Quantum biology. pi-pi entanglement signatures in protein-DNA interactions

The biological functions of DNA are carried out by individual proteins that interact with specific sequences along the DNA in order to prime the molecular processes required by the cellular metabolism. Protein-DNA interactions include DNA replication, gene expression and its regulation, DNA repair, DNA restriction and modification by endonucleases, generally classified as enzymatic functions, or transcription factors functions. To find specific binding target sequences and achieve their aims, in less than one second proteins operate in symbiosis with a crowded cellular environment, identifying extremely small cognate sequences along the DNA chain, which range from 15-20 bps for repressors to 4-6 bps for restriction enzymes. In a previous work, we proposed that the extraordinary ability of proteins to identify consensus sequences on DNA in a short time appears to be dependent on specific quantum signatures such as the entanglement of pi-pi electrons between DNA nucleotides and protein amino acids, where the couple of pi electrons function as a radical pair, one pi electron is located on a specific site of sequence to be identified and the other one performs a quantum walk to identify possible sites of consensus sequence. In this paper, we use the restriction endonucleases enzymes, EcoRV and EcoRI as a case study. These enzymes are able to recognize 3'-GATACT-5' or 3'-GAATCT-5' sequences, respectively. We exploit the analogy of a coin operator with a Bloch sphere to demonstrate that the entanglement between pi-pi electrons generated at the contacts on specific GA dimers between proteins and DNA relies on the spin of the electrons that form an initial singlet state. The latter is a maximally entangled state so that the identification of specific nucleotides is associated with the formation of singlet states. On the other hand, during the identification of subsequent GA dimers, the spin-orbit interaction on walking pi electron induces triplet transitions so that singlet-triplet transitions should manifest an experimentally measurable effect. We propose that the possible experimental evidence of entanglement between pi-pi electrons may be due to the phosphorescence signal correspondence to triplet decay processes.