(4)

)RMSDstralign: SSAP/DALI/CE/Contact Map Overlap

SCOPFSSPDALICATHSSAP

(1)

(2) vs.

RMSD(Root Mean Square Deviation)e.g., C O(n)

: stralignHGC [Akutsu 1996] : P=( p1,, pm ), Q=(q1,, qn), m n P,Q M T

stralign M0 {}for all triplets PP=(pi1,pi2,pi3) from P do for all triplets QQ=(qj1,qj2,qj3) from Q do Compute rigid motion TPP,QQ from PP to QQ Compute alignment M between TPP,QQ(P) and Q if |M| > |M0| then M0 MOutput M0

TPP,QQ PP=(p1,p2,p3)QQ=(q1,q2,q3) TPP,QQ p1 q1 PP p1p2 q1q2 PP PP QQ PP p1p2

T(P) Q M

(1) PP=(p1,p2,p3), QQ=(q1,q2,q3)T |T(pi) - qi| (i=1,2,3) p reg(p1,p2,p3) |T(p) - q| |T PP,QQ(p) - q| 8

(2) MOPT O(n8) M T MOPT P,Q P,Q P reg PPP MOPT PP QQ T(P) Q 8 |M||MOPT| 8

stralign O(n8) sparse DP O(n5)

PP,QQ 1020 fragment TPP,QQ rmsd O(n2) O(n2)DP= O(n4) rmsd DP rmsd fitting

SSAP (Double Dynamic Programming)DP [Taylor & Orengo 1989]High level DP Sij low level DP Low level DPpi P qj Q (i,j) ( Sij[i,j] = 0 )DP pk , ql ki, lj skl a,b skl = a / (| | pk - pi | - | ql qj| | + b)

DALI (Alignment of Distance Matrices)Distance Matrix [Holm & Sander 1993]Distance Matrix P P Q distance matrix Simulated Annealing

CE (Combinatorial Expansion) [Shindyalov & Bourne 1998]VAST (Vector Alignment Search Tool) [Gibrat et al. 1998]DP+Iterative Improvement [Gernstein & Levitt 1998]StrMul ( [Daiyasu & Toh 2000]

Contact Map Overlap (CMO) (1){vi,vj}E vi vj (vi,uk) (vj,ul) {vi,vj}Eif and only if {uk,ul}E

Contact Map Overlap (CMO) (2)CMONP [Goldman et al. 1999] [Caprara et al. 2004]RNA [G-H. Lin et al. 2002] [Akutsu & Miyano 1999]

( CE-MC, StrMul, ) (NP)NP(LCP) [Akutsu & Halldorson 2000] d S1, S2, , SN d C Si Ti T1(S1) T2(S2) TN(SN) = C

(ab initio)33.3%80%

NP

String Folding1/43/8 (Hart & Istrail, 1995) NP-Hard (Berger,Leighton,1998)NP-Hard (Crescenzi et al.,1998)1/3 (Newman, 2002)

Fold Recognition)fold)1000(Chotia, 1992)

-1D (Bowie et al., 1991)PSI-BLASTProfile-Profile etc.Frozen approximation, Double dynamic programming (Lathrop & Smith, 1996) (Xu et al., 2000) (Xu et al., 2003)

()

(DP)

fd(X,Y)

MAX CUT G(V,E) U V-U UMAX CUT ALALAL

RAPTOR (1)Ming Li (Xu et al., 2003)CASP5, CASP6

RAPTOR (2)g(i,j,l,k)i l j k i j

RAPTOR (3)y(i,l)(j,k): i l j k xi,l: i l D[i]: i R[i,j,l]: i l j

CASPCASP (Critical Assessment of Techniques for Protein Structure Prediction)

CASPCASP1 (1994), CASP2(1996), CASP3(1998), CASP4(2000), CASP5(2002), CASP6(2004)CAFASP(1998,2000,2002,2004)http://prediction center.llnl.gov/(Proteins)(E.E. Lattman et al. 2003)

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