Genetic code is a function

A function is a rule connecting each element of one set to one element of another set

Sometimes they are written with formulas

Sometimes they are written case-by-case

Example: NCBI

There’s a function connecting PubMed ids to PubMed records

Each PubMed ID points to one, and only one, PubMed record

The same is true for Nucleotide database, and protein database

(Obviously with different sets on each case)

Writing the genetic code

TTT F Phe      TCT S Ser      TAT Y Tyr      TGT C Cys  
TTC F Phe      TCC S Ser      TAC Y Tyr      TGC C Cys  
TTA L Leu      TCA S Ser      TAA * Ter      TGA * Ter  
TTG L Leu i    TCG S Ser      TAG * Ter      TGG W Trp  

CTT L Leu      CCT P Pro      CAT H His      CGT R Arg  
CTC L Leu      CCC P Pro      CAC H His      CGC R Arg  
CTA L Leu      CCA P Pro      CAA Q Gln      CGA R Arg  
CTG L Leu i    CCG P Pro      CAG Q Gln      CGG R Arg  

ATT I Ile      ACT T Thr      AAT N Asn      AGT S Ser  
ATC I Ile      ACC T Thr      AAC N Asn      AGC S Ser  
ATA I Ile      ACA T Thr      AAA K Lys      AGA R Arg  
ATG M Met i    ACG T Thr      AAG K Lys      AGG R Arg  

GTT V Val      GCT A Ala      GAT D Asp      GGT G Gly  
GTC V Val      GCC A Ala      GAC D Asp      GGC G Gly  
GTA V Val      GCA A Ala      GAA E Glu      GGA G Gly  
GTG V Val      GCG A Ala      GAG E Glu      GGG G Gly 

A shorter representation

For our purposes each genetic code is a vector indexed by codons

AAs    = FFLLSSSSYY**CC*WLLLLPPPPHHQQRRRRIIIMTTTTNNKKSSRRVVVVAAAADDEEGGGG
Starts = ---M------**--*----M---------------M----------------------------
Base1  = TTTTTTTTTTTTTTTTCCCCCCCCCCCCCCCCAAAAAAAAAAAAAAAAGGGGGGGGGGGGGGGG
Base2  = TTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGG
Base3  = TCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAG

The symbol ’*’ represents a stop codon

The line Starts = shows codons encoding start

(we will ignore the start codon information for now)

Genetic codes are different

We compare them by counting how many times they are different

01 FFLLSSSSYY**CC*WLLLLPPPPHHQQRRRRIIIMTTTTNNKKSSRRVVVVAAAADDEEGGGG
02 FFLLSSSSYY**CCWWLLLLPPPPHHQQRRRRIIMMTTTTNNKKSS**VVVVAAAADDEEGGGG

How many symbols are different?

Calculating a distance between strings

First idea:

• We count the number of mismatches

• Both strings must have the same length

    ASELLKYLTT
    ASELLKALTT

Here distance(ASELLKYLTT,ASELLKALTT) is 1

Hamming distance examples

How many substitutions we need to go from one sequence to the other

• CAT and CAT have a Hamming distance of 0
• CAT and BAT have a Hamming distance of 1
• CAT and BAG have a Hamming distance of 2

What if sequences have different length?

In that case we need to insert “gaps”

MOUSE
GROUSE

So, which one is the distance?

In geometry we say that “the distance between a point X and a line L is the length of the shortest path from X to any point in L”

Hamming versus Levenstein

Hamming distance counts substitutions

ABCDEFGHIJ
BCDEFGHIJA

Hamming distance=10

Levenstein counts substitutions, insertions and deletions

ABCDEFGHIJK-
-BCDEFGHIJKA

Levenstein distance=2

What is the best way to insert gaps?

If the sequence has m letters, there are 2^m+1 ways to insert a single gap

CAT
CAT-
CA-T
CA-T-
C-AT
C-AT-
C-A-T
C-A-T-

-CAT
-CAT-
-CA-T
-CA-T-
-C-AT
-C-AT-
-C-A-T
-C-A-T-

And that is not even counting larger gaps

We could also do

C--A-----T

or

----CA-T--

or

-C--A--T--

There is a better way to find the best

We will see more details later

The idea is to draw a rectangle

• One sequence in the rows
• Another sequence in the columns
• Mark the cells where row letter and column letter are equal

We move from one corner to the other

White blocks add to the distance

Summary

• Hamming distance
• Levenstein distance
• Dot plot