307 research outputs found
Exploring the correlation between the folding rates of proteins and the entanglement of their native states
The folding of a protein towards its native state is a rather complicated
process. However there are empirical evidences that the folding time correlates
with the contact order, a simple measure of the spatial organisation of the
native state of the protein. Contact order is related to the average length of
the main chain loops formed by amino acids which are in contact. Here we argue
that folding kinetics can be influenced also by the entanglement that loops may
undergo within the overall three dimensional protein structure. In order to
explore such possibility, we introduce a novel descriptor, which we call
"maximum intrachain contact entanglement". Specifically, we measure the maximum
Gaussian entanglement between any looped portion of a protein and any other
non-overlapping subchain of the same protein, which is easily computed by
discretized line integrals on the coordinates of the atoms. By
analyzing experimental data sets of two-state and multistate folders, we show
that also the new index is a good predictor of the folding rate. Moreover,
being only partially correlated with previous methods, it can be integrated
with them to yield more accurate predictions.Comment: 8 figures. v2: new titl
The Role of Non-native Interactions in the Folding of Knotted Proteins
Stochastic simulations of coarse-grained protein models are used to
investigate the propensity to form knots in early stages of protein folding.
The study is carried out comparatively for two homologous
carbamoyltransferases, a natively-knotted N-acetylornithine
carbamoyltransferase (AOTCase) and an unknotted ornithine carbamoyltransferase
(OTCase). In addition, two different sets of pairwise amino acid interactions
are considered: one promoting exclusively native interactions, and the other
additionally including non-native quasi-chemical and electrostatic
interactions. With the former model neither protein show a propensity to form
knots. With the additional non-native interactions, knotting propensity remains
negligible for the natively-unknotted OTCase while for AOTCase it is much
enhanced. Analysis of the trajectories suggests that the different entanglement
of the two transcarbamylases follows from the tendency of the C-terminal to
point away from (for OTCase) or approach and eventually thread (for AOTCase)
other regions of partly-folded protein. The analysis of the OTCase/AOTCase pair
clarifies that natively-knotted proteins can spontaneously knot during early
folding stages and that non-native sequence-dependent interactions are
important for promoting and disfavoring early knotting events.Comment: Accepted for publication on PLOS Computational Biolog
Linking in domain-swapped protein dimers
The presence of knots has been observed in a small fraction of single-domain
proteins and related to their thermodynamic and kinetic properties. The
exchanging of identical structural elements, typical of domain-swapped
proteins, make such dimers suitable candidates to validate the possibility that
mutual entanglement between chains may play a similar role for protein
complexes. We suggest that such entanglement is captured by the linking number.
This represents, for two closed curves, the number of times that each curve
winds around the other. We show that closing the curves is not necessary, as a
novel parameter , termed Gaussian entanglement, is strongly correlated with
the linking number. Based on non redundant domain-swapped dimers, our
analysis evidences a high fraction of chains with a significant intertwining,
that is with . We report that Nature promotes configurations with
negative mutual entanglement and surprisingly, it seems to suppress
intertwining in long protein dimers. Supported by numerical simulations of
dimer dissociation, our results provide a novel topology-based classification
of protein-swapped dimers together with some preliminary evidence of its impact
on their physical and biological properties.Comment: v2: some new paragraphs and new abstrac
The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein
The folding pathway and rate coefficients of the folding of a knotted protein
are calculated for a potential energy function with minimal energetic
frustration. A kinetic transition network is constructed using the discrete
path sampling approach, and the resulting potential energy surface is
visualized by constructing disconnectivity graphs. Owing to topological
constraints, the low-lying portion of the landscape consists of three distinct
regions, corresponding to the native knotted state and to configurations where
either the N- or C-terminus is not yet folded into the knot. The fastest
folding pathways from denatured states exhibit early formation of the
N-terminus portion of the knot and a rate-determining step where the C-terminus
is incorporated. The low-lying minima with the N-terminus knotted and the
C-terminus free therefore constitute an off-pathway intermediate for this
model. The insertion of both the N- and C-termini into the knot occur late in
the folding process, creating large energy barriers that are the rate limiting
steps in the folding process. When compared to other protein folding proteins
of a similar length, this system folds over six orders of magnitude more
slowly.Comment: 19 page
Proteins analysed as virtual knots
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, which are a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identifying topological interest in some new cases. The statistics of virtual knots in protein chains are compared with those of open random walks and Hamiltonian subchains on cubic lattices, identifying a regime of open curves in which the virtual knotting description is likely to be important
How to fold intricately: using theory and experiments to unravel the properties of knotted proteins.
Over the years, advances in experimental and computational methods have helped us to understand the role of thermodynamic, kinetic and active (chaperone-aided) effects in coordinating the folding steps required to achieving a knotted native state. Here, we review such developments by paying particular attention to the complementarity of experimental and computational studies. Key open issues that could be tackled with either or both approaches are finally pointed out.We acknowledge support from the Italian Ministry of Education, grant PRIN 2010HXAW77
Topological Models for Open-Knotted Protein Chains Using the Concepts of Knotoids and Bonded Knotoids
In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids and bonded knotoids. We show that the planar knotoids technique provides more refined information regarding the knottedness of a protein when compared to established methods in the literature. Moreover, we demonstrate that our topological model for bonded proteins is robust enough to distinguish all types of lassos in proteins
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