The Principle of Stationary Action in Biophysics: Stability in Protein Folding
We conceptualize protein folding as motion in a large dimensional dihedral angle space. We use Lagrangian mechanics and introduce an unspecified Lagrangian to study the motion. The fact that we have reliable folding leads us to conjecture the totality of paths forms caustics that can be recognized b...
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Hindawi Publishing Corporation
2013
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3888734/ |
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pubmed-38887342014-01-22 The Principle of Stationary Action in Biophysics: Stability in Protein Folding Simmons, Walter Weiner, Joel L. Research Article We conceptualize protein folding as motion in a large dimensional dihedral angle space. We use Lagrangian mechanics and introduce an unspecified Lagrangian to study the motion. The fact that we have reliable folding leads us to conjecture the totality of paths forms caustics that can be recognized by the vanishing of the second variation of the action. There are two types of folding processes: stable against modest perturbations and unstable. We also conjecture that natural selection has picked out stable folds. More importantly, the presence of caustics leads naturally to the application of ideas from catastrophe theory and allows us to consider the question of stability for the folding process from that perspective. Powerful stability theorems from mathematics are then applicable to impose more order on the totality of motions. This leads to an immediate explanation for both the insensitivity of folding to solution perturbations and the fact that folding occurs using very little free energy. The theory of folding, based on the above conjectures, can also be used to explain the behavior of energy landscapes, the speed of folding similar to transition state theory, and the fact that random proteins do not fold. Hindawi Publishing Corporation 2013 2013-12-28 /pmc/articles/PMC3888734/ /pubmed/24454360 http://dx.doi.org/10.1155/2013/697529 Text en Copyright © 2013 W. Simmons and J. L. Weiner. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Simmons, Walter Weiner, Joel L. |
| spellingShingle |
Simmons, Walter Weiner, Joel L. The Principle of Stationary Action in Biophysics: Stability in Protein Folding |
| author_facet |
Simmons, Walter Weiner, Joel L. |
| author_sort |
Simmons, Walter |
| title |
The Principle of Stationary Action in Biophysics: Stability in Protein Folding |
| title_short |
The Principle of Stationary Action in Biophysics: Stability in Protein Folding |
| title_full |
The Principle of Stationary Action in Biophysics: Stability in Protein Folding |
| title_fullStr |
The Principle of Stationary Action in Biophysics: Stability in Protein Folding |
| title_full_unstemmed |
The Principle of Stationary Action in Biophysics: Stability in Protein Folding |
| title_sort |
principle of stationary action in biophysics: stability in protein folding |
| description |
We conceptualize protein folding as motion in a large dimensional dihedral angle space. We use Lagrangian mechanics and introduce an unspecified Lagrangian to study the motion. The fact that we have reliable folding leads us to conjecture the totality of paths forms caustics that can be recognized by the vanishing of the second variation of the action. There are two types of folding processes: stable against modest perturbations and unstable. We also conjecture that natural selection has picked out stable folds. More importantly, the presence of caustics leads naturally to the application of ideas from catastrophe theory and allows us to consider the question of stability for the folding process from that perspective. Powerful stability theorems from mathematics are then applicable to impose more order on the totality of motions. This leads to an immediate explanation for both the insensitivity of folding to solution perturbations and the fact that folding occurs using very little free energy. The theory of folding, based on the above conjectures, can also be used to explain the behavior of energy landscapes, the speed of folding similar to transition state theory, and the fact that random proteins do not fold. |
| publisher |
Hindawi Publishing Corporation |
| publishDate |
2013 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3888734/ |
| _version_ |
1612046638756397056 |