The information isn't lost in gene expression

The present question is the possibility of information loss in gene expression? Information loss in the gene expression disrupts the cellular dynamics and can lead to serious defects, including cancer. Using Gottesman and Preskill method for calculating information loss in black holes,a mechanism for calculating the amount of information transformation in gene expression is proposed. In this proposal, there are three different Hilbert spaces that belong to degrees of freedom of DNA, RNA, and protein. The genetic sequence of the DNA is transcribed into protein at two stages. At first stage it is shown that the internal stationary state of the cell can be represented by a maximally entangled two-mode squeezed state of DNA and mRNA.At second stage, the state of the cell is described by a maximally entangled two-mode squeezed state of mRNA and protein. The amount of information transformation can be obtain by projecting the state at first stage on the state at second stage. Evidently for all finite values of the transcription factor concentration y, binding energy E and free energy F of the transcription factor, the information isn't lost in gene expression.