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Molecular models of DNA

About: Molecular models of DNA is a research topic. Over the lifetime, 300 publications have been published within this topic receiving 16805 citations.


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TL;DR: Simulations and detailed analysis such as those presented here provide molecular insights into strand displacement computation, that can be also be expected in chemical implementations.
Abstract: We perform a spatially resolved simulation study of an AND gate based on DNA strand displacement using several lengths of the toehold and the adjacent domains. DNA strands are modelled using a coarse-grained dynamic bonding model {[}C. Svaneborg, Comp. Phys. Comm. 183, 1793 (2012){]}. We observe a complex transition path from the initial state to the final state of the AND gate. This path is strongly influenced by non-ideal effects due to transient bubbles revealing undesired toeholds and thermal melting of whole strands. We have also characterized the bound and unbound kinetics of single strands, and in particular the kinetics of the total AND operation and the three distinct distinct DNA transitions that it is based on. We observe a exponential kinetic dependence on the toehold length of the competitive displacement operation, but that the gate operation time is only weakly dependent on both the toehold and adjacent domain length. Our gate displays excellent logical fidelity in three input states, and quite poor fidelity in the fourth input state. This illustrates how non-ideality can have very selective effects on fidelity. Simulations and detailed analysis such as those presented here provide molecular insights into strand displacement computation, that can be also be expected in chemical implementations.

2 citations

Posted Content
TL;DR: Geometric orthogonal codes as discussed by the authors abstractly model the engineered DNA macrobonds as two-dimensional binary codewords and share similar features to the optical orthogonality codes studied by Chung, Salehi, and Wei.
Abstract: An example of a nonspecific molecular bond is the affinity of any positive charge for any negative charge (like-unlike), or of nonpolar material for itself when in aqueous solution (like-like). This contrasts specific bonds such as the affinity of the DNA base A for T, but not for C, G, or another A. Recent experimental breakthroughs in DNA nanotechnology demonstrate that a particular nonspecific like-like bond ("blunt-end DNA stacking" that occurs between the ends of any pair of DNA double-helices) can be used to create specific "macrobonds" by careful geometric arrangement of many nonspecific blunt ends, motivating the need for sets of macrobonds that are orthogonal: two macrobonds not intended to bind should have relatively low binding strength, even when misaligned. To address this need, we introduce geometric orthogonal codes that abstractly model the engineered DNA macrobonds as two-dimensional binary codewords. While motivated by completely different applications, geometric orthogonal codes share similar features to the optical orthogonal codes studied by Chung, Salehi, and Wei. The main technical difference is the importance of 2D geometry in defining codeword orthogonality.

2 citations

Journal ArticleDOI
TL;DR: In this article, a generalized model for three-stranded DNA consisting of two chains of one type and a third chain of a different type was defined, and the DNA strands were modeled by random walks on the three-dimensional cubic lattice with different interactions between two chains.
Abstract: We define a generalized model for three-stranded DNA consisting of two chains of one type and a third chain of a different type. The DNA strands are modeled by random walks on the three-dimensional cubic lattice with different interactions between two chains of the same type and two chains of different types. This model may be thought of as a classical analog of the quantum three-body problem. In the quantum situation, it is known that three identical quantum particles will form a triplet with an infinite tower of bound states at the point where any pair of particles would have zero binding energy. The phase diagram is mapped out, and the different phase transitions are examined using finite-size scaling. We look particularly at the scaling of the DNA model at the equivalent Efimov point for chains up to 10 000 steps in length. We find clear evidence of several bound states in the finite-size scaling. We compare these states with the expected Efimov behavior.

2 citations

Journal ArticleDOI
TL;DR: This paper reviews different mechanical models of double DNA and considers multi-pendulum models appropriate for experimental testing of visco-elastic properties of DNA, which point to existence of independent eigen multi-frequency signals in double DNA chains.
Abstract: In this paper, we review different mechanical models of double DNA (polymer models, elastic rod model, network model, torsional springs model, soliton-existence supporting models) emphasising specifities of each model. We especially considered the DNA model of Kovaleva and Manevich (2005), and Kovaleva et al. (2007). On a basis of this model, we made double DNA helical models with ideally elastic, visco-elastic, hereditary properties and fractional order model and named them multi-pendulum/multi-chain models. For each of these models, we made systems of corresponding differential equations or integro-differential equations or differential fractional order equations. Our results point to existence of independent eigen multi-frequency signals in double DNA chains with subsets of the eigen frequencies as well as set of one eigen frequency normal modes. For some of these multi-pendulum models, we calculate transfer of energy trough the double DNA chains. We consider multi-pendulum models appropriate for experimental testing of visco-elastic properties of DNA.

2 citations

Journal ArticleDOI
12 Mar 1999-Science
TL;DR: The statement that DNA is like “chains or loops of linked rigid pieces, like bits of uncooked spaghetti joined by hinges,” rather than the more familiar “overcooked spaghetti” is misleading, and Rigidity matters.
Abstract: A recent Random Samples contribution “Locked but not knotted” (12 Feb. p. 931) describes a mathematically interesting result about locked, unknotted hexagons. We believe, however, that the statement that DNA is like “chains or loops of linked rigid pieces, like bits of uncooked spaghetti joined by hinges,” rather than the more familiar “overcooked spaghetti” is misleading. Piece-wise linear models of polymers were introduced by Kuhn in the 1930s to provide a tractable model simpler than the continuous description that he knew was closer to reality. His approximation and subsequent refinements have successfully allowed relatively simple mathematical and numerical treatments of physical phenomena in DNA. However, the effective physical properties of DNA are relatively uniform along the backbone and, in reality, there are no hinges interspersed with rigid regions (unless perhaps one reduces to a single base pair-level description). Electron microscopy of DNA has shown that on the wide range of viewable length scales the double helix appears as a continuous curve (Fig. 1). Any such smooth curve (in yellow) can be well approximated by n line segments, with n sufficiently large (the case n = 6 shown in red seems inadequate). The question of how large n needs to be depends on the smoothness of the underlying curve, or whether the spaghetti is cooked al dente or scotti. For models of DNA, this smoothness depends on the number of base pairs represented by the continuous curve (2686 for the data shown). ![Fig. 1.][1] Fig. 1. DNA model. We know of no realistic application involving a piece-wise linear model of a DNA loop where the number of links, n , can be as few as 6. Moreover, any conclusion that depends sensitively on n —for example, rigidity—for n = 6, which disappears for n = 7, cannot be physically pertinent for DNA. # DNA: Uncooked, al Dente, or Scotti ? {#article-title-2} The point of Stasiak et al. that DNA does not resemble a polygon of 6 or 7 rigid segments is absolutely correct. Such a model may be more realistic for an artificially synthesized polymer, and several mathematicians I spoke with suggested that this might be an interesting project for chemists to work on (similar to the synthesis of “rotaxanes,” in which two loops are geometrically linked without being topologically linked). For DNA, the best model may indeed be one that depends on the details of how the spaghetti is cooked, as Stasiak et al. suggest. The mathematical treatment of large molecules with a certain amount of rigidity is still very much in its infancy. If mathematicians continue to study models of molecules that are in some respects outdated or oversimplified, the reason is that there are still interesting questions about them that have not been answered. The mathematicians I spoke with felt that the shape presented by Jason Cantarella was a useful step toward understanding the effect of rigidity on conformation. The conclusion: Rigidity matters. [1]: pending:yes

2 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20216
20208
20194
201810
201712
201617