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Korneev A, Begun A, Liubimov S, Kachlishvili K, Molochkov A, Niemi AJ, Maisuradze GG. Exploring Structural Flexibility and Stability of α-Synuclein by the Landau-Ginzburg-Wilson Approach. J Phys Chem B 2022; 126:6878-6890. [PMID: 36053833 PMCID: PMC9482328 DOI: 10.1021/acs.jpcb.2c04651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
α-Synuclein (αS) is the principal protein component of the Lewy body and Lewy neurite deposits that are found in the brains of the victims of one of the most prevalent neurodegenerative disorders, Parkinson's disease. αS can be qualified as a chameleon protein because of the large number of different conformations that it is able to adopt: it is disordered under physiological conditions in solution, in equilibrium with a minor α-helical tetrameric form in the cytoplasm, and is α-helical when bound to a cell membrane. Also, in vitro, αS forms polymorphic amyloid fibrils with unique arrangements of cross-β-sheet motifs. Therefore, it is of interest to elucidate the origins of the structural flexibility of αS and what makes αS stable in different conformations. We address these questions here by analyzing the experimental structures of the micelle-bound, tetrameric, and fibrillar αS in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger equation. It is illustrated that without molecular dynamics simulations the kinks are capable of identifying the key residues causing structural flexibility of αS. Also, the stability of the experimental structures of αS is investigated by simulating heating/cooling trajectories using the Glauber algorithm. The findings are consistent with experiments.
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Affiliation(s)
- Anatolii Korneev
- Pacific Quantum Center, Far Eastern Federal University, 690922, Vladivostok, Russia
| | - Alexander Begun
- Pacific Quantum Center, Far Eastern Federal University, 690922, Vladivostok, Russia
| | - Sergei Liubimov
- Pacific Quantum Center, Far Eastern Federal University, 690922, Vladivostok, Russia
| | - Khatuna Kachlishvili
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, U. S. A
| | - Alexander Molochkov
- Pacific Quantum Center, Far Eastern Federal University, 690922, Vladivostok, Russia
| | - Antti J. Niemi
- Pacific Quantum Center, Far Eastern Federal University, 690922, Vladivostok, Russia
- Nordita, Stockholm University and Uppsala University, SE-106 91 Stockholm, Sweden
- Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, F37200, Tours, France
- School of Physics, Beijing Institute of Technology, Beijing 100081, P.R. China
| | - Gia G. Maisuradze
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, U. S. A
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2
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Lubecka EA, Liwo A. ESCASA: Analytical estimation of atomic coordinates from coarse-grained geometry for nuclear-magnetic-resonance-assisted protein structure modeling. I. Backbone and H β protons. J Comput Chem 2021; 42:1579-1589. [PMID: 34048074 DOI: 10.1002/jcc.26695] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Revised: 05/06/2021] [Accepted: 05/11/2021] [Indexed: 12/13/2022]
Abstract
A method for the estimation of coordinates of atoms in proteins from coarse-grained geometry by simple analytical formulas (ESCASA), for use in nuclear-magnetic-resonance (NMR) data-assisted coarse-grained simulations of proteins is proposed. In this paper, the formulas for the backbone Hα and amide (HN ) protons, and the side-chain Hβ protons, given the Cα -trace, have been derived and parameterized, by using the interproton distances calculated from a set of 140 high-resolution non-homologous protein structures. The mean standard deviation over all types of proton pairs in the set was 0.44 Å after fitting. Validation against a set of 41 proteins with NMR-determined structures, which were not considered in parameterization, resulted in average standard deviation from average proton-proton distances of the NMR-determined structures of 0.25 Å, compared to 0.21 Å obtained with the PULCHRA all-atom-chain reconstruction algorithm and to the 0.12 Å standard deviation of the average-structure proton-proton distance of NMR-determined ensembles. The formulas provide analytical forces and can, therefore, be used in coarse-grained molecular dynamics.
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Affiliation(s)
- Emilia A Lubecka
- Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Gdańsk, Poland
| | - Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland
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3
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Sieradzan AK, Korneev A, Begun A, Kachlishvili K, Scheraga HA, Molochkov A, Senet P, Niemi AJ, Maisuradze GG. Investigation of Phosphorylation-Induced Folding of an Intrinsically Disordered Protein by Coarse-Grained Molecular Dynamics. J Chem Theory Comput 2021; 17:3203-3220. [PMID: 33909430 DOI: 10.1021/acs.jctc.1c00155] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Apart from being the most common mechanism of regulating protein function and transmitting signals throughout the cell, phosphorylation has an ability to induce disorder-to-order transition in an intrinsically disordered protein. In particular, it was shown that folding of the intrinsically disordered protein, eIF4E-binding protein isoform 2 (4E-BP2), can be induced by multisite phosphorylation. Here, the principles that govern the folding of phosphorylated 4E-BP2 (pT37pT46 4E-BP218-62) are investigated by analyzing canonical and replica exchange molecular dynamics trajectories, generated with the coarse-grained united-residue force field, in terms of local and global motions and the time dependence of formation of contacts between Cαs of selected pairs of residues. The key residues involved in the folding of the pT37pT46 4E-BP218-62 are elucidated by this analysis. The correlations between local and global motions are identified. Moreover, for a better understanding of the physics of the formation of the folded state, the experimental structure of the pT37pT46 4E-BP218-62 is analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger equation. It is shown that without molecular dynamics simulations the kinks are able to identify not only the phosphorylated sites of protein, the key players in folding, but also the reasons for the weak stability of the pT37pT46 4E-BP218-62.
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Affiliation(s)
- Adam K Sieradzan
- Faculty of Chemistry, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland
| | - Anatolii Korneev
- Pacific Quantum Center, Far Eastern Federal University, 10 Ajax Bay, 690922 Russky Island, Vladivostok, Russia
| | - Alexander Begun
- Pacific Quantum Center, Far Eastern Federal University, 10 Ajax Bay, 690922 Russky Island, Vladivostok, Russia
| | - Khatuna Kachlishvili
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, United States
| | - Harold A Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, United States
| | - Alexander Molochkov
- Pacific Quantum Center, Far Eastern Federal University, 10 Ajax Bay, 690922 Russky Island, Vladivostok, Russia
| | - Patrick Senet
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, United States.,Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS-Université de Bourgogne Franche-Comté, 9 Av. A. Savary, BP 47 870, F-21078 Dijon Cedex, France
| | - Antti J Niemi
- Pacific Quantum Center, Far Eastern Federal University, 10 Ajax Bay, 690922 Russky Island, Vladivostok, Russia.,Laboratoire de Mathematiques et Physique Theorique, CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200 Tours, France.,Nordita, Stockholm University and Uppsala University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden.,School of Physics, Beijing Institute of Technology, Beijing 100081, P.R. China
| | - Gia G Maisuradze
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, United States
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4
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Kachlishvili K, Korneev A, Maisuradze L, Liu J, Scheraga HA, Molochkov A, Senet P, Niemi AJ, Maisuradze GG. New Insights into Folding, Misfolding, and Nonfolding Dynamics of a WW Domain. J Phys Chem B 2020; 124:3855-3872. [PMID: 32271570 DOI: 10.1021/acs.jpcb.0c00628] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Intermediate states in protein folding are associated with formation of amyloid fibrils, which are responsible for a number of neurodegenerative diseases. Therefore, prevention of the aggregation of folding intermediates is one of the most important problems to overcome. Recently, we studied the origins and prevention of formation of intermediate states with the example of the Formin binding protein 28 (FBP28) WW domain. We demonstrated that the replacement of Leu26 by Asp26 or Trp26 (in ∼15% of the folding trajectories) can alter the folding scenario from three-state folding, a major folding scenario for the FBP28 WW domain (WT) and its mutants, toward two-state or downhill folding at temperatures below the melting point. Here, for a better understanding of the physics of the formation/elimination of intermediates, (i) the dynamics and energetics of formation of β-strands in folding, misfolding, and nonfolding trajectories of these mutants (L26D and L26W) is investigated; (ii) the experimental structures of WT, L26D, and L26W are analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger equation. We show that the formation of each β-strand in folding trajectories is accompanied by the emergence of kinks in internal coordinate space as well as a decrease in local free energy. In particular, the decrease in downhill folding trajectory is ∼7 kcal/mol, while it varies between 31 and 48 kcal/mol for the three-state folding trajectory. The kink analyses of the experimental structures give new insights into formation of intermediates, which may become a useful tool for preventing aggregation.
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Affiliation(s)
- Khatuna Kachlishvili
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca 14853-1301, New York, United States
| | - Anatolii Korneev
- Laboratory of Physics of Living Matter, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950, Russia
| | - Luka Maisuradze
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca 14853-1301, New York, United States.,Biochemistry, Quantitative Biology, Biophysics, and Structural Biology (BQBS) Track, Yale University, New Haven 06520-8084, ConnecticutUnited States
| | - Jiaojiao Liu
- School of Physics, Beijing Institute of Technology, Beijing 100081, P. R. China
| | - Harold A Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca 14853-1301, New York, United States
| | - Alexander Molochkov
- Laboratory of Physics of Living Matter, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950, Russia
| | - Patrick Senet
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca 14853-1301, New York, United States.,Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS-Univ. de Bourgogne Franche-Comté, 9 Av. A. Savary, BP 47 870, Dijon Cedex F-21078, France
| | - Antti J Niemi
- Laboratory of Physics of Living Matter, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950, Russia.,School of Physics, Beijing Institute of Technology, Beijing 100081, P. R. China.,Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, Tours F37200, France.,Nordita, Stockholm University, Roslagstullsbacken 23, Stockholm SE-106 91, Sweden
| | - Gia G Maisuradze
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca 14853-1301, New York, United States
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5
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Melnikov D, Niemi AJ, Sedrakyan A. Topological Indices of Proteins. Sci Rep 2019; 9:14641. [PMID: 31601844 PMCID: PMC6787103 DOI: 10.1038/s41598-019-50809-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2019] [Accepted: 09/10/2019] [Indexed: 01/08/2023] Open
Abstract
Protein molecules can be approximated by discrete polygonal chains of amino acids. Standard topological tools can be applied to the smoothening of the polygons to introduce a topological classification of folded states of proteins, for example, using the self-linking number of the corresponding framed curves. In this paper we extend this classification to the discrete version, taking advantage of the “randomness” of such curves. Known definitions of the self-linking number apply to non-singular framings: for example, the Frenet framing cannot be used if the curve has inflection points. However, in the discrete proteins the special points are naturally resolved. Consequently, a separate integer topological characteristics can be introduced, which takes into account the intrinsic features of the special points. This works well for the proteins in our analysis, for which we compute integer topological indices associated with the singularities of the Frenet framing. We show how a version of the Calugareanu’s theorem is satisfied for the associated self-linking number of a discrete curve. Since the singularities of the Frenet framing correspond to the structural motifs of proteins, we propose topological indices as a technical tool for the description of the folding dynamics of proteins.
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Affiliation(s)
- Dmitry Melnikov
- International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal-RN, 59078-970, Brazil. .,Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, Moscow, 117218, Russia.
| | - Antti J Niemi
- Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours, France.,Nordita, Stockholm University, Roslagstullsbacken 23, SE-106 91, Stockholm, Sweden.,Laboratory of Physics of Living Matter, Far Eastern Federal University, Sukhanova 8, Vladivostok, 690950, Russia.,Department of Physics, Beijing Institute of Technology, Haidian District, Beijing, 100081, P. R. China
| | - Ara Sedrakyan
- International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal-RN, 59078-970, Brazil.,National Laboratory after Alikhanyan, Yerevan Physics Institute, Br.Alikhanyan 2, Yerevan, 0036, Armenia
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6
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Nasedkin A, Davidsson J, Niemi AJ, Peng X. Solution x-ray scattering and structure formation in protein dynamics. Phys Rev E 2018; 96:062405. [PMID: 29347365 DOI: 10.1103/physreve.96.062405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Indexed: 11/07/2022]
Abstract
We propose a computationally effective approach that builds on Landau mean-field theory in combination with modern nonequilibrium statistical mechanics to model and interpret protein dynamics and structure formation in small- to wide-angle x-ray scattering (S/WAXS) experiments. We develop the methodology by analyzing experimental data in the case of Engrailed homeodomain protein as an example. We demonstrate how to interpret S/WAXS data qualitatively with a good precision and over an extended temperature range. We explain experimental observations in terms of protein phase structure, and we make predictions for future experiments and for how to analyze data at different ambient temperature values. We conclude that the approach we propose has the potential to become a highly accurate, computationally effective, and predictive tool for analyzing S/WAXS data. For this, we compare our results with those obtained previously in an all-atom molecular dynamics simulation.
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Affiliation(s)
- Alexandr Nasedkin
- Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
| | - Jan Davidsson
- Department of Chemistry, Uppsala University, P. O. Box 803, S-75108, Uppsala, Sweden
| | - Antti J Niemi
- Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden.,Nordita, Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden.,Department of Physics and Astronomy, Uppsala University, P. O. Box 803, S-75108, Uppsala, Sweden.,Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours, France.,School of Physics, Beijing Institute of Technology, Beijing 100081, P.R. China.,Laboratory of Physics of Living Matter, School of Biomedicine, Far Eastern Federal University, Vladivostok 690090, Russia¶
| | - Xubiao Peng
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T1Z4, Canada
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Dai J, Niemi AJ, He J, Sieradzan A, Ilieva N. Bloch spin waves and emergent structure in protein folding with HIV envelope glycoprotein as an example. Phys Rev E 2016; 93:032409. [PMID: 27078392 DOI: 10.1103/physreve.93.032409] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2015] [Indexed: 06/05/2023]
Abstract
We inquire how structure emerges during the process of protein folding. For this we scrutinize collective many-atom motions during all-atom molecular dynamics simulations. We introduce, develop, and employ various topological techniques, in combination with analytic tools that we deduce from the concept of integrable models and structure of discrete nonlinear Schrödinger equation. The example we consider is an α-helical subunit of the HIV envelope glycoprotein gp41. The helical structure is stable when the subunit is part of the biological oligomer. But in isolation, the helix becomes unstable, and the monomer starts deforming. We follow the process computationally. We interpret the evolving structure both in terms of a backbone based Heisenberg spin chain and in terms of a side chain based XY spin chain. We find that in both cases the formation of protein supersecondary structure is akin the formation of a topological Bloch domain wall along a spin chain. During the process we identify three individual Bloch walls and we show that each of them can be modelled with a precision of tenths to several angstroms in terms of a soliton solution to a discrete nonlinear Schrödinger equation.
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Affiliation(s)
- Jin Dai
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
| | - Antti J Niemi
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
- Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala, Sweden
- Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours, France
| | - Jianfeng He
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
| | - Adam Sieradzan
- Faculty of Chemistry, University of Gdansk, Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Nevena Ilieva
- Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 25A, Acad. G. Bonchev Str., Sofia 1113, Bulgaria
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8
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Peng X, He J, Niemi AJ. Clustering and percolation in protein loop structures. BMC STRUCTURAL BIOLOGY 2015; 15:22. [PMID: 26510704 PMCID: PMC4625449 DOI: 10.1186/s12900-015-0049-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/07/2015] [Accepted: 10/13/2015] [Indexed: 11/24/2022]
Abstract
Background High precision protein loop modelling remains a challenge, both in template based and template independent approaches to protein structure prediction. Method We introduce the concepts of protein loop clustering and percolation, to develop a quantitative approach to systematically classify the modular building blocks of loops in crystallographic folded proteins. These fragments are all different parameterisations of a unique kink solution to a generalised discrete nonlinear Schrödinger (DNLS) equation. Accordingly, the fragments are also local energy minima of the ensuing energy function. Results We show how the loop fragments cover practically all ultrahigh resolution crystallographic protein structures in Protein Data Bank (PDB), with a 0.2 Ångström root-mean-square (RMS) precision. We find that no more than 12 different loop fragments are needed, to describe around 38 % of ultrahigh resolution loops in PDB. But there is also a large number of loop fragments that are either unique, or very rare, and examples of unique fragments are found even in the structure of a myoglobin. Conclusions Protein loops are built in a modular fashion. The loops are composed of fragments that can be modelled by the kink of the DNLS equation. The majority of loop fragments are also common, which are shared by many proteins. These common fragments are probably important for supporting the overall protein conformation. But there are also several fragments that are either unique to a given protein, or very rare. Such fragments are probably related to the function of the protein. Furthermore, we have found that the amino acid sequence does not determine the structure in a unique fashion. There are many examples of loop fragments with an identical amino acid sequence, but with a very different structure. Electronic supplementary material The online version of this article (doi:10.1186/s12900-015-0049-x) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Xubiao Peng
- Department of Physics and Astronomy, Uppsala University, P.O. Box 803, Uppsala, S-75108, Sweden.
| | - Jianfeng He
- School of Physics, Beijing Institute of Technology, Beijing, 100081, People's Republic of China.
| | - Antti J Niemi
- Department of Physics and Astronomy, Uppsala University, P.O. Box 803, Uppsala, S-75108, Sweden. .,Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, Tours, F37200, France.
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9
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He J, Dai J, Li J, Peng X, Niemi AJ. Aspects of structural landscape of human islet amyloid polypeptide. J Chem Phys 2015; 142:045102. [PMID: 25638009 DOI: 10.1063/1.4905586] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
The human islet amyloid polypeptide (hIAPP) co-operates with insulin to maintain glycemic balance. It also constitutes the amyloid plaques that aggregate in the pancreas of type-II diabetic patients. We have performed extensive in silico investigations to analyse the structural landscape of monomeric hIAPP, which is presumed to be intrinsically disordered. For this, we construct from first principles a highly predictive energy function that describes a monomeric hIAPP observed in a nuclear magnetic resonance experiment, as a local energy minimum. We subject our theoretical model of hIAPP to repeated heating and cooling simulations, back and forth between a high temperature regime where the conformation resembles a random walker and a low temperature limit where no thermal motions prevail. We find that the final low temperature conformations display a high level of degeneracy, in a manner which is fully in line with the presumed intrinsically disordered character of hIAPP. In particular, we identify an isolated family of α-helical conformations that might cause the transition to amyloidosis, by nucleation.
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Affiliation(s)
- Jianfeng He
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
| | - Jin Dai
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
| | - Jing Li
- Institute of Biopharmaceutical Research, Yangtze River Pharmaceutical Group Beijing Haiyan Pharmaceutical Co., Ltd, Beijing 102206, China
| | - Xubiao Peng
- Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108 Uppsala, Sweden
| | - Antti J Niemi
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
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10
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Krokhotin A, Liwo A, Maisuradze GG, Niemi AJ, Scheraga HA. Kinks, loops, and protein folding, with protein A as an example. J Chem Phys 2014; 140:025101. [PMID: 24437917 PMCID: PMC3899063 DOI: 10.1063/1.4855735] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2013] [Accepted: 12/10/2013] [Indexed: 02/02/2023] Open
Abstract
The dynamics and energetics of formation of loops in the 46-residue N-terminal fragment of the B-domain of staphylococcal protein A has been studied. Numerical simulations have been performed using coarse-grained molecular dynamics with the united-residue (UNRES) force field. The results have been analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger (DNLS) equation. In the case of proteins, the DNLS equation arises from a C(α)-trace-based energy function. Three individual kink profiles were identified in the experimental three-α-helix structure of protein A, in the range of the Glu16-Asn29, Leu20-Asn29, and Gln33-Asn44 residues, respectively; these correspond to two loops in the native structure. UNRES simulations were started from the full right-handed α-helix to obtain a clear picture of kink formation, which would otherwise be blurred by helix formation. All three kinks emerged during coarse-grained simulations. It was found that the formation of each is accompanied by a local free energy increase; this is expressed as the change of UNRES energy which has the physical sense of the potential of mean force of a polypeptide chain. The increase is about 7 kcal/mol. This value can thus be considered as the free energy barrier to kink formation in full α-helical segments of polypeptide chains. During the simulations, the kinks emerge, disappear, propagate, and annihilate each other many times. It was found that the formation of a kink is initiated by an abrupt change in the orientation of a pair of consecutive side chains in the loop region. This resembles the formation of a Bloch wall along a spin chain, where the C(α) backbone corresponds to the chain, and the amino acid side chains are interpreted as the spin variables. This observation suggests that nearest-neighbor side chain-side chain interactions are responsible for initiation of loop formation. It was also found that the individual kinks are reflected as clear peaks in the principal modes of the analyzed trajectory of protein A, the shapes of which resemble the directional derivatives of the kinks along the chain. These observations suggest that the kinks of the DNLS equation determine the functionally important motions of proteins.
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Affiliation(s)
- Andrey Krokhotin
- Department of Physics and Astronomy and Science for Life Laboratory, Uppsala University, P.O. Box 803, S-75108 Uppsala, Sweden
| | - Adam Liwo
- Faculty of Chemistry, University of Gdansk, ul. Sobieskiego 18, 80-952 Gdansk, Poland
| | - Gia G Maisuradze
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, USA
| | - Antti J Niemi
- Department of Physics and Astronomy and Science for Life Laboratory, Uppsala University, P.O. Box 803, S-75108 Uppsala, Sweden
| | - Harold A Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, USA
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11
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Niemi AJ. Gauge fields, strings, solitons, anomalies, and the speed of life. THEORETICAL AND MATHEMATICAL PHYSICS 2014; 181:1235-1262. [PMCID: PMC7149039 DOI: 10.1007/s11232-014-0210-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2014] [Indexed: 06/05/2023]
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.
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Affiliation(s)
- A. J. Niemi
- Laboratoire de Mathematiques et Physique Theorique CNRS UMR, Université de Tours, Tours, France
- Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
- Department of Physics, Beijing Institute of Technology, Beijing, China
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Krokhotin A, Niemi AJ, Peng X. On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics. J Chem Phys 2013; 138:175101. [PMID: 23656161 DOI: 10.1063/1.4801330] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
We construct an energy function that describes the crystallographic structure of sperm whale myoglobin backbone. As a model in our construction, we use the Protein Data Bank entry 1ABS that has been measured at liquid helium temperature. Consequently, the thermal B-factor fluctuations are very small, which is an advantage in our construction. The energy function that we utilize resembles that of the discrete nonlinear Schrödinger equation. Likewise, ours supports topological solitons as local minimum energy configurations. We describe the 1ABS backbone in terms of topological solitons with a precision that deviates from 1ABS by an average root-mean-square distance, which is less than the experimentally observed Debye-Waller B-factor fluctuation distance. We then subject the topological multi-soliton solution to extensive numerical heating and cooling experiments, over a very wide range of temperatures. We concentrate in particular to temperatures above 300 K and below the Θ-point unfolding temperature, which is around 348 K. We confirm that the behavior of the topological multi-soliton is fully consistent with Anfinsen's thermodynamic principle, up to very high temperatures. We observe that the structure responds to an increase of temperature consistently in a very similar manner. This enables us to characterize the onset of thermally induced conformational changes in terms of three distinct backbone ligand gates. One of the gates is made of the helix F and the helix E. The two other gates are chosen similarly, when open they provide a direct access route for a ligand to reach the heme. We find that out of the three gates we investigate, the one which is formed by helices B and G is the most sensitive to thermally induced conformational changes. Our approach provides a novel perspective to the important problem of ligand entry and exit.
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Affiliation(s)
- Andrey Krokhotin
- Department of Physics and Astronomy and Science for Life Laboratory, Uppsala University, P.O. Box 803, S-75108 Uppsala, Sweden.
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Krokhotin A, Liwo A, Niemi AJ, Scheraga HA. Coexistence of phases in a protein heterodimer. J Chem Phys 2012; 137:035101. [PMID: 22830730 DOI: 10.1063/1.4734019] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
A heterodimer consisting of two or more different kinds of proteins can display an enormous number of distinct molecular architectures. The conformational entropy is an essential ingredient in the Helmholtz free energy and, consequently, these heterodimers can have a very complex phase structure. Here, it is proposed that there is a state of proteins, in which the different components of a heterodimer exist in different phases. For this purpose, the structures in the protein data bank (PDB) have been analyzed, with radius of gyration as the order parameter. Two major classes of heterodimers with their protein components coexisting in different phases have been identified. An example is the PDB structure 3DXC. This is a transcriptionally active dimer. One of the components is an isoform of the intra-cellular domain of the Alzheimer-disease related amyloid precursor protein (AICD), and the other is a nuclear multidomain adaptor protein in the Fe65 family. It is concluded from the radius of gyration that neither of the two components in this dimer is in its own collapsed phase, corresponding to a biologically active protein. The UNRES energy function has been utilized to confirm that, if the two components are separated from each other, each of them collapses. The results presented in this work show that heterodimers whose protein components coexist in different phases, can have intriguing physical properties with potentially important biological consequences.
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Affiliation(s)
- Andrey Krokhotin
- Department of Physics and Astronomy and Science for Life Laboratory, Uppsala University, P.O. Box 803, S-75108 Uppsala, Sweden.
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Lundgren M, Niemi AJ. Correlation between protein secondary structure, backbone bond angles, and side-chain orientations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:021904. [PMID: 23005782 DOI: 10.1103/physreve.86.021904] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2011] [Revised: 05/24/2012] [Indexed: 06/01/2023]
Abstract
We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C(α) carbon of a protein backbone, and for this we develop new visualization techniques to analyze high-resolution x-ray structures in the Protein Data Bank. We observe that there is a correlation between the deformations of the ideal tetrahedral symmetry and the local secondary structure of the protein. We propose a universal coarse-grained energy function to describe the ensuing side-chain geometry in terms of the C(β) carbon orientations. The energy function can model the side-chain geometry with a subatomic precision. As an example we construct the C(α)-C(β) structure of HP35 chicken villin headpiece. We obtain a configuration that deviates less than 0.4 Å in root-mean-square distance from the experimental x-ray structure.
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Affiliation(s)
- Martin Lundgren
- Department of Physics and Astronomy, Uppsala University, PO Box 803, S-75108 Uppsala, Sweden.
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Krokhotin A, Lundgren M, Niemi AJ. Solitons and collapse in the λ-repressor protein. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:021923. [PMID: 23005801 DOI: 10.1103/physreve.86.021923] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2011] [Revised: 06/09/2012] [Indexed: 06/01/2023]
Abstract
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, which controls the transition from the lysogenic to the lytic state. We first investigate the supersecondary helix-loop helix 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 C(α) 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.
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Affiliation(s)
- Andrey Krokhotin
- Department of Physics and Astronomy, Uppsala University, PO Box 803, S-75108, Uppsala, Sweden.
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Krokhotin A, Niemi AJ, Peng X. Soliton concepts and protein structure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031906. [PMID: 22587122 DOI: 10.1103/physreve.85.031906] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2011] [Indexed: 05/31/2023]
Abstract
Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion from a relatively small number of components. Here we propose that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop-specific parameters, and we compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental B-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.
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Affiliation(s)
- Andrei Krokhotin
- Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden.
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Hu S, Lundgren M, Niemi AJ. Discrete Frenet frame, inflection point solitons, and curve visualization with applications to folded proteins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061908. [PMID: 21797404 DOI: 10.1103/physreve.83.061908] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2011] [Indexed: 05/31/2023]
Abstract
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. This 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 reproduces the generalized Frenet equation. In particular, we draw attention to the conceptual similarity between inflection points where the curvature vanishes and topologically stable solitons. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of C(β) 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(β) framing relates intimately to the discrete Frenet framing. We also explain how inflection points (a.k.a. soliton centers) can be located in the loops and clarify their distinctive rôle in determining the loop structure of folded proteins.
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Affiliation(s)
- Shuangwei Hu
- Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
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