The Musical Atlas
The NDB has developed Musical Atlas to provide a unique way to explore structures of DNA.
Two types of musical representations were recorded. Project 1 focuses on B-DNA base pairing, while Project 2 uses a more detailed scheme to represent DNA conformation, mismatches, modifications, and more.
(Plain Melody & Composition 1)
By Joanna de la Cruz (RU '98)
DNA can be represented in a variety of ways, which can provide different visual perspectives of molecular structure.
DNA can also be aurally represented when a correspondence is created between the bases and musical notes, as seen in Dr. David Deamer's earlier work DNA Suite (1983).
This Musical Atlas presents an aural representation of the B-DNA molecules without mismatches, drugs, or modifiers that were contained in the NDB as of July 25, 1996.
This atlas follows a newly created pattern. For each structure, there is a "Plain Melody," which follows a simple algorithm to highlight the structure's sequence, and a "Composition," which follows a more complicated algorithm that features the base pairing of the structure.
These algorithms contain rules for determining the meter and rhythm for each piece.
In each case, the notes are assigned to each base as follows:
These are found within the range a to g1. Thymine was assigned to E so that the four bases would fall into an a minor seventh chord. In each melody, each base in the sequence is played for one beat. If there are four adenines in a row, the note A will be played four (separated) times. If there is only one cytosine, it will be played for one beat, etc. In these melodies, the sequence for each structure is played once. The purpose of this Melody is to provide the listener with a 'feel' for the nucleotide without accompaniment. For each composition, there are four measures in which every quarter note gets one beat.
Each base of the asymmetric strand is given one note. The strand is read 5' to 3'.
The Plain Melody for BDF062, Strand A (C G C T G G)
The number of beats per measure is based upon the length of the nucleotide; the number of beats per measure is half the number of bases per strand. For example, if the nucleotide is 12 base pairs long, then the number of beats per measure will be 6 (time signature = 6/4).
The sequences used here all had an even number of base pairs. However, if a sequence contained an odd number of bases, the number of beats per measure will be half that amount minus the remainder. For example, a 13 base pair piece would get 6 beats per measure.
The compositions consist of two lines:
Thymine was assigned to E so that the four bases would fall into an a minor seventh chord.
In each melody, each base in the sequence is played for one beat. If there are four adenines in a row, the note A will be played four (separated) times. If there is only one cytosine, it will be played for one beat, etc. In these melodies, the sequence for each structure is played once. The purpose of this Melody is to provide the listener with a 'feel' for the nucleotide without accompaniment.
For each composition, there are four measures in which every quarter note gets one beat.
The melodic line is the melody derived directly from the sequence of the molecules. If the asymmetric strand is self-complementary, the DNA molecule will have only one melody. If the strand(s) in the asymmetrical unit is(are) not self-complementary, both the asymmetrical strand and its symmetry related strand each have a separate melody.
In this algorithm, there are four measures to each melody. The melodic line consists the sequence being repeated of the asymmetrical sequence being repeated four times.
If a base repeats itself in a sequence, the repeated note is tied (ie., if two adenines are in a row, then an A will play for a full quarter note.) For example, the sequence C G C A A A T T T G C G (BDL038) will have an A playing for one and a half beats (a dotted eighth note), and a E for one and a half beats. The cytosines and guanines are all eight notes.
The first measure is a full measure rest for the bass line while the full sequence is played on the melodic line.
The second measure begins with the complimentary strand. This strand is read 3' to 5' (essentially, it base pairs with the melody). For example, when a C is playing in the melodic line, a G is played in the bass line; when an A plays in one, an E will play in the other, etc. The bass line should be smooth as the line will allow and should follow fundamental rules of counterpoint. Both the melodic and the bass lines have the same rhythmic structure in this measure.
The third measure slightly expands upon the base pairing concept of the second measure. Using notes from the a minor scale, the base pairing note in the bass line is followed by specifically assigned notes to create counterpoint while the melody is being held.
|Base from asymmetrical strand||Note Played in Melodic Line
|Note Played in Bass Line
(Complementary Strand Sequence)
|Assigned note to follow Base Pairing note in Bass Line||Range for base pairs and assigned bass note|
The base pair will play at the same time as the base in the asymmetrical strand but will only play for half the amount of time given in the second measure. It will then be followed by the new note assigned by the algorithm having the same time length as the base pair preceding it. For example, using the same sequence as above, C G C A A A T T T G C G, cytosine's note is a C. When the C plays for half a beat (eighth note) a G plays in the bass line for one quarter of a beat (sixteenth note) followed by an F which is also played for one quarter of a beat (sixteenth note). For the dotted quarter note A, the bass line will have an E playing for half that time followed by a D played for the same amount of time.
The fourth measure ends in a somewhat static chord progression. Each base in the melodic line is accompanied by its corresponding chord in the bass line. To create a stable chord, it was decided that these chords should be a fifth down from the base note, and should be in the same key signature (a minor).The chords assigned by the algorithm will play simultaneously with the corresponding bases in the top line. Chord inversions are acceptable as long as the line is kept as smooth as possible.
Thanks to Jason Young for providing technical assistance.
By Gautam Malhotra (RU '96)
"Seeing" things on the molecular level is obviously impossible with the naked eye, as even the electron microscope provides limited visibility of molecules. Therefore, other ways of "looking" at structures have been developed. Since the majority of us have difficulty visualizing molecular structure by glancing at tables of numbers, a familiar adage can be altered to "a picture is worth a lot of data." Thus drawings and models are a necessary tool for understanding and interpreting scientific data.
However, perceptions of reality are not limited only to vision but to four other senses. The concept of "hearing" DNA through music as seen in Dr. David Deamer's DNA Suite (1983), motivated Joanna de la Cruz (Rutgers University '98 of the NDB) to further develop aural representations of molecular structures to aid in "hearing" things which could not be "seen." De la Cruz created compositions based around DNA sequences to provide a unique representation of B-DNA sequence.
The algorithm presented here builds on Deamer's and de la Cruz's ideas in a number of ways. First, the new algorithm represents more aspects of the DNA structure (conformation, mismatches, modifications, nicks, uracil, inosine, etc). Secondly, it uses more than one timbre or tone color to aid in representation (i.e. the main sequence is represented by a piano while the complementary sequence is represented by a string section). The primary goal of this project was to use music to identify structures. Thus the representational value of each musical idea was more important than its aesthetic consequence.
- Each piece of DNA music consists of 15 measures.
- Measure length is determined by the number of bases in the DNA strand. (Each base is equal to one beat.) For example, a strand which is 10 base pairs long will have 10-beat measures, while a 4 base pair strand will be represented by 4 beats per measure, and so on.
- In the time signature there are (# of nitrogenous bases) beats per measure with the eighth note getting the beat. The eighth note was arbitrarily chosen.
- The sequence is repeated in each measure.
- All MIDI composing and recording was done using LOGIC Audio PPC (version 2.5) and sounds were synthetically generated by QuickTimeTM (version 2.5). All work was done on a Power Macintosh 7100/80, System 7.5.5 .
SIGNIFICANCE OF EACH MEASURE
- A-DNA is represented by a ride cymbal.
- B-DNA is represented by a triangle (high pitched).
- Z-DNA is represented by a timpani (a low booming drum).
A number of equally spaced percussive clicks are sounded to represent the number of nitrogenous bases in the DNA strand. For example, if there are a total of 6 successive clicks, then there are 6 bases in the strand of DNA (and consequently the time signature is 6/8). The first sound establishes whether you are listening to A-, B-, or Z-DNA.
These sounds are repeated to signal the beginning of every new measure and were chosen purely for aesthetic reasons.
The melody, or main strand, is introduced by the piano and is repeated until the end of the piece. Notes are equidistant since the nitrogenous bases themselves are structurally an equal distance apart. Thus spaces in the melody can reveal missing bases and extra notes can represent hairpin loops and overhangs. Notational representation of bases is shown below.
- A-DNA is represented by a low range of pitches which correspond to low anti conformation. B-DNA's high range represents high anti conformation. Z-DNA has pitches between A-DNA & B-DNA ranges, which represent sequence only.
- A-DNA & B-DNA are both right handed helices which are being represented in the major mode. Z-DNA is a left handed helix and is therefore represented by the natural minor mode. This explains why the notes A, B and E in Z-DNA have been flatted. (Note: the keys of C major and c minor were chosen for convenience and clarity of identification.) Thus the left/right handedness of a strand can be identified by listening to the mode of each piece.
Note: c1 is "middle c." c2 is one octave above "middle c" and c is one octave below it. Capitalized letters are in the octave directly below c.
Exact repetition of measure 2.
- The pitch of the choir voice indicates high or low anti. (i.e. high pitch represents high anti and low pitch represents low anti.)
- If a base is in the syn configuration, the choir voice is silent.
- If a base is in the anti configuration a note is sounded. Therefore if all the bases are anti, the choir voice sustains a note; but if the strand alternates anti/syn, then the choir voice will alternate between sound and silence.
Syn/Anti configuration is represented by the choir voice.
Exact repetition of measure 4.
Measure 6 & 7:
The strings introduce the complementary strand using the algorithm described below. This introduction develops for two measures. The complementary strand's melody will always sound an octave below that of the main strand. Syn/Anti choir voice drops out.
Full sequence of the complementary strand is established using the same principles for pitch and duration as were used for the main strand. The syn/Anti choir voice re-enters.
Exact repetition of measure 8.
- If mismatches are present in the structure, they are represented in this measure by a layer of Orchestra Hits at the precise locations of the mismatches. (Orchestra Hits is a combination of strings, timpanis, brass, and woodwinds which achieves a loud staccato snap.) This measure will sound the same as measure 9 for structures without mismatches.
- Exact repetition of measure 8.
If present in the structure, mismatches are represented again. The Syn/Anti choir voice drops out.
Exact repetition of measure 12.
The complementary strand and any mismatches drop out.
Muted triangle sound indicates the end of the piece. Anything sounded after this is structurally meaningless. (However, for the sake of simplicity these pieces consistently end with single note cadences.)
REPRESENTING THE COMPLEMENTARY STRAND
The complementary strand, which is represented by the String Section sound, is preceded by a 2 measure melodic introduction. This melody is the result of an algorithm which was used purely for aesthetic purposes to relieve some of the monotony of the music. It does not signify structure.
- Measure 6 contains two notes. The first note is just the first note of the complementary strand.
- The second note is the note found halfway down the sequence. So for example, if the sixth note of a 10-base sequence is C, then the second note of measure of 6 is C.
- Measure 7 contains four notes. Two of them are the same as in measure 6. The other two are the final note of the sequece and the note just before halfway.
REPRESENTING SPECIAL DNA FEATURES
- Overhangs are represented by a rest (a space or silence) in the complementary strand at the site of the overhang (see UDI030).
- Flipped-out Bases are preceded by a quick grace note (see UDI047).
- Uracil and Inosine are treated as mismatches (see BDL075 & ZDH030).
table OF SOUND-STRUCTURE RELATIONSHIPS
BRIEF MEASURE BY MEASURE SYNOPSIS
Thanks to Joanna de la Cruz for helpful discussion.
Project 1 uses .au and .wav files.
Unlike MIDI files, audio files are actual sound recordings. These recordings are offered in two formats (.au and .wav) to accommodate different systems. Except for the format type, these files are identical. To hear these files, be sure that your browser matches the appropriate software with the MIME type for .au and .wav files.
Project 2 uses .mid files.The MIME type of the .mid files on this Atlas is audio/midi . If you are having trouble playing these files (e.g. your screen is filled with nonsense text) then you need to do one of the following:
- make sure you have selected a player/helper application in your options menu which can be called up to play the MIDI files
- download a player
- download the files and listen to them using your own computer's applications.