https://github.com/BioJulia/BioMarkovChains.jl

Representing biological sequences as Markov chains
https://github.com/BioJulia/BioMarkovChains.jl

bioinformatics biology dna julia julialang markov-chain

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Representing biological sequences as Markov chains

• Host: GitHub
• URL: https://github.com/BioJulia/BioMarkovChains.jl
• Owner: BioJulia
• License: mit
• Created: 2023-07-11T15:11:46.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2024-12-09T05:52:17.000Z (10 months ago)
• Last Synced: 2024-12-11T11:28:40.038Z (10 months ago)
• Topics: bioinformatics, biology, dna, julia, julialang, markov-chain
• Language: Julia
• Homepage: https://biojulia.dev/BioMarkovChains.jl/dev/
• Size: 3.57 MB
• Stars: 8
• Watchers: 1
• Forks: 2
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • Changelog: CHANGELOG.md
  • License: LICENSE.md
  • Citation: CITATION.cff

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  Representing biological sequences as Markov chains







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***

# BioMarkovChains

> A Julia package to represent biological sequences as Markov chains

## Installation



BioMarkovChains is a  

    

        

        Julia Language

    

      package. To install BioMarkovChains,

    please open

    Julia's interactive session (known as REPL) and press ]

    key in the REPL to use the package mode, then type the following command



```julia

pkg> add BioMarkovChains

```

## Creating Markov chain out of DNA sequences

An important step before developing several gene finding algorithms consist of having a Markov chain representation of the DNA. To do so, we implemented the `BioMarkovChain` method that will capture the initials and transition probabilities of a DNA sequence (`LongSequence`) and will create a dedicated object storing relevant information of a DNA Markov chain. Here an example:

Let find one ORF in a random `LongDNA` :

```julia

using BioSequences, BioMarkovChains, GeneFinder

# > 180195.SAMN03785337.LFLS01000089 -> finds only 1 gene in Prodigal (from Pyrodigal tests)

seq = dna"AACCAGGGCAATATCAGTACCGCGGGCAATGCAACCCTGACTGCCGGCGGTAACCTGAACAGCACTGGCAATCTGACTGTGGGCGGTGTTACCAACGGCACTGCTACTACTGGCAACATCGCACTGACCGGTAACAATGCGCTGAGCGGTCCGGTCAATCTGAATGCGTCGAATGGCACGGTGACCTTGAACACGACCGGCAATACCACGCTCGGTAACGTGACGGCACAAGGCAATGTGACGACCAATGTGTCCAACGGCAGTCTGACGGTTACCGGCAATACGACAGGTGCCAACACCAACCTCAGTGCCAGCGGCAACCTGACCGTGGGTAACCAGGGCAATATCAGTACCGCAGGCAATGCAACCCTGACGGCCGGCGACAACCTGACGAGCACTGGCAATCTGACTGTGGGCGGCGTCACCAACGGCACGGCCACCACCGGCAACATCGCGCTGACCGGTAACAATGCACTGGCTGGTCCTGTCAATCTGAACGCGCCGAACGGCACCGTGACCCTGAACACAACCGGCAATACCACGCTGGGTAATGTCACCGCACAAGGCAATGTGACGACTAATGTGTCCAACGGCAGCCTGACAGTCGCTGGCAATACCACAGGTGCCAACACCAACCTGAGTGCCAGCGGCAATCTGACCGTGGGCAACCAGGGCAATATCAGTACCGCGGGCAATGCAACCCTGACTGCCGGCGGTAACCTGAGC"

orfseq = findorfs(seq)[3] |> sequence

21nt DNA Sequence:

ATGCGTCGAATGGCACGGTGA

```

If we translate it, we get a 7aa sequence:

```julia

translate(orfseq)

7aa Amino Acid Sequence:

MRRMAR*

```

Now supposing I do want to see how transitions are occurring in this ORF sequence, the I can use the `BioMarkovChain` method and tune it to 2nd-order Markov chain:

```julia

BioMarkovChain(orfseq, 2)

BioMarkovChain of DNA alphabet and order 1:

  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):

   0.25    0.25    0.0     0.5

   0.25    0.0     0.75    0.0

   0.25    0.25    0.25    0.25

   0.0     0.25    0.75    0.0

  - Initial Probabilities -> Vector{Float64}(4 × 1):

   0.2     0.2     0.4     0.2

```

But I can also have a BioMarkovChain instance of the Ammino Acid sequence:

```julia

BioMarkovChain(translate(orfseq), 2)

BioMarkovChain of AminoAcid alphabet and order 1:

  - Transition Probability Matrix -> Matrix{Float64}(20 × 20):

   0.0    1.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.333  0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.5    0.5    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

   0.0    0.0    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

  - Initial Probabilities -> Vector{Float64}(20 × 1):

   0.167  0.5    0.0    0.0    0.0    0.0      …    0.0    0.0    0.0    0.0    0.0    0.0    0.0

```

This is  useful to later create HMMs and calculate sequence probability based on a given model, for instance we now have the *E. coli* CDS and No-CDS transition models or Markov chain implemented:

```julia

ECOLICDS

BioMarkovChain of DNA alphabet and order 1:

  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):

   0.31    0.224   0.199   0.268

   0.251   0.215   0.313   0.221

   0.236   0.308   0.249   0.207

   0.178   0.217   0.338   0.267

  - Initial Probabilities -> Vector{Float64}(4 × 1):

   0.245   0.243   0.273   0.239

```

What is then the probability of the previous DNA sequence given this model?

```julia

markovprobability(orfseq, model=ECOLICDS, logscale=true)

-39.71754773536592

```

This is off course not very informative, but we can later use different criteria to then classify new ORFs. For a more detailed explanation see the [docs](https://BioJulia.dev/BioMarkovChains.jl/dev/)