Difference between revisions of "Kinetic Tile Assembly Model (kTAM)"

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(Created page with "The ''kinetic tile assembly model''(KTAM) is a more realistic model that considers the rate of association and dissociation of basic molecular elements (so-called monomers, or [[...")
 
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The ''kinetic tile assembly model''(KTAM) is a more realistic model that considers the rate of association and dissociation of basic molecular elements (so-called monomers, or [[Tile]]s) within the original framework provided by the socalled abstract Tile Assembly Model [[ATAM]].
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In reality, DNA tile self-assembly is a more complicated process than that modeled by the [[Abstract Tile Assembly Model (aTAM) | aTAM]], and therefore a different model is required for a realistic simulation of the physical process of self-assembling DNA tiles.  Whereas the aTAM is a great model for studying the capabilities and limitations of tile assembly, and for programming tile sets to understand issues related to computation and geometry, the '''kinetic Tile Assembly Model''' (kTAM) <ref name=Winf98 /> was developed as a more physically realistic model for laboratory settings, and considers the reversible nature of self-assembly, factoring in the rates of association and dissociation of basic molecular elements (so-called monomers, or tiles) within the original framework provided by the aTAM.  The kTAM describes the dynamics of assembly according to a set of reversible chemical reactions: A tile can attach to an assembly anywhere that it makes even a weak bond, and any tile can dissociate from the assembly at a rate dependent on the total strength with which it adheres to the assembly.  In this section, we first give a more formal definition of the kTAM, then describe the types of errors that it captures, and then discuss several results which have successfully demonstrated methods for reducing those errors.  Techniques such as those discussed below have been responsible for a rapid and steady decline in the frequency of errors seen in laboratory experiments, plummeting from error rates of $10\%$ per tile in 2004 <ref name=RothTriangles /> to only $0.13\%$ by 2009 <ref name=OrigamiSeed />, and continuing to shrink.
  
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In practice, DNA self-assembly entails a more complicated process than the simple model described previously. For instance, there are an infinite number of different types of monomer (tile) and the bonding strength for each edge is not a discrete integer, but a continuous number. Therefore, a different model is required for a realistic simulation of this process.
 
  
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KTAM describes the dynamics of assembly according to an inclusive set of reversible chemical reactions: A tile can attach to an assembly anywhere that it makes even a weak bond, and any tile can dissociate from the assembly at a rate dependent on the total strength with which it adheres to the assembly
 
  
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== A Kinetic Model of DNA Self-Assembly ==
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==References==
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<references>
  
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The self-assembly of two-dimensional lattices from a heterogeneous mix of DX molecules is a far more complicated system than the hybridization of two oligonucleotides. Rather than having just three species to consider (ssDNA, ssDNAA, and dsDNA), we now have an infinite number of species (all possible aggregates). For each aggregate of tiles with available sites, there are association reactions and dissociation reactions. Note that at every available site, there is an association reaction for every possible monomer, regardless of whether the monomer is the “correct” one or not; to understand when correct behavior can be expected, we must look closely at the kinetics of all the reactions. The model we develop here can be seen as an extention of Erickson (1980), which considers the self-assembly of an isotropic two-dimensional lattice consisting of a single unit type. To model the kinetics of self-assembly, we make several simplifying assumptions:
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<ref name=Winf98><bibtex>
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@phdthesis{Winf98,
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  author = "Erik Winfree",
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  title = "Algorithmic Self-Assembly of DNA",
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  school = "California Institute of Technology",
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  year = "1998",
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  month = "June",
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}
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</bibtex></ref>
  
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1. Monomer concentrations will be held constant. Further, all monomer types will be held at the same concentration. Primarily we make this assumption because the analysis is easier. Later we show how the results found with the assumption can be used to understand the more general case when the assumption is not true.
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<ref name=RothTriangles><bibtex>
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@article{RothTriangles,
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    author = {Rothemund, Paul W. K AND Papadakis, Nick AND Winfree, Erik},
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    journal = {PLoS Biol},
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    publisher = {Public Library of Science},
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    title = {Algorithmic Self-Assembly of DNA Sierpinski Triangles},
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    year = {2004},
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    month = {12},
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    volume = {2},
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    url = {http://dx.doi.org/10.1371%2Fjournal.pbio.0020424},
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    pages = {e424},
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    abstract = {
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        <p>Engineered DNA self-assembly to produce a fractal pattern demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata.</p>
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      },
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    number = {12},
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    doi = {10.1371/journal.pbio.0020424}
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}
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</bibtex></ref>
  
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2.Aggregates do not interact with each other; thus the only reactions to model are the addition of a monomer to an aggregate, and the dissociation of a monomer from an aggregate. Potential drawbacks of this assumption will be discussed at the very end.
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<ref name=OrigamiSeed><bibtex>
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@article{OrigamiSeed,
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    author = {Barish, Robert D. and Schulman, Rebecca and Rothemund, Paul W. K. and Winfree, Erik},
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    day = {14},
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    doi = {10.1073/pnas.0808736106},
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    journal = {Proceedings of the National Academy of Sciences},
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    month = apr,
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    number = {15},
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    pages = {6054--6059},
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    title = {{An information-bearing seed for nucleating algorithmic self-assembly}},
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    url = {http://dx.doi.org/10.1073/pnas.0808736106},
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    volume = {106},
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    year = {2009}
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}
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</bibtex></ref>
  
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3. As in the hybridization of oligonucleotides, we assume that the forward rate constants for all monomers are identical. In particular, the forward rate constants for correct and incorrect additions are identical.
 
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4. As in the hybridization of oligonucleotides, we assume that the reverse rate depends exponentially on the number of base-pair bonds which must be broken, and that mismatched sticky ends make no base-pair bonds. This amounts to assuming that binding on multiple edges is cooperative and that mismatched sticky ends do not affect the dissociation rate in any way.
 
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==References==
 
  
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<references />
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</references>  
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Erik Winfree, Algorithmic Self-Assembly of DNA, PdD thesis, Caltech, 1998.
 
  
 
[[Category: Tile Assembly Models]]
 
[[Category: Tile Assembly Models]]

Revision as of 09:51, 22 May 2013

In reality, DNA tile self-assembly is a more complicated process than that modeled by the aTAM, and therefore a different model is required for a realistic simulation of the physical process of self-assembling DNA tiles. Whereas the aTAM is a great model for studying the capabilities and limitations of tile assembly, and for programming tile sets to understand issues related to computation and geometry, the kinetic Tile Assembly Model (kTAM) [1] was developed as a more physically realistic model for laboratory settings, and considers the reversible nature of self-assembly, factoring in the rates of association and dissociation of basic molecular elements (so-called monomers, or tiles) within the original framework provided by the aTAM. The kTAM describes the dynamics of assembly according to a set of reversible chemical reactions: A tile can attach to an assembly anywhere that it makes even a weak bond, and any tile can dissociate from the assembly at a rate dependent on the total strength with which it adheres to the assembly. In this section, we first give a more formal definition of the kTAM, then describe the types of errors that it captures, and then discuss several results which have successfully demonstrated methods for reducing those errors. Techniques such as those discussed below have been responsible for a rapid and steady decline in the frequency of errors seen in laboratory experiments, plummeting from error rates of \(10\%\) per tile in 2004 [2] to only \(0.13\%\) by 2009 [3], and continuing to shrink.


References

  1. ↑ Erik Winfree - Algorithmic Self-Assembly of DNA
    Ph.D. Thesis, California Institute of Technology , June 1998
    Bibtex
    Author : Erik Winfree
    Title : Algorithmic Self-Assembly of DNA
    In : Ph.D. Thesis, California Institute of Technology -
    Address :
    Date : June 1998
  2. ↑ Rothemund, Paul W. K AND Papadakis, Nick AND Winfree, Erik - Algorithmic Self-Assembly of DNA Sierpinski Triangles
    PLoS Biol 2(12):e424, 12 2004
    http://dx.doi.org/10.1371%2Fjournal.pbio.0020424
    Bibtex
    Author : Rothemund, Paul W. K AND Papadakis, Nick AND Winfree, Erik
    Title : Algorithmic Self-Assembly of DNA Sierpinski Triangles
    In : PLoS Biol -
    Address :
    Date : 12 2004
  3. ↑ Barish, Robert D., Schulman, Rebecca, Rothemund, Paul W. K., Winfree, Erik - {An information-bearing seed for nucleating algorithmic self-assembly}
    Proceedings of the National Academy of Sciences 106(15):6054--6059, @apr 2009
    http://dx.doi.org/10.1073/pnas.0808736106
    Bibtex
    Author : Barish, Robert D., Schulman, Rebecca, Rothemund, Paul W. K., Winfree, Erik
    Title : {An information-bearing seed for nucleating algorithmic self-assembly}
    In : Proceedings of the National Academy of Sciences -
    Address :
    Date : @apr 2009
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