Towards Quantitative Classification of Folded Proteins in Terms of Elementary Functions

A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a classification scheme that describes a protein starting from its well organized secondary structures and often involves direct human involvement, with an atomary level Physics based approach where a protein is fundamentally nothing more than an ensemble of mutually interacting carbon, hydrogen, oxygen and nitrogen atoms. In order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced. Here we explain how the geometrical shape of entire folded proteins can be described analytically in terms of a single explicit elementary function that is familiar from nonlinear physical systems where it is known as the kink-soliton. Our approach enables the conversion of hierarchical structural information into a quantitative form that allows for a folded protein to be characterized in terms of a small number of global parameters that are in principle computable from atomary level considerations. As an example we describe in detail how the native fold of the myoglobin 1M6C emerges from a combination of kink-solitons with a very high atomary level accuracy. We also verify that our approach describes longer loops and loops connecting $\alpha$-helices with $\beta$-strands, with same overall accuracy.Comment: 3 figure

Application de la symétrie de jauge et de la théorie des solitons aux protéines repliées

Le but de cette thèse est d étudier profondément le repliement des protéines, au moyendes concepts d invariance de jauge et d universalité. La structure de jauge émerge del équation de Frenet qui est utilisée pour décrire la forme de la chaîne principale de laprotéine. Le principe d invariance de jauge conduit à une fonctionnelle d énergieeffective pour une protéine, développée dans le but d extraire les propriétésuniverselles des protéines repliées durant la phase d effondrement, et qui estcaractérisée par la loi d échelle du rayon de giration au niveau tertiaire de la structureprotéique. Dans cette thèse, on étudie l existence d une large universalité au niveausecondaire de la structure protéique. La fonctionnelle d énergie invariante de jaugealliée à l équation de Frenet discrète conduit à une solution solitonique, identifiéecomme un motif hélice-boucle-hélice dans la protéine.The purpose of this thesis is to investigate protein folding, by means of the general concepts of gauge invariance and universality. The gauge structure emerges in the Frenet equation which is utilized to describe the shape of protein backbone. The gauge invariance principle leads us an effective energy functional for a protein, which bas been found to catch the universal properties of folded proteins in their collapse phase,characterized by the scaling law of gyration radius on the tertiary level of proteinstructure. In this thesis, the existence of wide universality on the secondary level of protein structure is investigated. The synthesis of the gauge-invariant energy functional with the discrete Frenet equation leads to a soliton solution, which is identified as the helix-loop-helix motif in protein.TOURS-Bibl.électronique (372610011) / SudocSudocFranceF

Topological Solitons and Folded Proteins

We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by assembling the solitons together, one after another. We present a simple theoretical model that realizes our proposal and apply it to a number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to construct solitons that reproduce secondary structural motifs such as alpha-helix-loop-alpha-helix and beta-sheet-loop-beta-sheet with an overall root-mean-square-distance accuracy of around 0.7 Angstrom or less for the central alpha-carbons, i.e. within the limits of current experimental accuracy.Comment: 4 pages, 4 figure

The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves. We verify that in the case of differentiable curves the continuum limit of our discrete equation does reproduce the generalized Frenet equation. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of $C_\beta$ carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this $C_\beta$ framing relates intimately to the discrete Frenet framing. We also explain how inflection points can be located in the loops, and clarify their distinctive r\^ole in determining the loop structure of foldel proteins.Comment: 14 pages 12 figure

Genetically predicted causal effects of gut microbiota on spinal pain: a two-sample Mendelian randomization analysis

BackgroundObservational studies have hinted at a correlation between the gut microbiota and spinal pain (SP). However, the impact of the gut microbiota on SP remains inconclusive.MethodsIn this study, we employed a two-sample Mendelian randomization (MR) analysis to explore the causal relationship between the gut microbiota and SP, encompassing neck pain (NP), thoracic spine pain (TSP), low back pain (LBP), and back pain (BP). The compiled gut microbiota data originated from a genome-wide association study (GWAS) conducted by the MiBioGen consortium (n = 18,340). Summary data for NP were sourced from the UK Biobank, TSP from the FinnGen Biobank, and LBP from both the UK Biobank and FinnGen Biobank. Summary data for BP were obtained from the UK Biobank. The primary analytical approach for assessing causal relationships was the Inverse Variance Weighted (IVW) method, supplemented by various sensitivity analyses to ensure result robustness.ResultsThe IVW analysis unveiled 37 bacterial genera with a potential causal relationship to SP. After Benjamini-Hochberg corrected test, four bacterial genera emerged with a strong causal relationship to SP. Specifically, Oxalobacter (OR: 1.143, 95% CI 1.061–1.232, P = 0.0004) and Tyzzerella 3 (OR: 1.145, 95% CI 1.059–1.238, P = 0.0007) were identified as risk factors for LBP, while Ruminococcaceae UCG011 (OR: 0.859, 95% CI 0.791–0.932, P = 0.0003) was marked as a protective factor for LBP, and Olsenella (OR: 0.893, 95% CI 0.839–0.951, P = 0.0004) was recognized as a protective factor for low back pain or/and sciatica. No significant heterogeneity or horizontal pleiotropy was observed through alternative testing methods.ConclusionThis study establishes a causal relationship between the gut microbiota and SP, shedding light on the “gut-spine” axis. These findings offer novel perspectives for understanding the etiology of SP and provide a theoretical foundation for potential interventions targeting the gut microbiota to prevent and treat SP

Application of gauge symmetry and soliton theory on folded proteins

Le but de cette thèse est d’étudier profondément le repliement des protéines, au moyendes concepts d’invariance de jauge et d’universalité. La structure de jauge émerge del’équation de Frenet qui est utilisée pour décrire la forme de la chaîne principale de laprotéine. Le principe d’invariance de jauge conduit à une fonctionnelle d’énergieeffective pour une protéine, développée dans le but d’extraire les propriétésuniverselles des protéines repliées durant la phase d’effondrement, et qui estcaractérisée par la loi d’échelle du rayon de giration au niveau tertiaire de la structureprotéique. Dans cette thèse, on étudie l’existence d’une large universalité au niveausecondaire de la structure protéique. La fonctionnelle d’énergie invariante de jaugealliée à l’équation de Frenet discrète conduit à une solution solitonique, identifiéecomme un motif hélice-boucle-hélice dans la protéine.The purpose of this thesis is to investigate protein folding, by means of the general concepts of gauge invariance and universality. The gauge structure emerges in the Frenet equation which is utilized to describe the shape of protein backbone. The gauge invariance principle leads us an effective energy functional for a protein, which bas been found to catch the universal properties of folded proteins in their collapse phase,characterized by the scaling law of gyration radius on the tertiary level of proteinstructure. In this thesis, the existence of wide universality on the secondary level of protein structure is investigated. The synthesis of the gauge-invariant energy functional with the discrete Frenet equation leads to a soliton solution, which is identified as the helix-loop-helix motif in protein