Conformational fluctuation and heterogeneity in biological molecules

Dynamic heterogeneity in the folding/unfolding transitions of FiP35

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 lead 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 D.E. et al. Science 330, 331 (2010)]. The approach successfully characterizes the slowest mode corresponding to the folding/unfolding transitions and determine 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.

Mori & Saito, J. Chem. Phys. (2015).
Couplings between hierarchical conformational dynamics from multi-time correlation functions and two-dimensional lifetime spectra: Application to adenylate kinase

An analytical method based on a three-time correlation function and the corresponding two-dimensional (2D) lifetime spectrum is developed to elucidate the time-dependent couplings between the multi-timescale (i.e., hierarchical) conformational dynamics in heterogeneous systems such as proteins. In analogy with 2D NMR, IR, electronic, and fluorescence spectroscopies, the waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra can provide a quantitative description of the dynamical correlations between the conformational motions with different lifetimes. The present method is applied to intrinsic conformational changes of substrate-free adenylate kinase (AKE) using long-time coarse-grained molecular dynamics simulations. It is found that the hierarchical conformational dynamics arise from the intra-domain structural transitions among conformational substates of AKE by analyzing the one-time correlation functions and one-dimensional lifetime spectra for the donor-acceptor distances corresponding to single-molecule Foerster resonance energy transfer (FRET) experiments with the use of the principal component analysis. In addition, the complicated waiting-time dependence of the off-diagonal peaks in the 2D lifetime spectra for the donor-acceptor distances is attributed to the fact that the time evolution of the couplings between the conformational dynamics depends upon both the spatial and temporal characters of the system. The present method is expected to shed light on the biological relationship among the structure, dynamics, and function.

Waiting-time dependence of two-dimensional lifetime spectra calculated from three-time distance fluctuation
Ono, Takada, & Saito, J. Chem. Phys. Special Topic on Multidimensional Spectroscopy, 142, 212404 (2015). invited
Relation between conformational heterogeneity and reaction cycle of Ras: Molecular simulation of Ras

Ras functions as a molecular switch by cycling between the active GTP-bound state and the inactive GDP-bound state. It is known experimentally that there is another GTP-bound state called state 1. We investigate the conformational changes and fluctuations arising from the difference in the coordinations between the switch regions and ligands in the GTP- and GDP-bound states by using 830 ns molecular dynamics simulations in total. The present result suggests that the large fluctuations among multiple conformations of switch I in state 1 owing to the absence of the coordination between Thr-35 and Mg2+ inhibit the binding of Ras to effectors. Furthermore, we elucidate the conformational heterogeneity in Ras by using principal component analysis and propose a two-step reaction path from the GDP-bound state to the active GTP-bound state via state 1. The present study suggests that state 1 plays an important role in the signal transduction as an intermediate state of the nucleotide exchange process, though state 1 itself is an inactive state for signal transduction.

Figure of Ras-GAP complex
Kobayashi & Saito, Biophys. J, 99, 3726 (2010).
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