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  • 1.
    Babaev, Egor
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Faddeev,
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Hidden symmetry and duality in a charged two-condensate Bose system2002In: Phys. Rev., Vol. B65, p. 100512-Article in journal (Refereed)
  • 2. Babaev, Egor
    et al.
    Faddeev, L
    Niemi,
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Hidden symmetry and knot solitons in a charged two-condensate Bose system2002In: Physical Review B, Vol. 65, p. 100512-Article in journal (Refereed)
  • 3.
    Chen, Si
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Electronics.
    Niemi, Antti J
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Univ Tours, Lab Math & Phys Theor, Federat Denis Poisson, CNRS UMR 6083, Parc Grandmont, F-37200 Tours, France.;Beijing Inst Technol, Dept Phys, Beijing 100081, Peoples R China..
    On Ramachandran angles, closed strings and knots in protein structure2016In: Journal of Physics D: Applied Physics, ISSN 0022-3727, E-ISSN 1361-6463, Vol. 49, no 31, article id 315401Article in journal (Refereed)
    Abstract [en]

    The Ramachandran angles (phi, psi) of a protein backbone form the vertices of a piecewise geodesic curve on the surface of a torus. When the ends of the curve are connected to each other similarly, by a geodesic, the result is a closed string that in general wraps around the torus a number of times both in the meridional and the longitudinal directions. The two wrapping numbers are global characteristics of the protein structure. A statistical analysis of the wrapping numbers in terms of crystallographic x-ray structures in the protein data bank (PDB) reveals that proteins have no net chirality in the phi direction but in the psi direction, proteins prefer to display chirality. A comparison between the wrapping numbers and the concept of folding index discloses a non-linearity in their relationship. Thus these three integer valued invariants can be used in tandem, to scrutinize and classify the global loop structure of individual PDB proteins, in terms of the overall fold topology.

  • 4. Chernodub, M. N.
    et al.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Embedding Brans-Dicke gravity into electroweak theory2008In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 77, no 12, p. 127902-Article in journal (Refereed)
    Abstract [en]

    We argue that a version of the four dimensional Brans-Dicke theory can be embedded in the standard flat spacetime electroweak theory. The embedding involves a change of variables that separates the isospin from the hypercharge in the electroweak theory.

  • 5.
    Dai, Jin
    et al.
    Beijing Inst Technol, Sch Phys, Beijing 100081, Peoples R China.
    Niemi, Antti
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Beijing Inst Technol, Sch Phys, Beijing 100081, Peoples R China.; Univ Tours, CNRS, UMR 6083, Lab Math & Phys Theor,Federat Denis Poisson, Parc Grandmont, F-37200 Tours, France.
    He, Jianfeng
    Beijing Inst Technol, Sch Phys, Beijing 100081, Peoples R China.
    Sieradzan, Adam
    Univ Gdansk, Fac Chem, Wita Stwosza 63, PL-80308 Gdansk, Poland.
    Ilieva, Nevena
    Bulgarian Acad Sci, Inst Informat & Commun Technol, 25A Acad G Bonchev Str, BU-1113 Sofia, Bulgaria.
    Bloch spin waves and emergent structure in protein folding with HIV envelope glycoprotein as an example2016In: Physical review E, ISSN 2470-0045, Vol. 93, no 3, article id 032409Article in journal (Refereed)
    Abstract [en]

    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.

  • 6.
    Faddeev, L
    et al.
    Uppsala University.
    Niemi, A
    Uppsala University.
    Decomposing the Yang-Mills field1999In: PHYSICS LETTERS B, ISSN 0370-2693, Vol. 464, no 1-2, p. 90-93Article in journal (Other scientific)
    Abstract [en]

    Recently we have proposed a set of variables for describing the physical parameters of SU(N) Yang-Mills field. Were we derive an off-shell generalization of this Ansatz, For this we envoke the Darboux theorem to decompose arbitrary one-form with respect t

  • 7.
    Faddeev, L
    et al.
    Uppsala University.
    Niemi, A
    Uppsala University.
    Partially dual variables in SU(2) Yang-Mills theory1999In: PHYSICAL REVIEW LETTERS, ISSN 0031-9007, Vol. 82, no 8, p. 1624-1627Article in journal (Other scientific)
    Abstract [en]

    We propose a reformulation of SU(2) Yang-Mills theory in terms of new variables, appropriate for describing the theory in its infrared limit. These variables suggest a dual picture of the Yang-Mills theory where the short distance limit describes asymptot

  • 8.
    Faddeev, L
    et al.
    Uppsala University.
    Niemi, A
    Uppsala University.
    Stable knot-like structures in classical field theory1997In: NATURE, ISSN 0028-0836, Vol. 387, no 6628, p. 58-61Article in journal (Other scientific)
    Abstract [en]

    In 1867, Lord Kelvin proposed that atoms-then considered to be elementary particles-could be described as knotted vortex tubes in ether(1). For almost two decades, this idea motivated an extensive study of the mathematical properties of knots, and the res

  • 9.
    Faddeev, L
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Electric-magnetic duality in infrared SU(2) Yang-Mills theory2002In: Phys. Lett., Vol. B525, p. 195-200Article in journal (Refereed)
  • 10. Faddeev, Ludwig D.
    et al.
    Freyhult, Lisa
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Rajan, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Shafranov's virial theorem and magnetic plasma confinement2002In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, no 11, p. L133-L139Article in journal (Refereed)
    Abstract [en]

    Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a nontrivial electric field, which implies that purely magnetohydrodynamical arguments are insufficient for describing stable, nontrivial structures within the bulk of a plasma.

  • 11.
    Freyhult, Lisa
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Chirality and fermion number in a knotted soliton background2003In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 557, no 1-2, p. 121-124Article in journal (Refereed)
    Abstract [en]

    We consider the coupling of a single Dirac fermion to the three component unit vector field which appears as an order parameter in the Faddeev model. Classically, the coupling is determined by requiring that it preserves a certain local frame independence. But quantum mechanically the separate left- and right-chiral fermion number currents suffer from a frame anomaly. We employ this anomaly to compute the fermion number of a knotted soliton. The result coincides with the self-linking number of the soliton. In particular, the anomaly structure of the fermions relates directly to the inherent chiral properties of the soliton. Our result suggests that interactions between fermions and knotted solitons can lead to phenomena akin the Callan–Rubakov effect.

  • 12. Gordeli, Ivan
    et al.
    Melnikov, Dmitry
    Niemi, Antti
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Sedrakyan, Ara
    Chern-Simons Improved Hamiltonians for Strings in Three Space Dimensions2016In: PHYSICAL REVIEW D, ISSN 2470-0010, Vol. 94, no 2, article id 021701Article in journal (Other academic)
    Abstract [en]

    The Frenet equation governs the extrinsic geometry of a string in three-dimensional ambient space in terms of the curvature and torsion, which are both scalar functions under string reparameterisations. The description engages a local SO(2) gauge symmetry, which emerges from the invariance of the extrinsic string geometry under local frame rotations around the tangent vector. Here we inquire how to construct the most general SO(2) gauge invariant Hamiltonian of strings, in terms of the curvature and torsion. The construction instructs us to introduce a long-range (self-) interaction between strings, which is mediated by a three dimensional bulk gauge field with a Chern-Simons self-interaction. The results support the proposal that fractional statistics should be prevalent in the case of three dimensional string-like configurations.

  • 13. He, Jianfeng
    et al.
    Dai, Jin
    Li, Jing
    Peng, Xubiao
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Aspects of structural landscape of human islet amyloid polypeptide2015In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 142, no 4, article id 045102Article in journal (Refereed)
    Abstract [en]

    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 a-helical conformations that might cause the transition to amyloidosis, by nucleation.

  • 14. Hinsen, Konrad
    et al.
    Hu, Shuangwei
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Kneller, Gerald R.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    A comparison of reduced coordinate sets for describing protein structure2013In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 139, no 12, p. 124115-Article in journal (Refereed)
    Abstract [en]

    In all-atom molecular simulation studies of proteins, each atom in the protein is represented by a point mass and interactions are defined in terms of the atomic positions. In recent years, various simplified approaches have been proposed. These approaches aim to improve computational efficiency and to provide a better physical insight. The simplified models can differ widely in their description of the geometry and the interactions inside the protein. This study explores the most fundamental choice in the simplified protein models: the choice of a coordinate set defining the protein structure. A simplified model can use fewer point masses than the all-atom model and/or eliminate some of the internal coordinates of the molecule by setting them to an average or ideal value. We look at the implications of such choices for the overall protein structure. We find that care must be taken for angular coordinates, where even very small variations can lead to significant changes in the positions of far away atoms. In particular, we show that the phi/psi torsion angles are not a sufficient coordinate set, whereas another coordinate set with two degrees of freedom per residue, virtual C-alpha backbone bond, and torsion angles performs satisfactorily.

  • 15. Hong, Soon-Tae
    et al.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics. Department of Physics and Materials Science, Theoretical Physics.
    BRST extension of the Faddeev model2005In: Physical Review D, Vol. 72, p. 127701-Article in journal (Refereed)
    Abstract [en]

    The Faddeev model is a second class constrained system. Here we construct its nilpotent BRST operator and derive the ensuing manifestly BRST invariant Lagrangian. Our construction employs the structure of Stuckelberg fields in a nontrivial fashion.

  • 16. Hong, Soon-Tae
    et al.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Topological aspects of dual superconductors2004In: Phys. Rev. B70Article in journal (Refereed)
    Abstract [en]

    We discuss topological aspects of two-gap superconductors with and without Josephson coupling between gaps. We address nontrivial topological aspects of the dual superconductors and its connections to Meissner effect and flux quantization. The topological knotted string geometry is also discussed in terms of the Hopf invariant, curvature and torsion of the strings associated with U(1)$\times$U(1) gauge group.

  • 17.
    Hu, Shuangwei
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Jiang, Ying
    Shanghai University.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Energy functions for stringlike continuous curves, discrete chains, and space-filling one dimensional structures2013In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 87, no 10, p. 105011-Article in journal (Refereed)
    Abstract [en]

    The theory of string-like continuous curves and discrete chains have numerous important physical applications. Here we develop a general geometrical approach, to systematically derive Hamiltonian energy functions for these objects. In the case of continuous curves, we demand that the energy function must be invariant under local frame rotations, and it should also transform covariantly under reparametrizations of the curve. This leads us to consider energy functions that are constructed from the conserved quantities in the hierarchy of the integrable nonlinear Schrödinger equation. We point out the existence of a Weyl transformation that we utilize to introduce a dual hierarchy to the standard nonlinear Schrödinger equation hierarchy. We propose that the dual hierarchy is also integrable, and we confirm this to the first nontrivial order. In the discrete case the requirement of reparametrization invariance is void. But the demand of invariance under local frame rotations prevails, and we utilize it to introduce a discrete variant of the Zakharov-Shabat recursion relation. We use this relation to derive frame-independent quantities that we propose are the essentially unique and as such natural candidates for constructing energy functions for piecewise linear polygonal chains. We also investigate the discrete version of the Weyl duality transformation. We confirm that in the continuum limit the discrete energy functions go over to their continuum counterparts, including the perfect derivative contributions.

  • 18.
    Ilieva, N.
    et al.
    Bulgarian Aacademy Sci, Inst Informat & Commun Technol, Sofia, Bulgaria..
    Dai, J.
    Beijing Inst Technol, Sch Phys, Beijing 100081, Peoples R China..
    Sieradzan, A.
    Univ Gdansk, Fac Chem, PL-80952 Gdansk, Poland..
    Niemi, Antti
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Solitons And Protein Folding: An In Silico Experiment2015In: Application of Mathematics in Technical and Natural Sciences (AMiTaNS'15), 2015, article id 030006Conference paper (Refereed)
    Abstract [en]

    Protein folding [1] is the process of formation of a functional 3D structure from a random coil - the shape in which amino-acid chains leave the ribosome. Anfinsen's dogma states that the native 3D shape of a protein is completely determined by protein's amino acid sequence. Despite the progress in understanding the process rate and the success in folding prediction for some small proteins, with presently available physics-based methods it is not yet possible to reliably deduce the shape of a biologically active protein from its amino acid sequence. The protein-folding problem endures as one of the most important unresolved problems in science; it addresses the origin of life itself. Furthermore, a wrong fold is a common cause for a protein to lose its function or even endanger the living organism. Soliton solutions of a generalized discrete non-linear Schrodinger equation (GDNLSE) obtained from the energy function in terms of bond and torsion angles kappa and tau provide a constructive theoretical framework for describing protein folds and folding patterns [2]. Here we study the dynamics of this process by means of molecular-dynamics simulations. The soliton manifestation is the pattern helix-loop-helix in the secondary structure of the protein, which explains the importance of understanding loop formation in helical proteins. We performed in silico experiments for unfolding one subunit of the core structure of gp41 from the HIV envelope glycoprotein (PDB ID: 1AIK [3]) by molecular-dynamics simulations with the MD package GROMACS. We analyzed 80 ns trajectories, obtained with one united-atom and two different all-atom force fields, to justify the side-chain orientation quantification scheme adopted in the studies and to eliminate force-field based artifacts. Our results are compatible with the soliton model of protein folding and provide first insight into soliton-formation dynamics.

  • 19.
    Ilieva, N.
    et al.
    Inst Informat & Commun Technol BAS, Sofia, Bulgaria..
    Liu, J.
    Beijing Inst Technol, Sch Phys, Beijing, Peoples R China..
    Marinova, R.
    Sofia Univ St Kliment Ohridski, Fac Phys, Sofia, Bulgaria..
    Petkov, P.
    Sofia Univ St Kliment Ohridski, Fac Phys, Sofia, Bulgaria..
    Litov, L.
    Sofia Univ St Kliment Ohridski, Fac Phys, Sofia, Bulgaria..
    He, J.
    Beijing Inst Technol, Sch Phys, Beijing, Peoples R China..
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Univ Tours, LMPT CNRS, Tours, France..
    Are There Folding Pathways in the Functional Stages of Intrinsically Disordered Proteins?2016In: Application Of Mathematics In Technical And Natural Sciences (AMITANS'16), 2016, article id 110008Conference paper (Refereed)
    Abstract [en]

    We proceed from the description of protein folding by means of molecular dynamics (MD) simulations with all-atom force fields, with folding pathways interpreted in terms of soliton structures, to identify possible systematic dynamical patterns of self-organisation that govern protein folding process. We perform in silico investigations of the conformational transformations of three different proteins MYC protein (an alpha-helical protein), amylin and indolicidin (IDPs with different length and binding dynamics). We discuss the emergence of soliton-mediated secondary motifs, in the case of IDPs in the context of their functional activity. We hypothesize that soliton-like quasi-ordered conformations appear as an important intermediate stage in this process.

  • 20. Ioannidou, Theodora
    et al.
    Jiang, Ying
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Spinors, strings, integrable models, and decomposed Yang-Mills theory2014In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 90, no 2, p. 025012-Article in journal (Refereed)
    Abstract [en]

    This paper deals with various interrelations between strings and surfaces in three-dimensional ambient space, two-dimensional integrable models, and two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three-dimensional stringlike structures. Then its relation to the structure of the su(2) Lie algebra valued Maurer-Cartan one-form is presented, while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is shown how the Lax pair of the integrable nonlinear Schrodinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation, and it is described how a spinor-based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schrodinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two-dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauss-Codazzi equation that describes surfaces in three-dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two-dimensional integrable models as embedded structures in the four-dimensional decomposed SU(2) Yang-Mills theory are presented.

  • 21.
    Ioannidou, Theodora
    et al.
    Aristotle Univ Thessaloniki, Sch Engn, Fac Civil Engn, Thessaloniki 54249, Greece..
    Niemi, A
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Stockholm Univ, Nordita, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.;Far Eastern Fed Univ, Sch Biomed, Phys Living Matter, Vladivostok 690950, Russia.;Beijing Inst Technol, Dept Phys, Beijing 100081, Peoples R China..
    Relation between discrete Frenet frames and the bi- Hamiltonian structure of the discrete nonlinear Schrödinger equation2017In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 95, no 8, article id 085003Article in journal (Refereed)
    Abstract [en]

    The discrete Frenet equation entails a local framing of a discrete, piecewise linear polygonal chain in terms of its bond and torsion angles. In particular, the tangent vector of a segment is akin to the classical O(3) spin variable. Thus there is a relation to the lattice Heisenberg model that can be used to model physical properties of the chain. On the other hand, the Heisenberg model is closely related to the discrete nonlinear Schrodinger equation. Here we apply these interrelations to develop a perspective on discrete chains dynamics: We employ the properties of a discrete chain in terms of a spinorial representation of the discrete Frenet equation, to introduce a bi-Hamiltonian structure for the discrete nonlinear Schrodinger equation, which we then use to produce integrable chain dynamics.

  • 22.
    Ioannidou, Theodora
    et al.
    Aristotle Univ Thessaloniki, Sch Engn, Fac Civil Engn, Thessaloniki 54249, Greece..
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Univ Tours, Federat Denis Poisson, CNRS UMR 6083, Lab Math & Phys Theor, F-37200 Tours, France.;Beijing Inst Technol, Dept Phys, Beijing 100081, Peoples R China..
    Poisson hierarchy of discrete strings2016In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 380, no 3, p. 333-336Article in journal (Refereed)
    Abstract [en]

    The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra.

  • 23.
    Krokhotin, Andrei
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Univ Tours, Lab Math & Phys Theor, CNRS, UMR 6083, F-37200 Tours, France.
    Peng, Xubiao
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Soliton concepts and protein structure2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 85, no 3, article id 031906Article in journal (Refereed)
    Abstract [en]

    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.

  • 24.
    Krokhotin, Andrey
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Liwo, Adam
    Maisuradze, Gia G.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Scheraga, Harold A.
    Kinks, loops, and protein folding, with protein A as an example2014In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 140, no 2, p. 025101-Article in journal (Refereed)
    Abstract [en]

    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 Cα-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 Cα 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.

  • 25.
    Krokhotin, Andrey
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Liwo, Adam
    Niemi, Antti J
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Scheraga, Harold A
    Coexistence of phases in a protein heterodimer2012In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 137, no 3, p. 035101-Article in journal (Refereed)
    Abstract [en]

    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.

  • 26. Krokhotin, Andrey
    et al.
    Lundgren, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Soliton driven relaxation dynamics and universality in protein collapseArticle in journal (Refereed)
    Abstract [en]

    Protein collapse can be viewed as a dynamical phase transition, during which new scales and collective variables become excited while the old ones recede and fade away. This causes formidable computational bottle-necks in approaches that are based on atomic scale scrutiny. Here we consider an effective dynamical Landau theory to model the folding process at biologically relevant time and distance scales. We reach both a substantial decrease in the execution time and improvement in the accuracy of the final configuration, in comparison to more conventional approaches. As an example we inspect the collapse of HP35 chicken villin headpiece subdomain, where there are detailed molecular dynamics simulations to compare with. We start from a structureless, unbend and untwisted initial configuration. In less than one second of wall-clock time on a single processor personal computer we consistently reach the native state with 0.5 Angstrom root mean square distance (RMSD) precision. We confirm that our folding pathways are indeed akin those obtained in recent atomic level molecular dynamics simulations. We conclude that our approach appears to have the potential for a computationally economical method to accurately understand theoretical aspects of protein collapse. 

  • 27.
    Krokhotin, Andrey
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Lundgren, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Solitons and collapse in the lambda-repressor protein2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, no 2, p. 021923-Article in journal (Refereed)
    Abstract [en]

    The enterobacteria lambda phage is a paradigm temperate bacteriophage. Its lysogenic and lytic life cycles echo competition between the DNA binding lambda-repressor (CI) and CRO proteins. Here we scrutinize the structure, stability, and folding pathways of the lambda-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 Schrodinger 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 lambda-repressor protein. We introduce a coarse-grained energy function to model the backbone in terms of the C-alpha atoms and the side chains in terms of the relative orientation of the C-beta 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.

  • 28.
    Krokhotin, Andrey
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Lundgren, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Peng, Xubiao
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Soliton driven relaxation dynamics and protein collapse in the villin headpiece2013In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 25, no 32, p. 325103-Article in journal (Refereed)
    Abstract [en]

    Protein collapse from a random chain to the native state involves a dynamical phase transition. During the process, new scales and collective variables become excited while old ones recede and fade away. The presence of different phases and many scales causes formidable computational bottle-necks in approaches that are based on full atomic scale scrutiny. Here we propose a way to describe the folding and unfolding processes effectively, using only the biologically relevant time and distance scales. We merge a coarse grained Landau theory that models the static collapsed protein in the low-temperature limit with a Glauber protocol that describes finite-temperature relaxation dynamics in a statistical system which is out of thermal equilibrium. As an example we inspect the collapse of a HP35 chicken villin headpiece subdomain, a paradigm specimen in protein folding studies. We simulate the folding and unfolding process by repeated heating and cooling cycles between a given low-temperature, i.e. bad solvent, environment where the protein is collapsed and various different high-temperature, i.e. good solvent, environments. We find that as long as the high temperature value stays below a value in the range that separates the random walk phase from the self-avoiding walk phase, we consistently recover the native state upon cooling. But, when heated to sufficiently high temperatures, the native state practically never recurs. Our result confirms Anfinsen's thermodynamical hypothesis and estimates a temperature range for its validity, in the case of villin.

  • 29.
    Krokhotin, Andrey
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Nicolis, Stam
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Long range correlations and folding angle with applications to alpha-helical proteins2014In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 140, no 9, p. 095103-Article in journal (Refereed)
    Abstract [en]

    The conformational complexity of chain-like macromolecules such as proteins and other linear polymers is much larger than that of point-like atoms and molecules. Unlike particles, chains can bend, twist, and even become knotted. Thus chains might also display a much richer phase structure. Unfortunately, it is not very easy to characterize the phase of a long chain. Essentially, the only known attribute is the radius of gyration. The way how it changes when the degree of polymerization becomes different, and how it evolves when the ambient temperature and solvent properties change, is commonly used to disclose the phase. But in any finite length chain there are corrections to scaling that complicate the detailed analysis of the phase structure. Here we introduce a quantity that we call the folding angle to identify and scrutinize the phase structure, as a complement to the radius of gyration. We argue for a mean-field level relationship between the folding angle and the scaling exponent in the radius of gyration. We then estimate the value of the folding angle in the case of crystallographic a-helical protein structures in the Protein Data Bank. We also show how the experimental value of the folding angle can be obtained computationally, using a semiclassical Born-Oppenheimer description of alpha-helical chiral chains. (C) 2014 AIP Publishing LLC.

  • 30.
    Krokhotin, Andrey
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Peng, Xubiao
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics2013In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 138, no 17, p. 175101-Article in journal (Refereed)
    Abstract [en]

    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 Schrodinger 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 Theta-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.

  • 31.
    Liu, Jiaojiao
    et al.
    Beijing Inst Technol, Sch Phys, Beijing 100081, Peoples R China..
    Dai, Jin
    Beijing Inst Technol, Sch Phys, Beijing 100081, Peoples R China..
    He, Jianfeng
    Beijing Inst Technol, Sch Phys, Beijing 100081, Peoples R China..
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Beijing Inst Technol, Sch Phys, Beijing 100081, Peoples R China.;Stockholm Univ, Nordita, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.;Univ Tours, Federat Denis Poisson, Lab Math & Phys Theor, CNRS,UMR 6083, Parc Grandmt, F-37200 Tours, France.;Far Eastern Fed Univ, Sch Biomed, Phys Living Matter, Vladivostok 690950, Russia..
    Ilieva, Nevena
    Bulgarian Acad Sci, Inst Informat & Commun Technol, 25A Acad G Bonchev Str, BU-1113 Sofia, Bulgaria..
    Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 95, no 3, article id 032406Article in journal (Refereed)
    Abstract [en]

    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 modeling 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 C alpha 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 C alpha profile with ultrahigh 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 analyze the thermal stability of this Glauber attractor using room-temperature molecular dynamics. We identify and scrutinize 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 alpha 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.

  • 32. Liwo, Jozef A.
    et al.
    Sieradzan, Adam K.
    He, Yi
    Krupa, Pawel
    Czaplewski, Cezary R.
    Krokhotin, Andrey
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Scheraga, Harold A.
    Origin of the Architecture of Biological Macromolecules - A Mean-Field Perspective2014In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 106, no 2, p. 256A-256AArticle in journal (Other academic)
    Abstract [en]

    The structures of the key classes of biological macromolecules: proteins, nucleic acids and polysaccharides can be dissected into very regular motifs, which are alpha-, beta, and double helices and sheets. In this communication we demonstrate that these regular patterns arise as a result of dipole-dipole interactions of the polar groups (peptide, nucleic-acid-base or sugar-ring groups) and the coupling of these interactions with backbone-local interactions, described at the mean-field level; the averaging is carried out by rotating the dipole of a polar unit about its virtual-bond axis.

  • 33.
    Lubcke, M.
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Nasir, S. M.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Niemi, A
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Torokoff, K.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Twisted plasma column2002In: Phys. Lett., Vol. B534, p. 195-200Article in journal (Refereed)
    Abstract [en]

    We inspect a particular gauge field theory model that describes the properties of a variety of physical systems, including a charge neutral two-component plasma, a Gross-Pitaevskii functional of two charged Cooper pair condensates, and a limiting case of the bosonic sector in the Salam-Weinberg model. It has been argued that this field theory model also admits stable knot-like solitons. Here we produce numerical evidence in support for the existence of these solitons, by considering stable axis-symmetric solutions that can be thought of as straight twisted vortex lines clamped at the two ends. We compute the energy of these solutions as a function of the amount of twist per unit length. The result can be described in terms of a energy spectral function. We find that this spectral function acquires a minimum which corresponds to a nontrivial twist per unit length, strongly suggesting that the model indeed supports stable toroidal solitons.

  • 34.
    Lubcke, M
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Niemi,
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Torokoff, K.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Asymptotically free Yang-Mills classical mechanics with self-linked orbits2003In: Phys. Lett., Vol. B568, p. 176-180Article in journal (Refereed)
  • 35.
    Lundgren, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Krokhotin, Andrey
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Topology and structural self-organization in folded proteins2013In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 88, no 4, p. 042709-Article in journal (Refereed)
    Abstract [en]

    Topological methods are indispensable in theoretical studies of particle physics, condensed matter physics, and gravity. These powerful techniques have also been applied to biological physics. For example, knowledge of DNA topology is pivotal to the understanding as to how living cells function. Here, the biophysical repertoire of topological methods is extended, with the aim to understand and characterize the global structure of a folded protein. For this, the elementary concept of winding number of a vector field on a plane is utilized to introduce a topological quantity called the folding index of a crystallographic protein. It is observed that in the case of high resolution protein crystals, the folding index, when evaluated over the entire length of the crystallized protein backbone, has a very clear and strong propensity towards integer values. The observation proposes that the way how a protein folds into its biologically active conformation is a structural self-organization process with a topological facet that relates to the concept of solitons. It is proposed that the folding index has a potential to become a useful tool for the global, topological characterization of the folding pathways.

  • 36.
    Lundgren, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Correlation between protein secondary structure, backbone bond angles, and side-chain orientations2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, no 2, p. 021904-Article in journal (Refereed)
    Abstract [en]

    We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C-alpha 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-beta carbon orientations. The energy function can model the side-chain geometry with a subatomic precision. As an example we construct the C-alpha-C-beta structure of HP35 chicken villin headpiece. We obtain a configuration that deviates less than 0.4 angstrom in root-mean-square distance from the experimental x-ray structure.

  • 37.
    Lundgren, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Niemi, Antti
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Sha, Fan
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Protein loops, solitons and side-chain visualization with applications to the left-handed helix region2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 85, no 6, p. 061909-Article in journal (Refereed)
    Abstract [en]

    Folded proteins have a modular assembly. They are constructed from regular secondary structures like alpha helices and beta strands that are joined together by loops. Here we develop a visualization technique that is adapted to describe this modular structure. In complement to the widely employed Ramachandran plot that is based on toroidal geometry, our approach utilizes the geometry of a two sphere. Unlike the more conventional approaches that describe only a given peptide unit, ours is capable of describing the entire backbone environment including the neighboring peptide units. It maps the positions of each atom to the surface of the two-sphere exactly how these atoms are seen by an observer who is located at the position of the central C-alpha atom. At each level of side-chain atoms we observe a strong correlation between the positioning of the atom and the underlying local secondary structure with very little if any variation between the different amino acids. As a concrete example we analyze the left-handed helix region of nonglycyl amino acids. This region corresponds to an isolated and highly localized residue independent sector in the direction of the C-beta carbons on the two-sphere. We show that the residue independent localization extends to C gamma and C-delta carbons and to side-chain oxygen and nitrogen atoms in the case of asparagine and aspartic acid. When we extend the analysis to the side-chain atoms of the neighboring residues, we observe that left-handed beta turns display a regular and largely amino acid independent structure that can extend to seven consecutive residues. This collective pattern is due to the presence of a backbone soliton. We show how one can use our visualization techniques to analyze and classify the different solitons in terms of selection rules that we describe in detail.

  • 38.
    Molochkov, Alexander
    et al.
    Far Eastern Fed Univ, Lab Phys Living Matter, Sukhanova 8, Vladivostok 690950, Russia..
    Begun, Alexander
    Far Eastern Fed Univ, Lab Phys Living Matter, Sukhanova 8, Vladivostok 690950, Russia..
    Niemi, Antti
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Univ Tours, Lab Math & Phys Theor, Federat Denis Poisson, France.; Beijing Inst Technol, Dept Phys, Beijing, Peoples R China..
    Gauge symmetries and structure of proteins2017In: XIITH QUARK CONFINEMENT AND THE HADRON SPECTRUM / [ed] Foka, Y Brambilla, N Kovalenko, V, E D P SCIENCES , 2017, article id UNSP 04004Conference paper (Refereed)
    Abstract [en]

    We discuss the gauge field theory approach to protein structure study, which allows a natural way to introduce collective degrees of freedom and nonlinear topological structures. Local symmetry of proteins and its breaking in the medium is considered, what allows to derive Abelian Higgs model of protein backbone, correct folding of which is defined by gauge symmetry breaking due hydrophobic forces. Within this model structure of protein backbone is defined by superposition of one-dimensional topological solitons (kinks), what allows to reproduce the three-dimensional structure of the protein backbone with precision up to 1A and to predict its dynamics.

  • 39.
    Morozov, Alexei
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Can renormalization group flow end in a big mess?2003In: Nucl. Phys., Vol. B666, p. 311-336Article in journal (Refereed)
  • 40.
    Nasedkin, Alexandr
    et al.
    Chalmers Univ Technol, Dept Phys, Gothenburg.
    Davidsson, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Physical Chemistry.
    Niemi, Antti J.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Chalmers Univ Technol, Dept Phys, Gothenburg; Stockholm Univ, NORDITA, Stockholm; Univ Tours, Federat Denis Poisson, CNRS UMR 6083, Lab Math & Phys Theor, Parc Grandmont, Tours; Beijing Inst Technol, Sch Phys, Beijing; Far Eastern Fed Univ, Sch Biomed, Lab Phys Living Matter, Vladivostok.
    Peng, Xubiao
    Univ British Columbia, Dept Phys & Astron, Vancouver.
    Solution x-ray scattering and structure formation in protein dynamics2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 6, article id 062405Article in journal (Refereed)
    Abstract [en]

    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.

  • 41. Nasir, S.
    et al.
    Niemi, A
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Effective string theories and field theories in four dimensions2002In: Mod. Phys. Lett., Vol. A17, p. 1445-1453Article in journal (Refereed)
  • 42.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Are glueballs knotted closed strings?2003In: Wako 2003, Color confinement and hadrons in quantum chromodynamics, 2003Conference paper (Other scientific)
    Abstract [en]

    Glueballs have a natural interpretation as closed strings in Yang-Mills theory. Their stability requires that the string carries a nontrivial twist, or then it is knotted. Since a twist can be either left-handed or right-handed, this implies that the glueball spectrum must be degenerate. This degeneracy becomes consistent with experimental observations, when we identify the $\eta_L(1410)$ component of the $\eta(1440)$ pseudoscalar as a $0^{-+}$ glueball, degenerate in mass with the widely accepted $0^{++}$ glueball $f_0(1500)$. In addition of qualitative similarities, we find that these two states also share quantitative similarity in terms of equal production ratios, which we view as further evidence that their structures must be very similar. We explain how our string picture of glueballs can be obtained from Yang-Mills theory, by employing a decomposed gauge field. We also consider various experimental consequences of our proposal, including the interactions between glueballs and quarks and the possibility to employ glueballs as probes for extra dimensions: The coupling of strong interactions to higher dimensions seems to imply that absolute color confinement becomes lost.

  • 43.
    Niemi, Antti
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Benchmark Computations of stresses in a spherical dome with shell finite elements2015Article in journal (Other academic)
  • 44.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics. Department of Physics and Materials Science, Theoretical Physics.
    Could Spin-Charge Separation be the Source of Confinement?2006In: AIP Conference Proceedings, Vol. 806, p. 114-123Article in journal (Other (popular scientific, debate etc.))
  • 45.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Dual Superconductors and SU(2) Yang-Mills2004In: JHEP 0408Article in journal (Refereed)
    Abstract [en]

    We propose that the SU(2) Yang-Mills theory can be interpreted as a two-band dual superconductor with an interband Josephson coupling. We discuss various consequences of this interpretation including electric flux quantization, confinement of vortices with fractional flux, and the possibility that a closed vortex loop exhibits exotic exchange statistics.

  • 46.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Phases of bosonic strings and two dimensional gauge theories2003In: Phys. Rev., Vol. D67, p. 106004-Article in journal (Refereed)
  • 47.
    Niemi, Antti
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Physics, Department of Theoretical Physics.
    Three dimensional gravity from SU(2) Yang-Mills theory in two dimensions2004In: Phys. Rev., Vol. D70, p. 045017-Article in journal (Refereed)
    Abstract [en]

    We argue that two dimensional classical SU(2) Yang-Mills theory describes the embedding of Riemann surfaces in three dimensional curved manifolds. Specifically, the Yang-Mills field strength tensor computes the Riemannian curvature tensor of the ambient space in a thin neighborhood of the surface. In this sense the two dimensional gauge theory then serves as a source of three dimensional gravity. In particular, if the three dimensional manifold is flat it corresponds to the vacuum of the Yang-Mills theory. This implies that all solutions to the original Gauss-Codazzi surface equations determine two dimensional integrable models with a SU(2) Lax pair. Furthermore, the three dimensional SU(2) Chern-Simons theory describes the Hamiltonian dynamics of two dimensional Riemann surfaces in a four dimensional flat space-time.

  • 48.
    Niemi, Antti
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    WHAT IS LIFE - Sub-cellular Physics of Live Matter2014Article in journal (Other academic)
    Abstract [en]

    This is a set of lectures that I presented at the Les Houches 2014 Summer School "Topological Aspects in Condensed Matter Physics". The lectures are an introduction to physics of proteins. To physicists, and by a physicist. My lectures at les Houches were also celebration of the anniversary of Schroedinger's 1944 lectures, and for that reason I decided to share my title with his book.

  • 49.
    Niemi, Antti
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Calo, Victor
    Collier, Nathaniel
    Analysis of the discontinuous Petrov–Galerkin method with optimal test functions for the Reissner–Mindlin plate bending model2014In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668Article in journal (Refereed)
  • 50.
    Niemi, Antti
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Collier, Nathaniel
    Calo, Victor
    Automatically stable discontinuous Petrov–Galerkin methods for stationary transport problems: Quasi-optimal test space norm2013In: Computers & Mathematics with Applications, ISSN 0898-1221Article in journal (Refereed)
    Abstract [en]

    We investigate the application of the discontinuous Petrov–Galerkin (DPG) finite element framework to stationary convection–diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view.

12 1 - 50 of 69
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