Sir John, Mark Quinn and the new portrait
The portrait, on show from Wednesday, is by Marc Quinn, one of the UK's most controversial young artists.
Sir John contributed a sample of DNA from his sperm to be used by Quinn in the work.
The result is a picture about the size of an A4 piece of paper surrounded by a stainless steel frame - representative of a sterile scientific environment.
Sir John led the British effort to decode the human genome. Quinn rose to fame in the early 90s with his picture Self, a sculpture made from a cast of his head in nine pints of his own deep-frozen blood.
Sense of communality
Commenting on his work, Quinn said: "Even though in artistic terms it seems to be abstract, in fact it is the most realistic portrait in the Portrait Gallery.
"It carries the actual instructions that led to the creation of John. It is a portrait of his parents, and every ancestor he ever had back to the beginning of life in the Universe."
To make the image on display at the gallery, Quinn placed Sir John's DNA in agar jelly. Bacterial cultures were then grown from the sample.
Sir John is the former director of the Sanger Centre in Cambridge, which deciphered about one-third of the genetic instructions for human life. The other two-thirds were decoded in labs around the world - mostly in the US.
Sir John Sulston said: "The portrait contains a small fraction of my DNA, though there is ample information to identify me.
"I like that it makes the invisible visible, and brings the inside out. This is a portrait of our shared inheritance and communality, as well as of one person."
Major prize
Quinn, who has had solo exhibitions at some of the world's leading galleries, is no stranger to mixing art with science.
One of his recent exhibitions was an installation made from a test tube containing a thread of his own DNA.
In 1999, he began a body of work that consisted of sculptural portraits of people who had lost limbs.
His life-size cast Catherine Long 2000 won the Wollaston prize at the Royal Academy.
Quinn's portrait of Sir John was acquired by the National Portrait Gallery as part of its aim to take a broader view of portraiture.
It follows the gallery's unveiling earlier this month of portraits of the pop group Blur by Julian Opie, along with self-portraits by important British female artists, Tracey Emin and Sarah Lucas.