Spend enhancement materials to raise a piece from +0 to +10. Each level makes all of its stats and ability bonuses 8% stronger. +3 and +5 add extra rolls, and every enhance has a chance to mutate the piece. There's no level requirement, only the materials. The Viral Genome can't be enhanced.
Polymerase Shards also scale by tier: ×10 on Common, then 30% more for each tier up (×13, ×16.9 … about ×48 on Prismatic; the list above already includes Common's ×10)
+3% per item level above 1 (rounded up)
Example: a Prismatic piece at item level 1 costs about 445,000 Shards, 2,010 Chaperones and 530 Ribozyme Cores from +0 to +10
From the Codex
RNA molecules that act as enzymes, cutting and joining RNA without any protein help.
Fun fact: The ribosome's core catalytic site is a ribozyme, a living fossil of an early "RNA world".