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(        ) 

               
1
                                                                          
                              


              O              E               

     
                        2            F2             
                                                                             3 1  

                                                            2              2  
         O
            E
                 (O‐E)
       (O‐E)2
       (O‐E)2/E 

       5475
         5493
               ‐19
         361
          0.06572

       1850
         1831
                19
         361
          0.19716



    1   5%             3.84                             chi square
                                                             F2
                  :    3:1                                
1                     
5%             3.84, 1%            6.63 
      3.84                                 0.95(95%)
0.05(5%)                           3.84        5%
                




                                            O          E   




             3.84
                     6.63
1 R                         
                                     2       F2                                        
                                                                                 3 1  
> obs1 <‐ 5474 
> obs2 <‐ 1850 
> exp1 <‐ (obs1+obs2)*(3/4)                                        3:1
> exp1                                                                             
> exp2 <‐ (obs1+obs2)*(1/4) 
> exp2                                                         
         
> dev1 <‐ obs1‐exp1 
                                                          
 5474
 1850
> num1 <‐ (dev1)^2 
> dev2 <‐ obs2‐exp2                                       
 5493
 1831
> num2 <‐ (dev2)^2 
> chi1 <‐ num1/exp1 
> chi2 <‐ num2/exp2 

> chi <‐ chi1+chi2                                    O        E             
> chi 
[1] 0.2628800 
2
Makorin1‐p1                     regionB regionC                                                 
                  regionB regionC                 number of differences                                  
               (region B   617bp, regionC   639bp      ) 

          domesVcus molossinus                                  

                                                                        2                2  
                  O
           E
              (O‐E)
              (O‐E)2
         (O‐E)2/E 
 regionB
         6
        6.758998         ‐0.758998         0.576078
          0.08523127
 regionC
         7
        6.213938         0.786062         0.6178935
          0.0994367




*                regionB         regionC                      (7/639)*617            
regionC           regionB             (6/617)*639                        
                                                           
              processed pseudogene                                             
                                          
2 R                 
Makorin1‐p1                     regionB regionC
              regionB regionC                     number of differences                    
               
region B   617bp, regionC   639bp          
                                                                   regionB
 regionC
> obsB <‐ 6 
                                              dom‐mol                 6         7 
> obsC <‐ 7 
> expB <‐ (obsC/639)*617                      dom‐mol              6.758998  6.213938 
> expB 
[1] 6.758998 
expC <‐ (obsB/617)*639 
> expC 
[1] 6.213938 
> devB <‐ (obsB‐expB)                                   O            E          
> devC <‐ (obsC‐expC) 
> chiB <‐ (devB^2) /expB 
> chiC <‐ (devC^2)/expC 
> chisqrt <‐ chiB+chiC 
> chisqrt        
[1] 0.1846679   #           3                        
region B    617  bp
           region C     639  bp
pair 
        observed
    expected
         observed
     expected
   chi square
dom – mol
       6
         6.758998            7          6.213938
      0.18 
dom – cas
       6
                             7
dom – mus
       8
                             8
dom – spr
      16
                            14
dom – car
      30
                            39
mol – spr
      14
                            17
mol – car
      28
                            38
cas – spr
      14
                            17
cas – car
      28
                            38
mus – spr 
     14
                            18
mus – car
      28
                            39
spr – car
      32
                            37
3 R                     
CotEditor                                  chi‐square‐test.R        
[Macintosh HD/        /tg03/bin]                     
expB <‐ (obsC/639)*617 
expC <‐ (obsB/617)*639 
devB <‐ (obsB‐expB) 
devC <‐ (obsC‐expC) 
chiB <‐ (devB^2) /expB                                         O       E       
chiC <‐ (devC^2)/expC 
chisqrt <‐ chiB+chiC 
                                                         obsB obsC          
> obsB <‐  
> obsC <‐  
> source("/Users/tg03/bin/chi‐square‐test.R") 
                            bin                    
> source("chi‐square‐test.R") 
                      
> expB 
> expC 
> chisqrt 
(             )
Makorin1‐p1                                    regionB regionC
               regionB regionC                                       number of differences        
                



                            O                    E         

                                        pair                             
 regionB regionC                                                                         

                95%,                1                 
> qchisq(0.95, 1) 
                         
                                                                  
                                 
(           )
              region B    617  bp
        region C     639  bp
pair 
        observed
    expected
      observed
         expected
    chi square
dom – mol
        6
           6.759         7               6.214      0.18  
dom – cas
        6
           6.759         7
              6.214      0.18  
dom – mus
        8
           7.725         8
              8.285      0.02  
dom – spr
        16
          13.518       14
             16.571      0.85  
dom – car
        30
          37.657       39
             31.070      3.58  
mol – spr
        14
          16.415       17
             14.499      0.79  
mol – car
        28
          36.692       38
             28.998      4.85 * 
cas – spr
        14
          16.415       17
             14.499      0.79  
cas – car
        28
          36.692       38
             28.998      4.85 * 
mus – spr 
       14
          17.380       18
             14.499      1.50  
mus – car
        28
          37.657       39
             28.998      5.93 * 
spr – car
        32
          35.726       37
             33.141      0.84  
* : p < 0.05 
molossinus, castaneus, musculus caroli                      regionB regionC
                             5%                          
Makorin1‐p1    Makorin1      mRNA                                                      
      Makorin1‐p1 regionB Makorin1                                                              
Makorin1‐p1 regionB                                                   
                                                   regionC            
regionB regionC                                                                

          molossinus, castaneus, musculus caroli                         regionB regionC
                                  5%                          
           regionB
               

‐    ‐ 



Makorin1‐p1              M. caroli                                
regionI                                                                                             
      processed pseudogene      CpG                                                             
               regionII 600bp                                                      
                                   5                                      
                                                     
‐hemoglobin       ‐ 
           (molecular clock)
                                         
1960                                c                      
DNA
                                            


Hemoglobin subunit alpha (Hemoglobin alpha chain) 




        3 exons,   CDS 577bp (142a.a.) 




                                   2
1 – hemoglobin‐
1) TogoWS REST                                                      
2) R                   p distance                     
3) x                 y     p distance                           

                     human                                              

                            human             
              uniprot ID
                        p distance
                              (         )

  human
     HBA_HUMAN
            ‐
  horse
     HBA_HORSE
           80
  wallaby
   HBA_MACEU
           150
  chicken
   HBA_CHICK
           300
  frog
      HBA_XENTR
           350
  zebra fish
 HBA_DANRE
           420
2 – hemoglobin‐
1) TogoWS REST                                                      
apple mark+a                         R                      

2) R                           p distance               
> library(Biostrings) 
> human <‐ “HBA_human                       ” 
> len <‐ AAString(human)           
> total <‐ length(len)  #                        
> horse <‐ “” 
> comp <‐ c(compareStrings(human, horse))  #                                                
> subs <‐ gsub(“([‘?’])”, “”, comp)   #compareStrings                      ?            
> aas <‐ AAString(subs)            
> aasame <‐ length(aas)   #                           
> dif <‐ (total‐aasame)  #                 
> pdis <‐ dif/total 

#human‐horse, human‐wallaby, human‐chicken, human‐frog, human‐zebra fish             
#compareStrings()                               zebra fish                       
YFSHW A DLSPG      A(48        ) R                                      

3) x                       y         p distance                 
– hemoglobin‐
 x <‐ c(80,150,300,350,420) 
 y <‐ c(0.120,0.197,0.296,0.423,0.465) 
 plot(x,y,xlim=c(0,450), ylim=c(0,0.5)) 

                           human                  
             uniprot ID
                      
                                                     p distance 
                             (          )

human
      HBA_HUMAN
            ‐

horse
      HBA_HORSE
           80
                   0.120 

wallaby
    HBA_MACEU
           150
                  0.197

chicken
    HBA_CHICK
           300
                  0.296

frog
       HBA_XENTR
           350
                  0.423

zebra fish
 HBA_DANRE
            420
                  0.465


                      1960
                                                                     
                                                                        olfactory receptor

         
–Makorin1, Makorin2‐
1) TogoWS REST                                                              
2) R                       p distance               
3) x                     y     p distance                         

                         human                                                              
          alignment                                                             
*        1 Makorin1                                                                         
         2 Makorin2 Makorin1 alignment                                                  


                                             human                    
                   uniprot ID
           
                               p distance
                                               (            )

     human
     MKRN1_HUMAN
 193‐401
                  ‐
     mouse
     MKRN1_MOUSE
 193‐401
              80
     wallaby
   MKRN1_MACEU
 189‐397
              150
     frog
      MKRN1_XENLA
      159‐367
         350
     zebra fish
 MKRN1_DANRE
      148‐356
         420
     mouse
     MKRN2_MOUSE
 150‐358
              80
–Makorin1, Makorin2‐
1) TogoWS REST                                                 

2) R                          p distance          
library(Biostrings) 
> human <‐ "" 
> all1 <‐ AAString(human) 
> humanc <‐ substring(all1, 193, 401)   #                             
> total <‐length(humanc) 
> mouse <‐ "" 
> all2 <‐ AAString(mouse) 
> mousec <‐ substring(all2, 193, 401)  
> comp <‐c(compareStrings(humanc, mousec))  #                             
> subs <‐gsub("(['?'])", "", comp) 
> aas <‐ AAString(subs)           
> aasame <‐ length(aas) 
> diff <‐ (total‐aasame) 
> pdis <‐ diff/total 
#human‐mouse, human‐wallaby, human‐frog, human‐zebra fish, human‐mouse2        

3) x                    y    p distance                 
–Makorin1, Makorin2‐
 x <‐ c(80,150,420,350,80) 
 y <‐ c(0.024,0.053,0.177,0.139,0.407) 
 plot(x,y,xlim=c(0,450), ylim=c(0,0.5)) 
                              human                 
              uniprot ID
                              p distance
                                (         )

human
      MKRN1_HUMAN
             ‐

mouse
      MKRN1_MOUSE
            80
                  0.024

wallaby
    MKRN1_MACEU
            150
                 0.053

frog
       MKRN1_XENLA
            350
                 0.139

zebra fish
 MKRN1_DANRE
             420
                 0.177

mouse
      MKRN2_MOUSE
            80
                  0.407

 Makorin1                                                                                     hemoglobin
                            Makorin1
         Makorin1                                                                      
      Makorin1                        Makorin2                        Makorin1                        
 Makorin1 human‐zebra fish                                                                                 
                                                            Makorin2                                          
                                                                 ortholog
                                                                                           
 

R   Biostrings
                  
 

         




     

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100701_statistics3

  • 1. 2010/07/01    kaneko.satoko(at)ocha.ac.jp   
  • 2. (      )   
  • 3. 1     O E   2 F2   3 1         2   2   O E (O‐E) (O‐E)2 (O‐E)2/E  5475 5493 ‐19 361 0.06572 1850 1831 19 361 0.19716 1 5% 3.84 chi square F2 : 3:1  
  • 4. 1   5%  3.84, 1%  6.63  3.84 0.95(95%) 0.05(5%) 3.84 5%   O E 3.84 6.63
  • 5. 1 R 2 F2                     3 1   > obs1 <‐ 5474  > obs2 <‐ 1850  > exp1 <‐ (obs1+obs2)*(3/4)  3:1 > exp1    > exp2 <‐ (obs1+obs2)*(1/4)  > exp2  > dev1 <‐ obs1‐exp1  5474 1850 > num1 <‐ (dev1)^2  > dev2 <‐ obs2‐exp2  5493 1831 > num2 <‐ (dev2)^2  > chi1 <‐ num1/exp1  > chi2 <‐ num2/exp2  > chi <‐ chi1+chi2  O E > chi  [1] 0.2628800 
  • 6. 2 Makorin1‐p1 regionB regionC   regionB regionC number of differences   (region B 617bp, regionC 639bp )  domesVcus molossinus         2   2   O E (O‐E) (O‐E)2 (O‐E)2/E  regionB 6 6.758998  ‐0.758998  0.576078 0.08523127 regionC 7 6.213938  0.786062  0.6178935 0.0994367 * regionB regionC (7/639)*617   regionC regionB (6/617)*639     processed pseudogene    
  • 7. 2 R Makorin1‐p1 regionB regionC regionB regionC number of differences     region B 617bp, regionC 639bp   regionB regionC > obsB <‐ 6  dom‐mol   6  7  > obsC <‐ 7  > expB <‐ (obsC/639)*617  dom‐mol   6.758998  6.213938  > expB  [1] 6.758998  expC <‐ (obsB/617)*639  > expC  [1] 6.213938  > devB <‐ (obsB‐expB)  O E > devC <‐ (obsC‐expC)  > chiB <‐ (devB^2) /expB  > chiC <‐ (devC^2)/expC  > chisqrt <‐ chiB+chiC  > chisqrt      [1] 0.1846679   # 3  
  • 8. region B    617  bp region C     639  bp pair  observed expected observed expected chi square dom – mol 6  6.758998   7   6.213938  0.18  dom – cas 6 7 dom – mus 8 8 dom – spr 16 14 dom – car 30 39 mol – spr 14 17 mol – car 28 38 cas – spr 14 17 cas – car 28 38 mus – spr  14 18 mus – car 28 39 spr – car 32 37
  • 9. 3 R CotEditor chi‐square‐test.R   [Macintosh HD/ /tg03/bin]   expB <‐ (obsC/639)*617  expC <‐ (obsB/617)*639  devB <‐ (obsB‐expB)  devC <‐ (obsC‐expC)  chiB <‐ (devB^2) /expB  O E chiC <‐ (devC^2)/expC  chisqrt <‐ chiB+chiC  obsB obsC   > obsB <‐   > obsC <‐   > source("/Users/tg03/bin/chi‐square‐test.R")  bin   > source("chi‐square‐test.R")    > expB  > expC  > chisqrt 
  • 10. ( ) Makorin1‐p1 regionB regionC regionB regionC number of differences     O E pair   regionB regionC   95%,  1   > qchisq(0.95, 1)       
  • 11. ( ) region B    617  bp region C     639  bp pair  observed expected observed expected chi square dom – mol 6 6.759   7   6.214   0.18   dom – cas 6 6.759   7 6.214   0.18   dom – mus 8 7.725   8 8.285   0.02   dom – spr 16 13.518   14 16.571   0.85   dom – car 30 37.657   39 31.070   3.58   mol – spr 14 16.415   17 14.499   0.79   mol – car 28 36.692   38 28.998   4.85 *  cas – spr 14 16.415   17 14.499   0.79   cas – car 28 36.692   38 28.998   4.85 *  mus – spr  14 17.380   18 14.499   1.50   mus – car 28 37.657   39 28.998   5.93 *  spr – car 32 35.726   37 33.141   0.84   * : p < 0.05  molossinus, castaneus, musculus caroli regionB regionC 5%  
  • 12. Makorin1‐p1 Makorin1 mRNA   Makorin1‐p1 regionB Makorin1   Makorin1‐p1 regionB   regionC   regionB regionC   molossinus, castaneus, musculus caroli regionB regionC 5%   regionB   ‐ ‐  Makorin1‐p1 M. caroli   regionI   processed pseudogene CpG   regionII 600bp   5    
  • 13. ‐hemoglobin ‐  (molecular clock)   1960 c   DNA Hemoglobin subunit alpha (Hemoglobin alpha chain)  3 exons,   CDS 577bp (142a.a.)  2
  • 14. 1 – hemoglobin‐ 1) TogoWS REST   2) R p distance   3) x y p distance   human   human   uniprot ID p distance ( ) human HBA_HUMAN ‐ horse HBA_HORSE 80 wallaby HBA_MACEU 150 chicken HBA_CHICK 300 frog HBA_XENTR 350 zebra fish HBA_DANRE 420
  • 15. 2 – hemoglobin‐ 1) TogoWS REST   apple mark+a R   2) R p distance   > library(Biostrings)  > human <‐ “HBA_human ”  > len <‐ AAString(human)    > total <‐ length(len)  #   > horse <‐ “”  > comp <‐ c(compareStrings(human, horse))  #   > subs <‐ gsub(“([‘?’])”, “”, comp)   #compareStrings ?   > aas <‐ AAString(subs)      > aasame <‐ length(aas)   #   > dif <‐ (total‐aasame)  #   > pdis <‐ dif/total  #human‐horse, human‐wallaby, human‐chicken, human‐frog, human‐zebra fish   #compareStrings() zebra fish   YFSHW A DLSPG A(48 ) R   3) x y p distance  
  • 16. – hemoglobin‐ x <‐ c(80,150,300,350,420)  y <‐ c(0.120,0.197,0.296,0.423,0.465)  plot(x,y,xlim=c(0,450), ylim=c(0,0.5))  human   uniprot ID   p distance  ( ) human HBA_HUMAN ‐ horse HBA_HORSE 80 0.120  wallaby HBA_MACEU 150 0.197 chicken HBA_CHICK 300 0.296 frog HBA_XENTR 350 0.423 zebra fish HBA_DANRE 420 0.465 1960   olfactory receptor  
  • 17. –Makorin1, Makorin2‐ 1) TogoWS REST   2) R p distance   3) x y p distance   human   alignment   * 1 Makorin1      2 Makorin2 Makorin1 alignment   human   uniprot ID   p distance ( ) human MKRN1_HUMAN 193‐401 ‐ mouse MKRN1_MOUSE 193‐401 80 wallaby MKRN1_MACEU 189‐397 150 frog MKRN1_XENLA 159‐367 350 zebra fish MKRN1_DANRE 148‐356 420 mouse MKRN2_MOUSE 150‐358 80
  • 18. –Makorin1, Makorin2‐ 1) TogoWS REST   2) R p distance   library(Biostrings)  > human <‐ ""  > all1 <‐ AAString(human)  > humanc <‐ substring(all1, 193, 401)   #   > total <‐length(humanc)  > mouse <‐ ""  > all2 <‐ AAString(mouse)  > mousec <‐ substring(all2, 193, 401)   > comp <‐c(compareStrings(humanc, mousec))  #   > subs <‐gsub("(['?'])", "", comp)  > aas <‐ AAString(subs)      > aasame <‐ length(aas)  > diff <‐ (total‐aasame)  > pdis <‐ diff/total  #human‐mouse, human‐wallaby, human‐frog, human‐zebra fish, human‐mouse2   3) x y p distance  
  • 19. –Makorin1, Makorin2‐ x <‐ c(80,150,420,350,80)  y <‐ c(0.024,0.053,0.177,0.139,0.407)  plot(x,y,xlim=c(0,450), ylim=c(0,0.5))  human   uniprot ID   p distance ( ) human MKRN1_HUMAN ‐ mouse MKRN1_MOUSE 80 0.024 wallaby MKRN1_MACEU 150 0.053 frog MKRN1_XENLA 350 0.139 zebra fish MKRN1_DANRE 420 0.177 mouse MKRN2_MOUSE 80 0.407 Makorin1 hemoglobin Makorin1 Makorin1   Makorin1 Makorin2 Makorin1   Makorin1 human‐zebra fish   Makorin2   ortholog  
  • 20.   R Biostrings  
  • 21.