Inspired by the micro-dots used during the 2nd world war, Clelland et al. developed an extension of this principle 1. The scientists produced artificial DNA strands, which contained secret messages. A triplet encodes one character or number (Table 1). The Clelland algorithm is a simple substitution cipher which encodes characters into DNA sequences using the following encoding function

• E : X → Y

• X ∈ {A, B, C,..., Z, 0, 1,..., 9, ".",","," : ","⊔"}

• Y ∈ {xyz : x, y, z ∈ {A, C, G, T}}

The decoding function is corresponding D : Y → X.

Now Clelland et al. ligated two primers with the synthesized DNA sequences, a forward and a reverse primer. These ligated sequences were mixed up with dummy strands. Important preconditions are:

• length of dummy strand = length of message DNA with primers

• #copies of each dummy = #copies of message DNA

The receiver must know the decoding function and the primer to decode the message. The primers are used for the polymerase chain reaction and in the last step the amplified DNA sequence has to be sequenced and decoded. To improve the security one can use dummy strands, which are not random but correspond to words out of a dictionary.

The original One-Time pad uses the XOR – exclusive or (⊕). In the case of DNA, the XOR is very impracticable and therefore it is better to use the properties of DNA. Gehani et al. established a DNA One-Time pad by creating word pairs 2. The first word is the plain text and the second one is the cipher text. After such a block of plain and cipher text, there is a stop codon (Figure 1). The DNA polymerase completes the plain and cipher text.

To encode a message, the plain text is mixed with the DNA sequences. It binds directly to the corresponding complementary sequence. The DNA polymerase creates the cipher text accordingly and the decoding is functionally analogous. The cipher text binds to its complement and the DNA polymerase creates the plain text.

Leier et al. encoded binary information into DNA sequences. A short DNA sequence represents the binary 1₂, another one represents 0₂ 3. Further there are another two short DNA sequences, which represent start and end. The fragments have sticky ends and can be ligated (Figure 2). All resulting sequences are like this s{0₂|1₂}e. The start and end marker have primer sequences on one site for the polymerase chain reaction, which can not be ligated.

Although it seems to be more complicated, it is very similar to the algorithm of Clelland et al. The resulting DNA sequence is mixed with dummy strands and can only be detected and isolated knowing the primer sequences.

Wong et al. developed a steganographic algorithm based on DNA, which is able to store data in living organisms 4. The data are translated into a DNA sequence which is inserted into a vector. The insert sequence is flanked by two primer sequences which do not exist in the genome yet. This vector is introduced into a cell of a living organism where it coexists and is replicated with the genomic DNA. To extract the data they used a polymerase chain reaction.

Wong et al. used a substitution cipher similar to Clelland et al. to encode a song text into a DNA sequence and stored it in Deinococcus radiodurans. Deinococcus radiodurans survive extreme conditions, e.g. ionizing radiation, so the song text can be stored for hundreds of years.

Arita et al. developed a steganographic algorithm based on the degenerative genetic code. Amino acid codes are redundant so that the translation of mRNA into proteins is a substitution cipher with the following characteristics

• E : X → Y

• X ∈ {xyz : x, y, z ∈ {A, C, G, U}}

• Y ∈ {A, C, D, E, F, G, H, I, K, L, M, N, P, Q, R, S, T, V, W, Y, STOP}

But the inverse function D : Y → X is not injective.

An example:

threonine(T) = E(ACU) = E(ACC) = E(ACA) = E(ACG)

The triplet of threonine is redundant in the third base so mutations in the third base do not exert any influence on the translation of threonine and the translated protein. These mutations are called "synonymous substitutions", in contrast to the "non-synonymous substitutions".

Arita et al. translated each letter of the English alphabet into six codons (Table 2). A value of 0 means to keep the original base at the third position of a codon, while a value of 1 means to change the third base at that position. Arita et al. added a parity bit to each letter, to keep it odd for possible error detection 5. They encoded 'KEIO' into the ftsZ gene of Bacillus subtilis which is essential for cell division and demonstrated as expected that the changed codon sequences did not affect the cell division, colony morphology, growth rate and sporulation frequency of these bacteria. To extract the encoded message one has to know the original sequence so that one can decide whether the codon is the original or the altered sequence.

DNA-Crypt encodes binary information using the following substitution cipher:

• E : X → Y

• X = {xy : x, y ∈ {0₂, 1₂}}

• Y ∈ {A, C, G, T}

A standard setting is given in table 4.

The binary sequence 0111001001001111₂ would be encoded to E(0111001001001111₂) = GATCGTAA.

Two bits could be encoded by one base, so one byte needs four bases for its encoding.

Based on this binary encryption, several private and public key cryptographic algorithms are integrated in DNA-Crypt:

• One-Time pad 6

• AES 7

• Blowfish 6

• RSA 89

To use DNA-Crypt one has to register so that DNA-Crypt can create AES, Blowfish and RSA keys for the user. These keys can be used to encrypt the binary information which then gets integrated into the genome. In addition it is possible to export and to import these keys and to exchange them with other users. Further the user can create new keys in DNA-Crypt or delete old ones. Another possibility is to use a One-Time pad instead of an encryption key. Compared to Arita et al. our substitution cipher allows to use several encryption algorithms as decribed above. In addition DNA-Crypt offers a better storage utilization compared to the algorithm of Arita et al. (four instead of six synonomous codons per character).

Mutations do not occur very often, approximately 10^-10 to 10^-15 per cell division, but they can destroy the encrypted information in DNA sequences. To correct these failures DNA-Crypt uses a correction code based on binary correction. One of them is the 8/4 Hamming-code and another one is the WDH-code 10. The advantage of the WDH-code is that it can correct more mutations than the 8/4 Hamming-code. The n-times WDH-code repeats the enrypted DNA sequence n times. It can correct ⌊n−12⌋ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaGbdaqaamaalaaabaGaemOBa4MaeyOeI0IaeGymaedabaGaeGOmaidaaaGaayj84laawUp+aaaa@3608@ failures. All WDH-codes where n is an odd number are perfect.

The 8/4 Hamming-code can only correct ≤ 25% of the mutations. Four bits are used for information (b3,b2,b1,b0) and the other four bits as parity bits. A complete byte is represented by these eight bits b₃,b₃ ⊕ b₂ ⊕ b₁,b₂, ¬b₂ ⊕ b₁ ⊕ b₀,b₁, ¬b₃ ⊕ b₁ ⊕ b₀,b₀, ¬b₃ ⊕ b₂ ⊕ b₀

which are called h7, h6, h5, h4, h3, h2, h1, h0. To decode the byte, the following parity sums are build:

• p = h₇ ⊕ h₆ ⊕ h₅ ⊕ h₄ ⊕ h₃ ⊕ h₂ ⊕ h₁ ⊕ h₀

c₀ = h₇ ⊕ h₅ ⊕ h₁ ⊕ h₀

c₁ = h₇ ⊕ h₃ ⊕ h₂ ⊕ h₁

c₂ = h₅ ⊕ h₄ ⊕ h₃ ⊕ h₁

If p = 1 there are 0 or 2 failures in the byte. The byte was transmitted correct, if the parity bits c₀, c₁, c₂ are correct, which means equal to 1. If not, there happened 2 failures, which cannot be corrected.

If p = 0 there is 1 failure in the byte which can be corrected using table 5.

Only one of four bits can be corrected. But not all mutations can be corrected by the 8/4 Hamming-code. Failures which only differ in one bit can be corrected, e.g. 00 ↔ 01 or 11 ↔ 10. Failures like 00 ↔ 11 or 10 ↔ 01 cannot be corrected.

The limiting resource for mutation correction is not the time, but the space. The advantage of the 8/4 Hamming-code is that it is very compact. The space requirements of the 8/4 Hamming-code is f(n) = 2n ∈ Θ(n). In contrast to f(n)={n2, n is an odd numbern2+n, else}∈Θ(n2) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzcqGGOaakcqWGUbGBcqGGPaqkcqGH9aqpdaGadeqaauaabeqaceaaaeaacqWGUbGBdaahaaWcbeqaaiabikdaYaaakiabcYcaSiabbccaGiabd6gaUjabbccaGiabdMgaPjabdohaZjabbccaGiabdggaHjabd6gaUjabbccaGiabd+gaVjabdsgaKjabdsgaKjabbccaGiabd6gaUjabdwha1jabd2gaTjabdkgaIjabdwgaLjabdkhaYbqaaiabd6gaUnaaCaaaleqabaGaeGOmaidaaOGaey4kaSIaemOBa4MaeiilaWIaeeiiaaIaemyzauMaemiBaWMaem4CamNaemyzaugaaaGaay5Eaiaaw2haaiabgIGiolabfI5arjabcIcaOiabd6gaUnaaCaaaleqabaGaeGOmaidaaOGaeiykaKcaaa@620B@ for the WDH-code.

For example to encode one byte, which means a DNA sequence of four bases, the 8/4 Hamming-code needs eight synonymous codons instead of twenty synonymous codons for the 5-times WDH-code. In contrast to the data published by Arita et al. we can not only exibit error detection but error corrections which enables us to maintain the data. This obviously represents an important advantage.

The integrated fuzzy controller decides and recommends whether to use the 8/4 Hamming-code, the WDH-code or no mutation correction for optimal performance 11121314 [see Additional file 2]. It uses the Singleton-fuzzyfication and has three input dimensions with each separated into three triangular sets. The first dimension is the individual mutation rate (φ) of the DNA sequence containing the secret message (Figure 5). This is based on a standard mutation rate, by default 1 * 10^-7 for prokaryotes and 1 * 10^-10 for eukaryotes, which is changed by specific mutation rates (α_i) for each base pair. These changes are based on the transversion and transition rate and in addition on the stability (δ) of GC rich regions.

• φ=∑i=03αi/4 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFgpGzcqGH9aqpdaaeWaqaaiab=f7aHnaaBaaaleaacqWGPbqAaeqaaOGaei4la8IaeGinaqdaleaacqWGPbqAcqGH9aqpcqaIWaamaeaacqaIZaWma0GaeyyeIuoaaaa@3ABE@

• α0=#C∗(∑i=A,G,T3αCi/3)/δ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFXoqydaWgaaWcbaGaeGimaadabeaakiabg2da9iabcocaJiabdoeadjabgEHiQiabcIcaOmaaqadabaGae8xSde2aaSbaaSqaaiabdoeadjabdMgaPbqabaGccqGGVaWlcqaIZaWmcqGGPaqkcqGGVaWlcqWF0oazaSqaaiabdMgaPjabg2da9iabdgeabjabcYcaSiabdEeahjabcYcaSiabdsfaubqaaiabiodaZaqdcqGHris5aaaa@47FE@

• α1=#G∗(∑i=A,C,T3αGi/3)/δ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFXoqydaWgaaWcbaGaeGymaedabeaakiabg2da9iabcocaJiabdEeahjabgEHiQiabcIcaOmaaqadabaGae8xSde2aaSbaaSqaaiabdEeahjabdMgaPbqabaGccqGGVaWlcqaIZaWmcqGGPaqkcqGGVaWlcqWF0oazaSqaaiabdMgaPjabg2da9iabdgeabjabcYcaSiabdoeadjabcYcaSiabdsfaubqaaiabiodaZaqdcqGHris5aaaa@4808@

• α2=#A∗∑i=C,G,T3αAi/3 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFXoqydaWgaaWcbaGaeGOmaidabeaakiabg2da9iabcocaJiabdgeabjabgEHiQmaaqadabaGae8xSde2aaSbaaSqaaiabdgeabjabdMgaPbqabaGccqGGVaWlcqaIZaWmaSqaaiabdMgaPjabg2da9iabdoeadjabcYcaSiabdEeahjabcYcaSiabdsfaubqaaiabiodaZaqdcqGHris5aaaa@43C6@

• α3=#T∗∑i=A,C,G3αTi/3 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFXoqydaWgaaWcbaGaeG4mamdabeaakiabg2da9iabcocaJiabdsfaujabgEHiQmaaqadabaGae8xSde2aaSbaaSqaaiabdsfaujabdMgaPbqabaGccqGGVaWlcqaIZaWmaSqaaiabdMgaPjabg2da9iabdgeabjabcYcaSiabdoeadjabcYcaSiabdEeahbqaaiabiodaZaqdcqGHris5aaaa@43EE@

The first input dimension is separated into three triangular sets X_i = (a_m, a_λ, a_ρ) 151617181920. The first called "low" = (0, 0, 6) describes a low mutation rate. The second "middle" = (10, 4, 16) and the third "high" = (20, 14, 20) describes a middle and a high mutation rate.

The second input dimension is the length of the DNA sequence containing the secret message (Figure 6).

The triangular sets are "short" = (0, 0, 24), "middle" = (40, 16, 64) and "long" = (80, 56, 80).

The third input dimension is the stability over time, which is represented by the number of generations (Figure 7). It is separated into "low" = (0, 0, 400), "middle" = (500, 100, 900) and "high" = (1000, 600, 1000).

The three input dimensions are linked through a set of rules based on heuristics to one output dimension [see Additional file 3]. The maximum of each correction code means a cut on the y axis (Figure 8). In the next step the fuzzy controller decides, whether to use an 8/4 Hamming-code, a WDH-code or no mutation correction by using the first-maximum method and recommends it to the user.

The small GTPases termed Ypt in yeast and Rab in higher eukaryotes are molecular switches in cellular transport processes 21. Each Ypt protein is localized to the membrane of specific intracellular compartments and highly specific for a particular transport step 22.

The Ypt7 GTPase from S. cerevisiae is involved in late endosome-to-vacuole transport and vacuole fusion events 2324. Ypt7 is one of the 11 members of the S. cerevisiae Ypt family and is homologous to mammalian Rab7.

Analysis of the Ypt7 DNA sequence showed that 32% of the codons allow synonymous substitutions, resulting in 16 bytes, which could be encrypted (Table 6). The first steganogram contains the message "this is a test" and the second one "yet another test" [see Additional file 4].

The results of the analyses of these steganograms with the fuzzy controller are shown in table 7. Translation with DNA-Crypt and the Expasy Translate Tool shows that the translated amino acid sequences are identical 25.

The pairwise and the multiple sequence alignments show a few mismatches between the three sequences (Figures 9, 10, 11).

The pairwise sequence alignment was performed with Dotlet and the multiple sequence alignment was performed using ClustalW of the European Bioinformatics Institute with standard settings 2627.