Jakob Bohr

Technical University of Denmark, Lyngby, Capital Region, Denmark

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Publications (129)311.92 Total impact

  • Jakob Bohr · Steen Markvorsen

    No preview · Article · Feb 2016 · Physica Scripta
  • Jakob Bohr · Steen Markvorsen
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    ABSTRACT: A continuous autorotation vector field along a framed space curve is defined, which describes the rotational progression of the frame. We obtain an exact integral for the length of the autorotation vector. This invokes the infinitesimal rotation vector of the frame progression and the unit vector field for the corresponding autorotation vector field. For closed curves we define an autorotation number whose integer value depends on the starting point of the curve. Upon curve deformations, the autorotation number is either constant, or can make a jump of (multiples of) plus-minus two, which corresponds to a change in rotation of multiples of 4π. The autorotation number is therefore not topologically conserved under all transformations. We discuss this within the context of generalised inflection points and of frame revisit points. The results may be applicable to physical systems such as polymers, proteins, and DNA. Finally, turbulence is discussed in the light of autorotation, as is the Philippine wine dance, the Dirac belt trick, and the 4π cycle of the flying snake
    No preview · Article · Jan 2016 · Physica Scripta
  • Jakob Bohr · Kasper W Olsen
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    ABSTRACT: The properties of double-stranded DNA and other chiral molecules depend on the local geometry, i.e., on curvature and torsion, yet the paths of closed chain molecules are globally restricted by topology. When both of these characteristics are to be incorporated in the description of circular chain molecules, e.g., plasmids, it is shown to have implications for the total positive curvature integral. For small circular micro-DNAs it follows as a consequence of Fenchel's inequality that there must exist a minimum length for the circular plasmids to be double stranded. It also follows that all circular micro-DNAs longer than the minimum length must be concave, a result that is consistent with typical atomic force microscopy images of plasmids. Predictions for the total positive curvature of circular micro-DNAs are given as a function of length, and comparisons with circular DNAs from the literature are presented.
    No preview · Article · Nov 2013 · Physical Review E
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    Jakob Bohr · Steen Markvorsen
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    ABSTRACT: A repetitive crystal-like pattern is spontaneously formed upon the twisting of straight ribbons. The pattern is akin to a tessellation with isosceles triangles, and it can easily be demonstrated with ribbons cut from an overhead transparency. We give a general description of developable ribbons using a ruled procedure where ribbons are uniquely described by two generating functions. This construction defines a differentiable frame, the ribbon frame, which does not have singular points, whereby we avoid the shortcomings of the Frenet-Serret frame. The observed spontaneous pattern is modeled using planar triangles and cylindrical arcs, and the ribbon structure is shown to arise from a maximization of the end-to-end length of the ribbon, i.e. from an optimal use of ribbon length. The phenomenon is discussed in the perspectives of incompatible intrinsic geometries and of the emergence of long-range order.
    Full-text · Article · Oct 2013 · PLoS ONE
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    Kasper W Olsen · Jakob Bohr
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    ABSTRACT: Two separate regimes exist for the aspect ratio of DNA. A low aspect regime where DNA will twist further under strain and a high aspect regime where DNA will untwist under strain. The question of the overall geometry, i.e. the aspect ratio, of DNA is revisited from the perspective of a geometrical analysis of transcription. It is shown that under certain reasonable assumptions transcription is only possible if the aspect ratio is in the regime corresponding to further twisting. We find this constraint to be in agreement with long-established crystallographic studies of DNA.
    Preview · Article · Sep 2013 · New Journal of Physics
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    Kasper W Olsen · Jakob Bohr
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    ABSTRACT: We study simple, knotted and linked torus windings that are made of tubes of finite thickness. Knots which have the shortest rope length are often denoted ideal structures. Conventionally, the ideal structure are found by rope shortening routines. It is shown that alternatively they can be directly determined as maximally rotated structures. In many cases these structures are also zero-twist structures i.e. structures that neither rotate one or the other way under strain. We use this principle to implement rapid numerical calculations of the ideal structures and subsequently quantify them by their aspect ratio. The results are compared with the aspect ratios of biological torus molecules.
    Preview · Article · May 2013 · EPL (Europhysics Letters)
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    Nikolay N. Oskolkov · Jakob Bohr
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    ABSTRACT: Helical structures with Lennard-Jones self-interactions are studied for optimal conformations. For this purpose, their self-energy is analyzed for extrema with respect to the geometric parameters of the helices. It is found that Lennard-Jones helices exhibit a first order phase transition from a state with large curvature of the helical backbone to one with a small curvature. I.e. from a dense helix to an extended helix. A transition from one helical structure to another is a phenomenon known to take place in self-assembling helices formed in multicomponent solutions with cholesterol.
    Full-text · Article · Mar 2013 · Central European Journal of Physics
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    Jakob Bohr · Kasper W. Olsen
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    ABSTRACT: The interplay between global constraints and local material properties of chain molecules is a subject of emerging interest. Studies of molecules that are intrinsically chiral, such as double-stranded DNA, is one example. Their properties generally depend on the local geometry, i.e. on curvature and torsion, yet the paths of closed molecules are globally restricted by topology. Molecules that fulfill a twist neutrality condition, a zero sum rule for the incremental change in the rate of winding along the curve, will behave neutrally to strain. This has implications for plasmids. For small circular microDNAs it follows that there must exist a minimum length for these to be double-stranded. It also follows that all microDNAs longer than the minimum length must be concave. This counterintuitive result is consistent with the kink-like appearance which has been observed for circular DNA. A prediction for the total negative curvature of a circular microDNA is given as a function of its length.
    Preview · Article · Jan 2013
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    ABSTRACT: The newly proposed close-packed motif for collagen and the more established 7/2 structure are investigated and compared. First-principles semi-empirical wave function theory and Kohn-Sham density functional theory are applied in the study of these relatively large and complex structures. The structures are refined, and comparable stability is displayed using these methods. The electronic circular dichroism of the close-packed model is shown to have a significant negative bias and a large signal. This bias is consistent with existing experimental data, though it is not unambiguously possible from the circular dichroism calculations to select one structure over the other. An interesting feature of the close-packed structure is the existence of a central channel. Simulations show that, if hydrogen atoms are placed in the cavity, a chain of molecular hydrogens is formed suggesting a possible biological function for molecular hydrogen.
    Full-text · Article · Oct 2012 · EPL (Europhysics Letters)
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    ABSTRACT: This article reports on studies of the chemical alterations induced by synchrotron radiation at the calcite-ethanol interface, a simple model system for interfaces between minerals and more complex organic molecules containing OH groups. A combination of X-ray reflectivity and X-ray photoelectron spectroscopy of natural calcite, cleaved in distilled ethanol to obtain new clean interfaces, indicated that, during a 5 h period, the two top atomic layers of calcite, CaCO(3), transform into calcium oxide, CaO, by releasing CO(2). Also, the occupation of the first ordered layer of ethanol attached to calcite by hydrogen bonds almost doubles. Comparison between radiated and non-radiated areas of the same samples demonstrate that these effects are induced only by radiation and not caused by aging. These observations contribute to establishing a time limit for synchrotron experiments involving fluid-mineral interfaces where the polar OH group, as present in ethanol, plays a key role in their molecular structure and bonding. Also, the chemical evolution observed in the interface provides new insight into the behavior of some complex organic molecules involved in biomineralization processes.
    Full-text · Article · Jul 2012 · Journal of Synchrotron Radiation
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    Kasper W. Olsen · Jakob Bohr
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    ABSTRACT: The question of the value of the pitch angle of DNA is visited from the perspective of a geometrical analysis of transcription. It is suggested that for transcription to be possible, the pitch angle of B-DNA must be smaller than the angle of zero-twist. At the zero-twist angle the double helix is maximally rotated and its strain-twist coupling vanishes. A numerical estimate of the pitch angle for B-DNA based on differential geometry is compared with numbers obtained from existing empirical data. The crystallographic studies shows that the pitch angle is approximately 38 deg., less than the corresponding zero-twist angle of 41.8 deg., which is consistent with the suggested principle for transcription.
    Preview · Article · May 2012
  • Jakob Bohr · Kasper Olsen
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    ABSTRACT: The diameter of the nucleosome core particle is the same for all the eukaryotes. Here we discuss the possibility that this selectiveness is consistent with a propensity for twist neutrality, in particular, for the double helical DNA to stay rotationally neutral when strained. Reorganization of DNA cannot be done without some level of temporal tensile stress, and as a consequence chiral molecules, such as helices, will twist under strain. The requirement that the nucleosome, constituting the nucleosome core particle and linker DNA, has a vanishing strain-twist coupling leads to a requirement for the amount of bending. For the diameter of the coiled DNA we obtain the relatively accurate numerical estimate of 2R=82 Å.
    No preview · Article · Mar 2012 · Physical Review Letters
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    Kasper Olsen · Jakob Bohr
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    ABSTRACT: Two important geometrical properties of N-helix structures are influenced by bending. One is maximizing the volume fraction, which is called optimal-packing, and the other is having a vanishing strain-twist coupling, which is called zero-twist. Zero-twist helices rotate neither in one nor in the other direction under pull. The packing problem for tubular N-helices is extended to bent helices where the strands are coiled on toruses. We analyze the geometry of open circular helices and develop criteria for the strands to be in contact. The analysis is applied to a single, a double and a triple helix. General N-helices are discussed, as well as zero-twist helices for N > 1. The derived geometrical restrictions are gradually modified by changing the aspect ratio of the torus.
    Preview · Article · Feb 2012 · New Journal of Physics
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    ABSTRACT: A broad table-like entropy change (ΔS) at room temperature has been observed in the ferromagnetic compound La0.75Ca0.15Sr0.10MnO3, which is analyzed in the concept of Landau theory and with critical exponent analysis obtained from the magnetization measurements. The change in entropy in La0.75Ca0.15Sr0.10MnO3 is discussed in the light of magnetoelastic coupling between the magnetization and the lattice distortion. Application aspects of this unusual broad magnetocaloric effect with relative cooling power of 107 J kg−1 in an applied magnetic field of 1.6 T with an operating temperature range of 93 K around the room temperature are also discussed.
    No preview · Article · Jan 2012 · Materials Chemistry and Physics
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    ABSTRACT: To produce biominerals, such as shells, bones, and teeth, living beings create organic compounds that control the growth of the solid phase. Investigating the atomic scale behavior of individual functional groups at the mineral-fluid interface provides fundamental information that is useful for constructing accurate predictive models for natural systems. Previous investigations of the activity of coccolith-associated polysaccharides (CAP) on calcite, using atomic force microscopy (AFM) [Henriksen, K., Young, J. R., Bown, P. R., and Stipp, S. L. S. Palentology 2004, 43 (Part 3), 725-743] and molecular dynamics (MD) modeling [Yang, M., Stipp, S. L. S., and Harding, J. H. Cryst. Growth Des. 2008, 8 (11), 4066-4074], have suggested that OH functional groups control polysaccharide attachment. The purpose of this work was to characterize, using X-ray reflectivity (XR) combined with molecular dynamics (MD) simulations, the structuring on calcite of a layer of the simplest carbon chain molecule that contains an OH group, ethanol (CH(3)-CH(2)-OH). We found evidence that EtOH forms a highly ordered structure at the calcite surface, where the first layer molecules bond with calcite. The ethanol molecules stand up perpendicularly at the interface or nearly so. As a consequence, the fatty, CH(3) ends form a new surface, about 6 Å from the termination of the bulk calcite, and beyond that, there is a thin gap where ethanol density is low. Following is a more disordered layer that is two to three ethanol molecules thick, about 14 Å, where density more resembles that of bulk liquid ethanol. The good agreement between theory and experiment gives confidence that a theoretical approach can offer information about behavior in more complex systems.
    No preview · Article · Nov 2011 · Langmuir
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    Jakob Bohr · Kasper Olsen
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    ABSTRACT: The structural origin of the size of the 11 nm nucleosomal disc is addressed. On the nanometer length-scale the organization of DNA as chromatin in the chromosomes involves a coiling of DNA around the histone core of the nucleosome. We suggest that the size of the nucleosome core particle is dictated by the fulfillment of two criteria: One is optimizing the volume fraction of the DNA double helix; this requirement for close-packing has its root in optimizing atomic and molecular interactions. The other criterion being that of having a zero strain-twist coupling; being a zero-twist structure is a necessity when allowing for transient tensile stresses during the reorganization of DNA, e.g., during the reposition, or sliding, of a nucleosome along the DNA double helix. The mathematical model we apply is based on a tubular description of double helices assuming hard walls. When the base-pairs of the linker-DNA is included the estimate of the size of an ideal nucleosome is in close agreement with the experimental numbers. Interestingly, the size of the nucleosome is shown to be a consequence of intrinsic properties of the DNA double helix.
    Preview · Article · Feb 2011

  • No preview · Article · Jan 2011 · MRS Online Proceeding Library
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    ABSTRACT: Synchrotron X-ray reflectivity (SXR) was used to measure the thickness of the water film that adsorbs on a {} cleavage surface of calcite (CaCO3) in a sample chamber where relative humidity could be controlled within the range from <4% to 90%. Gases used to carry water vapour were initially either 100% N2 or 100% CO2. The product water film was remarkably constant in thickness at 15.5 Å (±1 Å) and independent of humidity. When N2 was used as the carrier gas, this film displayed a gap in its electron density at between 0.6 and 2 Å distance from the calcite surface, depending on humidity. This implies that a change in the arrangement of water molecules occurs in direct proximity to the surface. This electron density discontinuity was measurably further from the calcite surface, at 3.4 Å, when CO2 was used as the carrier gas. Except for this thin low density region proximate to the calcite surface, the density of the adsorbed water layer was 0.9 g cm−3, therefore suggesting a significant degree of ordering. Atomic force microscopy (AFM) images were completed in conjunction with the SXR measurements on similarly prepared calcite cleavage surfaces. AFM showed that terraces may be atomically flat over 1 μm or more. SXR corroborated this observation, with results showing that carefully cleaved surfaces had a starting root mean square (r.m.s.) roughness of ∼1.2 Å. Diffuse scatter measurements constrained the correlation lengths of these surfaces to be at least 18,000 Å. For comparison with the cleaved samples, a surface was also prepared by chemo-mechanical Syton polishing. This surface gave an r.m.s roughness by SXR that was an order of magnitude higher, equal to 12.1 Å. In this case, diffuse scatter resolved a correlation length of 950 Å, and revealed a fractal dimension that was higher than for the cleaved surface. On Syton polished samples, the water film determined by SXR was about twice as thick as for freshly cleaved surfaces, with a density of 1.0 g cm−3, equal to that of bulk water. However, surface roughness was too large to allow resolution of any gap in the electron density within the water layer proximate to the solid surface. Our AFM observations also confirm previous reports of calcite surface recrystallization. The electron density of the solid surface determined by SXR is indistinguishable from that of calcite, indicating that any material recrystallized within the adsorbed water film is compositionally indistinguishable from the calcite substrate.
    No preview · Article · Nov 2010 · Geochimica et Cosmochimica Acta
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    Kasper Olsen · Jakob Bohr
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    ABSTRACT: The pair-correlations between the positions of the six known planets in the exoplanetary system HD 10180 are studied. There are six non-trivial and almost equally spaced peaks. This demonstrates longer-ranged positional order between the orbits and suggests a seventh orbit at 0.92 AU that is consistent with these correlations. Comment: 5 pages, 4 figures
    Preview · Article · Sep 2010
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    Kasper Olsen · Jakob Bohr
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    ABSTRACT: Many hoards found in Ireland, Scotland, Orkney Islands, and Scandinavia demonstrate the vikings ability to fabricate beautiful arm and neck rings of twisted silver and gold rods. Characteristic for such rings is the uniform appearance of the twisted pattern along the length of the arm ring, as well as from one arm ring to another, also when found at distant geographical locations. How can the appearance of the twisted wires be so perfectly repetitive? We demonstrate that the answer is that the vikings utilized a self-forming motif: The pattern arises from a twisting of the wires to a maximally rotated configuration. That is why the twist patterns in these arm and neck rings are beautiful, repetitive, and universal. Comment: 4 pages, 3 figures
    Preview · Article · Aug 2010

Publication Stats

4k Citations
311.92 Total Impact Points

Institutions

  • 1995-2013
    • Technical University of Denmark
      • • National Laboratory for Sustainable Energy
      • • Department of Physics
      Lyngby, Capital Region, Denmark
  • 1996
    • Lomonosov Moscow State University
      Moskva, Moscow, Russia
    • Copenhagen University Hospital Hvidovre
      • Department of Infectious Diseases
      Hvidovre, Capital Region, Denmark
  • 1993
    • Odense University Hospital
      Odense, South Denmark, Denmark
  • 1985-1988
    • Brookhaven National Laboratory
      • Physics Department
      New York, New York, United States
    • Harvard University
      • Department of Physics
      Cambridge, Massachusetts, United States