Since there isn’t really a “pattern” as such, I borrowed notes from other knitters.

Short pattern below thanks to Cysiphist:
Cast on 4 stitches.
Row 1: kfb all around
Row 2: knit
Row 3: kfb all around
Row 4: Do two kfbs somewhere in the row, knit rest
Row 5: knit - 6 stitches per needle. 18 total.
Row 6: Start Right twist helix - use m1L for increase and decrease by binding off one.

Needle 1: k1, m1L k5;
Needle 2: k4, pass 3rd knit stitch over, k2;
Needle 3: k6.
Feed last stitch from Needle 1 to Needle 2. Repeat.

Used fbz’s suggestion for making the backbones/spirals

for the spirals: cast on 17 stitches,

working on double point needles divide up stitches across three needles. Join stitches and make sure they are not twisted. K17 for two set up rows.
every row: k1, m1L, k7, K2tog, K7.

joined for magic loop with 11 stitches on the front, 6 on the back. k17 for two set up rows.
every row: k1, m1L, k7, k2tog, k1 front, k6 back.

no need to move stitches around and no holes in the knitting to be stitched up later.

For the base pairs did 12 stitches and not 9.

Super detailed notes from Peckiepeck(!):
Using magic loop method. Start with cysiphist instructions for cast on and initial increases. Altered them slightly so finished with 17 stitches instead of 18, ready to follow rkaplan instructions for the main body of the backbones/spirals, which I also altered slightly as I prefer Kfb for increases.

Cast on 4 stitches. Join in the round.
Row 1: kfb all around = 8
Row 2: knit
Row 3: kfb all around = 16
Row 4: One more kfb somewhere in the row, knit rest = 17
Row 5: knit - 11 stitches front needle, 6 stitches on the back needle = 17 total.

Then every row: kfb (or if you prefer k1, m1L), k7, k2tog, k1 (end of front needle), k6 (end of back needle).
No need to move stitches around and no holes in the knitting to be stitched up later.
Don’t forget to stuff as you go! Stuffing at the end (I’ve been warned) is a nightmare!
I knitted until it measured 30cm when held straight, about 24cm in natural curved state.

To close - Row 1: K2tog all around ending with a K1 due to odd number of stitches = 9
Row 2: Knit
Row 3: K2tog all around ending with a K1 due to odd number of stitches = 5
Break yarn and weave through last 5 stitches and draw up, weave in ends.

For the base pairs (did 12 stitches and not 9)
Cast on 6 stitches. Join in the round.
Row 1: kfb all around = 12 (this makes a flat bottom for sewing to backbone twists.)
Row 2: knit all
Continue in knit doing colour change.
I didn’t do all of the bases with identical colour work, as I kept loosing count! Just tried to make them the same length!

The fiddliest bit is positioning the base pairs between the spiral backbones. I got my bloke to help and we used thin needles to spear straight through the spiral, down the centre of each base pair and out of the opposite spiral. When you are happy with the positioning of them all, start stitching them in place.

If I made it again, I think I would try to put something rattle like inside.

Nerdy Science Details from LauraPNW:
Choose your sequence of bases carefully. LauraPNW’s coding strand is ATG AGC TGA, which when translated into a protein will be Methionine (start codon), and then Serine, ending with a stop codon. It also contains a restriction site for the enzyme AluI, which is in the middle of the AGCT sequence.

Make it 9 base pairs long so that it contains 3 complete codon sequences.

I didn’t do the colorwork on the base pairs because I thought it made the size difference in the base lengths hard to see. I just made sure that one side of my base pair was twice as long as the other to represent purines and pyrimidines.
Purines: Adenine - Pink / Guanine - Blue
Pyrimidines: Thymine - Purple / Cytosine - Yellow