Random Numbers

 

Codon Numbers

( assign any numerical value to the bases )

permutation calculator

position from 5' end--> First Second Third
A
U
C
G
     

Result   

(codons with repeating bases, number-36 +*4=40)

AUA AAU UAA
ACA AAC CAA
AGA AAG GAA
UAU UUA AUU
UCU UUC CUU
UGU UUG GUU
CAC CCA ACC
CUC CCU UCC
CGC CCG GCC
GAG GGA AGG
GUG GGU UGG
GCG GGC CGG

(Codons with non-repeating bases, number=24)

AUC GAU    
CUA UAG    
AUG GAC    
GUA CAG    
UCG UAC *AAA
GCU CAU *UUU
UCA AGU *CCC
ACU UGA *GGG
CGA GCA    
AGC ACG    
CGU CUG    
UGC GUC    

Distribution of

Repeating Base & Non-repeating Base codons

in

Amino Acids

Amino Acid Total codons codons-repeating codons-nonrepeating
Trp 01 01 -
Met 01 - 01
Lys 02 02 -
His 02 01 01
Glu 02 02 -
Asp 02 - 02
Gln 02 01 01
Asn 02 02 --
Tyr 02 01 01
Cys 02 01 01
Phe 02 02 --
Ile 03 02 01
Thr 04 02 02
Gly 04 04 -
Val 04 02 02
Ala 04 02 02
Leu 04 02 02
Ser 06 02 04
Arg 06 04 02
Pro 06 06 -
termination 03 01 02
Total 64 40 24

 

Frequency Distribution of Amino Acids (AA/aa)

no. of codons in AA no. of AA total codons Presence of Base in middle Absence of base in middle
1 codon aa 2 02   C
2 codon aa 9 18 A or G C
3 codon aa 1 03   C/G/A
4 codon aa 5 20 C or U A
5 codon aa - --   ---
6 codon aa 3 18 C,G,U A
termination codon   03   C
TOTAL 20 64    

As a mathematical exercise, assign any value to bases in 1,2,3 positions and click, numbers shall be generated for each codon. Codons having same numbers are assumed to represent particular amino acids. How many aa can be generated through  different no. assigned to bases ? One can experiment.

         

 

Distribution of Bases

(total no. of codon:64 ; total no.of bases: 64*3=192)

Bases polar aa(10) nonpolar aa(10) initiation codon* termination codon total
A 33 10 01 04 48
U 14 30 01 03 48
C 24 24 - - 48
G 19 26 01 02 48
Total 90 90 03 09 192

*Met is included in non-polar aa but the bases are not included. They are shown separately in initiation codon.

Distribution of Bases position wise

(In each position, total no. of a base = 64*3/(3*4)=16)

Bases 1st position 2nd position 3rd position Total
A 16 16 (polar aa) 16 48
U 16 16 (non-polar aa) 16 48
C 16 16 (aaRS-II,8 polar,8 non-polar) 16 48
G 16 16 16 48
Total 64 64 64 192

AA distribution codon alphabet wise with a particular base in first & second position

(for 6 codon aa, 2 codons are made - from the total list to keep aa no. 20)

Base in 1st  & 2nd position U C A G Total
U 02-01(aa) 01 01 02 06 - 01
1codon aa -- -- -- 01 01
2codon aa 01 -- 01 01 03
3codon aa -- -- -- -- --
4codon aa -- -- -- -- --
6codon aa 01 01 -- -- 02
termination codon -- -- 02 01 03
C 01 (aa) 01 02 01 05
1codon aa -- -- -- -- --
2codon aa -- -- 02 -- 02
3codon aa -- -- -- -- --
4codon aa -- 01 -- -- 01
6codon aa 01 -- -- 01 02
termination codon -- -- -- -- --
A 02 (aa) 01 02 02-02 07-02
1codon aa 01 -- -- -- 01
2codon aa -- -- 02 -- 02
3codon aa 01 -- -- -- 01
4codon aa -- 01 -- -- 01
6codon aa -- -- -- 02 02
termination codon -- -- -- -- --
G 01(aa) 01 02 01 05
1codon aa -- -- -- -- --
2codon aa -- -- 02 -- 02
3codon aa -- -- -- -- --
4codon aa 01 01 -- 01 03
6codon aa -- -- -- -- --
termination codon -- -- -- -- --
Total          
1codon aa 01 -- -- 01  
2codon aa 01 -- 07 01  
3codon aa 01 -- --    
4codon aa 01 03 -- 01  
6codon aa 02-01 01 -- 03-02  
termination codon -- -- --    
  06-01(aa) 04 07 06-02 23-03=20

 

Distribution of aaRS-I & aaRS-II in codon table

  U C A G   no. of aa
U II, non-polar II, polar I, polar I, non-polar* U

C

A

G

6(1 common aa)+*+*
 
I, non-polar    
I, non-polar
C I, non-polar II, non-polar II, polar I, polar U/C

A/G

5
I, polar
A I, non-polar II, polar II, polar II, polar U

C

A

G

7(2 common aa)
 
  II, polar I, polar
I, non-polar
G I, non-polar II, non-polar II, polar II, non-polar* U/C

A/G

5
I, polar
  5 4 7+* 5(1 common aa) +*   23(includes 3 aa common) +* +*

(C in middle --> all aaRS-II, U in 1st --> all non-polar, aaRS-I except Phe which being a large molecule should have been associated with aaRS-I. To explore if something with Ala which is associated with aaRS-IIc as is Phe)

Distribution of aaRS-I & aaRS-II in codon table

(cytochrome oxidase of Human mitochondria)

  U C A G   no. of aa
U II, non-polar II, polar - Ser I, polar I, non-polar* U/C

 

A/G

 

6(1 common aa)+*
 
I, non-polar- Leu    
I, non-polar
C I, non-polar - Leu II, non-polar II, polar I, polar -Arg U/C

A/G

5
I, polar
A I, non-polar II, polar II, polar II, polar - Ser U/C

 

A/G

 

7(2 common aa)
 
  II, polar I, polar- Arg
I, non-polar
G I, non-polar II, non-polar II, polar II, non-polar* U/C

A/G

5
I, polar
no. of aa 5 4 7+* 5(1 common aa)   23(includes 3 aa common)+*

(C in middle --> all aaRS-II, U in 1st --> all non-polar, aaRS-I except Phe which being a large molecule should have been associated with aaRS-I. To explore if something with Ala which is associated with aaRS-IIc as is Phe)

Distribution of Doublets in codon table

(cytochrome oxidase of Human mitochondria)

  U C A G
U NP P P NP
C NP NP P P
A NP P P P
 
G NP NP P NP
Polar (P) & Non-Polar (NP) Amino Acids (aa)

NP- 8 blocks;

P- 8 blocks

* U in middle -> all NPs

*A in middle -> all Ps

*C in middle - 50% P, 50% NP  --- CC ->NP

*G in middle - 50% P, 50% NP  --- GG ->NP

*with 1st base as U or C, polarity of C & G blocks are opposite i.e. if C block is polar, G block is NP and vice versa.

*with 1st base as A or G, polarity of C & G blocks are identical i.e. if C block is polar, G block is also polar and vice versa.

Degeneracy

* click on blue colored NP, all yellow colored cells are doubly degenerate and black colored cells are fully degenerate.

8 blocks are fully degenerate

8 blocks are doubly degenerate.

* C in middle -> blocks fully degenerate

* A in middle -> blocks doubly degenerate

* U / G in middle -> doubly degenerate w.r.t. U & A

                         -> fully degenerate     w.r.t. C & G.

aaRS distribution

* C in middle -> aaRS-II - 4 blocks - 16 codons

* U in middle -> aaRS-I - 4 blocks - 16 codons (presume Phe to be of aaRS-I though it is aaRS-II)

* A in middle -> AA ->aaRS-II

* G in middle ->GG ->aaRS-II

* AG & GA -> aaRs-II (upper part) & aaRS-I (lower part)

*aaRS-I has 10+1(include Phe) aa, terminating codons -. total aggregate 32 codons

 Polar aa-      Arg(6 codon), nil (4 codons),                Glu, Gln, Tyr (all 2 codons)

 Non-Polar aa - nil(6 codon), Leu,Val (both 4 codons),Trp,Ile,Met,Cys,Phe (all 2 codons)

*aaRS-II has 10-01(exclude Phe) aa,                              total aggregate 32 codons

 Polar aa-      Ser(6 codon), Thr,Gly (both 4 codons),                Asp, Asn,Cys,His (all 2 codons)

Non-Polar aa - Pro(6 codon), Ala (4 codons),Nil (2 codons-Phe has been excluded)
 

 

Distribution of A among Amino Acids (total -48)

Codons with  codon no. in polar aa no. of bases in polar aa codon no. in non polar aa no. of bases in non polar aa  initiating codon no. no. of bases in initiating codon terminating codon. no no. of bases in terminating codons

total A

1 A 16 16 08 08 01 01 02 02 27
2 A 07 14 01 02 - - 01 02 18
3 A 01 03 -- -- -- - - - 03
Total 24 33 09 10 01 01 03 04 48
nil A 06 -- 21 -- -- -- -- -- --

 

Distribution of U among Amino Acids (total -48)

Codons with  codon no. in polar aa no. of bases in polar aa codon no. in non polar aa no. of bases in non polar aa  initiating codon no. no. of bases in initiating codon terminating codon. no no. of bases in terminating codons

total U

1 U 10 10 13 13 01 01 03 03 27
2 U 02 04 07 14 - - - - 18
3 U -- -- 01 03 -- - - - 03
Total 12 14 21 30 01 01 03 03 48
nil U 18 -- 09 -- -- -- -- -- --

Distribution of C among Amino Acids (total -48)

Codons with  codon no. in polar aa no. of bases in polar aa codon no. in non polar aa no. of bases in non polar aa  initiating codon no. no. of bases in initiating codon terminating codon. no no. of bases in terminating codons

total C

1 C 16 16 11 11 - - - - 27
2 C 04 08 05 10 - - - - 18
3 C - - 01 03 - - - - 03
Total 20 24 17 24 - - - - 48
nil C 10 -- 13 -- 01 - 03 - --

 

 

Distribution of G among Amino Acids (total -48)

Codons with  codon no. in polar aa no. of bases in polar aa codon no. in non polar aa no. of bases in non polar aa  initiating codon no. no. of bases in initiating codon terminating codon. no no. of bases in terminating codons

total G

1 G 13 13 11 11 01 01 02 02 27
2 G 03 06 06 12 - - - - 18
3 G 01 03 -- -- - - - - 03
Total 17 22 17 23 01 01 02 02 48
nil G 14?? -- 12?? -- - - 01 - --

Frequency of bases among 64 Codons ( Base A )

( frequency of other bases C, U, G are also same )

Frequency of A in codon Codons with repeating bases Codons with non-repeating bases Total
1 ( A,-,-; -,A,-; -,-,A ) 09 18 27
2 (A,-,A;A,A,-;-,A,A) 09 -- 09
3 (A,A,A) 01 -- 01
Nil(-,-,-) 21 *06 27
Total 40 24 64

Worksheet for above calculation of Frequency

no. of bases -(m)= 4
Each codon consists of n. number of bases, here n= 3
Total no. of codons m 43 =64
no. of codons with non-repeating bases -> mPn 4!/(4-3)! =24
no. of codons with repeating bases= (64-24)= 40
codons with 3 no. of A = (1/4)*(1/4)*(1/4)*64= 01
codons with nil A = (3/4)*(3/4)*(3/4)*64= 27
codons with 2 no. of  A = [(1/4)*(1/4)*(3/4)*64]+[(1/4)*(3/4)*(1/4)*64]+[(3/4)*(1/4)*(1/4)*64]= (1/4)*(1/4)*(3/4)*3*64 09
codons with 1 no. A = [(1/4)*(3/4)*(3/4)*64]+[(3/4)*(3/4)*(1/4)*64]+[(3/4)*(1/4)*(3/4)*64]= (3/4)*(3/4)*(1/4)*3*64 27
* in codons with non-repeating bases aggregating 24, total no. bases is 24*3=72 and each base has a frequency of 72/4=18 codons. So no. of  codons with non repeating bases where A is absent is 24-18=06 06
While doing the above exercise, one can think of three  4 sided dice being rolled  and outcome calculated.