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 TMF, 2014, Volume 181, Number 1, Pages 121–154 (Mi tmf8756)

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

A. J. Niemiabc

a Department of Physics, Beijing Institute of Technology, Beijing, China
b Laboratoire de Mathématiques et Physique Théorique, CNRS UMR, Université de Tours, Tours, France
c Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden

Abstract: Joel Cohen proposed that ‘mathematics is biology’s next microscope, only better; biology is mathematics' next physics, only better." 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 that were 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 stringlike configuration in the far infrared. We observe that the energy supports topological solitons that relate to an anomaly similarly to 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 multisolitons with experimental precision and investigate the nonequilibrium dynamics of proteins under temperature variations. We simulate the folding process of a protein at in vivo speed and with close to picoscale accuracy using a standard laptop computer. With picobiology as next pursuit of mathematical physics, things can only get better.

Keywords: physics of proteins, soliton, nonlinear Schrödinger equation, extrinsic string geometry

DOI: https://doi.org/10.4213/tmf8756

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English version:
Theoretical and Mathematical Physics, 2014, 181:1, 1235–1262

Bibliographic databases:

Citation: A. J. Niemi, “Gauge fields, strings, solitons, anomalies, and the speed of life”, TMF, 181:1 (2014), 121–154; Theoret. and Math. Phys., 181:1 (2014), 1235–1262

Citation in format AMSBIB
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• https://doi.org/10.4213/tmf8756
• http://mi.mathnet.ru/eng/tmf/v181/i1/p121

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. J. He, J. Dai, J. Li, X. Peng, A. J. Niemi, “Aspects of structural landscape of human islet amyloid polypeptide”, J. Chem. Phys., 142:4 (2015), 045102
2. X. Peng, J. He, A. J. Niemi, “Clustering and percolation in protein loop structures”, BMC Struct. Biol., 15 (2015), 22
3. A. Sinelnikova, A. J. Niemi, M. Ulybyshev, “Phase diagram and the pseudogap state in a linear chiral homopolymer model”, Phys. Rev. E, 92:3 (2015), 032602
4. T. Ioannidou, A. J. Niemi, “Poisson hierarchy of discrete strings”, Phys. Lett. A, 380:3 (2016), 333–336
5. J. Dai, A. J. Niemi, J. He, “Conformational landscape of an amyloid intra-cellular domain and Landau–Ginzburg–Wilson paradigm in protein dynamics”, J. Chem. Phys., 145:4 (2016), 045103
6. X. Peng, A. K. Sieradzan, A. J. Niemi, “Thermal unfolding of myoglobin in the Landau–Ginzburg–Wilson approach”, Phys. Rev. E, 94:6 (2016), 062405
7. N. Ilieva, J. Liu, R. Marinova, P. Petkov, L. Litov, J. He, A. J. Niemi, “Are there folding pathways in the functional stages of intrinsically disordered proteins?”, Application of Mathematics in Technical and Natural Sciences (AMITANS'16), AIP Conf. Proc., 1773, ed. M. Todorov, Amer. Inst. Phys., 2016, 110008
8. J. Liu, J. Dai, J. He, A. J. Niemi, N. Ilieva, “Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example”, Phys. Rev. E, 95:3 (2017), 032406
9. A. Molochkov, A. Begun, A. Niemi, “Gauge symmetries and structure of proteins”, XIIth Quark Confinement and the Hadron Spectrum, EPJ Web Conf., 137, eds. Y. Foka, N. Brambilla, V. Kovalenko, EDP Sciences, 2017, UNSP 04004
10. A. Begun, N. Gerasimenyuk, A. Korneev, A. Molochkov, A. Niemi, “Gauge theory: protein topology and dynamics”, J. Bioenerg. Biomembr., 50:6 (2018), 500–501
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