Building a dictionary for genomes

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Building a dictionary for genomes

• By Harmen J. Bussemaker, Hao Li, and Eric D.
  Siggia

Tal Frank
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Topics that will be discussed

• Biological background
• Present the biological problem
• Show an algorithm that treats this problem
• ?statistical mechanics methods
• Try our algorithm on two well known problems

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What we did so far

• Human Genome Project(2001)
• This article published(2000) Sequence is not
  everything - Lets do some theory
• Control over gene expression - when, how much
• Control element Regulator Sequence motif
  
• Genes are working together Co-regulated genes

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The goals of this work

• Identify the Control element
• Where are they located ?
• Identify co-regulated genes

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Multiple control elements

• Example where are the control elements located?
• Concepts directionality , upstream ,in the junk
• TACGAXTTCGA
• Example co-regulated genes
• naïve approach TACGAXTTTAAYATGGCA
• experimentally TACGAXTTCGAYATGGCA
• To activate set of genes multiple sequences
  needed

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New terminology

• DNA string of letters
• Control element word
• Multiple control element sentences
• Genes and junk background noise
• Example S GAGCXTGGYGCTT
• words GA,TG
• sentence GA.TG
• background genes and junk.

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MobyDick algorithm

• decipher a text consisting of a long string
  of letters written in an unknown language.
• Find the words in the text
• Find the right spacing
• example DA,T,AT SATT
  
• P1A.T.T
• P2AT.T

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How would you do it ?

• 1.Look for repeated substring in the string
• ? went, to, he? D (dictionary)
• 2.Space the text ooopps Spacing is not that
• simple.
• e.g. DA,T,AT SATT
• P1A.T.T ?p1
• P2AT.T ?p2

Tal went to Weizmann this morning. When he
arrived he didnt go to his office, he went to
drink a cup of coffee .
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MobyDick Blueprints
STAGATAT
DT,A,G
1 letter word
pw pA,pT..
Find pw
STAGATAT
DA,TA,
2 letter word
pw pA,pTA.
Find pw
No more optional words ? stop!
Find spacing
STA.G.A.TA.T
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statistical mechanics in order to ?

• 1.How does MobyDick decide pw?
• 2.When does MobyDick add a new
• word?
• 3.Space (parse) the text.

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The likelihood function

• k a possible spacing
• Nw number of times the word w appears
• Example D(T,AT,A) STATA
• k1T.A.T.A
• k2T.AT.A

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Likelihood function - intuition

• Z(D,pw)- partition function ltEgt,ltNgt,ltTgt,.
• Z(D,pw)- the probability to obtain a
• sequence S.
• Example D (T,AT,A) pT,pA,pAT
• Question what is the probability to STATA?
• 1st possibility T.A.T.A ? pApApTpT
• 2nd possibility T.AT.A ?pTpATpA

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Finding pw
Given D,S
Maximize Z(pw,D) with respect to pw
This pw gives the highest probability to get
the given S
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Lets find the pw !

• Definition - average number of
  the word w
• over the
  different spacings .
• Can prove
• maximize Z- solve
• solving is done by iteration

pw
ltNwgt
pw
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Enough is enough !!!

• When is pw good enough ?
• when the new pw dont give higher Z
• We say this method converges !
• Other methods dont converge.

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Why finding pw using this way ?

• Monte-Carlo methods dont converge.
• Slow method ? can transform to fast method
• Order of complexity O(LDl)
• L-the length of the string
• D-the size of the dictionary
• l-the length of the longest word in D

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Add new words ?
Look at dictionary
DT,A,C,G STATTGA
Compose new word ww
DT,A,C,G STATTGA wwTA
Check occurrence
DT,A,C,G STATTGA wwTA
DT,A,C,G,TA STATTGA
Yes- add to dictionary
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A problem and a bad solution

• The algorithm finds only the words which are
  composed from words already in the dictionary.
• Example SAATATAAA
• 1st step SAATATAAA
• D A
• 2nd step SAATATAAA
• AT is not a composition of
  words
• Solution Look for repeated long strings
• by consideration the problem

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Spacing

• Define number of times the word w occurs
  in
• a given spacing.
• Quality factor
• The required condition

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checking the algorithm

• Applying on the English novel Moby Dick
• Applying on Control elements on the yeast genome
• Not always possible - Voynich manuscript (1450)

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Preparing the book MobyDick

• Call me Ishmael. Some years ago- never mind how
  long precisely- having little
• or no money in my purse, and nothing particular
  tothought I would sail
• CallmeIshmaelSomeyearsagonevermindhowlongprecisely
  havingli
• ttleornomoneyinmypurseandnothingparticulartothough
  tIwouldsail..
• CallabajameIshmaelbjklmbbSomeyearsagonevermindhowl
  on
• Eciselyhavinglittlermsdrornomoneyinmypurseandnothi
  ngparticu
• artothoughtIwouldsail

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Results- MobyDick

• 10 first chapters
• Da,b,c.
• Text 4,214 unique words
• 2,630 occurred only once
• Background increases L by the factor of 3.
• 2,450 words found , 700 in English, 40 composite
  words.

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Results- yeast

• DT,A,C,G
• Text 443 experimentally determined sites
• Background genes and junk
• 500 words found
• 114 match the experimentally predictions
• Not that good it is a beginning!

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• The end