DNA recombination through assembly graphs

Angeleska, Aleksandra; Jonoska, Nataša; Saito, Masahico

doi:10.1016/j.dam.2009.06.011

Cited by 26 publications

(49 citation statements)

References 9 publications

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“…Considering that a virtual knot diagram could represent the physical structure of the micronuclear DNA at the time of recombination, in [4] it was shown that for every such virtual knot diagram there is an embedding of the molecule in space, and there is smoothing of the vertices (recombination along the pointers) such that the resulting molecule is always unlinked. Further it was shown that the smoothing guided by the pointers differs from the existent smoothing notions defined earlier for virtual knot diagrams [56].…”

Section: Discussionmentioning

confidence: 99%

Computational Nature of Gene Assembly in Ciliates

Brijder

Daley

Harju

et al. 2012

Handbook of Natural Computing

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Section: Discussionmentioning

confidence: 99%

Computational Nature of Gene Assembly in Ciliates

Brijder

Daley

Harju

et al. 2012

Handbook of Natural Computing

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“…For a more detailed explanation of the model and its connection to the genetic processes we refer the reader to [1,2].…”

Section: Preliminariesmentioning

confidence: 99%

“…Section 2 recalls the definitions of assembly graphs, assembly words, polygonal paths as well as some of the relevant properties shown in [1]. In Section 3, we develop formulas for the number of assembly words and graphs with a given number of vertices of various types and classes.…”

Section: Introductionmentioning

confidence: 99%

“…The recombination events are modeled by smoothing of the 4-valent vertices. In [1] each macronuclear gene is represented as a so-called polygonal path in the graph which in turn determines the smoothing type at the vertices along these paths. In this paper we study properties of assembly words and graphs as well as polygonal paths within these graphs.…”

Section: Introductionmentioning

confidence: 99%

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Four-regular graphs with rigid vertices associated to DNA recombination

Burns¹,

Dolzhenko²,

Jonoska³

et al. 2013

Discrete Applied Mathematics

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a b s t r a c tGenome rearrangement and homological recombination processes have been modeled by Angeleska et al. [A. Angeleska, N. Jonoska, M. Saito, DNA recombinations through assembly graphs, Discrete Appl. Math. 157 (2009) 3020-3037] as 4-regular spacial graphs with rigid vertices, called assembly graphs. These graphs can also be represented by double occurrence words called assembly words. The rearranged DNA segments are modeled by certain types of paths in the assembly graphs called polygonal paths. The minimum number of polygonal paths visiting all vertices in a graph is called an assembly number for the graph.In this paper, we give formulas for counting certain types of assembly graphs and assembly words. Some of these formulas produce sequences not previously reported at the Online Encyclopedia of Integer Sequences (http://oeis.org). We provide a sharp upper bound for the number of polygonal paths in Hamiltonian sets of polygonal paths, and present a family of graphs that achieves this bound. We investigate changes in the assembly numbers as a result of graph compositions. Finally, we introduce a polynomial invariant for assembly graphs and show properties of this invariant.

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“…Both operations are important in describing recombination enzymes (see, for example, Fig. 8 in Angeleska et al 2009), and the projected twist number T of DNA ribbon is decreased by 1/2 each step in the case of D configuration. If the crossing belongs to different strands, the smoothing unites these two strands (Cerf 1997), as shown in Fig.…”

Section: The Crossing Smoothing Operationmentioning

confidence: 99%

Topological Analysis of Enzymatic Actions on DNA Polyhedral Links

Wang

2011

Bull Math Biol

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Current synthetic biology has witnessed a revolution that natural DNA molecule steps onto a broad scientific area by assembling a large variety of three-dimensional structures with the connectivity of polyhedra. A mathematical model of these biomolecules is crucial to clarify the biological self-assembly principle, and unravel a first-step understanding of biological regulation and controlling mechanisms. In this paper, mechanisms of two different enzymatic actions on DNA polyhedra are elucidated through theoretical models of polyhedral links: (1) topoisomerase that untangles DNA polyhedral links produces separated single-stranded DNA circles through the crossing change operation; (2) recombinase generates a class of polyhedral circular paths or polyhedral knots by applying the crossing smoothing operation. Furthermore, we also discuss the possibility of applying two theoretical operations in molecular design of DNA polyhedra. Thus, our research provides a new sight of how geometry and topology of DNA polyhedra can be manipulated and controlled by enzymes, as well as has implications for molecular design and structural analysis of structural genome organization.

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DNA recombination through assembly graphs

Cited by 26 publications

References 9 publications

Computational Nature of Gene Assembly in Ciliates

Computational Nature of Gene Assembly in Ciliates

Four-regular graphs with rigid vertices associated to DNA recombination

Topological Analysis of Enzymatic Actions on DNA Polyhedral Links

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