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  • 1
    Publication Date: 2015-04-15
    Description: We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
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  • 2
    Publication Date: 2015-08-20
    Description: DNA origami is a robust assembly technique that folds a single-stranded DNA template into a target structure by annealing it with hundreds of short 'staple' strands. Its guiding design principle is that the target structure is the single most stable configuration. The folding transition is cooperative and, as in the case of proteins, is governed by information encoded in the polymer sequence. A typical origami folds primarily into the desired shape, but misfolded structures can kinetically trap the system and reduce the yield. Although adjusting assembly conditions or following empirical design rules can improve yield, well-folded origami often need to be separated from misfolded structures. The problem could in principle be avoided if assembly pathway and kinetics were fully understood and then rationally optimized. To this end, here we present a DNA origami system with the unusual property of being able to form a small set of distinguishable and well-folded shapes that represent discrete and approximately degenerate energy minima in a vast folding landscape, thus allowing us to probe the assembly process. The obtained high yield of well-folded origami structures confirms the existence of efficient folding pathways, while the shape distribution provides information about individual trajectories through the folding landscape. We find that, similarly to protein folding, the assembly of DNA origami is highly cooperative; that reversible bond formation is important in recovering from transient misfoldings; and that the early formation of long-range connections can very effectively enforce particular folds. We use these insights to inform the design of the system so as to steer assembly towards desired structures. Expanding the rational design process to include the assembly pathway should thus enable more reproducible synthesis, particularly when targeting more complex structures. We anticipate that this expansion will be essential if DNA origami is to continue its rapid development and become a reliable manufacturing technology.〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Dunn, Katherine E -- Dannenberg, Frits -- Ouldridge, Thomas E -- Kwiatkowska, Marta -- Turberfield, Andrew J -- Bath, Jonathan -- England -- Nature. 2015 Sep 3;525(7567):82-6. doi: 10.1038/nature14860. Epub 2015 Aug 19.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉University of Oxford, Department of Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK. ; University of Oxford, Department of Computer Science, Wolfson Building, Parks Road, Oxford OX1 3QD, UK. ; University of Oxford, Department of Physics, Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/26287459" target="_blank"〉PubMed〈/a〉
    Keywords: DNA, Single-Stranded/*chemistry/genetics ; Dimerization ; Kinetics ; Nanostructures/*chemistry ; Nanotechnology ; *Nucleic Acid Conformation
    Print ISSN: 0028-0836
    Electronic ISSN: 1476-4687
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
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  • 3
    Publication Date: 2017-12-14
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
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  • 4
    Publication Date: 2013-10-19
    Description: Although the thermodynamics of DNA hybridization is generally well established, the kinetics of this classic transition is less well understood. Providing such understanding has new urgency because DNA nanotechnology often depends critically on binding rates. Here, we explore DNA oligomer hybridization kinetics using a coarse-grained model. Strand association proceeds through a complex set of intermediate states, with successful binding events initiated by a few metastable base-pairing interactions, followed by zippering of the remaining bonds. But despite reasonably strong interstrand interactions, initial contacts frequently dissociate because typical configurations in which they form differ from typical states of similar enthalpy in the double-stranded equilibrium ensemble. Initial contacts must be stabilized by two or three base pairs before full zippering is likely, resulting in negative effective activation enthalpies. Non-Arrhenius behavior arises because the number of base pairs required for nucleation increases with temperature. In addition, we observe two alternative pathways—pseudoknot and inchworm internal displacement—through which misaligned duplexes can rearrange to form duplexes. These pathways accelerate hybridization. Our results explain why experimentally observed association rates of GC-rich oligomers are higher than rates of AT- rich equivalents, and more generally demonstrate how association rates can be modulated by sequence choice.
    Print ISSN: 0305-1048
    Electronic ISSN: 1362-4962
    Topics: Biology
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  • 5
    Publication Date: 2013-12-07
    Description: Dynamic DNA nanotechnology often uses toehold-mediated strand displacement for controlling reaction kinetics. Although the dependence of strand displacement kinetics on toehold length has been experimentally characterized and phenomenologically modeled, detailed biophysical understanding has remained elusive. Here, we study strand displacement at multiple levels of detail, using an intuitive model of a random walk on a 1D energy landscape, a secondary structure kinetics model with single base-pair steps and a coarse-grained molecular model that incorporates 3D geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Two factors explain the dependence of strand displacement kinetics on toehold length: (i) the physical process by which a single step of branch migration occurs is significantly slower than the fraying of a single base pair and (ii) initiating branch migration incurs a thermodynamic penalty, not captured by state-of-the-art nearest neighbor models of DNA, due to the additional overhang it engenders at the junction. Our findings are consistent with previously measured or inferred rates for hybridization, fraying and branch migration, and they provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.
    Print ISSN: 0305-1048
    Electronic ISSN: 1362-4962
    Topics: Biology
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  • 6
    Publication Date: 2015-07-25
    Description: The effect of secondary structure on DNA duplex formation is poorly understood. Using oxDNA, a nucleotide level coarse-grained model of DNA, we study how hairpins influence the rate and reaction pathways of DNA hybridzation. We compare to experimental systems studied by Gao et al . ( 1 ) and find that 3-base pair hairpins reduce the hybridization rate by a factor of 2, and 4-base pair hairpins by a factor of 10, compared to DNA with limited secondary structure, which is in good agreement with experiments. By contrast, melting rates are accelerated by factors of ~100 and ~2000. This surprisingly large speed-up occurs because hairpins form during the melting process, and significantly lower the free energy barrier for dissociation. These results should assist experimentalists in designing sequences to be used in DNA nanotechnology, by putting limits on the suppression of hybridization reaction rates through the use of hairpins and offering the possibility of deliberately increasing dissociation rates by incorporating hairpins into single strands.
    Print ISSN: 0305-1048
    Electronic ISSN: 1362-4962
    Topics: Biology
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  • 7
    Publication Date: 2015-04-14
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
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