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  • 1. Kierspel, Thomas
    et al.
    Kadek, Alan
    Barran, Perdita
    Bellina, Bruno
    Bijedic N, Adi
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Brodmerkel, Maxim N.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - BMC, Biochemistry.
    Commandeur, Jan
    Caleman, Carl
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics. Centre for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, E22607, Hamburg, Germany.
    Damjanović, Tomislav
    Dawod, Ibrahim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics. European XFEL, Holzkoppel 4, 22869, Schenefeld, Germany.
    De Santis, Emiliano
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - BMC, Biochemistry.
    Lekkas, Alexandros
    Lorenzen, Kristina
    López Morillo, Luis
    Mandl, Thomas
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics. University of Applied Sciences Technikum Wien, Höchstädtpl. 6, 1200, Vienna, Austria.
    Marklund, Erik G.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - BMC, Biochemistry.
    Papanastasiou, Dimitris
    Ramakers, Lennart A. I.
    Schweikhard, Lutz
    Simke, Florian
    Sinelnikova, Anna
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Smyrnakis, Athanasios
    Timneanu, Nicusor
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics.
    Uetrecht, Charlotte
    Coherent diffractive imaging of proteins and viral capsids: simulating MS SPIDOC2023In: Analytical and Bioanalytical Chemistry, ISSN 1618-2642, E-ISSN 1618-2650, Vol. 415, no 18 SI, p. 4209-4220Article in journal (Refereed)
    Abstract [en]

    MS SPIDOC is a novel sample delivery system designed for single (isolated) particle imaging at X-ray Free-Electron Lasers that is adaptable towards most large-scale facility beamlines. Biological samples can range from small proteins to MDa particles. Following nano-electrospray ionization, ionic samples can be m/z-filtered and structurally separated before being oriented at the interaction zone. Here, we present the simulation package developed alongside this prototype. The first part describes how the front-to-end ion trajectory simulations have been conducted. Highlighted is a quadrant lens; a simple but efficient device that steers the ion beam within the vicinity of the strong DC orientation field in the interaction zone to ensure spatial overlap with the X-rays. The second part focuses on protein orientation and discusses its potential with respect to diffractive imaging methods. Last, coherent diffractive imaging of prototypical T = 1 and T = 3 norovirus capsids is shown. We use realistic experimental parameters from the SPB/SFX instrument at the European XFEL to demonstrate that low-resolution diffractive imaging data (q < 0.3 nm−1) can be collected with only a few X-ray pulses. Such low-resolution data are sufficient to distinguish between both symmetries of the capsids, allowing to probe low abundant species in a beam if MS SPIDOC is used as sample delivery.

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  • 2.
    Sinelnikova, Anna
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Data Reduction & Error Analysis in brief2017Other (Other academic)
    Abstract [en]

    This booklet was written to give an idea about how errors propagate in physical measurements. For this purpose we will first discuss what a measurement of a physical quantity means and where errors come from. Then we will show how to write down the result in a proper way, using a scientific notation. We then discuss how to compute errors in different cases, in direct and indirect measurements. Finally, we give an example that explicitly shows how to use the methods.

    The booklet can be useful for students who do laboratory work in physics. It might be used as a reference source for data reduction and propagation of errors.

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  • 3.
    Sinelnikova, Anna
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Polymer and Protein Physics: Simulations of Interactions and Dynamics2021Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Proteins can, without any exaggeration, be called the "building blocks of life". Their physical properties depend not only on the chemical structure but also on their geometric shape. In this thesis, I investigate protein geometry using several different methods.

    We start with a coarse-graining model to study the general behavior of polymers. For this reason, we utilize an effective Hamiltonian that can describe the thermodynamic properties of polymer chains and reproduce secondary and tertiary structures. To investigate this model, I perform classical Monte Carlo simulations using my software package.

    Another problem we address in this thesis is how to distinguish thermodynamic phases of proteins. The conventional definition of phases of polymer systems uses scaling laws. However, this method needs the chain's length to be varied, which is impossible to do with heteropolymers where the number of sites is one of the system's characteristics. We will apply renormalization group (RG) theory ideas to overcome this difficulty. We present a scaling procedure and an observable through which RG flow can define a certain polymer chain's phase.

    Another part of the thesis is dedicated to the method of molecular dynamics. Our focus is on a novel experimental technique called Single Particle Imaging (SPI). The spatial orientation of the sample in this method is arbitrary. Scientists proposed to use a strong electric field to fix the orientation since most biological molecules have a non-zero dipole moment. Motivated by this, we investigate the influence of a strong electric field's ramping on the orientation of protein ubiquitin. For the same question of SPI and using the same protein, we study the reproducibility of unfolding it in a strong electric field. With the help of a new graph representation, I show different unfolding pathways as a function of the electric field's value and compare them with thermal and mechanical unfolding. I show that the RG flow observable can also detect the different ubiquitin unfolding pathways more simply.

    The study described in this thesis has two types of results. One is a very concrete type, which can be utilized right away in the SPI experiments, like MS SPIDOC on the European XFEL. The other type of results are more theoretical and opens up a new field for further research. However, all of them contribute to protein science, an area vital for humanity's ability to protect us from threats such as the current COVID-19 pandemic.

    List of papers
    1. Phase diagram and the pseudogap state in a linear chiral homopolymer model
    Open this publication in new window or tab >>Phase diagram and the pseudogap state in a linear chiral homopolymer model
    2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 92, no 3, article id 032602Article in journal (Refereed) Published
    Abstract [en]

    The phase structure of a single self-interacting homopolymer chain is investigated in terms of a universal theoretical model, designed to describe the chain in the infrared limit of slow spatial variations. The effects of chirality are studied and compared with the influence of a short-range attractive interaction between monomers, at various ambient temperature values. In the high-temperature limit the homopolymer chain is in the self-avoiding random walk phase. At very low temperatures two different phases are possible: When short-range attractive interactions dominate over chirality, the chain collapses into a space-filling conformation. But when the attractive interactions weaken, there is a low-temperature unfolding transition and the chain becomes like a straight rod. Between the high- and low-temperature limits, several intermediate states are observed, including the theta regime and pseudogap state, which is a novel form of phase state in the context of polymer chains. Applications to polymers and proteins, in particular collagen, are suggested.

    National Category
    Physical Sciences
    Identifiers
    urn:nbn:se:uu:diva-264627 (URN)10.1103/PhysRevE.92.032602 (DOI)000361310700003 ()
    Funder
    Swedish Research CouncilCarl Tryggers foundation
    Available from: 2015-10-26 Created: 2015-10-15 Last updated: 2021-02-08Bibliographically approved
    2. Multiple scales and phases in discrete chains with application to folded proteins
    Open this publication in new window or tab >>Multiple scales and phases in discrete chains with application to folded proteins
    2018 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 5, article id 052107Article in journal (Refereed) Published
    Abstract [en]

    Chiral heteropolymers such as large globular proteins can simultaneously support multiple length scales. The interplay between the different scales brings about conformational diversity, determines the phase properties of the polymer chain, and governs the structure of the energy landscape. Most importantly, multiple scales produce complex dynamics that enable proteins to sustain live matter. However, at the moment there is incomplete understanding of how to identify and distinguish the various scales that determine the structure and dynamics of a complex protein. Here we address this impending problem. We develop a methodology with the potential to systematically identify different length scales, in the general case of a linear polymer chain. For this we introduce and analyze the properties of an order parameter that can both reveal the presence of different length scales and can also probe the phase structure. We first develop our concepts in the case of chiral homopolymers. We introduce a variant of Kadanoff's block-spin transformation to coarse grain piecewise linear chains, such as the C alpha backbone of a protein. We derive analytically, and then verify numerically, a number of properties that the order parameter can display, in the case of a chiral polymer chain. In particular, we propose that in the case of a chiral heteropolymer the order parameter can reveal traits of several different phases, contingent on the length scale at which it is scrutinized. We confirm that this is the case with crystallographic protein structures in the Protein Data Bank. Thus our results suggest relations between the scales, the phases, and the complexity of folding pathways.

    Place, publisher, year, edition, pages
    American Physical Society, 2018
    National Category
    Physical Chemistry
    Identifiers
    urn:nbn:se:uu:diva-357014 (URN)10.1103/PhysRevE.97.052107 (DOI)000432978200001 ()
    Funder
    Knut and Alice Wallenberg FoundationSwedish Research Council
    Available from: 2018-08-13 Created: 2018-08-13 Last updated: 2021-02-08Bibliographically approved
    3. RG Smoothing Algorithm Which Makes Data Compression
    Open this publication in new window or tab >>RG Smoothing Algorithm Which Makes Data Compression
    2018 (English)In: arXiv preprint arXiv:1806.01663Article in journal (Other academic) Published
    Abstract [en]

    I describe a new method for smoothing a one-dimensional curve in Euclidian space with an arbitrary number of dimensions. The basic idea is borrowed from renormalization group theory which previously was applied to biological macromolecules. There are two crucial differences from other smoothing methods that make the algorithm unique: data compression and recursive implementation. One of the simplest forms of the method that is described in this article has only one free parameter - the number of iterative steps. This means that hardware implementation should be relatively easy because each loop is simple and strictly defined. The method could be beneficially applied to pattern recognition and data compression in future studies.

    National Category
    Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-434242 (URN)
    Available from: 2021-02-06 Created: 2021-02-06 Last updated: 2021-11-10Bibliographically approved
    4. Reproducibility in the unfolding process of protein induced by an external electric field
    Open this publication in new window or tab >>Reproducibility in the unfolding process of protein induced by an external electric field
    Show others...
    2021 (English)In: Chemical Science, ISSN 2041-6520, E-ISSN 2041-6539, Vol. 12, no 6, p. 2030-2038Article in journal (Refereed) Published
    Abstract [en]

    The dynamics of proteins are crucial for their function. However, commonly used techniques for studying protein structures are limited in monitoring time-resolved dynamics at high resolution. Combining electric fields with existing techniques to study gas phase proteins, such as Single Particle Imaging using Free-electron Lasers and gas phase Small Angle X-ray Scattering, has the potential to open up a new era in time-resolved studies of gas phase protein dynamics. Using molecular dynamics simulations, we identify well-defined unfolding pathways of a protein, induced by experimentally achievable external electric fields. Our simulations show that strong electric fields in conjunction with short pulsed X-ray sources such as Free-electron Lasers can be a new path for imaging dynamics of gas-phase proteins at high spatial and temporal resolution.

    Place, publisher, year, edition, pages
    Royal Society of ChemistryRoyal Society of Chemistry (RSC), 2021
    National Category
    Biophysics Physical Chemistry
    Identifiers
    urn:nbn:se:uu:diva-429912 (URN)10.1039/D0SC06008A (DOI)000619216100039 ()
    Funder
    EU, Horizon 2020, 801406Swedish Research Council, 2018-00740
    Available from: 2021-01-06 Created: 2021-01-06 Last updated: 2024-01-15Bibliographically approved
    5. Orientation before destruction. A multiscale molecular dynamics study
    Open this publication in new window or tab >>Orientation before destruction. A multiscale molecular dynamics study
    Show others...
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    The emergence of ultra-fast X-ray free-electron lasers opens the possibility of imaging single molecules in the gas phase at atomic resolution. The main disadvantage of this imaging technique is the unknown orientation of the sample exposed to the X-ray beam, making the three-dimensional reconstruction not trivial. The induced orientation of molecules prior to X-ray exposure can be highly beneficial, as it significantly reduces the number of collected diffraction patterns whilst improving the quality of the reconstructed structure. We present here the possibility of protein orientation using a time-dependent external electric field. We used ab initio simulations on Trp-cage protein to provide a qualitative estimation of the field strength required to break protein bonds, with 45 V/nm as a breaking point value. Furthermore, we simulated, in a classical molecular dynamics approach, the orientation of ubiquitin protein by exposing it to different time-dependent electric fields. The protein structure was preserved for all samples at the moment orientation was achieved, which we denote `orientation before destruction'. Moreover, we find that the minimal field strength required to induce orientation within ten ns of electric field exposure was of the order of 0.5 V/nm. Our results help explain the process of field orientation of proteins and can support the design of instruments for protein orientation.

    National Category
    Biophysics
    Identifiers
    urn:nbn:se:uu:diva-434280 (URN)
    Available from: 2021-02-08 Created: 2021-02-08 Last updated: 2021-02-08
    6. NMR Refinement and Peptide Folding Using the GROMACS Software
    Open this publication in new window or tab >>NMR Refinement and Peptide Folding Using the GROMACS Software
    2021 (English)In: Journal of Biomolecular NMR, ISSN 0925-2738, E-ISSN 1573-5001, Vol. 75, no 4-5, p. 143-149Article in journal (Refereed) Published
    Abstract [en]

    Nuclear magnetic resonance spectroscopy is used routinely for studying the three-dimensional structures and dynamics of proteins. Structure determination is usually done by adding restraints based upon NMR data to a classical energy function and performing restrained molecular simulations. Here we report on the implementation of a script to extract NMR restraints from a NMR-STAR file and export it to the GROMACS software. With this package, it is possible to model distance restraints, dihedral restraints, and orientation restraints. The output from the script is validated by performing simulations with and without restraints, including the ab initio refinement of one peptide.

    Place, publisher, year, edition, pages
    Springer NatureSpringer Nature, 2021
    Keywords
    Python, NMR-STAR, Force Field, Amber, Charmm
    National Category
    Biophysics Physical Chemistry
    Identifiers
    urn:nbn:se:uu:diva-434243 (URN)10.1007/s10858-021-00363-z (DOI)000634305400001 ()33778935 (PubMedID)
    Available from: 2021-02-06 Created: 2021-02-06 Last updated: 2024-01-15Bibliographically approved
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  • 4.
    Sinelnikova, Anna
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    RG Smoothing Algorithm Which Makes Data Compression2018In: arXiv preprint arXiv:1806.01663Article in journal (Other academic)
    Abstract [en]

    I describe a new method for smoothing a one-dimensional curve in Euclidian space with an arbitrary number of dimensions. The basic idea is borrowed from renormalization group theory which previously was applied to biological macromolecules. There are two crucial differences from other smoothing methods that make the algorithm unique: data compression and recursive implementation. One of the simplest forms of the method that is described in this article has only one free parameter - the number of iterative steps. This means that hardware implementation should be relatively easy because each loop is simple and strictly defined. The method could be beneficially applied to pattern recognition and data compression in future studies.

  • 5.
    Sinelnikova, Anna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Mandl, Thomas
    Agelii, Harald
    Grånäs, Oscar
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Marklund, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular biophysics. Uppsala University, Science for Life Laboratory, SciLifeLab. Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - BMC, Biochemistry.
    Caleman, Carl
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular biophysics.
    De Santis, Emiliano
    Orientation before destruction. A multiscale molecular dynamics studyManuscript (preprint) (Other academic)
    Abstract [en]

    The emergence of ultra-fast X-ray free-electron lasers opens the possibility of imaging single molecules in the gas phase at atomic resolution. The main disadvantage of this imaging technique is the unknown orientation of the sample exposed to the X-ray beam, making the three-dimensional reconstruction not trivial. The induced orientation of molecules prior to X-ray exposure can be highly beneficial, as it significantly reduces the number of collected diffraction patterns whilst improving the quality of the reconstructed structure. We present here the possibility of protein orientation using a time-dependent external electric field. We used ab initio simulations on Trp-cage protein to provide a qualitative estimation of the field strength required to break protein bonds, with 45 V/nm as a breaking point value. Furthermore, we simulated, in a classical molecular dynamics approach, the orientation of ubiquitin protein by exposing it to different time-dependent electric fields. The protein structure was preserved for all samples at the moment orientation was achieved, which we denote `orientation before destruction'. Moreover, we find that the minimal field strength required to induce orientation within ten ns of electric field exposure was of the order of 0.5 V/nm. Our results help explain the process of field orientation of proteins and can support the design of instruments for protein orientation.

  • 6.
    Sinelnikova, Anna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Mandl, Thomas
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics. ty of Applied Sciences Technikum Wien, Wien, Austria.
    Agelii, Harald
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Grånäs, Oscar
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Marklund, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - BMC, Biochemistry. Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular biophysics. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Caleman, Carl
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics. Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular biophysics. Center for Free-Electron Laser Science, DESY,Hamburg, Germany.
    De Santis, Emiliano
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics. Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - BMC, Biochemistry.
    Protein orientation in time-dependent electric fields: orientation before destruction2021In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 120, no 17, p. 3709-3717, article id S0006-3495(21)00603-2Article in journal (Refereed)
    Abstract [en]

    Proteins often have nonzero electric dipole moments, making them interact with external electric fields and offering a means for controlling their orientation. One application that is known to benefit from orientation control is single-particle imaging with x-ray free-electron lasers, in which diffraction is recorded from proteins in the gas phase to determine their structures. To this point, theoretical investigations into this phenomenon have assumed that the field experienced by the proteins is constant or a perfect step function, whereas any real-world pulse will be smooth. Here, we explore the possibility of orienting gas-phase proteins using time-dependent electric fields. We performed ab initio simulations to estimate the field strength required to break protein bonds, with 45 V/nm as a breaking point value. We then simulated ubiquitin in time-dependent electric fields using classical molecular dynamics. The minimal field strength required for orientation within 10 ns was on the order of 0.5 V/nm. Although high fields can be destructive for the structure, the structures in our simulations were preserved until orientation was achieved regardless of field strength, a principle we denote "orientation before destruction."

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  • 7.
    Sinelnikova, Anna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Mandl, Thomas
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics. University of Applied Sciences Technikum Wien, Höchstädtplatz 6, A-1200 Wien, Austria .
    Östlin, Christofer
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Grånäs, Oscar
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Brodmerkel, Maxim N.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - BMC, Biochemistry.
    Marklund, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - BMC, Biochemistry.
    Caleman, Carl
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Chemical and Bio-Molecular Physics.
    Reproducibility in the unfolding process of protein induced by an external electric field2021In: Chemical Science, ISSN 2041-6520, E-ISSN 2041-6539, Vol. 12, no 6, p. 2030-2038Article in journal (Refereed)
    Abstract [en]

    The dynamics of proteins are crucial for their function. However, commonly used techniques for studying protein structures are limited in monitoring time-resolved dynamics at high resolution. Combining electric fields with existing techniques to study gas phase proteins, such as Single Particle Imaging using Free-electron Lasers and gas phase Small Angle X-ray Scattering, has the potential to open up a new era in time-resolved studies of gas phase protein dynamics. Using molecular dynamics simulations, we identify well-defined unfolding pathways of a protein, induced by experimentally achievable external electric fields. Our simulations show that strong electric fields in conjunction with short pulsed X-ray sources such as Free-electron Lasers can be a new path for imaging dynamics of gas-phase proteins at high spatial and temporal resolution.

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  • 8.
    Sinelnikova, Anna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Niemi, Antti
    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, Lab Phys Living Matter, Vladivostok, Russia;Beijing Inst Technol, Dept Phys, Beijing 100081, Peoples R China.
    Nilsson, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Ulybyshev, M.
    Univ Regensburg, Inst Theoret Phys, Univ Str 31, D-93053 Regensburg, Germany.
    Multiple scales and phases in discrete chains with application to folded proteins2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 5, article id 052107Article in journal (Refereed)
    Abstract [en]

    Chiral heteropolymers such as large globular proteins can simultaneously support multiple length scales. The interplay between the different scales brings about conformational diversity, determines the phase properties of the polymer chain, and governs the structure of the energy landscape. Most importantly, multiple scales produce complex dynamics that enable proteins to sustain live matter. However, at the moment there is incomplete understanding of how to identify and distinguish the various scales that determine the structure and dynamics of a complex protein. Here we address this impending problem. We develop a methodology with the potential to systematically identify different length scales, in the general case of a linear polymer chain. For this we introduce and analyze the properties of an order parameter that can both reveal the presence of different length scales and can also probe the phase structure. We first develop our concepts in the case of chiral homopolymers. We introduce a variant of Kadanoff's block-spin transformation to coarse grain piecewise linear chains, such as the C alpha backbone of a protein. We derive analytically, and then verify numerically, a number of properties that the order parameter can display, in the case of a chiral polymer chain. In particular, we propose that in the case of a chiral heteropolymer the order parameter can reveal traits of several different phases, contingent on the length scale at which it is scrutinized. We confirm that this is the case with crystallographic protein structures in the Protein Data Bank. Thus our results suggest relations between the scales, the phases, and the complexity of folding pathways.

  • 9.
    Sinelnikova, Anna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Van der Spoel, David
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Computational Biology and Bioinformatics.
    NMR Refinement and Peptide Folding Using the GROMACS Software2021In: Journal of Biomolecular NMR, ISSN 0925-2738, E-ISSN 1573-5001, Vol. 75, no 4-5, p. 143-149Article in journal (Refereed)
    Abstract [en]

    Nuclear magnetic resonance spectroscopy is used routinely for studying the three-dimensional structures and dynamics of proteins. Structure determination is usually done by adding restraints based upon NMR data to a classical energy function and performing restrained molecular simulations. Here we report on the implementation of a script to extract NMR restraints from a NMR-STAR file and export it to the GROMACS software. With this package, it is possible to model distance restraints, dihedral restraints, and orientation restraints. The output from the script is validated by performing simulations with and without restraints, including the ab initio refinement of one peptide.

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