Knot theory in understanding proteins

Mishra, Rama K.; Bhushan, Shantha

doi:10.1007/s00285-011-0488-3

Cited by 12 publications

(12 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, a few hundred of the structures currently deposited in the Protein Data Bank (PDB) are known to contain knots [2,3,4,5,6,7,8,9,10,11] or, more precisely, physical knots (because a suitable arc closure of an open protein chain is needed to turn it into a ring with a mathematically well-defined topology [12,13]).…”

Section: Introductionmentioning

confidence: 99%

The Role of Non-Native Interactions in the Folding of Knotted Proteins: Insights from Molecular Dynamics Simulations

et al. 2013

View full text Add to dashboard Cite

For several decades, the presence of knots in naturally-occurring proteins was largely ruled out a priori for its supposed incompatibility with the efficiency and robustness of folding processes. For this very same reason, the later discovery of several unrelated families of knotted proteins motivated researchers to look into the physico-chemical mechanisms governing the concerted sequence of folding steps leading to the consistent formation of the same knot type in the same protein location. Besides experiments, computational studies are providing considerable insight into these mechanisms. Here, we revisit a number of such recent investigations within a common conceptual and methodological framework. By considering studies employing protein models with different structural resolution (coarse-grained or atomistic) and various force fields (from pure native-centric to realistic atomistic ones), we focus on the role of native and non-native interactions. For various unrelated instances of knotted proteins, non-native interactions are shown to be very important for favoring the emergence of conformations primed for successful self-knotting events.

show abstract

Section: Introductionmentioning

confidence: 99%

The Role of Non-Native Interactions in the Folding of Knotted Proteins: Insights from Molecular Dynamics Simulations

et al. 2013

View full text Add to dashboard Cite

show abstract

“…The existence of knotted proteins was first proposed in 1994 1 and discovered shortly after 2 . Today we know that knotted proteins are not uncommon as approximately 1% of all entries in the protein data bank (PDB) are knotted 3,4 . The function of protein knots is not yet completely understood, but it is hypothesized that knotedness increases thermal and kinetic stability of the molecule 5 …”

Section: Motivationmentioning

confidence: 99%

An invariant for colored bonded knots

Gabrovšek

2021

Stud Appl Math

View full text Add to dashboard Cite

We equip a knot K with a set of colored bonds, that is, colored intervals properly embedded into double-struckR3∖K. Such a construction can be viewed as a structure that topologically models a closed protein chain including any type of bridges connecting the backbone residues. We introduce an invariant of such colored bonded knots that respects the HOMFLYPT relation, namely, the HOMFLYPT skein module of colored bonded knots. We show that the rigid version of the module is freely generated by colored Θ‐curves and handcuff links, while the nonrigid version is freely generated by the trivially embedded Θ‐curve. The latter module, however, does not provide information about the knottedness of the bonds.

show abstract

“…considered in [ 32 ]. Conceptually, the main aim is to introduce homotopy of curve embeddings and Reidemeister moves to the field of computational structural biology as spoken for in [ 33 ].…”

Section: Introductionmentioning

confidence: 99%

Quantifying steric hindrance and topological obstruction to protein structure superposition

Røgen

2021

Algorithms Mol Biol

View full text Add to dashboard Cite

Background In computational structural biology, structure comparison is fundamental for our understanding of proteins. Structure comparison is, e.g., algorithmically the starting point for computational studies of structural evolution and it guides our efforts to predict protein structures from their amino acid sequences. Most methods for structural alignment of protein structures optimize the distances between aligned and superimposed residue pairs, i.e., the distances traveled by the aligned and superimposed residues during linear interpolation. Considering such a linear interpolation, these methods do not differentiate if there is room for the interpolation, if it causes steric clashes, or more severely, if it changes the topology of the compared protein backbone curves. Results To distinguish such cases, we analyze the linear interpolation between two aligned and superimposed backbones. We quantify the amount of steric clashes and find all self-intersections in a linear backbone interpolation. To determine if the self-intersections alter the protein’s backbone curve significantly or not, we present a path-finding algorithm that checks if there exists a self-avoiding path in a neighborhood of the linear interpolation. A new path is constructed by altering the linear interpolation using a novel interpretation of Reidemeister moves from knot theory working on three-dimensional curves rather than on knot diagrams. Either the algorithm finds a self-avoiding path or it returns a smallest set of essential self-intersections. Each of these indicates a significant difference between the folds of the aligned protein structures. As expected, we find at least one essential self-intersection separating most unknotted structures from a knotted structure, and we find even larger motions in proteins connected by obstruction free linear interpolations. We also find examples of homologous proteins that are differently threaded, and we find many distinct folds connected by longer but simple deformations. TM-align is one of the most restrictive alignment programs. With standard parameters, it only aligns residues superimposed within 5 Ångström distance. We find 42165 topological obstructions between aligned parts in 142068 TM-alignments. Thus, this restrictive alignment procedure still allows topological dissimilarity of the aligned parts. Conclusions Based on the data we conclude that our program provides significant additional information to alignment scores based solely on distances between aligned and superimposed residue pairs.

show abstract

Knot theory in understanding proteins

Cited by 12 publications

References 45 publications

The Role of Non-Native Interactions in the Folding of Knotted Proteins: Insights from Molecular Dynamics Simulations

The Role of Non-Native Interactions in the Folding of Knotted Proteins: Insights from Molecular Dynamics Simulations

An invariant for colored bonded knots

Quantifying steric hindrance and topological obstruction to protein structure superposition

Contact Info

Product

Resources

About