in the folding/unfolding transitions of FiP35

Abstract

Molecular dynamics simulations have become an important tool in studying protein dynamics over the last few decades. Atomistic simulations on the order of micro- to milliseconds are becoming feasible and are used to study the state-of-the-art experiments in atomistic detail. Yet, analyzing the high-dimensional-long-temporal trajectory data is still a challenging task and sometimes leads to contradictory results depending on the analyses. To reveal the dynamic aspect of the trajectory, here we propose a simple approach which uses a time correlation function matrix and apply to the folding/unfolding trajectory of FiP35 WW domain [Shaw et al., Science 330, 341 (2010)]. The approach successfully characterizes the slowest mode corresponding to the folding/unfolding transitions and determines the free energy barrier indicating that FiP35 is not an incipient downhill folder. The transition dynamics analysis further reveals that the folding/unfolding transition is highly heterogeneous, e.g., the transition path time varies by ∼100 fold. We identify two misfolded states and show that the dynamic heterogeneity in the folding/unfolding transitions originates from the trajectory being trapped in the misfolded and half-folded intermediate states rather than the diffusion driven by a thermal noise. The current results help reconcile the conflicting interpretations of the folding mechanism and highlight the complexity in the folding dynamics. This further motivates the need to understand the transition dynamics beyond a simple free energy picture using simulations and single-molecule experiments.

Investigating Molecular Kinetics by Variationally Optimized Diffusion Maps

“…The presence of this state shows that folding cannot be downhill incipient, in agreement with other studies. [46][47][48] In addition, there is an additional basin (C) just outside the unfolded state at ψ 1 ≈ 0.007 and a cloud of dispersed states (B) at ψ 1 ≈ 0.004 which elongates orthogonally to the horizontal folding direction. To better investigate the features of these states, heavy atom contact maps were built on sets of structures sampled from the trajectory.…”

“…Thus, state B represents a misfolded state, similar to those found in previous studies. 47,48 Finally, state (C) exhibits a random-coil structure, where the second hairpin starts being formed (a number of key contacts are being formed). Projecting productive trajectory portions onto the free energy plot in Fig.…”

Folding time dependence of the motions of a molecular motor in an amorphous medium

“…Indeed, characteristics of the glass-transition physics like cooperative motions called dynamic heterogeneities were reported to be generated during the motion of various motors [38][39][40][41][42]. The photo-fluidization and softening of the host material, or transient liquid-like behaviors, were also reported by different groups experimentally and by simulations [38,[43][44][45][46] with particular motors.…”

Analysis of molecular dynamics simulations of 10-residue peptide, chignolin, using statistical mechanics: Relaxation mode analysis and three-dimensional reference interaction site model theory

“…(Here, dynamic analysis methods mean that the variations of physical quantities with time are directly used in analysis.) Accordingly, many methods have been developed to analyze the dynamics and kinetics of protein simulations [47][48][49][50][51][52][53][54][55]. The Markov state model has been reported and applied to many protein systems [49,52,53,[56][57][58][59][60][61][62][63][64][65][66][67][68]; it can analyze transitions between local minimum-energy states, which are identified by using clustering analysis methods.…”

“…developed for molecular simulations of biopolymer systems. In these techniques, such as time structure-based independent component analysis (tICA) [50,51], time-lagged independent component analysis (TICA) [52,53], and dynamic component analysis (DCA) [54,55], time correlation matrices of certain physical quantities or states are used. Notably, tICA is a special case of RMA with t 0 =0, and gave rise to a different concept, the independent component analysis, to RMA with t 0 =0.…”