scholarly journals Sampling the Folding Transition State Ensemble in a Tube-Like Model of Protein

10.29007/ml3c ◽  
2020 ◽  
Author(s):  
Ba Hung Nguyen ◽  
Hoang Trinh Xuan
Keyword(s):  
Free Energy ◽  
Transition State ◽  
Energy Surface ◽  
Sampling Technique ◽  
Small Region ◽  
Umbrella Sampling ◽  
Free Energy Surface ◽  
State Ensemble ◽  
State Region ◽  
Transition State Ensemble

We used the tube model with Go-like potential for native contacts to study the folding transition of a designed three-helix bundle and a designed protein G-like structure. It is shown that both proteins in this model are two-state folders with a cooperative folding transition coincided with the collapse transition. We defined the transition states as protein conformations in a small region around the saddle point on a free energy surface with the energy and the conformational root-mean-square deviation (RMSD) from the native state as the coordinates. The transition state region on the free energy surface then was sampled by using the umbrella sampling technique. We show that the transition state ensemble is broad consisting of different conformations that have different folded and unfolded elements.

scholarly journals Sampling the Folding Transition State Ensemble in a Tube-like Model of Protein

2019 ◽  
Vol 29 (2) ◽  
pp. 129
Author(s):  
Nguyen Ba Hung ◽  
Trinh Xuan Hoang
Keyword(s):  
Free Energy ◽  
Transition State ◽  
Energy Surface ◽  
Sampling Technique ◽  
Small Region ◽  
Umbrella Sampling ◽  
Free Energy Surface ◽  
State Ensemble ◽  
State Region ◽  
Transition State Ensemble

We used the tube model with Go-like potential for native contacts to study the folding transition of a designed three-helix bundle and a designed protein G-like structure. It is shown that both proteins in this model are two-state folders with a cooperative folding transition coincided with the collapse transition. We defined the transition states as protein conformations in a small region around the saddle point on a free energy surface with the energy and the conformationalroot mean square deviation (rmsd) from the native state as the coordinates. The transition state region on the free energy surface then was sampled by using umbrella sampling technique. We show that the transition state ensemble is broad consisting of different conformations that have different folded and unfolded elements.

Optimizing the Structures of Minimum and Transition State on the Free Energy Surface

2005 ◽  
Vol 109 (1) ◽  
pp. 197-204 ◽  
Author(s):  
Sheng-Yong Yang ◽  
Iordan Hristov ◽  
Paul Fleurat-Lessard ◽  
Tom Ziegler
Keyword(s):  
Free Energy ◽  
Transition State ◽  
Energy Surface ◽  
Free Energy Surface

scholarly journals Stability and folding pathways of tetra-nucleosome from six-dimensional free energy surface

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xinqiang Ding ◽  
Xingcheng Lin ◽  
Bin Zhang
Keyword(s):  
Free Energy ◽  
Energy Surface ◽  
Sampling Technique ◽  
Thermal Fluctuations ◽  
Open Chromatin ◽  
Free Energy Surface ◽  
In Situ Experiments ◽  
Intermediate States ◽  
Folding Pathways

AbstractThe three-dimensional organization of chromatin is expected to play critical roles in regulating genome functions. High-resolution characterization of its structure and dynamics could improve our understanding of gene regulation mechanisms but has remained challenging. Using a near-atomistic model that preserves the chemical specificity of protein-DNA interactions at residue and base-pair resolution, we studied the stability and folding pathways of a tetra-nucleosome. Dynamical simulations performed with an advanced sampling technique uncovered multiple pathways that connect open chromatin configurations with the zigzag crystal structure. Intermediate states along the simulated folding pathways resemble chromatin configurations reported from in situ experiments. We further determined a six-dimensional free energy surface as a function of the inter-nucleosome distances via a deep learning approach. The zigzag structure can indeed be seen as the global minimum of the surface. However, it is not favored by a significant amount relative to the partially unfolded, in situ configurations. Chemical perturbations such as histone H4 tail acetylation and thermal fluctuations can further tilt the energetic balance to stabilize intermediate states. Our study provides insight into the connection between various reported chromatin configurations and has implications on the in situ relevance of the 30 nm fiber.

scholarly journals Dissecting the energetics of subunit rotation in the ribosome

2019 ◽  
Author(s):  
Mariana Levi ◽  
Paul C. Whitford
Keyword(s):  
Free Energy ◽  
Transition State ◽  
Energy Barrier ◽  
Small Subunit ◽  
Free Energy Barrier ◽  
Accurate Expression ◽  
State Ensemble ◽  
Subunit Rotation ◽  
Transition State Ensemble

AbstractThe accurate expression of proteins requires the ribosome to efficiently undergo elaborate conformational rearrangements. The most dramatic of these motions is subunit rotation, which is necessary for tRNA molecules to transition between ribosomal binding sites. While rigid-body descriptions provide a qualitative picture of the process, obtaining quantitative mechanistic insights requires one to account for the relationship between molecular flexibility and collective dynamics. Using simulated rotation events, we assess the quality of experimentally-accessible measures for describing the collective displacement of the ~ 4000-residue small subunit. For this, we ask whether each coordinate is able to identify the underlying free-energy barrier and transition state ensemble (TSE). We find that intuitive structurally-motivated coordinates (e.g. rotation angle, inter-protein distances) can distinguish between the endpoints, though they are poor indicators of barrier-crossing events, and they underestimate the free-energy barrier. In contrast, coordinates based on inter-subunit bridges can identify the TSE. We additionally verify that the committor probability for the putative TSE configurations is 0.5, a hallmark feature of any transition state. In terms of structural properties, these calculations implicate a transition state in which flexibility allows for asynchronous rearrangements of the bridges as the ribosome adopts a partially-rotated orientation. These calculations provide a theoretical foundation, upon which experimental techniques may precisely quantify the energy landscape of the ribosome.

scholarly journals Stability and folding pathways of tetra-nucleosome from six-dimensional free energy surface

2021 ◽  
Author(s):  
Xinqiang Ding ◽  
Xingcheng Lin ◽  
Bin Zhang
Keyword(s):  
Free Energy ◽  
Energy Surface ◽  
Three Dimensional ◽  
Sampling Technique ◽  
Thermal Fluctuations ◽  
Open Chromatin ◽  
Free Energy Surface ◽  
Intermediate States ◽  
Folding Pathways

The three-dimensional organization of chromatin is expected to play critical roles in regulating genome functions. High-resolution characterization of its structure and dynamics could improve our understanding of gene regulation mechanisms but has remained challenging. Using a near-atomistic model that preserves the chemical specificity of protein-DNA interactions at residue and base-pair resolution, we studied the stability and folding pathways of a tetra-nucleosome. Dynamical simulations performed with an advanced sampling technique uncovered multiple pathways that connect open chromatin configurations with the zigzag crystal structure. Intermediate states along the simulated folding pathways resemble chromatin configurations reported from in situ experiments. We further determined a six-dimensional free energy surface as a function of the inter-nucleosome distances via a deep learning approach. The zigzag structure can indeed be seen as the global minimum of the surface. However, it is not favored by a significant amount relative to the partially unfolded, in situ configurations. Chemical perturbations such as histone H4 tail acetylation and thermal fluctuations can further tilt the energetic balance to stabilize intermediate states. Our study provides insight into the connection between various reported chromatin configurations and has implications on the in situ relevance of the 30nm fiber.

The experimental survey of protein-folding energy landscapes

2005 ◽  
Vol 38 (3) ◽  
pp. 245-288 ◽  
Author(s):  
Mikael Oliveberg ◽  
Peter G. Wolynes
Keyword(s):  
Free Energy ◽  
Protein Folding ◽  
Transition State ◽  
Energy Landscape ◽  
Energy Profile ◽  
Global Features ◽  
Value Analysis ◽  
Free Energy Profile ◽  
State Ensemble ◽  
Transition State Ensemble

1. Introduction 22. The macroscopic and microscopic views of protein folding 22.1 The macroscopic view: the experimental folding free-energy profile 22.2 The microscopic view: an underlying energy landscape 33. The micro to macro projection: from an energy landscape to a free-energy profile 64. Global features of the protein folding transition-state ensemble 124.1 Overall transition state location β[Dagger]: a measure of compactness 124.2 What makes folding so robust ? 135. Structural characterization of the transition-state ensemble 165.1 Insights from ϕ-value analysis 166. Deviations from ideality 206.1 β[Dagger] shifts along seemingly robust trajectories 216.2 Anomalous ϕ values, frustration and inhomogeneities 257. Intermediates 288. Detours, traps and frustration 298.1 Premature collapse and non-native trapping 299. Diffusion on the energy landscape and the elementary events of protein folding 3010. Malleability of folding routes: changes of the dominant collective coordinates for folding 3311. The evolution of the shape of the energy landscape 3511.1 Negative design: the hidden dimension of the folding code 3512. Mechanistic multiplicity and evolutionary choice 3613. Acknowledgements 3714. References 38We review what has been learned about the protein-folding problem from experimental kinetic studies. These studies reveal patterns of both great richness and surprising simplicity. The patterns can be interpreted in terms of proteins possessing an energy landscape which is largely, but not completely, funnel-like. Issues such as speed limitations of folding, the robustness of folding, the origin of barriers and cooperativity and the ensemble nature of transition states, intermediate and traps are assessed using the results from several experimental groups highlighting energy-landscape ideas as an interpretive framework.

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