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Get started ​

Installation ​

You can install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the following:

julia
]add BioMarkovChains

If you are interested in the cutting edge of the development, please check out the main branch to try new features before release.

Create a BioMarkovChain of DNA ​

julia
using BioSequences, BioMarkovChains
+
+seq = dna"CCTCCCGGACCCTGGGCTCGGGAC"
+
+BioMarkovChain(sequence)
BioMarkovChain of DNAAlphabet{4}() and order 1:
+  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
+   0.0     1.0     0.0     0.0
+   0.0     0.5     0.2     0.3
+   0.25    0.125   0.625   0.0
+   0.0     0.6667  0.3333  0.0
+  - Initial Probabilities -> Vector{Float64}(4 × 1):
+   0.087   0.4348  0.3478  0.1304

Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.

`,9),r=t("em",null,"n-step transition probability matrix",-1),d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.679ex",height:"2.363ex",role:"img",focusable:"false",viewBox:"0 -750 6487.9 1044.2","aria-hidden":"true"},p=n('𝓂',1),h=[p],Q=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msup",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"M")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n")])]),t("mo",null,"="),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"m")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("mo",{stretchy:"false"},"("),t("mi",null,"n"),t("mo",{stretchy:"false"},")"),t("mo",{stretchy:"false"},")")])],-1),c={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),x=[g],u=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"n")])],-1),_={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"1.744ex",role:"img",focusable:"false",viewBox:"0 -721 1216 771","aria-hidden":"true"},w=n('',1),b=[w],v=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"M")])])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.985ex",height:"1.957ex",role:"img",focusable:"false",viewBox:"0 -661 2645.6 865","aria-hidden":"true"},C=n('',1),M=[C],L=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"→"),t("mi",null,"j")])],-1),H=t("em",null,"n",-1),A=n(`
julia
BioMarkovChain(sequence, 2)
BioMarkovChain of DNAAlphabet{4}() and order 2:
+  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
+   0.0     0.5     0.2     0.3
+   0.05    0.475   0.325   0.15
+   0.1562  0.3906  0.4156  0.0375
+   0.0833  0.375   0.3417  0.2
+  - Initial Probabilities -> Vector{Float64}(4 × 1):
+   0.087   0.4348  0.3478  0.1304
`,2);function D(j,E,B,S,P,V){return s(),e("div",null,[l,t("p",null,[a("A very nice nice property of the transition probability matrix is that the "),r,a(),t("mjx-container",d,[(s(),e("svg",T,h)),Q]),a(", that is the "),t("mjx-container",c,[(s(),e("svg",m,x)),u]),a("th power of "),t("mjx-container",_,[(s(),e("svg",k,b)),v]),a(" represents "),t("mjx-container",f,[(s(),e("svg",y,M)),L]),a(" transitions in "),H,a(" steps. We can also have higher order transition models as:")]),A])}const I=i(o,[["render",D]]);export{G as __pageData,I as default}; diff --git a/dev/assets/getstarted.md.CT3qMIGg.lean.js b/dev/assets/getstarted.md.CT3qMIGg.lean.js new file mode 100644 index 0000000..5b049dc --- /dev/null +++ b/dev/assets/getstarted.md.CT3qMIGg.lean.js @@ -0,0 +1 @@ +import{_ as i,c as e,j as t,a,a6 as n,o as s}from"./chunks/framework.Cvv1S4VC.js";const G=JSON.parse('{"title":"Get started","description":"","frontmatter":{},"headers":[],"relativePath":"getstarted.md","filePath":"getstarted.md","lastUpdated":null}'),o={name:"getstarted.md"},l=n("",9),r=t("em",null,"n-step transition probability matrix",-1),d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.679ex",height:"2.363ex",role:"img",focusable:"false",viewBox:"0 -750 6487.9 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We can also have higher order transition models as:")]),A])}const I=i(o,[["render",D]]);export{G as __pageData,I as default}; diff --git a/dev/assets/getstarted.md.YwYaJGOf.js b/dev/assets/getstarted.md.YwYaJGOf.js deleted file mode 100644 index f9fd491..0000000 --- a/dev/assets/getstarted.md.YwYaJGOf.js +++ /dev/null @@ -1,5 +0,0 @@ -import{_ as o,c as a,j as t,a as e,a6 as i,o as s}from"./chunks/framework.Cvv1S4VC.js";const G=JSON.parse('{"title":"Get started","description":"","frontmatter":{},"headers":[],"relativePath":"getstarted.md","filePath":"getstarted.md","lastUpdated":null}'),n={name:"getstarted.md"},l=i(`

Get started ​

Installation ​

You can install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the following:

julia
]add BioMarkovChains

If you are interested in the cutting edge of the development, please check out the main branch to try new features before release.

Create a BioMarkovChain of DNA ​

julia
using BioSequences, BioMarkovChains
-
-seq = dna"CCTCCCGGACCCTGGGCTCGGGAC"
-
-BioMarkovChain(sequence)

BioMarkovChain of DNAAlphabet{4}() and order 1: - Transition Probability Matrix -> Matrix{Float64}(4 × 4): 0.0 1.0 0.0 0.0 0.0 0.5 0.2 0.3 0.25 0.125 0.625 0.0 0.0 0.6667 0.3333 0.0 - Initial Probabilities -> Vector{Float64}(4 × 1): 0.087 0.4348 0.3478 0.1304

Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.

`,9),r=t("em",null,"n-step transition probability matrix",-1),T={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.679ex",height:"2.363ex",role:"img",focusable:"false",viewBox:"0 -750 6487.9 1044.2","aria-hidden":"true"},Q=i('𝓂',1),h=[Q],p=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msup",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"M")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n")])]),t("mo",null,"="),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"m")]),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"j")])]),t("mo",{stretchy:"false"},"("),t("mi",null,"n"),t("mo",{stretchy:"false"},")"),t("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),x=[g],u=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"n")])],-1),_={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.113ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.751ex",height:"1.744ex",role:"img",focusable:"false",viewBox:"0 -721 1216 771","aria-hidden":"true"},w=i('',1),f=[w],b=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"script"},"M")])])],-1),v={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.462ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.985ex",height:"1.957ex",role:"img",focusable:"false",viewBox:"0 -661 2645.6 865","aria-hidden":"true"},C=i('',1),M=[C],L=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"i"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",null," ")]),t("mo",{stretchy:"false"},"→"),t("mi",null,"j")])],-1),H=t("em",null,"n",-1),A=i('
julia
BioMarkovChain(sequence, 2)

BioMarkovChain of DNAAlphabet{4}() and order 2: - Transition Probability Matrix -> Matrix{Float64}(4 × 4): 0.0 0.5 0.2 0.3 0.05 0.475 0.325 0.15 0.1562 0.3906 0.4156 0.0375 0.0833 0.375 0.3417 0.2 - Initial Probabilities -> Vector{Float64}(4 × 1): 0.087 0.4348 0.3478 0.1304

',2);function D(j,E,B,S,P,V){return s(),a("div",null,[l,t("p",null,[e("A very nice nice property of the transition probability matrix is that the "),r,e(),t("mjx-container",T,[(s(),a("svg",d,h)),p]),e(", that is the "),t("mjx-container",m,[(s(),a("svg",c,x)),u]),e("th power of "),t("mjx-container",_,[(s(),a("svg",k,f)),b]),e(" represents "),t("mjx-container",v,[(s(),a("svg",y,M)),L]),e(" transitions in "),H,e(" steps. We can also have higher order transition models as:")]),A])}const I=o(n,[["render",D]]);export{G as __pageData,I as default}; diff --git a/dev/assets/getstarted.md.YwYaJGOf.lean.js b/dev/assets/getstarted.md.YwYaJGOf.lean.js deleted file mode 100644 index 6948b12..0000000 --- a/dev/assets/getstarted.md.YwYaJGOf.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as o,c as a,j as t,a as e,a6 as i,o as s}from"./chunks/framework.Cvv1S4VC.js";const G=JSON.parse('{"title":"Get started","description":"","frontmatter":{},"headers":[],"relativePath":"getstarted.md","filePath":"getstarted.md","lastUpdated":null}'),n={name:"getstarted.md"},l=i("",9),r=t("em",null,"n-step transition probability matrix",-1),T={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.666ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.679ex",height:"2.363ex",role:"img",focusable:"false",viewBox:"0 -750 6487.9 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BioMarkovChains.jl

Appearance

Towards Markov Chains ​

DNA as a Markov chain ​

Several packages (e.g. MarkovChainsHammer.jl, DiscreteMarkovChains.jl, etc.) in the Julia ecosystem have been implemented to work with Markov chains with a state space of integers, those could be efficient in many ways, but they are clumsy to work with a specialized biological types as in the BioJulia ecosystem. Therefore, in the GeneFinder package we dedicated some implementations to work with BioSequence types so that we can expand the functionality in an efficient way (see complete API).

One important step towards many gene finding algorithms is to represent a DNA sequence as a Markov chain. In this representation a DNA sequence of a reduced alphabet A = {A, C, G, T} is draw as a four-vertex graph, where each letter of A is a state (vertex) and the edges of the graph represent transitions from one nucleotide to another in a sequence (e.g. A → T represent a single nucleotide to nucleotide transition). This is also considered more specifically as a Discrete Markov chain (Axelson-Fisk 2015). The complete set of transitions and states of a DNA sequence of alphabet A.

More formally a Markov chain is a random process where each state is a random variable Xt where t∈T is a discrete time in a finite sequence T and the probability to jump from one state into another is only dependent of the current state. Therefore a definition of this Markov property is given by:

P(Xt=j|Xt−1=i)

where i, j ∈ A . This property led us to generalize a way to calculate the probability of a sequence T from a process (X1...XT) where each random variable is a nucleotide from A so that:

P(X1=i1,...,XT=iT)=P(X1=i1)∏t=2TP(Xt=it|Xt−1=it−1)

Note that previous equations has two terms, a initial probability P(X1=i1) and the the product of all transitions beginning at t=2. So, to calculate the initial probability distribution of each of the nucleotides of a string T with the alphabet 𝒜 we can first calculate the transition probability matrix M^ out of the frequency count of the transitions. In an alphabet 𝒜 we got 42 transitions of one order, that is the AA, AC, AG, ... which coincides with the frequency of the dinucleotides in the sequence. So we can later in fact build a 4x4 matrix representing all the transitions. For instance in a DNA sequence T of 24 nucleotides:

CCTCCCGGACCCTGGGCTCGGGAC

We can calculate each frequency nucleotide to any other nucleotide m^ij=cijci where cij is the actual count of the dinucleotide, and therefore ci is the counts of the nucleotide i to any other nucleotide and build the transition probability matrix:

[ACGTA0.001.000.000.00C0.000.560.220.30G0.250.120.620.00T0.000.670.330.00]

It is noteworthy that initial probabilities can also be obtained from the counts of each nucleotide transitions cij over the total sum of the dinucleotide counts ck:

π^i=ci∑kck

That way for the previous example example we can can calculate the initial probabilities π^ = (0.08,0.43,0.34,0.13). Both set of probabilities composed a transition model that can be used to predict the probability of any DNA sequence using equation (2).

References ​

Axelson-Fisk, Marina. 2015. Comparative Gene Finding. Vol. 20. Computational Biology. London: Springer London. http://link.springer.com/10.1007/978-1-4471-6693-1.

- + \ No newline at end of file diff --git a/dev/getstarted.html b/dev/getstarted.html index 00ecbff..cd8b7b0 100644 --- a/dev/getstarted.html +++ b/dev/getstarted.html @@ -8,11 +8,11 @@ - + - - + + @@ -21,8 +21,22 @@ seq = dna"CCTCCCGGACCCTGGGCTCGGGAC" -BioMarkovChain(sequence)

BioMarkovChain of DNAAlphabet{4}() and order 1: - Transition Probability Matrix -> Matrix{Float64}(4 × 4): 0.0 1.0 0.0 0.0 0.0 0.5 0.2 0.3 0.25 0.125 0.625 0.0 0.0 0.6667 0.3333 0.0 - Initial Probabilities -> Vector{Float64}(4 × 1): 0.087 0.4348 0.3478 0.1304

Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.

A very nice nice property of the transition probability matrix is that the n-step transition probability matrix Mn=(mij(n)), that is the nth power of M represents i →j transitions in n steps. We can also have higher order transition models as:

julia
BioMarkovChain(sequence, 2)

BioMarkovChain of DNAAlphabet{4}() and order 2: - Transition Probability Matrix -> Matrix{Float64}(4 × 4): 0.0 0.5 0.2 0.3 0.05 0.475 0.325 0.15 0.1562 0.3906 0.4156 0.0375 0.0833 0.375 0.3417 0.2 - Initial Probabilities -> Vector{Float64}(4 × 1): 0.087 0.4348 0.3478 0.1304

- +BioMarkovChain(sequence)
BioMarkovChain of DNAAlphabet{4}() and order 1:
+  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
+   0.0     1.0     0.0     0.0
+   0.0     0.5     0.2     0.3
+   0.25    0.125   0.625   0.0
+   0.0     0.6667  0.3333  0.0
+  - Initial Probabilities -> Vector{Float64}(4 × 1):
+   0.087   0.4348  0.3478  0.1304

Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.

A very nice nice property of the transition probability matrix is that the n-step transition probability matrix Mn=(mij(n)), that is the nth power of M represents i →j transitions in n steps. We can also have higher order transition models as:

julia
BioMarkovChain(sequence, 2)
BioMarkovChain of DNAAlphabet{4}() and order 2:
+  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
+   0.0     0.5     0.2     0.3
+   0.05    0.475   0.325   0.15
+   0.1562  0.3906  0.4156  0.0375
+   0.0833  0.375   0.3417  0.2
+  - Initial Probabilities -> Vector{Float64}(4 × 1):
+   0.087   0.4348  0.3478  0.1304
+ \ No newline at end of file diff --git a/dev/hashmap.json b/dev/hashmap.json index ee8ad04..51c18e3 100644 --- a/dev/hashmap.json +++ b/dev/hashmap.json @@ -1 +1 @@ -{"article01.md":"BrGXw77Y","getstarted.md":"YwYaJGOf","home.md":"DYCAAGxb","index.md":"C2Xkp6cL","api.md":"BiqC9tVJ","biomarkovchains.md":"0rg0z1ev"} +{"home.md":"DYCAAGxb","article01.md":"BrGXw77Y","index.md":"C2Xkp6cL","getstarted.md":"CT3qMIGg","api.md":"BiqC9tVJ","biomarkovchains.md":"0rg0z1ev"} diff --git a/dev/home.html b/dev/home.html index f410854..fafd433 100644 --- a/dev/home.html +++ b/dev/home.html @@ -8,17 +8,17 @@ - + - +
BioMarkovChains.jl

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Representing biological sequences as Markov chains

Overview ​

This package aim to represent BioSequences types as Markov chains to perform different operations and predictions

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BioMarkovChains.jl

Appearance

BioMarkovChains.jl

Representing biological sequences as Markov chains

Get Started
View on Github
BioMarkovChains

Install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the add BioMarkovChains command.

julia
(@v1.10) pkg> add BioMarkovChains

For more information, see the Get Started section.

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