Using DNA Self-assembly Design Strategies to Motivate Graph Theory Concepts

Ellis-Monaghan, Joanna A.; Pangborn, Greta

doi:10.1051/mmnp/20116606

Cited by 7 publications

(2 citation statements)

References 21 publications

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“…In a laboratory setting, an attempt to produce a target structure can result in an excess of costly branched junction molecules. Mathematical research done within the flexible tile model seeks to find a pot with the minimum numbers of bond-edge types and tile types required to construct a given target complex [6] [8]. We aim to find an accurate edge labeling of a specific graph with as few different half-edge labels as possible.…”

Section: Flexible Tile Based Modelmentioning

confidence: 99%

Tile Based Modeling of DNA Self-Assembly for Two Graph Families with Appended Paths

Griffin¹,

Sorrells²

2022

Preprint

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Branched molecules of deoxyribonucleic acid (DNA) can self-assemble into nanostructures through complementary cohesive strand base pairing. The production of DNA nanostructures is valuable in targeted drug delivery and biomolecular computing. With theoretical efficiency of laboratory processes in mind, we use a flexible tile model for DNA assembly. We aim to minimize the number of different types of branched junction molecules necessary to assemble certain target structures. We represent target structures as discrete graphs and branched DNA molecules as vertices with half-edges. We present the minimum numbers of required branched molecule and cohesive-end types under three levels of restrictive conditions for the tadpole and lollipop graph families. These families represent cycle and complete graphs with a path appended via a single cut-vertex. We include three general lemmas regarding such vertex-induced path subgraphs. Through proofs and examples, we demonstrate the challenges that can arise in determining optimal construction strategies.

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Section: Flexible Tile Based Modelmentioning

confidence: 99%

Tile Based Modeling of DNA Self-Assembly for Two Graph Families with Appended Paths

Griffin¹,

Sorrells²

2022

Preprint

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“…opening and closing of an active site of an enzyme and how that might be used to predict intermediate configurations of catalysis; Ellis-Monaghan and Pangborn (2011) [53] use graph theory to offer physical builders of DNA structures how to chose sequences that will self-assemble into particular three-dimensional lattices such as cubes, tetrahedra, and octahedral; and, Robic and Jungck (2011) [54] demonstrate the power of mathematical manipulatives in helping students understand topological processes accompanying replication, recombination and repair.…”

Section: Mathematical Challenges In Biology Educationmentioning

confidence: 99%

Mathematical Biology Education: Modeling Makes Meaning

Jungck

2011

Math. Model. Nat. Phenom.

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Abstract. This special issue of Mathematical Modelling of Natural Phenomena on biomathematics education shares the work of fifteen groups at as many different institutions that have developed beautiful biological applications of mathematics that are different in three ways from much of what is currently available. First, many of these selections utilize current research in biomathematics rather than the well-known textbook examples that are at least a half-century old. Second, the selections focus on modules that are intended for instant classroom adoption, adaptation, and implementation. Instead of focusing on how to overcome the challenges of implementing mathematics into biology or biology into mathematics or on educational research on the effectiveness of some small implementation, the authors develop individual biological models sufficiently well such that they can be easily adopted and adapted for use in both mathematics and biology classrooms. A third difference in this collection is the substantive inclusion of discrete mathematics and innovative pedagogies. Because calculus-based models have received the majority of the biomathematics modeling attention until very recently, the focus on discrete models may seem surprising. The examples range from DNA nanostructures through viral capsids to neuronal processes and ecosystem problems. Furthermore, a taxonomy of quantitative reasoning and the role of modeling per se as a different practice are contextualized in contemporary biomathematics education.Key words: biomathematics education, discrete mathematics, modeling AMS codes: 92-01 NarrativeMathematics plays an enormous role in the life sciences (Cohen, 2004) [1]. However, the amount and kind of mathematics used in most general biology education is woefully inadequate at most . While we were able to share many curricular successes, this issue did not afford us many opportunities to detail specific rich applications to biologists and mathematicians in a way that allowed easy adoption and adaptation into readers' classrooms. Thus, I welcomed the invitation from Editor Vitaly Volpert of Mathematical Modelling of Natural Phenomena to edit this special issue devoted to mathematical biology education. In particular, the congruence of interests of readers of this journal and the biomathematics education community are enormous. Besides such interesting biologically-oriented issues of MMNP on cancer, morphogenesis and development, plant structure, epidemiology, etc., MMNP's explicit focus on modeling per se lets us celebrate the tremendous importance of learning to model in the context of biomathematics education. Several articles herein, particularly by Weisstein, [5], Gaff et al. [6], Neuhauser and Stanley [7], and Koch [8], provide accessible approaches to introducing modeling to biology students with little or no prior experience in modeling.The considerable progress that has been made in addressing the challenges laid down in Bio 2010 [4] includes the mutual effort of biologists, mathematicians, and mathematic...

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