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A one-liner using ListLinePlot3D to visualize a gene

Lucien Grondin, hobbyist
Posted 4 years ago

I had already posted something similar but with the new 12.3.1 function ListLinePlot3D it becomes even easier so I thought it was worth sharing.

You can visualize a nucleic acid sequence in 3d with a few lines of code :

GenomeData["HOXA1", "FullSequence"] //
    Characters //
   # /. {
      "A" -> {1, 1, 1},
      "C" -> {-1, 1, -1},
      "G" -> {-1, -1, 1},
      "T" -> {1, -1, -1}
      } & //
  FoldList[Plus, #] & //
 ListLinePlot3D[#, BoxRatios -> {1, 1, 1}] &

enter image description here

The idea comes from this work : https://youtu.be/IjGZ6kF2gbQ The point is to make it possible to visually compare sequences to see if they are related.

I find that the colors don't matter much. With a long enough chain, they become indiscernable so only the overall shape of the curve is useful.
POSTED BY: Lucien Grondin
2 Replies
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One tactic that appears in the literature is to take Fourier transforms of the 3d sequences. And there are other methods as well. This Community post shows one such, by Mads Bahrami. It works with what are called "Z curves", but these are formed by accumulating the 3d sequences. This one (by me) uses Fourier computations on the sequence you describe, although I might have oriented the tetrahedron differently.

This is not to suggest that the plots you use are in any way bad, but rather to indicate some other possible modes of analyzing the sequences (and they too are amenable to plotting).
POSTED BY: Daniel Lichtblau

I didn't know about Z-curves, thanks. Here is my attempt at implementing it in the Wolfram language :

ZCurve[seq_String] := ListLinePlot3D[
  Transpose[
   {
      (#[["A"]] + #[["G"]]) - (#[["C"]] + #[["T"]]),
      (#[["A"]] + #[["C"]]) - (#[["G"]] + #[["T"]]),
      (#[["A"]] + #[["T"]]) - (#[["C"]] + #[["G"]])
      } &@
    Association[# -> FoldList[
         Plus, 0, Characters@seq /. {# -> 1, _String -> 0}
         ] & /@ Characters@"ACGT"
     ]
   ], BoxRatios -> {1, 1, 1}
  ]

ZCurve[GenomeData["HOXA1", "FullSequence"]]

It's a bit more complicated and less elegant but oh well.
POSTED BY: Lucien Grondin
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