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<a href=/index.xml target=_blank>RSS</a></nav></header><main><div><h1>Encoding binary data into DNA sequence</h1><p>Jan 3, 2019<div><h2 id=initial-thoughts>Initial thoughts</h2><p>Imagine a world where you could go outside and take a leaf from a tree and put
it through your personal DNA sequencer and get data like music, videos or
computer programs from it. Well, this is all possible now. It was not done on a
large scale because it is quite expensive to create DNA strands but it's
possible.<p>Encoding data into DNA sequence is relatively simple process once you understand
the relationship between binary data and nucleotides and scientists have been
making large leaps in this field in order to provide viable long-term storage
solution for our data that would potentially survive our specie if case of
global disaster. We could imprint all the world's knowledge into plants and
ensure the survival of our knowledge.<p>More optimistic usage for this technology would be easier storage of ever
growing data we produce every day. Once machines for sequencing DNA become fast
enough and cheaper this could mean the next evolution of storing data and
abandoning classical hard and solid state drives in data warehouses.<p>As we currently stand this is still not viable but it is quite an amazing and
cool technology.<p>My interests in this field are purely in encoding processes and experimental
testing mainly because I don't have the access to this expensive machines. My
initial goal was to create a toolkit that can be used by everybody to encode
their data into a proper DNA sequence.<h2 id=glossary>Glossary</h2><p><strong>deoxyribose</strong> A five-carbon sugar molecule with a hydrogen atom rather than a
hydroxyl group in the 2′ position; the sugar component of DNA nucleotides.<p><strong>double helix</strong> The molecular shape of DNA in which two strands of nucleotides
wind around each other in a spiral shape.<p><strong>nitrogenous base</strong> A nitrogen-containing molecule that acts as a base; often
referring to one of the purine or pyrimidine components of nucleic acids.<p><strong>phosphate group</strong> A molecular group consisting of a central phosphorus atom
bound to four oxygen atoms.<p><strong>RGB</strong> The RGB color model is an additive color model in which red, green and
blue light are added together in various ways to reproduce a broad array of
colors.<p><strong>GCC</strong> The GNU Compiler Collection is a compiler system produced by the GNU
Project supporting various programming languages.<h2 id=data-encoding>Data encoding</h2><p><strong>TL;DR:</strong> Encoding involves the use of a code to change original data into a
form that can be used by an external process.<p>Encoding is the process of converting data into a format required for a number
of information processing needs, including:<ul><li>Program compiling and execution<li>Data transmission, storage and compression/decompression<li>Application data processing, such as file conversion</ul><p>Encoding can have two meanings:<ul><li>In computer technology, encoding is the process of applying a specific code,
such as letters, symbols and numbers, to data for conversion into an
equivalent cipher.<li>In electronics, encoding refers to analog to digital conversion.</ul><h2 id=quick-history-of-dna>Quick history of DNA</h2><ul><li><strong>1869</strong> - Friedrich Miescher identifies "nuclein".<li><strong>1900s</strong> - The Eugenics Movement.<li><strong>1900</strong> – Mendel's theories are rediscovered by researchers.<li><strong>1944</strong> - Oswald Avery identifies DNA as the 'transforming principle'.<li><strong>1952</strong> - Rosalind Franklin photographs crystallized DNA fibres.<li><strong>1953</strong> - James Watson and Francis Crick discover the double helix structure of DNA.<li><strong>1965</strong> - Marshall Nirenberg is the first person to sequence the bases in each codon.<li><strong>1983</strong> - Huntington's disease is the first mapped genetic disease.<li><strong>1990</strong> - The Human Genome Project begins.<li><strong>1995</strong> - Haemophilus Influenzae is the first bacterium genome sequenced.<li><strong>1996</strong> - Dolly the sheep is cloned.<li><strong>1999</strong> - First human chromosome is decoded.<li><strong>2000</strong> – Genetic code of the fruit fly is decoded.<li><strong>2002</strong> – Mouse is the first mammal to have its genome decoded.<li><strong>2003</strong> – The Human Genome Project is completed.<li><strong>2013</strong> – DNA Worldwide and Eurofins Forensic discover identical twins have differences in their genetic makeup.</ul><h2 id=what-is-dna>What is DNA?</h2><p>Deoxyribonucleic acid, a self-replicating material which is <strong>present in nearly
all living organisms</strong> as the main constituent of chromosomes. It is the
<strong>carrier of genetic information</strong>.<blockquote><p>The nitrogen in our DNA, the calcium in our teeth, the iron in our blood,
the carbon in our apple pies were made in the interiors of collapsing stars.
We are made of starstuff.
<strong>-- Carl Sagan, Cosmos</strong></blockquote><p>The nucleotide in DNA consists of a sugar (deoxyribose), one of four bases
(cytosine (C), thymine (T), adenine (A), guanine (G)), and a phosphate.
Cytosine and thymine are pyrimidine bases, while adenine and guanine are purine
bases. The sugar and the base together are called a nucleoside.<p><img src=/assets/dna-sequence/dna-basics.jpg alt=DNA><p><em>DNA (a) forms a double stranded helix, and (b) adenine pairs with thymine and
cytosine pairs with guanine. (credit a: modification of work by Jerome Walker,
Dennis Myts)</em><h2 id=encode-binary-data-into-dna-sequence>Encode binary data into DNA sequence</h2><p>As an input file you can use any file you want:<ul><li>ASCII files,<li>Compiled programs,<li>Multimedia files (MP3, MP4, MVK, etc),<li>Images,<li>Database files,<li>etc.</ul><p>Note: If you would copy all the bytes from RAM to file or pipe data to file you
could encode also this data as long as you provide file pointer to the encoder.<h3 id=basic-encoding>Basic Encoding</h3><p>As already mentioned, the Basic Encoding is based on a simple mapping. Since DNA
is composed of 4 nucleotides (Adenine, Cytosine, Guanine, Thymine; usually
referred using the first letter). Using this technique we can encode<p>$$ log_2(4) = log_2(2^2) = 2 bits $$<p>using a single nucleotide. In this way, we are able to use the 4 bases that
compose the DNA strand to encode each byte of data.<table><thead><tr><th>Two bits<th>Nucleotides<tbody><tr><td>00<td><strong>A</strong> (Adenine)<tr><td>10<td><strong>G</strong> (Guanine)<tr><td>01<td><strong>C</strong> (Cytosine)<tr><td>11<td><strong>T</strong> (Thymine)</table><p>With this in mind we can simply encode any data by using two-bit to Nucleotides
conversion.<pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>{ Algorithm 1: Naive byte array to DNA encode }
</span></span><span style=display:flex><span>procedure EncodeToDNASequence(f) string
</span></span><span style=display:flex><span>begin
</span></span><span style=display:flex><span> enc string
</span></span><span style=display:flex><span> <span style=color:#00f>while</span> <span style=color:#00f>not</span> eof(f) do
</span></span><span style=display:flex><span> c byte := buffer[0] { Read 1 byte <span style=color:#00f>from</span> buffer }
</span></span><span style=display:flex><span> bin integer := sprintf(<span style=color:#a31515>'08b'</span>, c) { Convert to string binary }
</span></span><span style=display:flex><span> <span style=color:#00f>for</span> e <span style=color:#00f>in</span> range[0, 2, 4, 6] do
</span></span><span style=display:flex><span> <span style=color:#00f>if</span> e[0] == 48 <span style=color:#00f>and</span> e[1] == 48 then { 0x00 - A (Adenine) }
</span></span><span style=display:flex><span> enc += <span style=color:#a31515>'A'</span>
</span></span><span style=display:flex><span> <span style=color:#00f>else</span> <span style=color:#00f>if</span> e[0] == 48 <span style=color:#00f>and</span> e[1] == 49 then { 0x01 - G (Guanine) }
</span></span><span style=display:flex><span> enc += <span style=color:#a31515>'G'</span>
</span></span><span style=display:flex><span> <span style=color:#00f>else</span> <span style=color:#00f>if</span> e[0] == 49 <span style=color:#00f>and</span> e[1] == 48 then { 0x10 - C (Cytosine) }
</span></span><span style=display:flex><span> enc += <span style=color:#a31515>'C'</span>
</span></span><span style=display:flex><span> <span style=color:#00f>else</span> <span style=color:#00f>if</span> e[0] == 49 <span style=color:#00f>and</span> e[1] == 49 then { 0x11 - T (Thymine) }
</span></span><span style=display:flex><span> enc += <span style=color:#a31515>'T'</span>
</span></span><span style=display:flex><span> <span style=color:#00f>return</span> enc { Return DNA sequence }
</span></span><span style=display:flex><span>end
</span></span></code></pre><p>Another encoding would be <strong>Goldman encoding</strong>. Using this encoding helps with
Nonsense mutation (amino acids replaced by a stop codon) that occurs and is the
most problematic during translation because it leads to truncated amino acid
sequences, which in turn results in truncated proteins.<p><a href="https://www.youtube.com/watch?v=a4PiGWNsIEU">Where to store big data? In DNA: Nick Goldman at TEDxPrague</a><h3 id=fasta-file-format>FASTA file format</h3><p>In bioinformatics, FASTA format is a text-based format for representing either
nucleotide sequences or peptide sequences, in which nucleotides or amino acids
are represented using single-letter codes. The format also allows for sequence
names and comments to precede the sequences. The format originates from the
FASTA software package, but has now become a standard in the field of
bioinformatics.<p>The first line in a FASTA file started either with a ">" (greater-than) symbol
or, less frequently, a ";" (semicolon) was taken as a comment. Subsequent lines
starting with a semicolon would be ignored by software. Since the only comment
used was the first, it quickly became used to hold a summary description of the
sequence, often starting with a unique library accession number, and with time
it has become commonplace to always use ">" for the first line and to not use
";" comments (which would otherwise be ignored).<pre><code>;LCBO - Prolactin precursor - Bovine
; a sample sequence in FASTA format
MDSKGSSQKGSRLLLLLVVSNLLLCQGVVSTPVCPNGPGNCQVSLRDLFDRAVMVSHYIHDLSS
EMFNEFDKRYAQGKGFITMALNSCHTSSLPTPEDKEQAQQTHHEVLMSLILGLLRSWNDPLYHL
VTEVRGMKGAPDAILSRAIEIEEENKRLLEGMEMIFGQVIPGAKETEPYPVWSGLPSLQTKDED
ARYSAFYNLLHCLRRDSSKIDTYLKLLNCRIIYNNNC*
>MCHU - Calmodulin - Human, rabbit, bovine, rat, and chicken
ADQLTEEQIAEFKEAFSLFDKDGDGTITTKELGTVMRSLGQNPTEAELQDMINEVDADGNGTID
FPEFLTMMARKMKDTDSEEEIREAFRVFDKDGNGYISAAELRHVMTNLGEKLTDEEVDEMIREA
DIDGDGQVNYEEFVQMMTAK*
>gi|5524211|gb|AAD44166.1| cytochrome b [Elephas maximus maximus]
LCLYTHIGRNIYYGSYLYSETWNTGIMLLLITMATAFMGYVLPWGQMSFWGATVITNLFSAIPYIGTNLV
EWIWGGFSVDKATLNRFFAFHFILPFTMVALAGVHLTFLHETGSNNPLGLTSDSDKIPFHPYYTIKDFLG
LLILILLLLLLALLSPDMLGDPDNHMPADPLNTPLHIKPEWYFLFAYAILRSVPNKLGGVLALFLSIVIL
GLMPFLHTSKHRSMMLRPLSQALFWTLTMDLLTLTWIGSQPVEYPYTIIGQMASILYFSIILAFLPIAGX
IENY
</code></pre><p>FASTA format was extended by <a href=https://en.wikipedia.org/wiki/FASTQ_format>FASTQ</a>
format from the <a href=https://www.sanger.ac.uk/>Sanger Centre</a> in Cambridge.<h3 id=png-encoded-dna-sequence>PNG encoded DNA sequence</h3><table><thead><tr><th>Nucleotides<th>RGB<th>Color name<tbody><tr><td>A ➞ Adenine<td>(0,0,255)<td>Blue<tr><td>G ➞ Guanine<td>(0,100,0)<td>Green<tr><td>C ➞ Cytosine<td>(255,0,0)<td>Red<tr><td>T ➞ Thymine<td>(255,255,0)<td>Yellow</table><p>With this in mind we can create a simple algorithm to create PNG representation
of a DNA sequence.<pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>{ Algorithm 2: Naive DNA to PNG encode <span style=color:#00f>from</span> FASTA file }
</span></span><span style=display:flex><span>procedure EncodeDNASequenceToPNG(f)
</span></span><span style=display:flex><span>begin
</span></span><span style=display:flex><span> i image
</span></span><span style=display:flex><span> <span style=color:#00f>while</span> <span style=color:#00f>not</span> eof(f) do
</span></span><span style=display:flex><span> c char := buffer[0] { Read 1 char <span style=color:#00f>from</span> buffer }
</span></span><span style=display:flex><span> case c of
</span></span><span style=display:flex><span> <span style=color:#a31515>'A'</span>: color := RGB(0, 0, 255) { Blue }
</span></span><span style=display:flex><span> <span style=color:#a31515>'G'</span>: color := RGB(0, 100, 0) { Green }
</span></span><span style=display:flex><span> <span style=color:#a31515>'C'</span>: color := RGB(255, 0, 0) { Red }
</span></span><span style=display:flex><span> <span style=color:#a31515>'T'</span>: color := RGB(255, 255, 0) { Yellow }
</span></span><span style=display:flex><span> drawRect(i, [x, y], color)
</span></span><span style=display:flex><span> save(i) { Save PNG image }
</span></span><span style=display:flex><span>end
</span></span></code></pre><h2 id=encoding-text-file-in-practice>Encoding text file in practice</h2><p>In this example we will take a simple text file as our input stream for
encoding. This file will have a quote from Niels Bohr and saved as txt file.<blockquote><p>How wonderful that we have met with a paradox. Now we have some hope of
making progress.
― Niels Bohr</blockquote><p>First we encode text file into FASTA file.<pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>./dnae-encode -i quote.txt -o quote.fa
</span></span><span style=display:flex><span>2019/01/10 00:38:29 Gathering input file stats
</span></span><span style=display:flex><span>2019/01/10 00:38:29 Starting encoding ...
</span></span><span style=display:flex><span> 106 B / 106 B [==================================] 100.00% 0s
</span></span><span style=display:flex><span>2019/01/10 00:38:29 Saving to FASTA file ...
</span></span><span style=display:flex><span>2019/01/10 00:38:29 Output FASTA file length is 438 B
</span></span><span style=display:flex><span>2019/01/10 00:38:29 Process took 987.263µs
</span></span><span style=display:flex><span>2019/01/10 00:38:29 Done ...
</span></span></code></pre><p>Output of <code>quote.fa</code> file contains the encoded DNA sequence in ASCII format.<pre><code>>SEQ1
GACAGCTTGTGTACAAGTGTGCTTGCTCGCGAGCGGGTACGCGCGTGGGCTAACAAGTGA
GCCAGCAGGTGAACAAGTGTGCGGACAAGCCAGCAGGTGCGCGGACAAGCTGGCGGGTGA
ACAAGTGTGCCGGTGAGCCAACAAGCAGACAAGTAAGCAGGTACGCAGGCGAGCTTGTCA
ACTCACAAGATCGCTTGTGTACAAGTGTGCGGACAAGCCAGCAGGTGCGCGGACAAGTAT
GCTTGCTGGCGGACAAGCCAGCTTGTAAGCGGACAAGCTTGCGCACAAGCTGGCAGGCCT
GCCGGCTCGCGTACAAATTCACAAGTAAGTACGCTTGCGTGTACGCGGGTATGTATACTC
AACCTCACCAAACGGGACAAGATCGCCGGCGGGCTAGTATACAAGAACGCTTGCCAGTAC
AACC
</code></pre><p>Then we encode FASTA file from previous operation to encode this data into PNG.<pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>./dnae-png -i quote.fa -o quote.png
</span></span><span style=display:flex><span>2019/01/10 00:40:09 Gathering input file stats ...
</span></span><span style=display:flex><span>2019/01/10 00:40:09 Deconstructing FASTA file ...
</span></span><span style=display:flex><span>2019/01/10 00:40:09 Compositing image file ...
</span></span><span style=display:flex><span> 424 / 424 [==================================] 100.00% 0s
</span></span><span style=display:flex><span>2019/01/10 00:40:09 Saving output file ...
</span></span><span style=display:flex><span>2019/01/10 00:40:09 Output image file length is 1.1 kB
</span></span><span style=display:flex><span>2019/01/10 00:40:09 Process took 19.036117ms
</span></span><span style=display:flex><span>2019/01/10 00:40:09 Done ...
</span></span></code></pre><p>After encoding into PNG format this file looks like this.<p><img src=/assets/dna-sequence/quote.png alt="Encoded Quote in PNG format"><p>The larger the input stream is the larger the PNG file would be.<p>Compiled basic Hello World C program with
<a href=https://www.gnu.org/software/gcc/>GCC</a> would <a href=/assets/dna-sequence/sample.png>look
like</a>.<pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span><span style=color:green>// gcc -O3 -o sample sample.c
</span></span></span><span style=display:flex><span><span style=color:green></span><span style=color:#00f>#include</span> <span style=color:#00f><stdio.h></span><span style=color:#00f>
</span></span></span><span style=display:flex><span><span style=color:#00f></span>
</span></span><span style=display:flex><span>main() {
</span></span><span style=display:flex><span> printf(<span style=color:#a31515>"Hello, world!</span><span style=color:#a31515>\n</span><span style=color:#a31515>"</span>);
</span></span><span style=display:flex><span> <span style=color:#00f>return</span> 0;
</span></span><span style=display:flex><span>}
</span></span></code></pre><h2 id=toolkit-for-encoding-data>Toolkit for encoding data</h2><p>I have created a toolkit with two main programs:<ul><li>dnae-encode (encodes file into FASTA file)<li>dnae-png (encodes FASTA file into PNG)</ul><p>Toolkit with full source code is available on
<a href=https://github.com/mitjafelicijan/dna-encoding>github.com/mitjafelicijan/dna-encoding</a>.<h3 id=dnae-encode>dnae-encode</h3><pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>> ./dnae-encode --help
</span></span><span style=display:flex><span>usage: dnae-encode --input=INPUT [<flags>]
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span>A command-line application that encodes file into DNA sequence.
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span>Flags:
</span></span><span style=display:flex><span> --help Show context-sensitive help (also try --help-long and --help-man).
</span></span><span style=display:flex><span> -i, --input=INPUT Input file (ASCII or binary) which will be encoded into DNA sequence.
</span></span><span style=display:flex><span> -o, --output=<span style=color:#a31515>"out.fa"</span> Output file which stores DNA sequence in FASTA format.
</span></span><span style=display:flex><span> -s, --sequence=SEQ1 The description line (defline) or header/identifier line, gives a name and/or a unique identifier <span style=color:#00f>for</span> the sequence.
</span></span><span style=display:flex><span> -c, --columns=60 Row characters length (no more than 120 characters). Devices preallocate fixed line sizes in software.
</span></span><span style=display:flex><span> --version Show application version.
</span></span></code></pre><h3 id=dnae-png>dnae-png</h3><pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>> ./dnae-png --help
</span></span><span style=display:flex><span>usage: dnae-png --input=INPUT [<flags>]
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span>A command-line application that encodes FASTA file into PNG image.
</span></span><span style=display:flex><span>
</span></span><span style=display:flex><span>Flags:
</span></span><span style=display:flex><span> --help Show context-sensitive help (also try --help-long and --help-man).
</span></span><span style=display:flex><span> -i, --input=INPUT Input FASTA file which will be encoded into PNG image.
</span></span><span style=display:flex><span> -o, --output=<span style=color:#a31515>"out.png"</span> Output file in PNG format that represents DNA sequence in graphical way.
</span></span><span style=display:flex><span> -s, --size=10 Size of pairings of DNA bases on image in pixels (lower resolution lower file size).
</span></span><span style=display:flex><span> --version Show application version.
</span></span></code></pre><h2 id=benchmarks>Benchmarks</h2><p>First we generate some binary sample data with dd.<pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>dd <span style=color:#00f>if</span>=<(openssl enc -aes-256-ctr -pass pass:<span style=color:#a31515>"</span><span style=color:#00f>$(</span>dd <span style=color:#00f>if</span>=/dev/urandom bs=128 count=1 2>/dev/null | base64<span style=color:#00f>)</span><span style=color:#a31515>"</span> -nosalt < /dev/zero) of=1KB.bin bs=1KB count=1 iflag=fullblock
</span></span></code></pre><p>Our freshly generated 1KB file looks something like this (its full of garbage
data as intended).<p><img src=/assets/dna-sequence/sample-binary-file.png alt="Sample binary file 1KB"><p>We create following binary files:<ul><li>1KB.bin<li>10KB.bin<li>100KB.bin<li>1MB.bin<li>10MB.bin<li>100MB.bin</ul><p>After this we create FASTA files for all the binary files by encoding them
into DNA sequence.<pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>./dnae-encode -i 100MB.bin -o 100MB.fa
</span></span></code></pre><p>Then we GZIP all the FASTA files to see how much the can be compressed.<pre tabindex=0 style=background-color:#fff><code><span style=display:flex><span>gzip -9 < 10MB.fa > 10MB.fa.gz
</span></span></code></pre><p><a href=/dna-sequence/benchmarks.ods>Download ODS file with benchmarks</a>.<p><img src=/assets/dna-sequence/chart-1.png alt="Sample binary file 1KB"><p><img src=/assets/dna-sequence/chart-2.png alt="Sample binary file 1KB"><h2 id=references>References</h2><ul><li><a href=https://www.techopedia.com/definition/948/encoding>https://www.techopedia.com/definition/948/encoding</a><li><a href=https://www.dna-worldwide.com/resource/160/history-dna-timeline>https://www.dna-worldwide.com/resource/160/history-dna-timeline</a><li><a href=https://opentextbc.ca/biology/chapter/9-1-the-structure-of-dna/>https://opentextbc.ca/biology/chapter/9-1-the-structure-of-dna/</a><li><a href=https://arxiv.org/abs/1801.04774>https://arxiv.org/abs/1801.04774</a><li><a href=https://en.wikipedia.org/wiki/FASTA_format>https://en.wikipedia.org/wiki/FASTA_format</a></ul></div></div></main><footer><hr><div><h3>Want to comment or have something to add?</h3>You can write me an email at
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