Soliton concepts and protein structure

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

doi:10.1103/physreve.85.031906

Cited by 48 publications

(129 citation statements)

References 19 publications

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“…In [21] we have found that most crystallographic protein structures in PDB can be described in a modular fashion and with experimental B-factor precision, by combining together no more than 200 explicit soliton profiles. We propose that by learning how to compute the parameter values directly from the sequence, the geometric shape of most folded proteins can be constructed simply by solving the Master equation (28).…”

Section: G: Parametersmentioning

confidence: 99%

“…This makes a strong case that the solitons of the DNLS equation are the modular building blocks of folded proteins [21].…”

Section: D: Soliton Ansatzmentioning

confidence: 99%

“…In [21] it has been shown using the Ansatz (29) that over 92% of PDB configurations can be constructed in terms of 200 explicit soliton profiles. This makes a strong case that the solitons of the DNLS equation are the modular building blocks of folded proteins [21].…”

Section: D: Soliton Ansatzmentioning

confidence: 99%

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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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Section: G: Parametersmentioning

confidence: 99%

“…This makes a strong case that the solitons of the DNLS equation are the modular building blocks of folded proteins [21].…”

Section: D: Soliton Ansatzmentioning

confidence: 99%

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Solitons and collapse in theλ−repressor protein

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%

“…Indeed, it has been shown that over 92% of all Cα-traces of PDB proteins can be described by 200 different parametrizations of the discretized NLS kink (69), with better than 0.5Å root-mean-square-distance (RMSD) precision [34]. Accordingly, we set up to describe the modular building blocks of proteins in terms of various parametrizations of the DNLS soliton profile, that is described by the equations (68), (66), (58) and (59).…”

Section: Solitons and Proteinsmentioning

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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Comparison of the force fields on monomeric and fibrillar PHF6 of tau protein

Peng

2021

Biophysical Chemistry

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Soliton concepts and protein structure

Cited by 48 publications

References 19 publications

Solitons and collapse in theλ−repressor protein

Solitons and collapse in theλ−repressor protein

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

Comparison of the force fields on monomeric and fibrillar PHF6 of tau protein

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