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A number of methods have been proposed over the last decade for encoding information using deoxyribonucleic acid (DNA), giving rise to the emerging area of DNA data embedding. Since a DNA sequence is conceptually equivalent to a sequence of quaternary symbols (bases), DNA data embedding (diversely called DNA watermarking or DNA steganography) can be seen as a digital communications problem where channel errors are analogous to mutations of DNA bases. Depending on the use of coding or noncoding DNA host sequences, which, respectively, denote DNA segments that can or cannot be translated into proteins, DNA data embedding is essentially a problem of communications with or without side information at the encoder. In this paper, the Shannon capacity of DNA data embedding is obtained for the case in which DNA sequences are subject to substitution mutations modeled using the Kimura model from molecular evolution studies. Inferences are also drawn with respect to the biological implications of some of the results presented.