The experimental conditions by which electromagnetic signals (EMS) of low frequency can be emitted by diluted aqueous solutions of some bacterial and viral DNAs are described. That the recorded EMS and nanostructures induced in water carry the DNA information (sequence) is shown by retrieval of that same DNA by classical PCR amplification using the TAQ polymerase, including both primers and nucleotides. Moreover, such a transduction process has also been observed in living human cells exposed to EMS irradiation. These experiments suggest that coherent long-range molecular interaction must be present in water to observe the above-mentioned features. The quantum field theory analysis of the phenomenon is presented in this article.