Visualizing the Effects of Single Point Mutations on RNA Codons Using Graph Theory

Abstract

In our graph, vertices represent the 20 amino acids and the "Stop" signal. An edge connects two vertices if the amino acids they represent can be interchanged through a single point mutation in their corresponding codons. This graph is not just a visualization but an analytical tool, spotlighting the possible amino acid replacements due to minor genetic variations.

Using the computational capabilities of Mathematica, and with the expertise provided by Centaur Intelligence, each amino acid (and the Stop signal) is successively emphasized. When highlighted, all directly reachable amino acids through a single point mutation are illuminated, thus displaying the mutation landscape for each amino acid.

Full text

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Visualizing the Effects of Single Point Mutations on RNA
Codons Using Graph Theory
Douglas C. Youvan
doug@youvan.com
September 28, 2023
The genetic code serves as the blueprint of life, guiding the
synthesis of proteins from RNA sequences. Although extensively
studied, new methodologies can provide fresh perspectives on its
intricate nature. In this work, utilizing graph theory and aided by
Centaur Intelligence, we dissected the genetic code to illuminate
the potential impacts of single point mutations on RNA codons.
Introduction: Every RNA codon, a triplet of nucleotides,
translates to an amino acid or a stop signal. A single point
mutation in this codon can either have no effect or result in the
coding of a different amino acid. Understanding these potential
transitions provides insights into the robustness and
vulnerabilities of the genetic code.
YouTube video:
https://www.youtube.com/watch?v=WsGw5w6tiyE

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Methods:
1. Graph Construction: In our graph, vertices represent the 20
amino acids and the "Stop" signal. An edge connects two
vertices if the amino acids they represent can be
interchanged through a single point mutation in their
corresponding codons. This graph is not just a visualization
but an analytical tool, spotlighting the possible amino acid
replacements due to minor genetic variations.
2. Highlighting Mechanism: Using the computational
capabilities of Mathematica, and with the expertise provided
by Centaur Intelligence, each amino acid (and the Stop
signal) is successively emphasized. When highlighted, all
directly reachable amino acids through a single point
mutation are illuminated, thus displaying the mutation
landscape for each amino acid.
Results: The resultant graph unravels the dense web of
interconnections among amino acids based on single point
mutations. As we animate through each amino acid, patterns
emerge, revealing which amino acids can easily mutate into
others and which remain more isolated.
Discussion: This visualization offers a unique vantage point on
the genetic code. For instance, amino acids with numerous
connections can transition to a variety of other amino acids with
just a minor mutation. This might imply a greater evolutionary
flexibility but also suggests vulnerabilities to mutations causing
diseases.
In addition, by utilizing a graphical approach, the often abstract
concept of single point mutations becomes tangible and
comprehensible, even for those not deeply versed in genetics.

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Conclusion:
In collaboration with Centaur Intelligence, we have married
biology with mathematics to yield a fresh, intuitive perspective on
the genetic code. This method not only aids in comprehension but
also serves as a foundation for further explorations into the
resilience and adaptability of life at the molecular level.