Gauge field theory of chirally folded homopolymers with applications to folded proteins

Danielsson, Ulf H.; Lundgren, Martin; Niemi, Antti J.

doi:10.1103/physreve.82.021910

Cited by 43 publications

(115 citation statements)

References 14 publications

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“…The parameter m is the main regulator of the secondary structure, its value specifies whether we have an α-helix, a β-strand, or some other kind of regular pattern. Details can be found in [9][10][11][12][13][14][15][16][17].…”

Section: Validation Of Mean Field Approachmentioning

confidence: 99%

“…Thus, the Landau free energy E(κ, τ ) can be expanded in powers of these differences. A detailed analysis in [9][10][11][12][13][14][15][16][17] shows that in the limit of small ∆κ i the free energy admits the following expansion…”

Section: Mean Field Theorymentioning

confidence: 99%

“…In such cases the concept of a mean field theory can provide a pragmatic alternative [8]. It has been proposed that a mean field approach could be introduced to model proteins in terms of the Cα backbone [9][10][11][12][13][14][15][16][17]. For this we note that any biologically relevant time scale is long in comparison to the period of a covalent bond oscillation.…”

Section: Introductionmentioning

confidence: 99%

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Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example

Liu

Dai

et al. 2017

Phys. Rev. E

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We propose to combine a mean field approach with all atom molecular dynamics (MD), into a multistage algorithm that can model protein folding and dynamics over very long time periods yet with atomic level precision. As an example we investigate an isolated monomeric Myc oncoprotein that has been implicated in carcinomas including those in colon, breast and lungs. Under physiological conditions a monomeric Myc is presumed to be an example of intrinsically disordered proteins, that pose a serious challenge to existing modelling techniques. We argue that a room temperature monomeric Myc is in a dynamical state, it oscillates between different conformations that we identify. For this we adopt the Cα backbone of Myc in a crystallographic heteromer as an initial Ansatz for the monomeric structure. We construct a multisoliton of the pertinent Landau free energy, to describe the Cα profile with ultra high precision. We use Glauber dynamics to resolve how the multisoliton responds to repeated increases and decreases in ambient temperature. We confirm that the initial structure is unstable in isolation. We reveal a highly degenerate ground state landscape, an attractive set towards which Glauber dynamics converges in the limit of vanishing ambient temperature. We analyse the thermal stability of this Glauber attractor using room temperature molecular dynamics. We identify and scrutinise a particularly stable subset in which the two helical segments of the original multisoliton align in parallel, next to each other. During the MD time evolution of a representative structure from this subset, we observe intermittent quasiparticle oscillations along the C-terminal α-helix, some of which resemble a translating Davydov's Amide-I soliton. We propose that the presence of oscillatory motion is in line with the expected intrinsically disordered character of Myc.

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Section: Validation Of Mean Field Approachmentioning

confidence: 99%

Section: Mean Field Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example

Liu

Dai

et al. 2017

Phys. Rev. E

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“…A: Backbone geometry Our analysis of the λ-repressor protein will be based on an effective, coarse grained energy function approach that has been recently developed in [9]- [13]. In this approach the protein geometry is described in terms of the backbone C α atoms.…”

Section: Ii: Methodsmentioning

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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“…The only exception is cis-proline in which case the distance 2.8Å should be used; these are very rare. In our computations we shall also impose the steric constraint that prevents backbone self-crossing, in terms of the selfavoidance condition [36] …”

Section: Discretized Solitonsmentioning

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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Gauge field theory of chirally folded homopolymers with applications to folded proteins

Cited by 43 publications

References 14 publications

Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example

Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example

Solitons and collapse in theλ−repressor protein

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

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