A topological study of protein folding
                    kinetics

Panagiotou, Eleni

doi:10.1090/conm/746/15010

Cited by 17 publications

(27 citation statements)

References 22 publications

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“…We analyze a set of simple, single domain, non-disulfide-bonded proteins that have been reported to fold in a concerted, all-or-none, two-state fashion, whose experimental folding rates in water were obtained in [29]. In [25] it was shown that the logarithm of the experimental folding rate decreases with decreasing global Writhe and Torsion of the protein backbone. In this section we examine how the total local topological free energy correlates with folding rate.…”

Section: Local Topological Free Energy and Protein Folding Ratesmentioning

confidence: 99%

“…Studies have applied the Gauss linking integral to measure the entanglement of the protein backbone by taking the entire backbone of the protein or by looking at linking between parts of the protein. Both approaches have found a correlation between folding rates and these measures of conformational complexity [5][6][7]25]. However, this does not answer how local properties of proteins relate to its tertiary structure.…”

Section: Introductionmentioning

confidence: 98%

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The local topological free energy of proteins

Baldwin

Panagiotou

2021

Preprint

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Protein folding, the process by which proteins attain a 3-dimensional conformation necessary for their function, remains an important unsolved problem in biology. A major gap in our understanding is how local properties of proteins relate to their global properties. In this manuscript, we use the Writhe and Torsion to introduce a new local topological/geometrical free energy that can be associated to 4 consecutive residues along protein backbone. By analyzing a culled protein dataset from the PDB, our results show that high local topological free energy conformations are independent of sequence and may be involved in the rate limiting step in protein folding. By analyzing a set of 2-state single domain proteins, we find that the total local topological free energy of these proteins correlates with the experimentally observed folding rates reported in [29].

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Section: Local Topological Free Energy and Protein Folding Ratesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

The local topological free energy of proteins

Baldwin

Panagiotou

2021

Preprint

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“…More precisely, it was shown that the writhe in combination with the Z1 algorithm can provide a new estimator of the entanglement length with several advantages over other estimators and our proposed measures have also been used to understand the dis-entanglement of polymer chains in a melt under an elongational force [36,37,38]. Recently, the Gauss linking integral has been also used to study protein folding kinetics [39]. These results indicate the promise of such topology-based estimators in polymer theories.…”

Section: Introductionmentioning

confidence: 99%

Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

2019

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We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees–Edwards boundary conditions. We show how our topological characteristics can be used to capture key features of the polymer entanglements related to the viscoelastic responses. We find there is a linear relation over a significant range of frequencies between the mean absolute Writhe W r and the Loss Tangent tan ( δ ) . We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number L K P and the Loss Tangent tan ( δ ) . Our results show some of the ways topological methods can be used to characterize chain entanglements to better understand the origins of mechanical responses in polymeric materials.

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“…Our proof-of-concept-the restricted and unrestricted searches-and rar0 make use only of the writhe for identifying locally entangled configurations. Several authors have recently made similar use of the writhe, but for defining a global entanglement of one or more polymers (Baiesi et al, 2016;Baiesi et al, 2017;Baiesi et al, 2019;Panagiotou & Kröger, 2014;Panagiotou, Kröger & Millett, 2013;Panagiotou & Plaxco, 2019;Panagiotou, Millett & Atzberger, 2019). A general aim there is to relate such an entanglement measure to physical properties of the molecules.…”

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confidence: 99%

“…A general aim there is to relate such an entanglement measure to physical properties of the molecules. In these works the writhe is applied to open curves (Baiesi et al, 2016;Panagiotou & Kröger, 2014;Panagiotou, Kröger & Millett, 2013;Panagiotou & Plaxco, 2019;Panagiotou, Millett & Atzberger, 2019). Closest to our application of the local writhe numbers are Baiesi et al (2017); Baiesi et al (2019).…”

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confidence: 99%

GISA: using Gauss Integrals to identify rare conformations in protein structures

Grønbæk

Hamelryck

Røgen

2020

PeerJ

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The native structure of a protein is important for its function, and therefore methods for exploring protein structures have attracted much research. However, rather few methods are sensitive to topologic-geometric features, the examples being knots, slipknots, lassos, links, and pokes, and with each method aimed only for a specific set of such configurations. We here propose a general method which transforms a structure into a ”fingerprint of topological-geometric values” consisting in a series of real-valued descriptors from mathematical Knot Theory. The extent to which a structure contains unusual configurations can then be judged from this fingerprint. The method is not confined to a particular pre-defined topology or geometry (like a knot or a poke), and so, unlike existing methods, it is general. To achieve this our new algorithm, GISA, as a key novelty produces the descriptors, so called Gauss integrals, not only for the full chains of a protein but for all its sub-chains. This allows fingerprinting on any scale from local to global. The Gauss integrals are known to be effective descriptors of global protein folds. Applying GISA to sets of several thousand high resolution structures, we first show how the most basic Gauss integral, the writhe, enables swift identification of pre-defined geometries such as pokes and links. We then apply GISA with no restrictions on geometry, to show how it allows identifying rare conformations by finding rare invariant values only. In this unrestricted search, pokes and links are still found, but also knotted conformations, as well as more highly entangled configurations not previously described. Thus, an application of the basic scan method in GISA’s tool-box revealed 10 known cases of knots as the top positive writhe cases, while placing at the top of the negative writhe 14 cases in cis-trans isomerases sharing a spatial motif of little secondary structure content, which possibly has gone unnoticed. Possible general applications of GISA are fold classification and structural alignment based on local Gauss integrals. Others include finding errors in protein models and identifying unusual conformations that might be important for protein folding and function. By its broad potential, we believe that GISA will be of general benefit to the structural bioinformatics community. GISA is coded in C and comes as a command line tool. Source and compiled code for GISA plus read-me and examples are publicly available at GitHub (https://github.com).

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A topological study of protein folding kinetics

Cited by 17 publications

References 22 publications

The local topological free energy of proteins

The local topological free energy of proteins

Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

GISA: using Gauss Integrals to identify rare conformations in protein structures

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