March 1st, 2016

## Identity

We recognize patterns, such as

• the same object from different angles
• the same object in different times
• objects of the same class
• hierarchy of classes
• abstractions of language: letters
• abstractions of sets: numbers
• abstractions of rules: algebra

## Clustering

• split all the samples into meaningful classes
• Find the characteristic of each class
• classify all instances into classes
• determine the class of new instances
• determine the number of classes

## A CorrectUseful Clustering

• Different groupings can be correct at the same time
• The number of clusters depending on the context
• This is called granularity level
• meaning “the size of the grains”

Tree of Life

## Hierarchical Clustering

Bottom up: joining one by one

• if $$\textrm{dist}(x, y)$$ is the smallest distance, we join $$x$$ and $$y$$
• we create cluster $$C$$
• we repeat until we have only one cluster

## Application

microarray <- read.table("microarray.txt")
d <- dist(microarray, method="euclidean")
tree <- hclust(d, method = "average")

### Euclidean Distance

$\text{dist}_2(x,y)=\sqrt{(x_1-y_1)^2+\cdots +(x_n-y_n)^2}$

### Average Linkage

$\text{dist}(x, C)=\text{mean} (\text{dist}(x, y): y \in C)$

## Hierarchical clustering

plot(tree, labels = FALSE)

## Which are the clusters?

Since this is a hierarchical clustering, the number of clusters depends on the distance threshold.

Higher cut value means less clusters

## Doing the job

To finally split the samples into the clusters defined by the tree, we use the function cutree

cutree(tree, k = NULL, h = NULL)
• tree: a tree as produced by hclust.
• k: an integer scalar or vector with the desired number of groups
• h: numeric scalar or vector with heights where the tree should be cut
• sounds like cut tree

## Example

cluster <- cutree(tree, h = 5)
cluster
b4634 b3241 b3240 b3243 b3242 b2836 b0885 b1338 b1337 b1339
1     2     3     4     3     1     5     6     3     3
[ reached getOption("max.print") -- omitted 4287 entries ]
table(cluster)
cluster
1   2   3   4   5   6   7   8   9  10
277  74 386 440 327 486  78 223  22  38
[ reached getOption("max.print") -- omitted 166 entries ]

## FASTA file

>gi|556503834|ref|NC_000913.3| Escherichia coli str. K-12 substr. MG1655, complete genome
AGCTTTTCATTCTGACTGCAACGGGCAATATGTCTCTGTGTGGATTAAAAAAAGAGTGTCTGATAGCAGC
TTCTGAACTGGTTACCTGCCGTGAGTAAATTAAAATTTTATTGACTTAGGTCACTAAATACTTTAACCAA
TATAGGCATAGCGCACAGACAGATAAAAATTACAGAGTACACAACATCCATGAAACGCATTAGCACCACC
ATTACCACCACCATCACCATTACCACAGGTAACGGTGCGGGCTGACGCGTACAGGAAACACAGAAAAAAG
CCCGCACCTGACAGTGCGGGCTTTTTTTTTCGACCAAAGGTAACGAGGTAACAACCATGCGAGTGTTGAA
GTTCGGCGGTACATCAGTGGCAAATGCAGAACGTTTTCTGCGTGTTGCCGATATTCTGGAAAGCAATGCC
AGGCAGGGGCAGGTGGCCACCGTCCTCTCTGCCCCCGCCAAAATCACCAACCACCTGGTGGCGATGATTG
AAAAAACCATTAGCGGCCAGGATGCTTTACCCAATATCAGCGATGCCGAACGTATTTTTGCCGAACTTTT
GACGGGACTCGCCGCCGCCCAGCCGGGGTTCCCGCTGGCGCAATTGAAAACTTTCGTCGATCAGGAATTT
GCCCAAATAAAACATGTCCTGCATGGCATTAGTTTGTTGGGGCAGTGCCCGGATAGCATCAACGCTGCGC
TGATTTGCCGTGGCGAGAAAATGTCGATCGCCATTATGGCCGGCGTATTAGAAGCGCGCGGTCACAACGT
TACTGTTATCGATCCGGTCGAAAAACTGCTGGCAGTGGGGCATTACCTCGAATCTACCGTCGATATTGCT
GAGTCCACCCGCCGTATTGCGGCAAGCCGCATTCCGGCTGATCACATGGTGCTGATGGCAGGTTTCACCG
CCGGTAATGAAAAAGGCGAACTGGTGGTGCTTGGACGCAACGGTTCCGACTACTCTGCTGCGGTGCTGGC
TGCCTGTTTACGCGCCGATTGTTGCGAGATTTGGACGGACGTTGACGGGGTCTATACCTGCGACCCGCGT
CAGGTGCCCGATGCGAGGTTGTTGAAGTCGATGTCCTACCAGGAAGCGATGGAGCTTTCCTACTTCGGCG
CTAAAGTTCTTCACCCCCGCACCATTACCCCCATCGCCCAGTTCCAGATCCCTTGCCTGATTAAAAATAC
CGGAAATCCTCAAGCACCAGGTACGCTCATTGGTGCCAGCCGTGATGAAGACGAATTACCGGTCAAGGGC
ATTTCCAATCTGAATAACATGGCAATGTTCAGCGTTTCTGGTCCGGGGATGAAAGGGATGGTCGGCATGG
CGGCGCGCGTCTTTGCAGCGATGTCACGCGCCCGTATTTCCGTGGTGCTGATTACGCAATCATCTTCCGA
ATACAGCATCAGTTTCTGCGTTCCACAAAGCGACTGTGTGCGAGCTGAACGGGCAATGCAGGAAGAGTTC
TACCTGGAACTGAAAGAAGGCTTACTGGAGCCGCTGGCAGTGACGGAACGGCTGGCCATTATCTCGGTGG
TAGGTGATGGTATGCGCACCTTGCGTGGGATCTCGGCGAAATTCTTTGCCGCACTGGCCCGCGCCAATAT
CAACATTGTCGCCATTGCTCAGGGATCTTCTGAACGCTCAATCTCTGTCGTGGTAAATAACGATGATGCG
ACCACTGGCGTGCGCGTTACTCATCAGATGCTGTTCAATACCGATCAGGTTATCGAAGTGTTTGTGATTG
GCGTCGGTGGCGTTGGCGGTGCGCTGCTGGAGCAACTGAAGCGTCAGCAAAGCTGGCTGAAGAATAAACA
TATCGACTTACGTGTCTGCGGTGTTGCCAACTCGAAGGCTCTGCTCACCAATGTACATGGCCTTAATCTG
GAAAACTGGCAGGAAGAACTGGCGCAAGCCAAAGAGCCGTTTAATCTCGGGCGCTTAATTCGCCTCGTGA
AAGAATATCATCTGCTGAACCCGGTCATTGTTGACTGCACTTCCAGCCAGGCAGTGGCGGATCAATATGC
CGACTTCCTGCGCGAAGGTTTCCACGTTGTCACGCCGAACAAAAAGGCCAACACCTCGTCGATGGATTAC
TACCATCAGTTGCGTTATGCGGCGGAAAAATCGCGGCGTAAATTCCTCTATGACACCAACGTTGGGGCTG
GATTACCGGTTATTGAGAACCTGCAAAATCTGCTCAATGCAGGTGATGAATTGATGAAGTTCTCCGGCAT
TCTTTCTGGTTCGCTTTCTTATATCTTCGGCAAGTTAGACGAAGGCATGAGTTTCTCCGAGGCGACCACG
CTGGCGCGGGAAATGGGTTATACCGAACCGGACCCGCGAGATGATCTTTCTGGTATGGATGTGGCGCGTA
AACTATTGATTCTCGCTCGTGAAACGGGACGTGAACTGGAGCTGGCGGATATTGAAATTGAACCTGTGCT
GCCCGCAGAGTTTAACGCCGAGGGTGATGTTGCCGCTTTTATGGCGAATCTGTCACAACTCGACGATCTC
TTTGCCGCGCGCGTGGCGAAGGCCCGTGATGAAGGAAAAGTTTTGCGCTATGTTGGCAATATTGATGAAG
ATGGCGTCTGCCGCGTGAAGATTGCCGAAGTGGATGGTAATGATCCGCTGTTCAAAGTGAAAAATGGCGA
AAACGCCCTGGCCTTCTATAGCCACTATTATCAGCCGCTGCCGTTGGTACTGCGCGGATATGGTGCGGGC
AATGACGTTACAGCTGCCGGTGTCTTTGCTGATCTGCTACGTACCCTCTCATGGAAGTTAGGAGTCTGAC
ATGGTTAAAGTTTATGCCCCGGCTTCCAGTGCCAATATGAGCGTCGGGTTTGATGTGCTCGGGGCGGCGG
TGACACCTGTTGATGGTGCATTGCTCGGAGATGTAGTCACGGTTGAGGCGGCAGAGACATTCAGTCTCAA
CAACCTCGGACGCTTTGCCGATAAGCTGCCGTCAGAACCACGGGAAAATATCGTTTATCAGTGCTGGGAG
CGTTTTTGCCAGGAACTGGGTAAGCAAATTCCAGTGGCGATGACCCTGGAAAAGAATATGCCGATCGGTT
CGGGCTTAGGCTCCAGTGCCTGTTCGGTGGTCGCGGCGCTGATGGCGATGAATGAACACTGCGGCAAGCC
GCTTAATGACACTCGTTTGCTGGCTTTGATGGGCGAGCTGGAAGGCCGTATCTCCGGCAGCATTCATTAC
GACAACGTGGCACCGTGTTTTCTCGGTGGTATGCAGTTGATGATCGAAGAAAACGACATCATCAGCCAGC
AAGTGCCAGGGTTTGATGAGTGGCTGTGGGTGCTGGCGTATCCGGGGATTAAAGTCTCGACGGCAGAAGC
CAGGGCTATTTTACCGGCGCAGTATCGCCGCCAGGATTGCATTGCGCACGGGCGACATCTGGCAGGCTTC
ATTCACGCCTGCTATTCCCGTCAGCCTGAGCTTGCCGCGAAGCTGATGAAAGATGTTATCGCTGAACCCT
ACCGTGAACGGTTACTGCCAGGCTTCCGGCAGGCGCGGCAGGCGGTCGCGGAAATCGGCGCGGTAGCGAG
CGGTATCTCCGGCTCCGGCCCGACCTTGTTCGCTCTGTGTGACAAGCCGGAAACCGCCCAGCGCGTTGCC

## FASTA file (amino acids)

>NC_000913.3_prot_NP_414542.1_1 [gene=thrL] [protein=thr operon leader peptide] [protein_id=NP_414542.1] [location=190..255]
MKRISTTITTTITITTGNGAG
>NC_000913.3_prot_NP_414543.1_2 [gene=thrA] [protein=Bifunctional aspartokinase/homoserine dehydrogenase 1] [protein_id=NP_414543.1] [location=337..2799]
MRVLKFGGTSVANAERFLRVADILESNARQGQVATVLSAPAKITNHLVAMIEKTISGQDALPNISDAERI
FAELLTGLAAAQPGFPLAQLKTFVDQEFAQIKHVLHGISLLGQCPDSINAALICRGEKMSIAIMAGVLEA
RGHNVTVIDPVEKLLAVGHYLESTVDIAESTRRIAASRIPADHMVLMAGFTAGNEKGELVVLGRNGSDYS
AAVLAACLRADCCEIWTDVDGVYTCDPRQVPDARLLKSMSYQEAMELSYFGAKVLHPRTITPIAQFQIPC
LIKNTGNPQAPGTLIGASRDEDELPVKGISNLNNMAMFSVSGPGMKGMVGMAARVFAAMSRARISVVLIT
QSSSEYSISFCVPQSDCVRAERAMQEEFYLELKEGLLEPLAVTERLAIISVVGDGMRTLRGISAKFFAAL
ARANINIVAIAQGSSERSISVVVNNDDATTGVRVTHQMLFNTDQVIEVFVIGVGGVGGALLEQLKRQQSW
LKNKHIDLRVCGVANSKALLTNVHGLNLENWQEELAQAKEPFNLGRLIRLVKEYHLLNPVIVDCTSSQAV
ADQYADFLREGFHVVTPNKKANTSSMDYYHQLRYAAEKSRRKFLYDTNVGAGLPVIENLQNLLNAGDELM
KFSGILSGSLSYIFGKLDEGMSFSEATTLAREMGYTEPDPRDDLSGMDVARKLLILARETGRELELADIE
IEPVLPAEFNAEGDVAAFMANLSQLDDLFAARVAKARDEGKVLRYVGNIDEDGVCRVKIAEVDGNDPLFK
VKNGENALAFYSHYYQPLPLVLRGYGAGNDVTAAGVFADLLRTLSWKLGV
>NC_000913.3_prot_NP_414544.1_3 [gene=thrB] [protein=homoserine kinase] [protein_id=NP_414544.1] [location=2801..3733]
MVKVYAPASSANMSVGFDVLGAAVTPVDGALLGDVVTVEAAETFSLNNLGRFADKLPSEPRENIVYQCWE
RFCQELGKQIPVAMTLEKNMPIGSGLGSSACSVVAALMAMNEHCGKPLNDTRLLALMGELEGRISGSIHY
DNVAPCFLGGMQLMIEENDIISQQVPGFDEWLWVLAYPGIKVSTAEARAILPAQYRRQDCIAHGRHLAGF
IHACYSRQPELAAKLMKDVIAEPYRERLLPGFRQARQAVAEIGAVASGISGSGPTLFALCDKPETAQRVA
DWLGKNYLQNQEGFVHICRLDTAGARVLEN
>NC_000913.3_prot_NP_414545.1_4 [gene=thrC] [protein=L-threonine synthase] [protein_id=NP_414545.1] [location=3734..5020]
MKLYNLKDHNEQVSFAQAVTQGLGKNQGLFFPHDLPEFSLTEIDEMLKLDFVTRSAKILSAFIGDEIPQE
ILEERVRAAFAFPAPVANVESDVGCLELFHGPTLAFKDFGGRFMAQMLTHIAGDKPVTILTATSGDTGAA
VAHAFYGLPNVKVVILYPRGKISPLQEKLFCTLGGNIETVAIDGDFDACQALVKQAFDDEELKVALGLNS
ANSINISRLLAQICYYFEAVAQLPQETRNQLVVSVPSGNFGDLTAGLLAKSLGLPVKRFIAATNVNDTVP
RFLHDGQWSPKATQATLSNAMDVSQPNNWPRVEELFRRKIWQLKELGYAAVDDETTQQTMRELKELGYTS
EPHAAVAYRALRDQLNPGEYGLFLGTAHPAKFKESVEAILGETLDLPKELAERADLPLLSHNLPADFAAL
RKLMMNHQ
>NC_000913.3_prot_NP_414546.1_5 [gene=yaaX] [protein=DUF2502 family putative periplasmic protein] [protein_id=NP_414546.1] [location=5234..5530]
MKKMQSIVLALSLVLVAPMAAQAAEITLVPSVKLQIGDRDNRGYYWDGGHWRDHGWWKQHYEWRGNRWHL
HGPPPPPRHHKKAPHDHHGGHGPGKHHR
>NC_000913.3_prot_NP_414547.1_6 [gene=yaaA] [protein=peroxide resistance protein, lowers intracellular iron] [protein_id=NP_414547.1] [location=complement(5683..6459)]
MLILISPAKTLDYQSPLTTTRYTLPELLDNSQQLIHEARKLTPPQISTLMRISDKLAGINAARFHDWQPD
FTPANARQAILAFKGDVYTGLQAETFSEDDFDFAQQHLRMLSGLYGVLRPLDLMQPYRLEMGIRLENARG

## GFF file

##gff-version 3
#!gff-spec-version 1.20
#!processor NCBI annotwriter
##sequence-region NC_000913.3 1 4641652
##species http://www.ncbi.nlm.nih.gov/Taxonomy/Browser/wwwtax.cgi?id=511145
NC_000913.3 RefSeq  region  1   4641652 .   +   .   ID=id0;Name=ANONYMOUS;Dbxref=taxon:511145;Is_circular=true;gbkey=Src;genome=chromosome;mol_type=genomic DNA;strain=K-12;substrain=MG1655
NC_000913.3 RefSeq  gene    190 255 .   +   .   ID=gene0;Name=thrL;Dbxref=EcoGene:EG11277,GeneID:944742;gbkey=Gene;gene=thrL;gene_synonym=ECK0001,JW4367;locus_tag=b0001
NC_000913.3 RefSeq  CDS 190 255 .   +   0   ID=cds0;Name=NP_414542.1;Parent=gene0;Dbxref=ASAP:ABE-0000006,UniProtKB%2FSwiss-Prot:P0AD86,Genbank:NP_414542.1,EcoGene:EG11277,GeneID:944742;gbkey=CDS;gene=thrL;product=thr operon leader peptide;protein_id=NP_414542.1;transl_table=11
NC_000913.3 RefSeq  gene    337 2799    .   +   .   ID=gene1;Name=thrA;Dbxref=EcoGene:EG10998,GeneID:945803;gbkey=Gene;gene=thrA;gene_synonym=ECK0002,Hs,JW0001,thrA1,thrA2,thrD;locus_tag=b0002
NC_000913.3 RefSeq  CDS 337 2799    .   +   0   ID=cds1;Name=NP_414543.1;Parent=gene1;Note=bifunctional: aspartokinase I %28N-terminal%29%3B homoserine dehydrogenase I %28C-terminal%29;Dbxref=ASAP:ABE-0000008,UniProtKB%2FSwiss-Prot:P00561,Genbank:NP_414543.1,EcoGene:EG10998,GeneID:945803;gbkey=CDS;gene=thrA;product=Bifunctional aspartokinase%2Fhomoserine dehydrogenase 1;protein_id=NP_414543.1;transl_table=11
NC_000913.3 RefSeq  gene    2801    3733    .   +   .   ID=gene2;Name=thrB;Dbxref=EcoGene:EG10999,GeneID:947498;gbkey=Gene;gene=thrB;gene_synonym=ECK0003,JW0002;locus_tag=b0003
NC_000913.3 RefSeq  CDS 2801    3733    .   +   0   ID=cds2;Name=NP_414544.1;Parent=gene2;Dbxref=ASAP:ABE-0000010,UniProtKB%2FSwiss-Prot:P00547,Genbank:NP_414544.1,EcoGene:EG10999,GeneID:947498;gbkey=CDS;gene=thrB;product=homoserine kinase;protein_id=NP_414544.1;transl_table=11
NC_000913.3 RefSeq  gene    3734    5020    .   +   .   ID=gene3;Name=thrC;Dbxref=EcoGene:EG11000,GeneID:945198;gbkey=Gene;gene=thrC;gene_synonym=ECK0004,JW0003;locus_tag=b0004
NC_000913.3 RefSeq  CDS 3734    5020    .   +   0   ID=cds3;Name=NP_414545.1;Parent=gene3;Dbxref=ASAP:ABE-0000012,UniProtKB%2FSwiss-Prot:P00934,Genbank:NP_414545.1,EcoGene:EG11000,GeneID:945198;gbkey=CDS;gene=thrC;product=L-threonine synthase;protein_id=NP_414545.1;transl_table=11
NC_000913.3 RefSeq  gene    5234    5530    .   +   .   ID=gene4;Name=yaaX;Dbxref=EcoGene:EG14384,GeneID:944747;gbkey=Gene;gene=yaaX;gene_synonym=ECK0005,JW0004;locus_tag=b0005
NC_000913.3 RefSeq  CDS 5234    5530    .   +   0   ID=cds4;Name=NP_414546.1;Parent=gene4;Dbxref=ASAP:ABE-0000015,UniProtKB%2FSwiss-Prot:P75616,Genbank:NP_414546.1,EcoGene:EG14384,GeneID:944747;gbkey=CDS;gene=yaaX;product=DUF2502 family putative periplasmic protein;protein_id=NP_414546.1;transl_table=11
NC_000913.3 RefSeq  repeat_region   5565    5669    .   +   .   ID=id1;Note=RIP1 %28repetitive extragenic palindromic%29 element%3B contains 2 REP sequences and 1 IHF site;gbkey=repeat_region
NC_000913.3 RefSeq  gene    5683    6459    .   -   .   ID=gene5;Name=yaaA;Dbxref=EcoGene:EG10011,GeneID:944749;gbkey=Gene;gene=yaaA;gene_synonym=ECK0006,JW0005;locus_tag=b0006
NC_000913.3 RefSeq  CDS 5683    6459    .   -   0   ID=cds5;Name=NP_414547.1;Parent=gene5;Dbxref=ASAP:ABE-0000018,UniProtKB%2FSwiss-Prot:P0A8I3,Genbank:NP_414547.1,EcoGene:EG10011,GeneID:944749;gbkey=CDS;gene=yaaA;product=peroxide resistance protein%2C lowers intracellular iron;protein_id=NP_414547.1;transl_table=11
NC_000913.3 RefSeq  gene    6529    7959    .   -   .   ID=gene6;Name=yaaJ;Dbxref=EcoGene:EG11555,GeneID:944745;gbkey=Gene;gene=yaaJ;gene_synonym=ECK0007,JW0006;locus_tag=b0007
NC_000913.3 RefSeq  CDS 6529    7959    .   -   0   ID=cds6;Name=NP_414548.1;Parent=gene6;Note=inner membrane transport protein;Dbxref=ASAP:ABE-0000020,UniProtKB%2FSwiss-Prot:P30143,Genbank:NP_414548.1,EcoGene:EG11555,GeneID:944745;gbkey=CDS;gene=yaaJ;product=putative transporter;protein_id=NP_414548.1;transl_table=11
NC_000913.3 RefSeq  gene    8238    9191    .   +   .   ID=gene7;Name=talB;Dbxref=EcoGene:EG11556,GeneID:944748;gbkey=Gene;gene=talB;gene_synonym=ECK0008,JW0007,yaaK;locus_tag=b0008
NC_000913.3 RefSeq  CDS 8238    9191    .   +   0   ID=cds7;Name=NP_414549.1;Parent=gene7;Dbxref=ASAP:ABE-0000027,UniProtKB%2FSwiss-Prot:P0A870,Genbank:NP_414549.1,EcoGene:EG11556,GeneID:944748;gbkey=CDS;gene=talB;product=transaldolase B;protein_id=NP_414549.1;transl_table=11
NC_000913.3 RefSeq  gene    9306    9893    .   +   .   ID=gene8;Name=mog;Dbxref=EcoGene:EG11511,GeneID:944760;gbkey=Gene;gene=mog;gene_synonym=bisD,chlG,ECK0009,JW0008,mogA,yaaG;locus_tag=b0009
NC_000913.3 RefSeq  CDS 9306    9893    .   +   0   ID=cds8;Name=NP_414550.1;Parent=gene8;Note=putative molybdochetalase in molybdopterine biosynthesis;Dbxref=ASAP:ABE-0000030,UniProtKB%2FSwiss-Prot:P0AF03,Genbank:NP_414550.1,EcoGene:EG11511,GeneID:944760;gbkey=CDS;gene=mog;product=molybdochelatase incorporating molybdenum into molybdopterin;protein_id=NP_414550.1;transl_table=11
NC_000913.3 RefSeq  gene    9928    10494   .   -   .   ID=gene9;Name=satP;Dbxref=EcoGene:EG11512,GeneID:944792;gbkey=Gene;gene=satP;gene_synonym=ECK0010,JW0009,yaaH;locus_tag=b0010
NC_000913.3 RefSeq  CDS 9928    10494   .   -   0   ID=cds9;Name=NP_414551.1;Parent=gene9;Dbxref=ASAP:ABE-0000032,UniProtKB%2FSwiss-Prot:P0AC98,Genbank:NP_414551.1,EcoGene:EG11512,GeneID:944792;gbkey=CDS;gene=satP;product=succinate-acetate transporter;protein_id=NP_414551.1;transl_table=11
NC_000913.3 RefSeq  gene    10643   11356   .   -   .   ID=gene10;Name=yaaW;Dbxref=EcoGene:EG14340,GeneID:944771;gbkey=Gene;gene=yaaW;gene_synonym=ECK0011,JW0010;locus_tag=b0011
NC_000913.3 RefSeq  CDS 10643   11356   .   -   0   ID=cds10;Name=NP_414552.1;Parent=gene10;Dbxref=ASAP:ABE-0000037,UniProtKB%2FSwiss-Prot:P75617,Genbank:NP_414552.1,EcoGene:EG14340,GeneID:944771;gbkey=CDS;gene=yaaW;product=UPF0174 family protein;protein_id=NP_414552.1;transl_table=11
NC_000913.3 RefSeq  gene    11382   11786   .   -   .   ID=gene11;Name=yaaI;Dbxref=EcoGene:EG11513,GeneID:944751;gbkey=Gene;gene=yaaI;gene_synonym=ECK0013,JW0012;locus_tag=b0013
NC_000913.3 RefSeq  CDS 11382   11786   .   -   0   ID=cds11;Name=NP_414554.1;Parent=gene11;Dbxref=ASAP:ABE-0000043,UniProtKB%2FSwiss-Prot:P28696,Genbank:NP_414554.1,EcoGene:EG11513,GeneID:944751;gbkey=CDS;gene=yaaI;product=UPF0412 family protein;protein_id=NP_414554.1;transl_table=11
NC_000913.3 RefSeq  gene    12163   14079   .   +   .   ID=gene12;Name=dnaK;Dbxref=EcoGene:EG10241,GeneID:944750;gbkey=Gene;gene=dnaK;gene_synonym=ECK0014,groPAB,groPC,groPF,grpC,grpF,JW0013,seg;locus_tag=b0014
NC_000913.3 RefSeq  CDS 12163   14079   .   +   0   ID=cds12;Name=NP_414555.1;Parent=gene12;Note=chaperone Hsp70%3B DNA biosynthesis%3B autoregulated heat shock proteins;Dbxref=ASAP:ABE-0000052,UniProtKB%2FSwiss-Prot:P0A6Y8,Genbank:NP_414555.1,EcoGene:EG10241,GeneID:944750;gbkey=CDS;gene=dnaK;product=chaperone Hsp70%2C with co-chaperone DnaJ;protein_id=NP_414555.1;transl_table=11
NC_000913.3 RefSeq  gene    14168   15298   .   +   .   ID=gene13;Name=dnaJ;Dbxref=EcoGene:EG10240,GeneID:944753;gbkey=Gene;gene=dnaJ;gene_synonym=ECK0015,faa,groP,grpC,JW0014;locus_tag=b0015
NC_000913.3 RefSeq  CDS 14168   15298   .   +   0   ID=cds13;Name=NP_414556.1;Parent=gene13;Note=chaperone with DnaK%3B heat shock protein;Dbxref=ASAP:ABE-0000054,UniProtKB%2FSwiss-Prot:P08622,Genbank:NP_414556.1,EcoGene:EG10240,GeneID:944753;gbkey=CDS;gene=dnaJ;product=chaperone Hsp40%2C DnaK co-chaperone;protein_id=NP_414556.1;transl_table=11

## GenBank file (partial)

LOCUS       NC_000913            4641652 bp    DNA     circular CON 15-MAY-2014
DEFINITION  Escherichia coli str. K-12 substr. MG1655, complete genome.
ACCESSION   NC_000913
VERSION     NC_000913.3  GI:556503834
DBLINK      BioProject: PRJNA57779
BioSample: SAMN02604091
KEYWORDS    RefSeq.
SOURCE      Escherichia coli str. K-12 substr. MG1655
ORGANISM  Escherichia coli str. K-12 substr. MG1655
Bacteria; Proteobacteria; Gammaproteobacteria; Enterobacteriales;
Enterobacteriaceae; Escherichia.
FEATURES             Location/Qualifiers
source          1..4641652
/organism="Escherichia coli str. K-12 substr. MG1655"
/mol_type="genomic DNA"
/strain="K-12"
/sub_strain="MG1655"
/db_xref="taxon:511145"
gene            190..255
/gene="thrL"
/locus_tag="b0001"
/gene_synonym="ECK0001; JW4367"
/db_xref="EcoGene:EG11277"
/db_xref="GeneID:944742"
CDS             190..255
/gene="thrL"
/locus_tag="b0001"
/gene_synonym="ECK0001; JW4367"
ORIGIN
1 agcttttcat tctgactgca acgggcaata tgtctctgtg tggattaaaa aaagagtgtc
61 tgatagcagc ttctgaactg gttacctgcc gtgagtaaat taaaatttta ttgacttagg
121 tcactaaata ctttaaccaa tataggcata gcgcacagac agataaaaat tacagagtac
181 acaacatcca tgaaacgcat tagcaccacc attaccacca ccatcaccat taccacaggt
241 aacggtgcgg gctgacgcgt acaggaaaca cagaaaaaag cccgcacctg acagtgcggg
301 cttttttttt cgaccaaagg taacgaggta acaaccatgc gagtgttgaa gttcggcggt
361 acatcagtgg caaatgcaga acgttttctg cgtgttgccg atattctgga aagcaatgcc
421 aggcaggggc aggtggccac cgtcctctct gcccccgcca aaatcaccaa ccacctggtg

## GC-content

### From Wikipedia, the free encyclopedia

The percentage of nitrogenous bases on a DNA molecule that are either guanine or cytosine.

• GC content is found to be variable with different organisms.
• The committee on bacterial systematics has recommended use of GC ratios in higher level hierarchical classification

The GC-content can be measured by several means,

• Measuring the melting temperature of the DNA double helix using spectrophotometry
• The absorbance of DNA at a wavelength of 260 nm increases sharply when the double-stranded DNA separates into two single strands when sufficiently heated.

## Determination of GC content

In alternative manner, if the DNA has been sequenced then the GC-content can be accurately calculated by simple arithmetic.

GC-content percentage is calculated as $\frac{G+C}{A+T+G+C}$

## Exercise 1

Determine the GC content of E.coli

Is this GC content uniform through all genome?

## Chargaff’s rules

### From Wikipedia, the free encyclopedia

Discovered by Austrian chemist Erwin Chargaff in 1952.

DNA from any cell of all organisms has a 1:1 ratio of pyrimidine and purine bases

The amount of guanine is equal to cytosine and the amount of adenine is equal to thymine.

Elson D, Chargaff E (1952). On the deoxyribonucleic acid content of sea urchin gametes. Experientia 8 (4): 143–145

Chargaff E, Lipshitz R, Green C (1952). Composition of the deoxypentose nucleic acids of four genera of sea-urchin. J Biol Chem 195 (1): 155–160

## Chargaff’s rules

### First parity rule

A double-stranded DNA molecule globally has percentage base pair equality: $$\%A = \%T$$ and $$\%G = \%C$$

• The rigorous validation of the rule constitutes the basis of Watson-Crick pairs

### Second parity rule

Both $$\%A \approx \%T$$ and $$\%G \approx \%C$$ are valid for each of the two DNA strands

• This describes only a global feature of the base composition in a single DNA strand

## Exercise 2

Why the first rule is always valid?

How do you determine if $$\%G \approx \%C$$?

Is this valid through all the genome?

## GC Skew

What is the difference $$G-C$$ respect to the total $$G+C$$?

Calculate the ratio $\frac{G-C}{G+C}$ using sliding windows and plot it

What do you see?

## Chargaff second rule

In each DNA strand the frequency of occurrence of G is equal to C because the substitution rate is presumably equal

Hence, the second parity rule only exists when there is no mutation or substitution

There is a richness of G over C and T over A in the leading strand

• and vice versa for the lagging strand

GC skew changes sign at the boundaries of the two replichores

This corresponds to DNA replication origin or terminus

## Comparative Genometrics

Roten C-AH, Gamba P, Barblan J-L, Karamata D. Comparative Genometrics (CG): a database dedicated to biometric comparisons of whole genomes. Nucleic Acids Research. 2002;30(1):142-144

## Credits of Images

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• dogs By YellowLabradorLooking_new.jpg: derivative work: Djmirko (talk)YellowLabradorLooking.jpg: User:HabjGolden_Retriever_Sammy.jpg: Pharaoh HoundCockerpoo.jpg: ALMMLonghaired_yorkie.jpg: Ed Garcia from United StatesBoxer_female_brown.jpg: Flickr user boxercabMilù_050.JPG: AleRBeagle1.jpg: TobycatBasset_Hound_600.jpg: ToBNewfoundland_dog_Smoky.jpg: Flickr user DanDee Shotsderivative work: December21st2012Freak (talk) - YellowLabradorLooking_new.jpg Golden_Retriever_Sammy.jpg Cockerpoo.jpg Longhaired_yorkie.jpg Boxer_female_brown.jpg Milù_050.JPGBeagle1.jpgBasset_Hound_600.jpg Newfoundland_dog_Smoky.jpg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=10793219

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