Towards quantitative classification of folded proteins in terms of elementary functions

Hu, Shuangwei; Krokhotin, Andrei; Niemi, Antti J.; Peng, Xubiao

doi:10.1103/physreve.83.041907

Cited by 34 publications

(96 citation statements)

References 13 publications

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“…Elsewhere [11], [12] it has been shown that loops in the chicken villin headpiece with PDB code 1YRF and the myoglobin 1ABS can be described in terms of the dark soliton of the generalized discrete nonlinear Schrödinger equation that derives from the energy function…”

Section: Modelmentioning

confidence: 99%

“…The soliton evokes a deformation of the protein shape, and as a consequence a trapped soliton is a natural cause for protein folding. The present generalization of the original DNLS equation is motivated by recent observations that protein loops in the HP35 villin headpiece with Protein Data Bank (PDB) [10] code 1YRF [11], and in the myoglobin with PDB code 1ABS [12] are accurately described in terms of its dark soliton. In this article we extend this observation to essentially all proteins in PDB.…”

Section: Introductionmentioning

confidence: 99%

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Soliton concepts and protein structure

2012

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Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion, from a relatively small number of components. Here we propose to identify the modular building blocks of proteins with the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. For this we show that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop specific parameters and we identify their possible values in Protein Data Bank. We show that with a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop, we cover over 90 % of all proteins with experimental accuracy. We also present two examples that describe how the loop library can be employed both to model and to analyze the structure of folded proteins.

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Soliton concepts and protein structure

2012

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“…But we have found [32][33][34] that an excellent approximative solution can be obtained by discretizing the topological soliton (43).…”

Section: Discretized Solitonsmentioning

confidence: 99%

“…Hence we compensate for the extension of κ to negative values, by engaging a discrete Z 2 symmetry [33]. An (isolated) point where the curvature κ(s) vanishes is an inflection point.…”

Section: Frame Anomalymentioning

confidence: 99%

Gauge fields, strings, solitons, anomalies, and the speed of life

Niemi

2014

Theor Math Phys

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It's been said that mathematics is biology's next microscope, only better; biology is mathematics' next physics, only better [1]. Here we aim for something even better. We try to combine mathematical physics and biology into a picoscope of life. For this we merge techniques which have been introduced and developed in modern mathematical physics, largely by Ludvig Faddeev to describe objects such as solitons and Higgs and to explain phenomena such as anomalies in gauge fields. We propose a synthesis that can help to resolve the protein folding problem, one of the most important conundrums in all of science. We apply the concept of gauge invariance to scrutinize the extrinsic geometry of strings in three dimensional space. We evoke general principles of symmetry in combination with Wilsonian universality and derive an essentially unique Landau-Ginzburg energy that describes the dynamics of a generic string-like configuration in the far infrared. We observe that the energy supports topological solitons, that pertain to an anomaly in the manner how a string is framed around its inflection points. We explain how the solitons operate as modular building blocks from which folded proteins are composed. We describe crystallographic protein structures by multi-solitons with experimental precision, and investigate the non-equilibrium dynamics of proteins under varying temperature. We simulate the folding process of a protein at in vivo speed and with close to pico-scale accuracy using a standard laptop computer: With pico-biology as mathematical physics' next pursuit, things can only get better.This article is dedicated to Ludvig Faddeev on the occasion of his 80 th birthday. * Electronic address: Antti.Niemi@physics.uu.se 1 arXiv:1406.7468v3 [math-ph]

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“…But a numerical approximation can be easily constructed using the procedure described in [11]. Furthermore, since it turns out that in the case of proteins the first term in (25) is small, an excellent approximation [12] is given by the naive discretization of the continuum dark NLSE soliton [20],…”

Section: D: Soliton Ansatzmentioning

confidence: 99%

Solitons and collapse in theλ−repressor protein

2012

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The enterobacteria lambda phage is a paradigm temperate bacteriophage. Its lysogenic and lytic life cycles echo competition between the DNA binding λ-repressor (CI) and CRO proteins. Here we scrutinize the structure, stability and folding pathways of the λ-repressor protein, that controls the transition from the lysogenic to the lytic state. We first investigate the super-secondary helix-loophelix composition of its backbone. We use a discrete Frenet framing to resolve the backbone spectrum in terms of bond and torsion angles. Instead of four, there appears to be seven individual loops. We model the putative loops using an explicit soliton Ansatz. It is based on the standard soliton profile of the continuum nonlinear Schrödinger equation. The accuracy of the Ansatz far exceeds the B-factor fluctuation distance accuracy of the experimentally determined protein configuration. We then investigate the folding pathways and dynamics of the λ-repressor protein. We introduce a coarse-grained energy function to model the backbone in terms of the Cα atoms and the side-chains in terms of the relative orientation of the C β atoms. We describe the folding dynamics in terms of relaxation dynamics, and find that the folded configuration can be reached from a very generic initial configuration. We conclude that folding is dominated by the temporal ordering of soliton formation. In particular, the third soliton should appear before the first and second. Otherwise, the DNA binding turn does not acquire its correct structure. We confirm the stability of the folded configuration by repeated heating and cooling simulations. I: INTRODUCTIONThe transition between the lysogenic and the lytic state in bacteriophage λ infected E. coli cell is the paradigm genetic switch mechanism. It is described in numerous molecular biology textbooks and review articles [1]- [7]. The interplay between the lysogeny maintaining λ-repressor (CI) protein and the CRO regulator protein that controls the transition to the lytic state is a simple model for more complex regulatory networks, including those that can lead to cancer in humans.In the present article we describe the physical properties of the λ-repressor protein, that controls the lysogenic-to-lytic transition. We investigate in detail the stability of its native conformation, the dynamics of the folding process, and the landscape of folding pathways. We find that the folded configuration displays a structure which is unique among all known protein structures. We also conclude that the folding pathways are entirely dominated by the loop regions. In particular, the temporal ordering of loop formation appears to be the decisive factor for the protein's ability to reach its native fold. If solitons form in a wrong order the protein may misfold.Full crystallographic information of the experimental λ-repressor structure that we use in our investigation is available in Protein Data Bank (PDB) [8] under the code 1LMB. This structure is a homo-dimer with 92 residues in each of the two monomers. It maintain...

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Towards quantitative classification of folded proteins in terms of elementary functions

Cited by 34 publications

References 13 publications

Soliton concepts and protein structure

Soliton concepts and protein structure

Gauge fields, strings, solitons, anomalies, and the speed of life

Solitons and collapse in theλ−repressor protein

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