Genomic signal processing- An introduction

In short: after a biophysics class I went looking for work on programming biomolecules and found Dimitris Anastassiou's paper on genomic signal processing. These are the parts I kept.

The paper is here: Genomic signal processing on IEEE Xplore.

Genomes are already digital

Genomic information is digital in a very real sense; it is represented in the form of sequences of which each element can be one out of a finite number of entities. Such sequences, like DNA and proteins, have been mathematically represented by character strings, in which each character is a letter of an alphabet. In the case of DNA, the alphabet is size 4 and consists of the letters A, T, C and G; in the case of proteins, the size of the corresponding alphabet is 20.

Genomic signal processing, Dimitris Anastassiou

Why signal processing has not taken over yet

The main reason that the field of signal processing does not yet have significant impact in the field is because it deals with numerical sequences rather than character strings. However, if we properly map a character string into one or more numerical sequences, then digital signal processing (DSP) provides a set of novel and useful tools for solving highly relevant problems.

Genomic signal processing, Dimitris Anastassiou

What proteins do

Protein molecules tend to fold into complex three-dimensional (3-D) structures forming weak bonds between their own atoms, and they are responsible for carrying out nearly all of the essential functions in the living cell by properly binding to other molecules with a number of chemical bonds connecting neighboring atoms.

Genomic signal processing, Dimitris Anastassiou

Start and stop codons

A particular triplet, ATG, serves as the START codon and it also codes for the M amino acid (methionine); thus, methionine appears as the first amino acid of proteins, but it may also appear in other locations. We also see that there are three STOP codons (TAA, TAG, TGA) indicating termination of amino acid chain synthesis, and the last amino acid is the one generated by the codon preceding the STOP codon.

Mapping letters to numbers

In a DNA sequence of length N, assume that we assign the numbers a, t, c, g to the characters A, T, C, G, respectively. A proper choice of the numbers a, t, c and g can provide potentially useful properties to the numerical sequence x[n].
For example, if we choose complex conjugate pairs t = a* and g = c*, then the complementary DNA strand is represented by
~x[n] = x*[−n + N −1], n = 0, 1, …, N −1

That last one is the trick the whole field hangs on. Pick the mapping well and the complementary strand falls out as a time reversal and conjugation, which is something a DSP toolbox already knows how to do.