Instructions for Thoki Yenn’s original DNA model can be found in his Orikata book. I think there are also some tutorials on YouTube.
Once you know how to fold that model, instead of an A4 sheet, use a long strip, around 1:8 or longer (I used ca. 5×40 cm paper). Fold it in half so that you get a strip with ca 1:4 proportions, and then fold the DNA model using this strip, through both layers. It requires some modification: you do not fold the model in half lengthwise as in the original, and the edges require a bit of change. Basically, you only precrease the “ladder” part of the model. Finally, after precreasing and twisting the model, at the end with two separate raw edges, separate the two layers, thus partially unwinding the double helix.