Methods of gene assembly using DNAzymes and use in DNA data storage

A system for DNA synthesis, comprising:

• a first DNA symbol library comprising a number of single strand oligo first nibble symbols, each first nibble symbol having a base section and a 3′-phosphorimidazolide S1 end;
• a second DNA symbol library comprising a number of single strand oligo second nibble symbols, each second nibble symbol having a base section and a 5′-hydroxyl S2 end;
• a DNA linker library comprising a first set of single strand oligo linkers each having a 3′-phosphorimidazolide S1 end and a 5′-hydroxyl S2 end, and a second set of single strand oligo linkers each having a 3′-phosphorimidazolide S1 end and a 5′-hydroxyl S2 end;
• and
• a DNAzyme library comprising a number of DNA ligating DNAzymes, each DNA ligating DNAzyme having a 3′-phosphorimidazolide complementary S1 end and a 5′-hydroxyl complementary S2 end;
• wherein:
• wherein each of the linkers has a sequence specificity for the DNA ligating DNAzymes, and one or both of the S1 end and the S2 end of each of the linkers hybridizes to a complementary one of the DNA ligating DNAzymes;
• the base section of a first nibble symbol joins the base section of a second nibble symbol;
• the S1 end of a first DNA ligating DNAzyme joins the S1 end of one of the first nibble symbols and the S2 end of the first DNA ligating DNAzyme joins the S2 end of a first linker, and
• the S1 end of a second DNA ligating DNAzyme joins the S1 end of a second linker and the S2 end of the second DNA ligating DNAzyme joins the S2 end of one of the second nibble symbols.

A method of making a DNA strand, comprising:

• providing a DNA symbol library comprising a number of single strand DNA oligo symbols, each symbol having a 3′-phosphorimidazolide S1 end and a 5′-hydroxyl S2 end;
• providing a DNA linker library comprising a first set of single strand DNA oligo linkers having a 3′-phosphorimidazolide S1 end and a second set of single strand DNA oligo linkers having a 5′-hydroxyl S2 end, wherein each of the linkers has a sequence specificity for the DNA ligating DNAzymes, and one or both of the S1 end and the S2 end of each of the linkers hybridizes to a complementary one of the DNA ligating DNAzymes;
• providing a DNAzyme comprising a number of DNA ligating DNAzymes having a 3′-phosphorimidazolide complementary S1 end and a 5′-hydroxyl complementary S2 end;
• joining the S1 end of a first DNA ligating DNAzyme to the S1 end of a symbol and the S2 end of the first DNA ligating DNAzyme to the S2 end of a first linker;
• and
• joining the S1 end of a second DNA ligating DNAzyme to the S1 end of a second linker and the S2 end of the second DNA ligating DNAzyme to the S2 end of the symbol.