Topology and structural self-organization in folded proteins

Lundgren, Martin; Krokhotin, A.; Niemi, Antti J.

doi:10.1103/physreve.88.042709

Cited by 15 publications

(29 citation statements)

References 60 publications

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“…It turns out that this kind of encircling is quite generic for loops. Consequently, each loop can be assigned a winding number termed folding index, Ind f , 47 which is defined by Eq. 14:…”

Section: Figmentioning

confidence: 99%

Kinks, loops, and protein folding, with protein A as an example

Krokhotin

Liwo

Maisuradze

et al. 2014

The Journal of Chemical Physics

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The dynamics and energetics of formation of loops in the 46-residue N-terminal fragment of the B-domain of staphylococcal protein A has been studied. Numerical simulations have been performed using coarse-grained molecular dynamics with the united-residue (UNRES) force field. The results have been analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger (DNLS) equation. In the case of proteins, the DNLS equation arises from a C(α)-trace-based energy function. Three individual kink profiles were identified in the experimental three-α-helix structure of protein A, in the range of the Glu16-Asn29, Leu20-Asn29, and Gln33-Asn44 residues, respectively; these correspond to two loops in the native structure. UNRES simulations were started from the full right-handed α-helix to obtain a clear picture of kink formation, which would otherwise be blurred by helix formation. All three kinks emerged during coarse-grained simulations. It was found that the formation of each is accompanied by a local free energy increase; this is expressed as the change of UNRES energy which has the physical sense of the potential of mean force of a polypeptide chain. The increase is about 7 kcal/mol. This value can thus be considered as the free energy barrier to kink formation in full α-helical segments of polypeptide chains. During the simulations, the kinks emerge, disappear, propagate, and annihilate each other many times. It was found that the formation of a kink is initiated by an abrupt change in the orientation of a pair of consecutive side chains in the loop region. This resembles the formation of a Bloch wall along a spin chain, where the C(α) backbone corresponds to the chain, and the amino acid side chains are interpreted as the spin variables. This observation suggests that nearest-neighbor side chain-side chain interactions are responsible for initiation of loop formation. It was also found that the individual kinks are reflected as clear peaks in the principal modes of the analyzed trajectory of protein A, the shapes of which resemble the directional derivatives of the kinks along the chain. These observations suggest that the kinks of the DNLS equation determine the functionally important motions of proteins.

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“…It turns out that this kind of encircling is quite generic for loops. Consequently, each loop can be assigned a winding number termed folding index, Ind f , 47 which is defined by Eq. 14:…”

Section: Figmentioning

confidence: 99%

Kinks, loops, and protein folding, with protein A as an example

Krokhotin

Liwo

Maisuradze

et al. 2014

The Journal of Chemical Physics

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“…Here we propose an alternative ab-initio technique which uses a curve model of the 3D structure of the polypeptide chain, this description has a much reduced number of parameters by comparison to all atomistic models. Similar curve models have been previously proposed (14)(15)(16) but not for the purpose of interpreting BioSAXS data. The model is parameterised by consecutive discretised descriptions of the four major secondary structural elements, α-helices, β-strands, flexible sections and random coils.…”

Section: Introductionmentioning

confidence: 73%

Obtaining tertiary protein structures by the ab-initio interpretation of small angle X-ray scattering data

Prior

Davies

Pohl

2019

Preprint

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Small angle X-ray scattering (SAXS) has become an important tool to investigate the structure of proteins in solution. In this paper we present a novel ab-initio method to represent polypeptide chains as discrete curves that can be used to derive a meaningful three-dimensional model from only the primary sequence and experimental SAXS data. High resolution crystal structures were used to generate probability density functions for each of the common secondary structural elements found in proteins. These are used to place realistic restraints on the model curve's geometry. To evaluate the quality of potential models and demonstrate the efficacy of this novel technique we developed a new statistic to compare the entangled geometry of two open curves, based on mathematical techniques from knot theory. The chain model is coupled with a novel explicit hydration shell model in order derive physically meaningful 3D models by optimizing configurations against experimental SAXS data using a monte-caro based algorithm. We show that the combination of our ab-initio method with spatial restraints based on contact predictions successfully derives a biologically plausible model of the coiled-coil component of the human synaptonemal complex central element protein.SIGNIFICANCE Small-angle X-ray scattering allows for structure determination of biological macromolecules and their complexes in aqueous solution. Using a discrete curve representation of the polypeptide chain and combining it with empirically determined constraints and a realistic solvent model we are now able to derive realistic ab-initio 3-dimensional models from BioSAXS data. The method only require a primary sequence and the scattering data form the user.

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“…4 b is that it encircles the north-pole of the two-sphere. It turns out that this kind of encircling is quite generic for loops, even entire folded proteins [ 47 ]. Consequently, we assign to each loop a winding number which we term folding index that we denote I n d f [ 47 ] and define as follows, …”

Section: Methodsmentioning

confidence: 99%

Clustering and percolation in protein loop structures

Peng

Niemi

2015

BMC Struct Biol

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BackgroundHigh precision protein loop modelling remains a challenge, both in template based and template independent approaches to protein structure prediction.MethodWe introduce the concepts of protein loop clustering and percolation, to develop a quantitative approach to systematically classify the modular building blocks of loops in crystallographic folded proteins. These fragments are all different parameterisations of a unique kink solution to a generalised discrete nonlinear Schrödinger (DNLS) equation. Accordingly, the fragments are also local energy minima of the ensuing energy function.ResultsWe show how the loop fragments cover practically all ultrahigh resolution crystallographic protein structures in Protein Data Bank (PDB), with a 0.2 Ångström root-mean-square (RMS) precision. We find that no more than 12 different loop fragments are needed, to describe around 38 % of ultrahigh resolution loops in PDB. But there is also a large number of loop fragments that are either unique, or very rare, and examples of unique fragments are found even in the structure of a myoglobin.ConclusionsProtein loops are built in a modular fashion. The loops are composed of fragments that can be modelled by the kink of the DNLS equation. The majority of loop fragments are also common, which are shared by many proteins. These common fragments are probably important for supporting the overall protein conformation. But there are also several fragments that are either unique to a given protein, or very rare. Such fragments are probably related to the function of the protein. Furthermore, we have found that the amino acid sequence does not determine the structure in a unique fashion. There are many examples of loop fragments with an identical amino acid sequence, but with a very different structure.Electronic supplementary materialThe online version of this article (doi:10.1186/s12900-015-0049-x) contains supplementary material, which is available to authorized users.

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Topology and structural self-organization in folded proteins

Cited by 15 publications

References 60 publications

Kinks, loops, and protein folding, with protein A as an example

Kinks, loops, and protein folding, with protein A as an example

Obtaining tertiary protein structures by the ab-initio interpretation of small angle X-ray scattering data

Clustering and percolation in protein loop structures

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