Building a dictionary
for genomes
By Harmen J. Bussemaker, Hao Li, and Eric
D. Siggia
Tal Frank
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
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
The goals of this work
 Identify the Control element
 Where are they located ?
 Identify co-regulated genes
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
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.
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 : D={A,T,AT} S=ATT
P1=A.T.T
P2=AT.T
How would you do it ?
1.Look for repeated substring in the string :
Tal went to Weizmann this morning. When he arrived he
didn’t go to his office, he went to drink a cup of coffee ….
 {went, to, he} D (dictionary)
2.Space the text – ooopps Spacing is not that
simple.
e.g.– D={A,T,AT} S=ATT
P1=A.T.T
p1
P2=AT.T
p2
MobyDick Blueprints
1 letter word
S=TAGATAT
Find pw
D={T,A,G}
pw ={pA,pT..}
2 letter word
D={A,TA,…}
S=TAGATAT
Find pw
pw ={pA,pTA.}
No more optional words  stop!
Find spacing
S=TA.G.A.TA.T
statistical mechanics in
order to ?
1.How does MobyDick decide {pw}?
2.When does MobyDick add a new
word?
3.Space (parse) the text.
The likelihood function
z     pw 
k
k:
Nw ( k )
w
a possible spacing
Nw: number of times the word w appears
Example : D=(T,AT,A) S=TATA
k1=T.A.T.A
Z  p A2 pT2  p A pT p AT
k2=T.AT.A
Likelihood function - intuition
Z(D,{pw})- partition function: <E>,<N>,<T>,….
Z(D,{pw})- the probability to obtain a
sequence S.
Example : D =(T,AT,A) {pT,pA,pAT}
Question : what is the probability to S=TATA?
1st possibility : T.A.T.A  pA*pA*pT*pT
2nd possibility: T.AT.A pT*pAT*pA
p  p A p  p A pT p AT  Z
2
2
T
Finding {pw}
Given : D,S
Maximize Z({pw},D) with respect to {pw}
This {pw} gives the highest probability
to get the given S
Lets find the {pw} !
Definition : N w  - average number of the word w
over the different spacings .

Can prove:  N w  pw ( ) ln Z
pw
 Nw 
maximize Z- solve: pw 
 w'  N w' 
solving : is done by iteration:
pw’
<Nw’>
pw
Enough is enough !!!
 When is pw good enough ?
when the new {pw} don’t give higher Z
 We say : this method converges !
 Other methods don’t converge.
Why finding {pw} using this
way ?
 Monte-Carlo methods don’t 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
Add new words ?
Look at dictionary
D={T,A,C,G} S=TATTGA
Compose new word ww’
D={T,A,C,G} S=TATTGA ww’=TA
Check occurrence
D={T,A,C,G} S=TATTGA ww’=TA
[ N _ ww ']  [ N w  pw' ]?
Yes- add to dictionary
D={T,A,C,G,TA} S=TATTGA
A problem and a bad
solution
 The algorithm finds only the words which are
composed from words already in the dictionary.
 Example : S=AATATAAA
1st step : S=AATATAAA
D= {A}
2nd step : S=AATATAAA
AT is not a composition of words
 Solution: Look for repeated long strings
by consideration the problem
Spacing
 Define :
 w number of times the word w occurs in
a given spacing.
 Quality factor :
 Nw 
Qw 
w
 The required condition :
Qw  1
checking the algorithm
 Applying on the English novel Moby Dick
 Applying on Control elements on the yeast
genome
 Not always possible - Voynich manuscript
(1450)
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 …
CallmeIshmaelSomeyearsagonevermindhowlongpreciselyhavingli
ttleornomoneyinmypurseandnothingparticulartothoughtIwouldsail..
CallabajameIshmaelbjklmbbSomeyearsagonevermindhowlon
Eciselyhavinglittlermsdrornomoneyinmypurseandnothingparticu
artothoughtIwouldsail …
Results- MobyDick
 10 first chapters
 D={a,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.
Results- yeast
 D={T,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!
The end