α A G C T 國立交通大學生物資訊及系統生物研究所林勇欣老師
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- בַּעַל־זְבוּל Βάμβας
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1 A G C T
2 Juks and Cantor s (969) on-aramtr modl A T C G A G C T A() A( t ) ( 3 ) ( ) A() A() ( 3 ) ( ) A( A( A( A( t ) A( 3 A( t ) ( ) A( A(
3 Juks and Cantor s (969) on-aramtr modl A( A( t ) A( d A( 3 A( dt A( A(0) A( ( ) A( t A( A(0) A( 3 t A(0) A( 0 t In th abov, w focusd on a articular nuclotid sit and tratd A( as a robability. Howvr, A( can also b intrrtd as th frquncy of A in a DNA squnc.
4 Juks and Cantor s (969) on-aramtr modl A(0) A( 3 t A(0) A( 0 t AA( 3 t GA( t 3 t ii ( t ij (
5 Purins A G Pyrimidins C T
6 Kimura s (980) two-aramtr modl A T C G A G C T ( ) A( T( C( t ) G( A( ( ) T( C( G( A( T( ( ) C( G( A( T( C( ( ) G( A( t ) T( t ) C( t ) G( t )
7 國立交通大學國立交通大學國立交通大學國立交通大學生物資訊及系統生物研究所生物資訊及系統生物研究所生物資訊及系統生物研究所生物資訊及系統生物研究所林勇欣老師林勇欣老師林勇欣老師林勇欣老師 ( ) ( )t t t t t t t t t t ) AG( ) AC( ) AT( ) AA( Kimura s (980) two-aramtr modl
8 3 t ii ( t ij ( X Y Z AA( AG( AT( t t t ( ) ( ) t t Probability Gnration X Y Z Pii Pij
9 Li (997) Molcular Evolution
10 Li (997) Molcular Evolution
11 Ancstral squnc ATGACAGTATAGGACATAGAC ATGACAGTATAGGACATAGAC A T G ATCACAGTATAGGACATAGAC Singl substitution T C C T C A Multil substitutions G G G Coincidntal substitutions Paralll substitutions Convrgnt substitution Back substitution
12 Juks and Cantor s (969) on-aramtr modl Suos that th nuclotid at a givn sit was A at tim 0. At tim t, th robability that th nuclotid in both squncs is th sam: Ancstral squnc t t Squnc Squnc A( AA( AT( AC( AG( I( I 3 t ii ( t ij ( I ( ii( 3 ij( 3 8t I( ii ( t )
13 Kimura s (980) two-aramtr modl Suos that th nuclotid at a givn sit was A at tim 0. At tim t, th robability that th nuclotid in both squncs is th sam: Ancstral squnc t t Squnc Squnc A( AA( AT( AC( AG( I( I I ( 8 t ( )t AA( AT( AG( AC( t t t ( ) t ( )t
14 Gnral modl Suos that th nuclotid at a givn sit was A at tim 0. At tim t, th robability that th nuclotid in both squncs is th sam: Ancstral squnc t t Squnc Squnc A( AA( AT( AC( AG( I I I I I ( A A( T T( C C( G G( I I ˆ ˆ ˆ ˆ A T C ˆ G
15 Homwork: Us th "gnral substitution modl" (th aramtrs rfr to th substitution numbrs obsrvd in sudogns as shown in slid 9) to dislay th nuclotid (A, T, C, G) frquncy changs with tim, as wll as th chang of th similarity, I. You can dfin diffrnt initial frquncis for A, T, C, and G.
16 Squnc dissimilarity D is simly I Transitional diffrncs (ts) Transvrsional diffrncs (tv)
17 Juks and Cantor s (969) on-aramtr modl Suos that th nuclotid at a givn sit was A at tim 0. At tim t, th robability that th nuclotid in both squncs is transitional diffrnc: Ancstral squnc t t Squnc Squnc ts ( ij AA( ( t ) AG( 8t AT( AC( 3 t ii ( t ij (
18 Kimura s (980) two-aramtr modl Suos that th nuclotid at a givn sit was A at tim 0. At tim t, th robability that th nuclotid in both squncs is transitional diffrnc: Ancstral squnc t t Squnc Squnc ts ( AA( AG( AG( GA( AT( TC(t ) 8 t ( )t AC( CT(
19 Juks and Cantor s (969) on-aramtr modl Suos that th nuclotid at a givn sit was A at tim 0. At tim t, th robability that th nuclotid in both squncs is transvrsional diffrnc: Ancstral squnc t t Squnc Squnc tv ( AA( ij ( t ) AT( 8t AA( AC( AG( AT( AG( AC(
20 Kimura s (980) two-aramtr modl Suos that th nuclotid at a givn sit was A at tim 0. At tim t, th robability that th nuclotid in both squncs is transvrsional diffrnc: Ancstral squnc t t Squnc Squnc tv ( AA( AT( AA( AC( AG( AT( AG( AC( AT(t ) AC(t ) 8t
21 0.6 Squnc divrgnc ts, on aramtr tv, on aramtr ts, two aramtr tv, two aramtr Gnration
22 Nonuniform rats 0 5*0-3 Solid 5% 95%.75*0-3 Squnc similarity *0-3 Dottd 0% 00%.75*0-3 A G Gnration C T
23 Th substitution rat λ varis among sits according to th gamma distribution among sits: g(λ) g Γ ( λ) b Γ ( a) a λ / V b λ / V ( ) a a t 0 a λ λ bλ t dt λ a > sha > scal a0.5 a.0 a λ
24 A G g ( λ) b Γ a ( a) bλ λ a I 0 Ig ( λ) 3 dλ a a 8 t a C T Squnc similarity Squnc similarity a.75* Gnration Gnration
25 Estimating th numbr of nuclotid substitutions btwn squncs
26 Juks and Cantor s (969) on-aramtr modl At tim t, th robability that th nuclotid in both squncs is th sam: I ( 3 8t Ancstral squnc Squnc Squnc Th robability that th two squncs ar diffrnt at a sit at tim tis: 3 ( 8t D I ) ( D 8t ln 3 Th actual numbr of substitutions r sit sinc th divrgnc btwn th two squncs, K (3 t t K 3 ln D 3
27 Kimura s (980) two-aramtr modl At tim t, th robability that th nuclotid in both squncs is th sam: I ( 8 t ( )t Ancstral squnc t t Squnc Squnc ts ( 8 t ( )t 8t tv( t ) K ts tv tv ( ) t ln ln
28 Juks and Cantor s (969) on-aramtr modl K 3 ln D 3 Tajima and Ni s(98) mthod This mthod dos not rquir th assumtion of qual frquncis of th four nuclotids D K b ln b qa qt qc q b q is th quilibrium frquncy ( ) G
29 Tajima and Ni s(98) mthod This mthod dos not rquir th assumtion of qual frquncis of th four nuclotids D K b ln b qa qt qc q b q is th quilibrium frquncy ( ) This formula also holds undr th qual-inut modl, i.., ij j for all i j If th condition ij j dos not hold for all i j, this formula tnds to giv an undrstimat. To rmov this dficincy, 3 D D K bln b x b b h ij h i j i qiq j G
30 Th substitution rat λ varis among sits according to th gamma distribution among sits: g(λ) g Γ ( λ) b Γ ( a) a λ / V b λ / V ( ) a a t 0 a λ λ bλ t dt λ a > sha > scal a0.5 a.0 a λ
31 Nonuniform rats g ( λ) b Γ a λ a ( a) / V b λ / V λ λ bλ a λ Ancstral squnc t t Squnc Squnc A G 3a D K λ t 3 / a C T
32 Nonuniform rats g ( λ) b Γ a λ a ( a) / V b λ / V λ λ bλ a λ Ancstral squnc t t Squnc Squnc A G K a [ ( ) ( ) 3] / a / a ts tv tv C T
33 Homwork: Calculat th numbr of nuclotid diffrncs, th roortion of nuclotid diffrncs, JC69 on-aramtr distanc, and K80 twoaramtr distanc for (art of) th alignmnt squncs you constructd in HW. Comar your rsults with what MEGA comuts for you.
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