Our DNA strands are tight together by hydrogen bonds. Can the proton of Hydrogen tunnel to the other complementary strand, and by this during the replication bind to a different/wrong nucleotide, causing a point mutation?
Keto-enol tautomerism involving proton transfer within a single DNA base can lead to mispairing and mutation during replication. This is touched on in the previous citation provided by tsttst as well as this section from An Introduction to Genetic Analysis. 7th edition: https://www.ncbi.nlm.nih.gov/books/NBK21897/ I have not found a clear statement of whether the proton transfer is over sufficient distance to constitute "tunneling".