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Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would hav...

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Autores principales: Mohazab, Ali R., Plotkin, Steven S.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3554774/
https://www.ncbi.nlm.nih.gov/pubmed/23365638
http://dx.doi.org/10.1371/journal.pone.0053642
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author Mohazab, Ali R.
Plotkin, Steven S.
author_facet Mohazab, Ali R.
Plotkin, Steven S.
author_sort Mohazab, Ali R.
collection PubMed
description We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold [Image: see text], [Image: see text], [Image: see text], and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation “alignment”. The consensus minimal pathway is constructed and shown schematically for representative cases of an [Image: see text], [Image: see text], and knotted protein. An overlap parameter is defined between pathways; we find that [Image: see text] proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and [Image: see text] proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.
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spelling pubmed-35547742013-01-30 Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways Mohazab, Ali R. Plotkin, Steven S. PLoS One Research Article We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold [Image: see text], [Image: see text], [Image: see text], and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation “alignment”. The consensus minimal pathway is constructed and shown schematically for representative cases of an [Image: see text], [Image: see text], and knotted protein. An overlap parameter is defined between pathways; we find that [Image: see text] proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and [Image: see text] proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding. Public Library of Science 2013-01-24 /pmc/articles/PMC3554774/ /pubmed/23365638 http://dx.doi.org/10.1371/journal.pone.0053642 Text en © 2013 Mohazab, Plotkin http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Mohazab, Ali R.
Plotkin, Steven S.
Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways
title Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways
title_full Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways
title_fullStr Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways
title_full_unstemmed Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways
title_short Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways
title_sort polymer uncrossing and knotting in protein folding, and their role in minimal folding pathways
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3554774/
https://www.ncbi.nlm.nih.gov/pubmed/23365638
http://dx.doi.org/10.1371/journal.pone.0053642
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