A code for protein folding and bio-catalysis

The TGD inspired model for the evolution of genetic code leads to the idea that the folding of proteins obeys a folding code inherited from the genetic code. After some trials one ends up with a general conceptualization of the situation with the identification of wormhole magnetic flux tubes as correlates of attention at molecular level so that a direct connection with TGD inspired theory of consciousness emerges at quantitative level. This allows a far reaching generalization of the DNA as topological quantum computer paradigm and makes it much more detailed. By their asymmetric character hydrogen bonds are excellent candidates for magnetic flux tubes serving as correlates of attention at molecular level.

The constant part of free amino-acid containing O-H, O=, and NH₂ would correspond to the codon XYZ in the sense that the flux tubes would carry the "color" representing the four nucleotides in terms of quark pairs. Color inheritance by flux tube reconnection makes this possible. For the amino-adics inside protein O= and N-H would correspond to YZ. Also flux tubes connecting the acceptor atoms of hydrogen bonds are required by the model of DNA as topological quantum computer. The long flux tubes between O= atoms and their length reduction in a phase transition reducing Planck constant could be essential in protein-ligand interaction.

The model predicts a code for protein folding: depending on whether also =O-O= flux tubes are allowed or not, Y=Z or Y=Z_c condition is satisfied by the amino-acids having N-H-O= hydrogen bond. For =O-O= bonds Y-Y_c pairing holds true. Y=Z_c option predicts the average length of alpha bonds correctly. Y=Z rule is favored by the study of alpha helices for four enzymes: the possible average length of alpha helix is considerably longer than the average length of alpha helix if gene is the unique gene allowing to satisfy Y=Z rule. The explicit study of alpha helices for four enzymes demonstrates that the failure to satisfy the condition for the existence of hydrogen bond fails rarely and at most for two amino-acids (for 2 amino-acids in single case only). For beta sheets there ar no failures for Y=Z option.

The information apparently lost in the many-to-one character of the codon-amino-acid correspondence would code for the folding of the protein and similar amino-acid sequences could give rise to different foldings. Also catalyst action would reduce to effective base pairing and one can speak about catalyst code. The DNA sequences associated with alpha helices and beta sheets are completely predictable unless one assumes a quantum counterpart of wobble base pairing meaning that N-H flux tubes are before hydrogen bonding in quantum superpositions of braid colors associated with the third nucleotides Z of codons XYZ coding for amino-acid. Only the latter option works. The outcome is very simple quantitative model for folding and catalyst action based on minimization of energy and predicting as its solutions alpha helices and beta sheets.

I want to express my gratitude for Dale Trenary for interesting discussions, for suggesting proteins which could allow to test the model, as well as providing concrete help in loading data help from protein data bank. Also I want to thank Timo Immonen for loaning the excellent book "Proteins: Structures and Molecular Properties" of Creighton. Also Pekka Rapinoja for writing the program transforming protein data file to a form readable by MATLAB.

For details see the new chapter A Model for Protein Folding and Bio-catalysis of "Genes and Memes".