| 1. |
- Ilieva, N., et al.
(författare)
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Are There Folding Pathways in the Functional Stages of Intrinsically Disordered Proteins?
- 2016
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Ingår i: Application Of Mathematics In Technical And Natural Sciences (AMITANS'16). - 9780735414310
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 2. |
- Nummela, Aleksi J., et al.
(författare)
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Effects of dexmedetomidine, propofol, sevoflurane and S-ketamine on the human metabolome : A randomised trial using nuclear magnetic resonance spectroscopy
- 2022
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Ingår i: European Journal of Anaesthesiology. - : Wolters Kluwer. - 0265-0215 .- 1365-2346. ; 39:6, s. 521-532
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: Pharmacometabolomics uses large-scale data capturing methods to uncover drug-induced shifts in the metabolic profile. The specific effects of anaesthetics on the human metabolome are largely unknown.OBJECTIVE: We aimed to discover whether exposure to routinely used anaesthetics have an acute effect on the human metabolic profile.DESIGN: Randomised, open-label, controlled, parallel group, phase IV clinical drug trial.SETTING: The study was conducted at Turku PET Centre, University of Turku, Finland, 2016 to 2017.PARTICIPANTS: One hundred and sixty healthy male volunteers were recruited. The metabolomic data of 159 were evaluable.INTERVENTIONS: Volunteers were randomised to receive a 1-h exposure to equipotent doses (EC50 for verbal command) of dexmedetomidine (1.5 ng ml-1; n = 40), propofol (1.7 μg ml-1; n = 40), sevoflurane (0.9% end-tidal; n = 39), S-ketamine (0.75 μg ml-1; n = 20) or placebo (n = 20).MAIN OUTCOME MEASURES: Metabolite subgroups of apolipoproteins and lipoproteins, cholesterol, glycerides and phospholipids, fatty acids, glycolysis, amino acids, ketone bodies, creatinine and albumin and the inflammatory marker GlycA, were analysed with nuclear magnetic resonance spectroscopy from arterial blood samples collected at baseline, after anaesthetic administration and 70 min postanaesthesia.RESULTS: All metabolite subgroups were affected. Statistically significant changes vs. placebo were observed in 11.0, 41.3, 0.65 and 3.9% of the 155 analytes in the dexmedetomidine, propofol, sevoflurane and S-ketamine groups, respectively. Dexmedetomidine increased glucose, decreased ketone bodies and affected lipoproteins and apolipoproteins. Propofol altered lipoproteins, fatty acids, glycerides and phospholipids and slightly increased inflammatory marker glycoprotein acetylation. Sevoflurane was relatively inert. S-ketamine increased glucose and lactate, whereas branched chain amino acids and tyrosine decreased.CONCLUSION: A 1-h exposure to moderate doses of routinely used anaesthetics led to significant and characteristic alterations in the metabolic profile. Dexmedetomidine-induced alterations mirror α2-adrenoceptor agonism. Propofol emulsion altered the lipid profile. The inertness of sevoflurane might prove useful in vulnerable patients. S-ketamine induced amino acid alterations might be linked to its suggested antidepressive properties.TRIAL REGISTRATION: ClinicalTrials.gov identifier: NCT02624401. URL: https://clinicaltrials.gov/ct2/show/NCT02624401.
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| 3. |
- Alekseev, Anton, et al.
(författare)
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Provenance of classical Hamiltonian time crystals
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :8
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Tidskriftsartikel (refereegranskat)abstract
- Classical Hamiltonian systems with conserved charges and those with constraints often describe dynamics on a pre-symplectic manifold. Here we show that a pre-symplectic manifold is also the proper stage to describe autonomous energy conserving Hamiltonian time crystals. We explain how the occurrence of a time crystal relates to the wider concept of spontaneously broken symmetries; in the case of a time crystal, the symmetry breaking takes place in a dynamical context. We then analyze in detail two examples of timecrystalline Hamiltonian dynamics. The first example is a piecewise linear closed string, with dynamics determined by a Lie-Poisson bracket and Hamiltonian that relates to membrane stability. We explain how the Lie-Poisson brackets descents to a time-crystalline pre-symplectic bracket, and we show that the Hamiltonian dynamics supports two phases; in one phase we have a time crystal and in the other phase time crystals are absent. The second example is a discrete one dimensional model of a Hamiltonian chain. It is obtained by a reduction from the Q-ball Lagrangian that describes time dependent nontopological solitons. We show that a time crystal appears as a minimum energy domain wall configuration, along the chain.
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| 4. |
- Begun, Alexander, et al.
(författare)
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On topology and knotty entanglement in protein folding
- 2021
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Ingår i: PLOS ONE. - : Public Library of Science (PLoS). - 1932-6203. ; 16:1
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Tidskriftsartikel (refereegranskat)abstract
- We investigate aspects of topology in protein folding. For this we numerically simulate the temperature driven folding and unfolding of the slipknotted archaeal virus protein AFV3-109. Due to knottiness the (un)folding is a topological process, it engages the entire backbone in a collective fashion. Accordingly we introduce a topological approach to model the process. Our simulations reveal that the (un)folding of AFV3-109 slipknot proceeds through a folding intermediate that has the topology of a trefoil knot. We observe that the final slipknot causes a slight swelling of the folded AFV3-109 structure. We disclose the relative stability of the strands and helices during both the folding and unfolding processes. We confirm results from previous studies that pointed out that it can be very demanding to simulate the formation of knotty self-entanglement, and we explain how the problems are circumvented: The slipknotted AFV3-109 protein is a very slow folder with a topologically demanding pathway, which needs to be properly accounted for in a simulation description. When we either increase the relative stiffness of bending, or when we decrease the speed of ambient cooling, the rate of slipknot formation rapidly increases.
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| 5. |
- Begun, Alexander, et al.
(författare)
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Protein tertiary structure and the myoglobin phase diagram
- 2019
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Ingår i: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 9
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Tidskriftsartikel (refereegranskat)abstract
- We develop an effective theory approach to investigate the phase properties of globular proteins. Instead of interactions between individual atoms or localized interaction centers, the approach builds directly on the tertiary structure of a protein. As an example we construct the phase diagram of (apo) myoglobin with temperature (T) and acidity (pH) as the thermodynamical variables. We describe how myoglobin unfolds from the native folded state to a random coil when temperature and acidity increase. We confirm the presence of two molten globule folding intermediates, and we predict an abrupt transition between the two when acidity changes. When temperature further increases we find that the abrupt transition line between the two molten globule states terminates at a tricritical point, where the helical structures fade away. Our results also suggest that the ligand entry and exit is driven by large scale collective motions that destabilize the myoglobin F-helix.
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| 6. |
- Chen, Si, et al.
(författare)
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On Ramachandran angles, closed strings and knots in protein structure
- 2016
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Ingår i: Journal of Physics D. - : IOP Publishing. - 0022-3727 .- 1361-6463. ; 49:31
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Chernodub, M. N., et al.
(författare)
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Baryon number violation and a new electroweak interaction
- 2009
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Ingår i: Physical Review D. - 1550-7998. ; 79:7, s. 077901-
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a new supercurrent in the electroweak sector of the standard model. Its interaction with the hypergauge field influences the mass of the Z boson but has no effect on the W-+/- boson masses. In the leptonic sector it affects the numerical value of the vector and axial coupling constants between neutral currents and the Z boson, and a comparison with experimental values yields an upper bound to the strength of the coupling between the supercurrent and the hypergauge field. In the baryonic sector the supercurrent gives a new contribution to the anomaly equation for baryon number current. As a consequence it may have an effect on baryogenesis.
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| 8. |
- Chernodub, M.N., et al.
(författare)
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Elastic Energy and Phase Structure in a Continuous Spin Ising Chain with Applications to the Protein Folding Problem
- 2011
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 83:1
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Tidskriftsartikel (refereegranskat)abstract
- We present a numerical Monte Carlo analysis of a continuos spin Ising chain that can describe the statistical proterties of folded proteins. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a cross-over transition. We also compare the predictions of the model to a phenomenological elastic energy formula, proposed by Huang and Lei to describe folded proteins.
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| 9. |
- Chernodub, M. N., et al.
(författare)
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Embedding Brans-Dicke gravity into electroweak theory
- 2008
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Ingår i: Physical Review D. - 1550-7998 .- 1550-2368. ; 77:12, s. 127902-
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 10. |
- Chernodub, M. N., et al.
(författare)
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Non-abelian supercurrents and de Sitter ground state in electroweak theory
- 2008
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :12, s. 014-
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Tidskriftsartikel (refereegranskat)abstract
- We show that gauge symmetry breaking in the Weinberg-Salam model can be implemented by a mere change of variables and without any explicit gauge fixing. The change of variables entails the concept of supercurrent which has been widely employed in the study of superconductivity. It also introduces a separation between the isospin and the hypercharge, suggesting that our new variables describe a strongly coupled regime of the electroweak theory. We discuss the description of various embedded topological defects in terms of these variables. We also propose that in terms of our variables the Weinberg-Salam model can be interpreted in terms of a gravity theory with the modulus of Higgs field as dilaton and the de Sitter space as the ground state.
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| 11. |
- Chernodub, Maxim N., et al.
(författare)
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Spin-Charge Separation and the Pauli Electron
- 2007
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Ingår i: JETP Letters. - 0021-3640 .- 1090-6487. ; 85:8, s. 353-357
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Tidskriftsartikel (refereegranskat)abstract
- The separation between the spin and the charge converts the quantum mechanical Pauli Hamiltonian into the Hamiltonian of the non-Abelian Georgi-Glashow model, which is notorious for its magnetic monopoles and confinement. The independent spin and charge fluctuations both lead to the Faddeev model, suggesting the existence of a deep duality structure and indicating that the fundamental carriers of the spin and charge are knotted solitons.
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| 12. |
- Chernodub, Maxim, et al.
(författare)
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Topological solitons and folded proteins
- 2010
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 82:1, s. 011916-
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Tidskriftsartikel (refereegranskat)abstract
- We argue that protein loops can be described by topological domain-wall solitons that interpolate between ground states which are the alpha helices and beta strands. We present an energy function that realizes loops as soliton solutions to its equation of motion, and apply these solitons to model a number of biologically active proteins including 1VII, 2RB8, and 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to numerically construct soliton solutions that reproduce secondary structural motifs such as alpha-helix-loop-alpha-helix and beta-sheet-loop-beta-sheet with an overall root-mean-square-distance accuracy of around 1.0 angstrom or less for the central alpha-carbons, i.e., close to the limits of current experimental accuracy.
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| 13. |
- Dai, Jin, et al.
(författare)
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Autonomous topological time crystals and knotty molecular motors
- 2021
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Ingår i: Journal of Physics. - 0953-8984 .- 1361-648X. ; 33:1
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Tidskriftsartikel (refereegranskat)abstract
- We show that topology is a very effective tool, to construct classical Hamiltonian time crystals. For this we numerically analyze a general class of time crystalline Hamiltonians that are designed to model the dynamics of molecular closed strings. We demonstrate how the time crystalline qualities of a closed string are greatly enhanced when the string becomes knotted. The Hamiltonians that we investigate include a generalized Kratky-Porod wormlike chain model in combination with long range Coulomb and Lennard-Jones interactions. Such energy functions are commonplace in coarse grained molecular modeling. Thus we expect that physical realizations of Hamiltonian time crystals can be constructed in terms of knotted ring molecules.
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| 14. |
- Dai, Jin, et al.
(författare)
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Classical Hamiltonian time crystals-general theory and simple examples
- 2020
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 22:8
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Tidskriftsartikel (refereegranskat)abstract
- We focus on a Hamiltonian system with a continuous symmetry, and dynamics that takes place on a presymplectic manifold. We explain how the symmetry can become spontaneously broken by a time crystal, that we define as the minimum of the available mechanical free energy that is simultaneously a time dependent solution of Hamilton's equation. The mathematical description of such a timecrystalline spontaneous symmetry breaking builds on concepts of equivariant Morse theory in the space of Hamiltonian flows. As an example we analyze a general family of timecrystalline Hamiltonians that is designed to model polygonal, piecewise linear closed strings. The vertices correspond to the locations of pointlike interaction centers; the string is akin a chain of atoms, that are joined together by covalent bonds, modeled by the links of the string. We argue that the timecrystalline character of the string can be affected by its topology. For this we show that a knotty string is usually more timecrystalline than a string with no self-entanglement. We also reveal a relation between phase space topology and the occurrence of timecrystalline dynamics. For this we show that in the case of three point particles, the presence of a time crystal can relate to a Dirac monopole that resides in the phase space. Our results propose that physical examples of Hamiltonian time crystals can be realized in terms of closed, knotted molecular rings.
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| 15. |
- Dai, Jin, et al.
(författare)
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Conformational landscape of an amyloid intra-cellular domain and Landau-Ginzburg-Wilson paradigm in protein dynamics
- 2016
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 145:4
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Tidskriftsartikel (refereegranskat)abstract
- The Landau-Ginzburg-Wilson paradigm is proposed as a framework, to investigate the conformational landscape of intrinsically unstructured proteins. A universal Ca-trace Landau free energy is deduced from general symmetry considerations, with the ensuing all-atom structure modeled using publicly available reconstruction programs Pulchra and Scwrl. As an example, the conformational stability of an amyloid precursor protein intra-cellular domain (AICD) is inspected; the reference conformation is the crystallographic structure with code 3DXC in Protein Data Bank (PDB) that describes a heterodimer of AICD and a nuclear multi-domain adaptor protein Fe65. Those conformations of AICD that correspond to local or near-local minima of the Landau free energy are identified. For this, the response of the original 3DXC conformation to variations in the ambient temperature is investigated, using the Glauber algorithm. The conclusion is that in isolation the AICD conformation in 3DXC must be unstable. A family of degenerate conformations that minimise the Landau free energy is identified, and it is proposed that the native state of an isolated AICD is a superposition of these conformations. The results are fully in line with the presumed intrinsically unstructured character of isolated AICD and should provide a basis for a systematic analysis of AICD structure in future NMR experiments.
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| 16. |
- Dai, Jin, et al.
(författare)
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SU(2) Lie-Poisson algebra and its descendants
- 2022
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Ingår i: Physical Review D. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 106:5
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, a novel discrete algebra is presented which follows by combining the SU(2) Lie-Poisson bracket with the discrete Frenet equation. Physically, the construction describes a discrete piecewise linear string in R3. The starting point of our derivation is the discrete Frenet frame assigned at each vertex of the string. Then the link vector that connects the neighboring vertices is assigned the SU(2) Lie-Poisson bracket. Moreover, the same bracket defines the transfer matrices of the discrete Frenet equation which relates two neighboring frames along the string. The procedure extends in a self-similar manner to an infinite hierarchy of Poisson structures. As an example, the first descendant of the SU(2) Lie-Poisson structure is presented in detail. For this, the spinor representation of the discrete Frenet equation is employed, as it converts the brackets into a computationally more manageable form. The final result is a nonlinear, nontrivial, and novel Poisson structure that engages four neighboring vertices.
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| 17. |
- Dai, Jin, et al.
(författare)
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Truncated dynamics, ring molecules, and mechanical time crystals
- 2019
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : AMER PHYSICAL SOC. - 2469-9926 .- 2469-9934. ; 99:2
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Tidskriftsartikel (refereegranskat)abstract
- We identify circumstances where the effective descriptions of microscopic physical systems leads to a self-consistent reduced dynamics for a truncated subset of the original variables. The effective Hamiltonian involves unusual Poisson brackets that bring in noncommutative geometry. In idealized models of ring molecules, we find time crystal behavior is widespread.
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| 18. |
- Danielsson, Ulf H., et al.
(författare)
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Gauge field theory of chirally folded homopolymers with applications to folded proteins
- 2010
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Ingår i: Physical Review E. - 1539-3755. ; 82:2, s. 021910-
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Tidskriftsartikel (refereegranskat)abstract
- We combine the principle of gauge invariance with extrinsic string geometry to develop a lattice model that can be employed to theoretically describe properties of chiral, unbranched homopolymers. We find that in its low temperature phase the model is in the same universality class with proteins that are deposited in the Protein Data Bank, in the sense of the compactness index. We apply the model to analyze various statistical aspects of folded proteins. Curiously we find that it can produce results that are a very good good match to the data in the Protein Data Bank.
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| 19. |
- Faddeev, Ludwig D., et al.
(författare)
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Shafranov's virial theorem and magnetic plasma confinement
- 2002
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Ingår i: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 35:11, s. L133-L139
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 20. |
- Faddeev, Ludvig D., et al.
(författare)
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Spin-charge separation, conformal covariance and the SU(2) Yang–Mills theory
- 2007
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Ingår i: Nuclear Physics B. - : Elsevier BV. - 0550-3213 .- 1873-1562. ; 776:1-2, s. 38-65
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Tidskriftsartikel (refereegranskat)abstract
- In the low energy domain of four-dimensional SU(2) Yang–Mills theory the spin and the charge of the gauge field can become separated from each other. The ensuing field variables describe the interacting dynamics between a version of the O(3) nonlinear σ-model and a nonlinear Grassmannian σ-model, both of which may support closed knotted strings as stable solitons. Lorentz transformations act projectively in the O(3) model which breaks global internal rotation symmetry and removes massless Goldstone bosons from the particle spectrum. The entire Yang–Mills Lagrangian can be recast into a generally covariant form with a conformally flat metric tensor. The result contains the Einstein–Hilbert Lagrangian together with a nonvanishing cosmological constant, and insinuates the presence of a novel dimensionfull parameter in the Yang–Mills theory.
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| 21. |
- Freyhult, Lisa, et al.
(författare)
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Chirality and fermion number in a knotted soliton background
- 2003
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Ingår i: Physics Letters B. - 0370-2693 .- 1873-2445. ; 557:1-2, s. 121-124
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 22. |
- Garaud, Julien, et al.
(författare)
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Poincaré index formula and analogy with the Kosterlitz-Thouless transition in a non-rotated cold atom Bose-Einstein condensate
- 2022
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :9
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Tidskriftsartikel (refereegranskat)abstract
- A dilute gas of Bose-Einstein condensed atoms in a non-rotated and axially symmetric harmonic trap is modelled by the time dependent Gross-Pitaevskii equation. When the angular momentum carried by the condensate does not vanish, the minimum energy state describes vortices (or antivortices) that propagate around the trap center. The number of (anti)vortices increases with the angular momentum, and they repel each other to form Abrikosov lattices. Besides vortices and antivortices there are also stagnation points where the superflow vanishes; to our knowledge the stagnation points have not been analyzed previously, in the context of the Gross-Pitaevskii equation. The Poincare index formula states that the difference in the number of vortices and stagnation points can never change. When the number of stagnation points is small, they tend to aggregate into degenerate propagating structures. But when the number becomes sufficiently large, the stagnation points tend to pair up with the vortex cores, to propagate around the trap center in regular lattice arrangements. There is an analogy with the geometry of the Kosterlitz-Thouless transition, with the angular momentum of the condensate as the external control parameter instead of the temperature.
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| 23. |
- Garaud, Julien, et al.
(författare)
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Vortex precession and exchange in a Bose-Einstein condensate
- 2021
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :7
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Tidskriftsartikel (refereegranskat)abstract
- Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially symmetric trap, the core of a single vortex precesses around the trap center and, at the same time, the phase of its wave function shifts at a constant rate. The precession velocity, the speed of phase shift, and the distance between the vortex core and the trap center, depend continuously on the value of the conserved angular momentum that is carried by the entire condensate. In the case of a symmetric pair of identical vortices, the precession engages an emergent gauge field in their relative coordinate, with a flux that is equal to the ratio between the precession and shift velocities.
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| 24. |
- He, Jianfeng, et al.
(författare)
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Aspects of structural landscape of human islet amyloid polypeptide
- 2015
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 142:4
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Tidskriftsartikel (refereegranskat)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 a-helical conformations that might cause the transition to amyloidosis, by nucleation.
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| 25. |
- Hinsen, Konrad, et al.
(författare)
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A comparison of reduced coordinate sets for describing protein structure
- 2013
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 139:12, s. 124115-
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 26. |
- Hinsen, Konrad, et al.
(författare)
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On Coarse Grained Representations And the Problem of Protein Backbone Reconstruction
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Crystallographic protein structures reveal that generically, only two of the Ramachandran angles are flexible. The third Ramachandran angle, all the backbone bond angles, and also all the covalent bond lengths are quite rigid, displaying only insignificant deviations from their optimal values. This empirical observation is among the rationale for the construction of coarse grained force fields where only a subset of the full set of atomic coordinates is utilized as dynamically active variables. The present article addresses in a systematic manner the question, to what extent the various angles andbond lengths can be replaced by their optimal values. In the case of bond lengths, it is found that the optimal values are in practice sufficient. But a coarse graining where a subset of angular variables is replaced by optimal values, commonly yields geometrically incorrect protein structures. There appears to be an inherent numerical instability, which seems to reflect the presence of a positive Liapunov exponent in the iterative reconstruction algorithm. Besides the full and complete set of individual atomic angles, essentially only one numerically stable coarse grained subset of angular variables is found. It consists of variable virtual Cα backbone bond and torsion angles. In combination with fixed, constant valued virtual bond lengths these two angles reproduce the original structure with high precision. The present observations impose strong limitations on the subset of backbone coordinates that can be utilized, even in principle, for the development of coarse grained force fields.
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| 27. |
- Hou, Yanzhen, et al.
(författare)
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Intrinsic protein geometry with application to non-proline cis peptide planes
- 2019
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Ingår i: Journal of Mathematical Chemistry. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 57:1, s. 263-279
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Tidskriftsartikel (refereegranskat)abstract
- The shape of a protein can be modeled by the C atoms of its backbone, the mathematical description employing the notion of extrinsic geometry of a discrete piecewise linear chain. We advance differential geometry of a natively framed discrete chain to argue the existence of two additional, independent and intrinsic geometric structures, provided by the peptide planes and side chains, respectively. We develop our general methodology within a case study: analysis of the intrinsic geometry of atoms that are located around a non-proline cis peptide plane. We show that the native peptide plane framing allows for revealing of atomic positions anomalies. That way, we identify a number of entries that display such anomalies around their non-proline cis peptide planes within the ultrahigh-resolution structures in PDB. We propose that our approach can be extended into a visual analysis and refinement tool that is applicable even when resolution is limited or data is incomplete, for example when there are atoms missing in an experimental construct.
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| 28. |
- Hou, Yanzhen, et al.
(författare)
-
Myoglobin ligand gate mechanism analysis by a novel 3D visualization technique
- 2019
-
Ingår i: Journal of Mathematical Chemistry. - : Springer Science and Business Media LLC. - 0259-9791 .- 1572-8897. ; 57:6, s. 1586-1597
-
Tidskriftsartikel (refereegranskat)abstract
- A protein is commonly visualized as a discrete piecewise linear curve, conventionally characterized in terms of the extrinsically determined Ramachandran angles. However, in addition to the extrinsic geometry, the protein has also two independent intrinsic geometric structures, determined by the peptide planes and the side chains respectively. Here we develop a novel 3D visualization method that instead of the extrinsic geometry utilizes the intrinsic geometry of side chains. We base our approach on a series of orthonormal coordinate frames along the protein side chains in combination with a mapping of the atoms positions onto a unit sphere, for visualization purposes. We develop our methodology in terms of an example, by analyzing the acidity dependence of the presumed myoglobin ligand gate. In the literature, the ligand gate is often asserted to be highly localized at the distal histidine, its functioning being regulated by environmental changes. Thus, we investigate whether any pH dependence can be detected in the orientation of the distal and proximal histidine residues, using existing crystallographic data. We observe no pH dependence, in support of the alternative proposals that the ligand gate is more complex and might even be located elsewhere. Our methodology should help the planning of future myoglobin structure experiments, to identify the ligand gate position and its mechanism. More generally, our methodology is designed to visually depict the spatial orientation of side chain covalent bonds in a protein. As such, it can be eventually advanced into a general visual 3D tool for protein structure analysis for purposes of prediction, validation and refinement. It can serve as a complement to widely used visualization suites such as VMD, Jmol, PyMOL and others.
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| 29. |
- Hou, Yanzhen, et al.
(författare)
-
Study of correlations between protein peptide plane dynamics and side chain dynamics
- 2019
-
Ingår i: PLOS ONE. - : Public Library of Science (PLoS). - 1932-6203. ; 14:4
-
Tidskriftsartikel (refereegranskat)abstract
- Protein dynamics is pivotal to biological processes. However, experiments are very demanding and difficult to perform, and all-atom molecular dynamics simulations can still not provide all the answers. This motivates us to analyze protein dynamics in terms of different reduced coordinate representations. We then need to resolve how to reconstruct the full all-atom dynamics from its coarse grained approximation. Accordingly we scrutinize all-atom molecular dynamics trajectories in terms of crystallographic Protein Data Bank (PDB) structures, and inquire to what extent is it possible to predict the dynamics of side chain C beta atoms in terms of the static properties of backbone Ca and O atoms. Here we find that simulated C beta dynamics at near physiological conditions can be reconstructed with very high precision, using the knowledge of the crystallographic backbone Ca and O positions. The precision we can reach with our PDB-based Statistical Method reconstruction exceeds that of popular all-atom reconstruction methods such as Remo and Pulchra, and is fully comparable with the precision of the highly elaborate Scwrl4 all-atom reconstruction method that we have enhanced with the knowledge of the backbone Ca and O atom positions. We then conclude that in a dynamical protein that moves around at physiological conditions, the relative positions of its C beta atoms with respect to the backbone Ca and O atoms, deviate very little from their relative positions in static crystallographic PDB structures. This proposes that the dynamics of a biologically active protein could remain subject to very similar, stringent stereochemical constraints that dictate the structure of a folded crystallographic protein. Thus, our results provide a strong impetus to the development of coarse grained techniques that are based on reduced coordinate representations.
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| 30. |
- Hu, Shuangwei, et al.
(författare)
-
Discrete Frenet frame, inflection point solitons, and curve visualization with applications to folded proteins
- 2011
-
Ingår i: Physical Review E. - 1539-3755. ; 83:6, s. 061908-
-
Tidskriftsartikel (refereegranskat)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-beta carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this C-beta framing relates intimately to the discrete Frenet framing. We also explain how inflection points (a.k.a. soliton centers) can be located in the loops and clarify their distinctive role in determining the loop structure of folded proteins.
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| 31. |
- Hu, Shuangwei
(författare)
-
Dynamics of Discrete Curves with Applications to Protein Structure
- 2013
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In order to perform a specific function, a protein needs to fold into the proper structure. Prediction the protein structure from its amino acid sequence has still been unsolved problem. The main focus of this thesis is to develop new approach on the protein structure modeling by means of differential geometry and integrable theory. The start point is to simplify a protein backbone as a piecewise linear polygonal chain, with vertices recognized as the central alpha carbons of the amino acids. Frenet frame and equations from differential geometry are used to describe the geometric shape of the protein linear chain. Within the framework of integrable theory, we also develop a general geometrical approach, to systematically derive Hamiltonian energy functions for piecewise linear polygonal chains. These theoretical studies is expected to provide a solid basis for the general description of curves in three space dimensions. An efficient algorithm of loop closure has been proposed.
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| 32. |
- Hu, Shuangwei, et al.
(författare)
-
Energy functions for stringlike continuous curves, discrete chains, and space-filling one dimensional structures
- 2013
-
Ingår i: Physical Review D. - : APS. - 1550-7998 .- 1550-2368. ; 87:10, s. 105011-
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 33. |
- Hu, Shuangwei, et al.
(författare)
-
Towards quantitative classification of folded proteins in terms of elementary functions
- 2011
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 83:4, s. 041907-
-
Tidskriftsartikel (refereegranskat)abstract
- A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a classification scheme that describes a protein starting from its well-organized secondary structures and often involves direct human involvement, with an atomary-level physics-based approach where a protein is fundamentally nothing more than an ensemble of mutually interacting carbon, hydrogen, oxygen, and nitrogen atoms. In order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced. Here we explain how an approach toward geometric characterization of entire folded proteins can be based on a single explicit elementary function that is familiar from nonlinear physical systems where it is known as the kink soliton. Our approach enables the conversion of hierarchical structural information into a quantitative form that allows for a folded protein to be characterized in terms of a small number of global parameters that are in principle computable from atomary-level considerations. As an example we describe in detail how the native fold of the myoglobin 1M6C emerges from a combination of kink solitons with a very high atomary-level accuracy. We also verify that our approach describes longer loops and loops connecting alpha helices with beta strands, with the same overall accuracy.
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| 34. |
- Ilieva, N., et al.
(författare)
-
Solitons And Protein Folding : An In Silico Experiment
- 2015
-
Ingår i: Application of Mathematics in Technical and Natural Sciences (AMiTaNS'15). - : AIP Publishing LLC. - 9780735413313
-
Konferensbidrag (refereegranskat)abstract
- 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.
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| 35. |
- Ioannidou, Theodora, et al.
(författare)
-
Poisson hierarchy of discrete strings
- 2016
-
Ingår i: Physics Letters A. - : Elsevier BV. - 0375-9601 .- 1873-2429. ; 380:3, s. 333-336
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 36. |
- Ioannidou, Theodora, et al.
(författare)
-
Spinors, strings, integrable models, and decomposed Yang-Mills theory
- 2014
-
Ingår i: Physical Review D. - 1550-7998 .- 1550-2368. ; 90:2, s. 025012-
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 37. |
- Kachlishvili, Khatuna, et al.
(författare)
-
New Insights into Folding, Misfolding, and Nonfolding Dynamics of a WW Domain
- 2020
-
Ingår i: Journal of Physical Chemistry B. - : American Chemical Society (ACS). - 1520-6106 .- 1520-5207. ; 124:19, s. 3855-3872
-
Tidskriftsartikel (refereegranskat)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 similar to 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 beta-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 Schrodinger equation. We show that the formation of each beta-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 similar to 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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| 38. |
- Krokhotin, Andrey, et al.
(författare)
-
Coexistence of phases in a protein heterodimer
- 2012
-
Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 137:3, s. 035101-
-
Tidskriftsartikel (refereegranskat)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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| 39. |
- Krokhotin, Andrey, et al.
(författare)
-
Kinks, loops, and protein folding, with protein A as an example
- 2014
-
Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 140:2, s. 025101-
-
Tidskriftsartikel (refereegranskat)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 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.
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| 40. |
- Krokhotin, Andrey, et al.
(författare)
-
Long range correlations and folding angle with applications to alpha-helical proteins
- 2014
-
Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 140:9, s. 095103-
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 41. |
- Krokhotin, Andrey, et al.
(författare)
-
On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics
- 2013
-
Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 138:17, s. 175101-
-
Tidskriftsartikel (refereegranskat)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 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.
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| 42. |
- Krokhotin, Andrei, et al.
(författare)
-
Soliton concepts and protein structure
- 2012
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : APS. - 1539-3755 .- 1550-2376. ; 85:3
-
Tidskriftsartikel (refereegranskat)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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| 43. |
- Krokhotin, Andrey, et al.
(författare)
-
Soliton driven relaxation dynamics and protein collapse in the villin headpiece
- 2013
-
Ingår i: Journal of Physics. - : IOP Publishing. - 0953-8984 .- 1361-648X. ; 25:32, s. 325103-
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 44. |
- Krokhotin, Andrey, et al.
(författare)
-
Soliton driven relaxation dynamics and universality in protein collapse
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 45. |
- Krokhotin, Andrey, et al.
(författare)
-
Solitons and collapse in the lambda-repressor protein
- 2012
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 86:2, s. 021923-
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 46. |
- Liu, Jiaojiao, et al.
(författare)
-
Can the geometry of all-atom protein trajectories be reconstructed from the knowledge of C time evolution? A study of peptide plane O and side chain C atoms
- 2019
-
Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 150:22
-
Tidskriftsartikel (refereegranskat)abstract
- We inquire to what extent can the geometry of protein peptide plane and side chain atoms be reconstructed from the knowledge of C time evolution. Due to the lack of experimental data, we analyze all atom molecular dynamics trajectories from the Anton supercomputer, and for clarity, we limit our attention to the peptide plane O atoms and side chain C atoms. We reconstruct their positions using four different approaches. Three of these are the publicly available reconstruction programs Pulchra, Remo, and Scwrl4. The fourth, Statistical Method, builds entirely on the statistical analysis of Protein Data Bank structures. All four methods place the O and C atoms accurately along the Anton trajectories; the Statistical Method gives results that are closest to the Anton data. The results suggest that when a protein moves under physiological conditions, its all atom structures can be reconstructed with high accuracy from the knowledge of the C atom positions. This can help to better understand and improve all atom force fields, and advance reconstruction and refinement methods for reduced protein structures. The results provide impetus for the development of effective coarse grained force fields in terms of reduced coordinates.
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| 47. |
- Liu, Jiaojiao, et al.
(författare)
-
Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example
- 2017
-
Ingår i: Physical review. E. - : AMER PHYSICAL SOC. - 2470-0045 .- 2470-0053. ; 95:3
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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- Liwo, Jozef A., et al.
(författare)
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Origin of the Architecture of Biological Macromolecules - A Mean-Field Perspective
- 2014
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Ingår i: Biophysical Journal. - : Elsevier BV. - 0006-3495 .- 1542-0086. ; 106:2, s. 256A-256A
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 49. |
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