J. Bohr

Technical University of Denmark, Copenhagen, Capital Region, Denmark

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Publications (123)295.3 Total impact

  • 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.
    Physical Review E 11/2013; 88(5-1):052714. · 2.31 Impact Factor
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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.
    New Journal of Physics 09/2013; 15(9):093008. · 4.06 Impact Factor
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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.
    EPL (Europhysics Letters) 05/2013; 103(3). · 2.26 Impact Factor
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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.
    01/2013;
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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.
    PLoS ONE 01/2013; 8(10):e74932. · 3.53 Impact Factor
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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.
    EPL (Europhysics Letters) 10/2012; 100(2):28003. · 2.26 Impact Factor
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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.
    Journal of Synchrotron Radiation 07/2012; 19(Pt 4):530-5. · 2.19 Impact Factor
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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.
    05/2012;
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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.
    05/2012;
  • 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.
    Physical Review Letters 03/2012; 108(9):098101. · 7.73 Impact Factor
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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.
    New Journal of Physics 02/2012; 14(2):023063. · 4.06 Impact Factor
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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.
    Langmuir 11/2011; 28(5):2545-50. · 4.38 Impact Factor
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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.
    02/2011;
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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.
    Geochimica et Cosmochimica Acta 11/2010; 74(21):5985-5999. · 3.88 Impact Factor
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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
    09/2010;
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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
    08/2010;
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    Jakob Bohr, Kasper Olsen
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    ABSTRACT: The one-dimensional problem of selecting the triple helix with the highest volume fraction is solved and hence the condition for a helix to be close-packed is obtained. The close-packed triple helix is shown to have a pitch angle of $v_{CP} =43.3 ^\circ$. Contrary to the conventional notion, we suggest that close packing form the underlying principle behind the structure of collagen, and the implications of this suggestion are considered. Further, it is shown that the unique zero-twist structure with no strain-twist coupling is practically identical to the close-packed triple helix. Some of the difficulties for the current understanding of the structure of collagen are reviewed: The ambiguity in assigning crystal structures for collagen-like peptides, and the failure to satisfactorily calculate circular dichroism spectra. Further, the proposed new geometrical structure for collagen is better packed than both the 10/3 and the 7/2 structure. A feature of the suggested collagen structure is the existence of a central channel with negatively charged walls. We find support for this structural feature in some of the early x-ray diffraction data of collagen. The central channel of the structure suggests the possibility of a one-dimensional proton lattice. This geometry can explain the observed magic angle effect seen in NMR studies of collagen. The central channel also offers the possibility of ion transport and may cast new light on various biological and physical phenomena, including biomineralization. Comment: 15 pages, 7 figures
    Theoretical Chemistry Accounts 04/2010; · 2.14 Impact Factor
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    Jakob Bohr, Kasper Olsen
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    ABSTRACT: We describe a geometrical property of helical structures and show how it accounts for the early art of ropemaking. Helices have a maximum number of rotations that can be added to them -- and it is shown that this is a geometrical feature, not a material property. This geometrical insight explains why nearly identically appearing ropes can be made from very different materials and it is also the reason behind the unyielding nature of ropes. The maximally rotated strands behave as zero-twist structures. Under strain they neither rotate one or the other way. The necessity for the rope to be stretched while being laid, known from Egyptian tomb scenes, follows straightforwardly, as does the function of the top, an old tool for laying ropes.
    EPL (Europhysics Letters) 04/2010; · 2.26 Impact Factor
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    Kasper Olsen, Jakob Bohr
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    ABSTRACT: The geometrical coupling between strain and twist in double helices is investigated. Overwinding, where strain leads to further winding, is shown to be a universal property for helices, which are stretched along their longitudinal axis when the initial pitch angle is below the zero-twist angle (39.4 deg). Unwinding occurs at larger pitch angles. The zero-twist angle is the unique pitch angle at the point between overwinding and unwinding, and it is independent of the mechanical properties of the double helix. This suggests the existence of zero-twist structures, i.e. structures that display neither overwinding, nor unwinding under strain. Estimates of the overwinding of DNA, chromatin, and RNA are given. Comment: 8 pages, 4 figures; typos fixed; added ref. and acknowledgement
    03/2010;
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    Jakob Bohr, Kasper Olsen
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    ABSTRACT: The Solar system is investigated for positional correlations between the planets using a logarithmic distance scale. The pair correlation function for the logarithm of the semimajor axis shows a regular distribution with five to seven consecutive peaks, and the Fourier transform hereof shows reciprocal peaks of first and second order. A procedure involving random permutations for the shuffling of the inter-logarithmic distances is employed. This probes for the presence of correlations of longer range than neighbouring planets. The use of permutations is, in particular, a helpful analysis when the number of data points is small. The pair correlation function of the permutated planets lacks the sequence of equidistant peaks, and its Fourier transform has no second-order peak. This analysis demonstrates the existence of longer ranged correlations in the Solar system.
    Monthly Notices of the Royal Astronomical Society Letters 02/2010; 403(1):L59 - L63. · 5.52 Impact Factor

Publication Stats

2k Citations
295.30 Total Impact Points

Institutions

  • 1989–2013
    • Technical University of Denmark
      • • Department of Micro- and Nanotechnology
      • • Department of Physics
      Copenhagen, Capital Region, Denmark
  • 1990–2012
    • University of Copenhagen
      • Department of Chemistry
      Copenhagen, Capital Region, Denmark
  • 1998–2001
    • Lomonosov Moscow State University
      • • Faculty of Physics
      • • Department of Biophysics at the Faculty of Physics
      Moscow, Moscow, Russia
  • 1996
    • University of Antwerp
      Antwerpen, Flanders, Belgium
    • Copenhagen University Hospital Hvidovre
      Hvidovre, Capital Region, Denmark
  • 1983–1987
    • Brookhaven National Laboratory
      • Physics Department
      New York City, New York, United States