JavaScript (node + browser) bioinformatics library for nucleotide sequence manipulation and analysis.
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README.md

NtSeq

NtSeq is an open source Bioinformatics library written in JavaScript that provides DNA sequence manipulation and analysis tools for node and the browser.

More specifically, it's a library for dealing with all kinds of nucleotide sequences, including degenerate nucleotides. It's built with the developer (and scientist) in mind with simple, readable methods that are part of the standard molecular biologist's vocabulary.

Sequence Alignment / Mapping

Additionally, NtSeq comes with a novel, highly optimized exhaustive sequence mapping / comparison tool known as Nt.MatchMap.

Nt.MatchMap allows you to find all ungapped alignments between two degenerate nucleotide sequences, ordered by the number of matches. Also provided is a list of results showing the number of each match count, which can be useful for determining if certain sequences or variations are over-represented in a target genome. (P-values, unfortunately, are out of the scope of this project.)

MatchMap uses bit operations to exhaustively scan a search sequence at a rate of up to 10x faster than a standard naive alignment implementation that uses string comparisons. It can run at a rate of up to approximately 500,000,000 nucleotide comparisons per second single-threaded on a 2.4GHz processor.

An explanation of the algorithm used will be made available shortly. In the meantime, the code is open source and MIT-licensed so feel free to figure it out!

Tests and benchmarks are included in this repository which can be easily run from the command line using node / npm. A sample benchmark is also included in this README. :)

New to bioinformatics, or never played with a nucleotide sequence before? Check out Nucleic Acid Notation to get started.

What can I do with NtSeq?

  • Quickly scan genomic data for target sequences or ungapped relatives using .mapSequence()

  • Grab the 5' -> 3' complement of a sequence with .complement()

  • Manipulate sequences easily using .replicate(), .deletion(), .insertion(), .repeat() and .polymerize()

  • Translate your nucleotide sequences in a single line of code using .translate() or .translateFrame()

  • Quickly determine AT% content with .content() or .fractionalContent()

  • Grab approximate AT% content for degenerate sequences using .contentATGC() or .fractionalContentATGC()

  • Load FASTA files into memory from your machine (node) with .loadFASTA() or from a string if you use an external AJAX request (web) using .readFASTA()

  • Save large sequences for easy accession in the future using a new filetype, .4bnt that will cut your FASTA file sizes in half with .save4bnt() and .load4bnt() (node only)

Installation

Node

NtSeq is available as a node package, and can be installed with:

$ npm install ntseq

You can use NtSeq in your node project by using:

var Nt = require('ntseq');

(The node.js version has some useful additional tools as compared to the web version.)

Web

In order to use NtSeq on a webpage, download ntseq.js from the web folder of this repository and include it in a script tag, like so (assuming it is in the same directory as your page):

<script src="ntseq.js"></script>

If you're new to writing web applications, a sample page that uses NtSeq is available as index.html (in the web directory).

Quick Usage

The Nt namespace contains two constructor methods, Nt.Seq and Nt.MatchMap. You can use these by calling:

// Create and put data into a new nucleotide sequence
var seqA = new Nt.Seq();
seqA.read('ATGC');

// Create an RNA sequence - identical to DNA, but RNA will output 'U' instead of 'T'
var seqB = new Nt.Seq('RNA');
seqB.read('ATGCATGC');

// Create a MatchMap of seqA aligned against seqB.
var map = new Nt.MatchMap(seqA, seqB);

// Additionally, this line is equivalent to the previous
var map = seqB.mapSequence(seqA);

Examples

Let's start with a simple sequence...

var seq = new Nt.Seq();
seq.read('AATT');

Great, now I can start playing around with it. :)

var repeatedSeq = seq.repeat(3);

// Logs 'AATT'
console.log(seq.sequence());
// Logs 'AATTAATTAATT'
console.log(repeatedSeq.sequence());

// Can shorten to one line...
var gcSeq = (new Nt.Seq()).read('GCGC');

var insertedSeq = repeatedSeq.insertion(gcSeq, 4);

// Logs 'AATTGCGCAATTAATT'
console.log(insertedSeq.sequence());

We can combine sequences together...

// is 'AATTGCGCAATTAATTGCGC'
insertedSeq.polymerize(gcSeq).sequence();

And we find the reverse complement in a flash!

var complementMe = (new Nt.Seq()).read('CCAATT');
// is 'AATTGG'
complementMe.complement().sequence();

Translating sequences to amino acid sequences is trivial...

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
// Translate at nucleotide offset 0
seq.translate(); // === 'MPDC'
// Translate at nucleotide offset 1
seq.translate(1); // === 'CPTA'
// Translate at nucleotide offset 0, 1 amino acid into the frame
seq.translateFrame(0, 1); // === 'PDC'

Determine the AT% Content of my sequence... what fraction is A?

seq.fractionalContent()['A'] // === 0.23076923076923078, about 23%!

Hmm, well this is a small sequence but I want to find where "CCCG" matches

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('CCCG');
var map = seq.mapSequence(querySeq).initialize().sort();
map.best().position; // === 3

What about degenerate matching, 'ASTG'?

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('ASTG');
var map = seq.mapSequence(querySeq).initialize().sort();
map.best().position; // === 7

What if there are no perfect matches?

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('CCCW');
var map = seq.mapSequence(querySeq).initialize().sort();
map.best().position; // === 3
map.best().matches; // === 3
map.best().alignment().sequence(); // === 'CCCG'

// this is the actual nucleotides that match, gaps for non-matches
map.best().alignmentMask().sequence(); // === 'CCC-'

// this is the optimistic sequence that could match both
map.best().alignmentCover().sequence(); // === 'CCCD'

// .matchFrequencyData provides the number of times a certain number of matches were
//    found. In this example, the sequence didn't find any matches at 6
//    locations. Keep in mind the sequence attempts to align outside of the
//    upper and lower bounds of the search space.
//      i.e.     ATGC
//             CCCW
map.matchFrequencyData(); // === [ 6, 8, 3, 2, 0 ]

Benchmarks and Tests

NtSeq has a number of integration tests that you can access (after cloning the repository).

Run tests with

$ npm test

And run benchmarks with

$ npm run benchmark

You should get an output that looks (roughly) like the following (taken Feb 7th, 2015 on a 2.4GHz processor).

Benchmark         |        naive |       search |   naiveScore |  searchScore
--------------------------------------------------------------------------------
1,000,000, 0%     |          9ms |          3ms |    9.00ns/nt |    3.00ns/nt
10,000,000, 0%    |         63ms |          5ms |    6.30ns/nt |    0.50ns/nt
100,000,000, 0%   |        621ms |         60ms |    6.21ns/nt |    0.60ns/nt
1,000,000, 25%    |         15ms |          6ms |   15.00ns/nt |    6.00ns/nt
10,000,000, 25%   |        124ms |         17ms |   12.40ns/nt |    1.70ns/nt
100,000,000, 25%  |       1249ms |        233ms |   12.49ns/nt |    2.33ns/nt
1,000,000, 50%    |         15ms |          2ms |   15.00ns/nt |    2.00ns/nt
10,000,000, 50%   |        131ms |         20ms |   13.10ns/nt |    2.00ns/nt
100,000,000, 50%  |       1305ms |        234ms |   13.05ns/nt |    2.34ns/nt
1,000,000, 100%   |         14ms |          2ms |   14.00ns/nt |    2.00ns/nt
10,000,000, 100%  |        144ms |         18ms |   14.40ns/nt |    1.80ns/nt
100,000,000, 100% |       1471ms |        240ms |   14.71ns/nt |    2.40ns/nt

naive refers to a simple string implementation of exhaustive alignment mapping (no heuristics), and search refers to the MatchMap optimized bit op alignment mapping, providing the same result (no heuristics either!).

The scores (lower is better) are calculated by dividing the total execution time in nanoseconds by the input size in (m x n where m is search (large) sequence length and n is query sequence length).

The benchmark titles indicate the total size of the search space, and what percent identity (similarity) the sequences have to one another.

Library Reference

Nt.Seq

(constructor) Nt.Seq( [optional String seqType] )

Construct a new Nt.Seq object. seqType can be 'DNA' or 'RNA'.

var seq = (new Nt.Seq());

Nt.Seq#read( [String sequenceData] )

returns self

Reads the sequenceData into the Nt.Seq object.

Expects the sequence data to be read 5' -> 3' (left to right).

seq.read('ATGCATGC');

Nt.Seq#readFASTA( [String fastaData] )

returns self

Reads a lone FASTA file into the Nt.Seq object, removing comments and ignoring line breaks.


Nt.Seq#size()

returns Integer

Returns the size (length in nucleotides) of the sequence.


Nt.Seq#sequence()

returns String

Returns the nucleotide sequence as a string


Nt.Seq#complement()

returns Nt.Seq

Creates a new Nt.Seq object with complementary sequence data.

var seq = (new Nt.Seq()).read('ATGC');
var complement = seq.complement();

// Will read: 'GCAT'
complement.sequence();

Nt.Seq#equivalent( [Nt.Seq compareSequence] )

returns Boolean

Tells us whether two sequences are equivalent (same nucleotide data and type, RNA or DNA).


Nt.Seq#replicate( [optional Integer offset], [optional Integer length] )

returns Nt.Seq

Creates a new Nt.Seq object, starting at an optional offset and continuing to the specified length. If length is unspecified, will continue until the end of the sequence.


Nt.Seq#polymerize( [Nt.Seq sequence] )

returns Nt.Seq

Creates a new Nt.Seq object that is the result of concatenating the current and provided sequence together.


Nt.Seq#insertion( [Nt.Seq insertedSequence], [Integer offset] )

returns Nt.Seq

Creates a new Nt.Seq object that is the result of inserting insertedSequence at the specified offset.


Nt.Seq#deletion( [Nt.Seq offset], [Integer length] )

returns Nt.Seq

Creates a new Nt.Seq object that is the result of deleting (removing) nucleotides from the current sequence beginning at offset and continue to length.


Nt.Seq#repeat( [Integer count] )

returns Nt.Seq

Creates a new Nt.Seq object that is the result of repeating the current sequence count number of times. (0 will return an empty sequence, 1 will return an identical sequence.)


Nt.Seq#mask( [Nt.Seq sequence] )

returns Nt.Seq

Creates a new Nt.Seq object that is the result of aligning the current sequence and provided sequence and choosing this most pessimistic match between nucleotides. (Provides a sequence containing only exactly matching nucleotides.)

See Nucleic Acid Notation for more information

var seqA = (new Nt.Seq()).read('ATGC');
var seqB = (new Nt.Seq()).read('AWTS')

var seqC = seqA.mask(seqB);
seqC.sequence(); // === 'AT-C'

Nt.Seq#cover( [Nt.Seq sequence] )

returns Nt.Seq

Creates a new Nt.Seq object that is the result of aligning the current sequence and provided sequence and choosing this most optimistic match between nucleotides. (Provides a sequence that will match both.)

See Nucleic Acid Notation for more information

var seqA = (new Nt.Seq()).read('ATGC');
var seqB = (new Nt.Seq()).read('AWTS')

var seqC = seqA.cover(seqB);
seqC.sequence(); // === 'AWKS'

Nt.Seq#content()

returns Object

Returns a Object (hash table) containing the frequency counts of nucleotides, including degenerate nucleotides (16 results total).

var seqA = (new Nt.Seq()).read('ATGC');

var content = seqA.content();
/* Looks like:
  {
    'A': 1, 'T': 1, 'G': 1, 'C': 1, 'S': 0, 'W': 0, 'N': 0 [...]
  }
*/

var Acontent = content['A']; // === 1

Nt.Seq#fractionalContent()

returns Object

Returns a Object (hash table) containing the fraction of nucleotides present in the sequence, including degenerate nucleotides (16 results total).

var seqA = (new Nt.Seq()).read('ATGC');

var content = seqA.fractionalContent();
/* Looks like:
  {
    'A': 0.25, 'T': 0.25, 'G': 0.25, 'C': 0.25, 'S': 0, 'W': 0, 'N': 0 [...]
  }
*/

var Acontent = content['A']; // === 0.25

Nt.Seq#contentATGC()

returns Object

Returns a Object (hash table) containing frequency counts of only the four non-degenerate nucleotides.

NOTE: Degenerate nucleotides are counted as fractions of A, T, G, or C with this method. (N = 0.25 x A, 0.25 x G, 0.25 x T, 0.25 x C).

var seqA = (new Nt.Seq()).read('ATNN');

var content = seqA.contentATGC();
/* Looks like:
  {
    'A': 1.5,
    'T': 1.5,
    'G': 0.5,
    'C': 0.5
  }
*/

var Acontent = content['A']; // === 1.5

Nt.Seq#fractionalContentATGC()

returns Object

Returns a Object (hash table) containing the fraction of only the four non-degenerate nucleotides.

NOTE: Degenerate nucleotides are counted as fractions of A, T, G, or C with this method. (N = 0.25 x A, 0.25 x G, 0.25 x T, 0.25 x C).

var seqA = (new Nt.Seq()).read('ATNN');

var content = seqA.fractionalContentATGC();
/* Looks like:
  {
    'A': 0.375,
    'T': 0.375,
    'G': 0.125,
    'C': 0.125
  }
*/

var Acontent = content['A']; // === 0.375

Nt.Seq#translate( [optional Integer offset], [optional Integer length] )

returns String

Returns a string containing the Amino Acid sequence represented by the nucleotide sequence, starting at a nucleotide provided by offset and continuing for length nucleotides (not amino acids!). If offset is not provided, the entire sequence will be translated. If length is not provided, translation will continue until the end of the sequence.

See Amino Acid Abbreviations for more details.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
// Translate at nucleotide offset 0
seq.translate(); // === 'MPDC'
// Translate at nucleotide offset 1
seq.translate(1); // === 'CPTA'
// Translate at nucleotide offset 1, continue for 6 nucleotides (2 AAs)
seq.translate(1, 6); // === 'CP'

Nt.Seq#translateFrame( [optional Integer frame], [optional Integer AAoffset], [optional Integer AAlength] )

returns String

Returns a string containing the Amino Acid sequence represented by the current nucleotide sequence. Translation can begin at one of three frames (0, 1 or 2) and then begin at an Amino Acid specified by AAoffset and continuing for AAlength Amino Acids. If AAoffset is not provided, the entire sequence will be translated. If AAlength is not provided, translation will continue until the end of the sequence.

NOTE: Remember the difference! .translateFrame() uses amino acid offsets, while .translate() uses nucleotide offsets.

See Amino Acid Abbreviations for more details.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
// Translate entire sequence
seq.translateFrame(); // === 'MPDC'
// Translate beginning at frame 1 (offset by 1 nt)
seq.translateFrame(1); // === 'CPTA'
// Translate from frame 1 (offset by 1 nt), start by offset of 1 amino acid
//   and continue for 2 amino acids
seq.translateFrame(1, 1, 2); // === 'PT'

Nt.Seq#mapSequence( [Nt.Seq querySequence] )

returns Nt.MatchMap

Creates a new Nt.MatchMap object using the provided querySequence as a search query in the larger sequence. Equivalent to new MatchMap(querySequence, currentSequence).

See Nt.MatchMap for more details.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('TGC');

var map = seq.mapSequence(querySeq); // === (new Nt.MatchMap(querySeq, seq))

Nt.Seq#loadFASTA( [String pathname] )

returns self

NODE ONLY

Will load sequence data from a FASTA file located at the provided pathname


Nt.Seq#load4bnt( [String pathname] )

returns self

NODE ONLY

Will load sequence data from a .4bnt file located at the provided pathname

(.4bnt is short for "4-bit nucleotide")


Nt.Seq#save4bnt( [optional String name], [optional String path] )

returns self

NODE ONLY

Will save sequence data as name.4bnt in a directory located at path.

If name is not provided, it will be automatically generated as sequence_TIME.4bnt where TIME is the current UNIX timestamp in milliseconds.

If path is not provided, the directory you're running the process from will be used.

(.4bnt is short for "4-bit nucleotide")


Nt.MatchMap

(constructor) Nt.MatchMap( [Nt.Seq querySeq], [Nt.Seq searchSeq] )

Construct a new Nt.MatchMap object that queries searchSeq for matches of querySeq. Performs exhaustive degenerate nucleotide matching at every combination of nucleotides and stores the results. Results are ordered by alignment of position 0 of querySeq with a position in searchSeq (starting with negative offsets).

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('TGC');

var map = new Nt.MatchMap(querySeq, seq); // === seq.mapSequence(querySeq);

Nt.MatchMap#initialize()

Initialises the MatchMap so you can query the results.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('TGC');

var map = new Nt.MatchMap(querySeq, seq);
var initializedMap = map.initialize();

Nt.MatchMap#results( [optional Integer offset], [optional Integer count] )

returns Array (of Object)

Provides results in an array, ordered from the leftmost offset (negative alignment of querySeq relative to searchSeq) as element 0.

Objects returned will be hashes containing the following:

{
  position: [Integer],
  matches: [Integer]
}

Will Array#slice on the result array depending on offset and count. (Returns subset of the Array).


Nt.MatchMap#sort()

Sorts the results of MatchMap so you can return top, best and bottom MatchResults.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('TGC');

var map = new Nt.MatchMap(querySeq, seq).initialize().sort(); // === seq.mapSequence(querySeq);
map.best();
map.top();
map.bottom();

Nt.MatchMap#best()

returns Nt.MatchResult

Provides the best possible alignment match of querySeq in searchSeq as a new Nt.MatchResult object. See Nt.MatchResult for more details.

NOTE: There is no guarantee that the sorted results based on matches will be stable, do not write code that expects this to always be identical given ties of top match counts.


Nt.MatchMap#top( [Integer count] )

returns Array (of Nt.MatchResult)

Provides an Array containing the best possible alignment matches of querySeq in searchSeq as new Nt.MatchResult objects. See Nt.MatchResult for more details.

NOTE: There is no guarantee that the sorted results based on matches will be stable, do not write code that expects this to always be identical given ties of top match counts.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('TGC');

var map = new Nt.MatchMap(querySeq, seq).initialize();
var topArray = map.top(2); // === [ Nt.MatchResult, Nt.MatchResult ]

Nt.MatchMap#bottom( [Integer count] )

returns Array (of Nt.MatchResult)

Provides an Array containing the worst possible alignment matches of querySeq in searchSeq as new Nt.MatchResult objects. See Nt.MatchResult for more details.

NOTE: There is no guarantee that the sorted results based on matches will be stable, do not write code that expects this to always be identical given ties of bottom match counts.


Nt.MatchMap#matchFrequencyData()

returns Array (of Integers)

Provides an Array containing the frequency distribution of all matches. The Array will be the same length as querySequence.size(), the 0-indexed element represents the number of times no (0) matches were found considering all possible alignments, and the n-indexed element represents the number of times n matches were found considering all possible alignments.


Nt.MatchResult

INACCESSIBLE (constructor) Nt.MatchResult

Create Nt.MatchResult using the Nt.MatchMap#best, Nt.MatchMap#top and Nt.MatchMap#bottom methods.

Properties

.position

The alignment position of this MatchResult in searchSequence of your Nt.MatchMap.

.matches

The number of matches between querySequence and searchSequence at this alignment position.


Nt.MatchResult#alignment()

returns Nt.Seq

Creates a new Nt.Seq instance representing the portion of your searchSequence aligned at the associated Nt.MatchResult position. Will be querySequence.size() nucleotides long.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('TGCTC');

var map = new Nt.MatchMap(querySeq, seq);
var bestMatch = map.best();

bestMatch.alignment().sequence(); // === 'TGCCC'

Nt.MatchResult#alignmentMask()

returns Nt.Seq

Creates a new Nt.Seq instance representing a Nt.Seq#mask() of the portion of your searchSequence aligned at the associated Nt.MatchResult position. Will be querySequence.size() nucleotides long.

See Nt.Seq#mask for more information.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('TGCTC');

var map = new Nt.MatchMap(querySeq, seq);
var bestMatch = map.best();

bestMatch.alignmentMask().sequence(); // === 'TGC-C'

Nt.MatchResult#alignmentCover()

returns Nt.Seq

Creates a new Nt.Seq instance representing a Nt.Seq#cover() of the portion of your searchSequence aligned at the associated Nt.MatchResult position. Will be querySequence.size() nucleotides long.

See Nt.Seq#cover for more information.

var seq = (new Nt.Seq()).read('ATGCCCGACTGCA');
var querySeq = (new Nt.Seq()).read('TGCTC');

var map = new Nt.MatchMap(querySeq, seq);
var bestMatch = map.best();

bestMatch.alignmentCover().sequence(); // === 'TGCYC'

Appendix

Background

The initial purpose for developing this library was to find all sequences similar to a consensus sequence for a protein's DNA-binding domain in a genome. It was hypothesized that this protein could act to inhibit transcription by occluding the binding of RNA polymerase in multiple locations. I wanted a tool that could generate a list of all of these potential sites of inhibition (sites that the protein could potentially bind) ordered by their similarity to a consensus sequence.

I had previous experimental results listing a number of nucleotide sequences that this DNA-binding domain had high-affinity for. I had to use multiple tools to A) generate the consensus from identified binding sequences for this protein, B) use BLAST to try and find sequences that matched. Unfortunately, BLAST did not support the use the degenerate consensus sequence that I felt would give the best and largest set of results (potential binding sites in the genome) to test.

Using NtSeq, the Nt.Seq#cover method can generate consensus sequences quickly (though the resulting sequence is unweighted), and Nt.MatchMap supports degenerate nucleotide matching and can provide all ungapped matches (ordered by relevance) of moderately-sized query sequences in the genomic data I was looking through (~200kbp) in milliseconds.

This project sat unfinished for years, and I felt the need to clean it up and release it. I hope a new generation of young scientists and developers will be help develop and permeate small, focused, well-documented open source JavaScript libraries to create beautiful online experiences. :)

The Future, p-Values and Over / Under-Represented Sequences

Though it is outside of the scope of this project, I have done some work on determining whether sequences in a genome are over- or under-represented in a genome based on the statistical likelihood of finding a specific frequency of k matches given the ATGC content of the genome and search sequence. (i.e. How many times would I expect to find sequence identity of 15 (k) of 20 nucleotides if I aligned my query sequence at every possible location in a genome?)

Between non-degenerate sequences, you can approximate each alignment check between two nucleotides as a Bernoulli trial, where your probability of success (a match) is based upon the chance of randomly matching a nucleotide from your query sequence with your search sequence (for evenly-distributed ATGC content this is 0.25).

You can calculate the probability of matching two nucleotides for your input sequences by just calculating a sum of probabilities:

  Pr(match) = (Pr(SeqA, 'A') * Pr(SeqB, 'A')) +
    (Pr(SeqA, 'T') * Pr(SeqB, 'T')) +
    (Pr(SeqA, 'G') * Pr(SeqB, 'G')) +
    (Pr(SeqA, 'C') * Pr(SeqB, 'C'));

Where Pr(SeqA, 'A') would be the fractional A content of SeqA. (The probability of randomly choosing an 'A' nucleotide in SeqA). (This is available from Nt.Seq#fractionalContentATGC).

You can then calculate the probability of getting exactly k matches on any one alignment (say 15 of 20 for a length-20 query sequence) using the Probability Mass Function of a Binomial Distribution.

I've written an approximation for calculating the binomial distribution probability mass function in JavaScript as follows:

p is the probability of a match between two randomly selected nucleotides (calculated above).

n is the number of trials (the length of your query sequence)

k should be your number of matches.

function binomialPMF(p, n, k) {

  /*
    k = # of matches
    n = # of trials (length of query sequence)
    p = probability of success on a given trial
  */

  if (p === 0) {
    return 0;
  }

  if (p === 1) {
    return k === n ? 1 : 0;
  }

  // use symmetry
  if (k > (n / 2)) {
    k = n - k;
    p = 1 - p;
  };

  /*
    Binomial PMF:

      (n! / (k! * (n - k)!)) * p^k * (1 - p)^(n - k)

    Take the natural logarithm so we can add floats instead of multiply ints
    Lose some sensitivity, but if we don't, JS will overflow Number type

      log(n! / (k! * (n - k)!)) + (k * log(p)) + ((n - k) * log(1 - p))

  */
  var r = logBinomial(n, k) + (k * Math.log(p)) + ((n - k) * Math.log(1 - p));

  return Math.exp(r);

}

function logBinomial(n, k) {

  var r = 0;
  var i;

  /*

    (n! / (k! * (n - k)!)) can be represented as
    Product (i = (n - k + 1) to n): ( i / (n - i + 1) )

    i.e. n = 5, k = 2
      5! / (2! * 3!) = (5 * 4) / (2 * 1) = (4/2) * (5/1)

    Can be represented in log form as
    Sum (i = (n - k + 1) to n): ( log(i) - log(n - i + 1) )

  */

  for (i = n - k + 1; i <= n; i++) {
    r += Math.log(i) - Math.log(n - i + 1);
  }

  return r;

};

You can use Nt.MatchMap#matchFrequencyData() to view your match frequencies. You can calculate the probability of finding that many matches on a given random alignment trial by using binomialPMF(probability_match, matchFrequencyData[i], querySeq.size()). (Where i is the number of matches). We can then approximate the number of expected frequencies for each match amount by multiplying this by searchSeq.size() + querySeq.size() (the number of actual trials, Nt.MatchMap uses negative alignment offsets) by your probability result from binomialPMF.

I have not included this work in the library at present time, as it represents only a preliminary entry into determining the statistical significance of sequence match count frequencies. It is nowhere near complete, and if anybody can offer additional insight it would be great to extend the library further to offer useful p-values to scientists. It is important to note that this approach only provides a useful model when mapping and comparing two non-degenerate sequences.

Acknowledgements

Thanks for reading. Hope it's helpful! This library is MIT-licensed and completely open source. Use it (and any part of it) wherever you'd like, but credit is always appreciated. :)

You can feel free to follow me on Twitter:

@keithwhor

Check out my other projects on GitHub:

github.com/keithwhor

Or check out my personal website:

keithwhor.com