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|
*************************************************************************
* This program is to compare two protein structures and identify the
* best superposition that has the highest TM-score. Input structures
* must be in the PDB format. By default, TM-score is normalized by
* the second protein. Users can obtain a brief instruction by simply
* running the program without arguments. For comments/suggestions,
* please contact email: zhng@umich.edu.
*
* Reference:
* Yang Zhang, Jeffrey Skolnick, Proteins, 2004 57:702-10.
*
* Permission to use, copy, modify, and distribute this program for
* any purpose, with or without fee, is hereby granted, provided that
* the notices on the head, the reference information, and this
* copyright notice appear in all copies or substantial portions of
* the Software. It is provided "as is" without express or implied
* warranty.
******************* Updating history ************************************
* 2005/10/19: the program was reformed so that the score values.
* are not dependent on the specific compilers.
* 2006/06/20: selected 'A' if there is altLoc when reading PDB file.
* 2007/02/05: fixed a bug with length<15 in TMscore_32.
* 2007/02/27: rotation matrix from Chain-1 to Chain-2 was added.
* 2007/12/06: GDT-HA score was added, fixed a bug for reading PDB.
* 2010/08/02: A new RMSD matrix was used and obsolete statement removed.
* 2011/01/03: The length of pdb file names were extended to 500.
* 2011/01/30: An open source license is attached to the program.
* 2012/05/07: Improved RMSD calculation subroutine which speeds up
* TM-score program by 30%.
*************************************************************************
program TMscore
PARAMETER(nmax=5000)
common/stru/xt(nmax),yt(nmax),zt(nmax),xb(nmax),yb(nmax),zb(nmax)
common/nres/nresA(nmax),nresB(nmax),nseqA,nseqB
common/para/d,d0,d0_fix
common/align/n_ali,iA(nmax),iB(nmax)
common/nscore/i_ali(nmax),n_cut ![1,n_ali],align residues for the score
dimension k_ali(nmax),k_ali0(nmax)
character*500 fnam,pdb(100),outname
character*3 aa(-1:20),seqA(nmax),seqB(nmax)
character*500 s,du
character seq1A(nmax),seq1B(nmax),ali(nmax)
character sequenceA(nmax),sequenceB(nmax),sequenceM(nmax)
dimension L_ini(100),iq(nmax)
common/scores/score,score_maxsub,score_fix,score10
common/GDT/n_GDT05,n_GDT1,n_GDT2,n_GDT4,n_GDT8
double precision score,score_max,score_fix,score_fix_max
double precision score_maxsub,score10
dimension xa(nmax),ya(nmax),za(nmax)
ccc RMSD:
double precision r_1(3,nmax),r_2(3,nmax),r_3(3,nmax),w(nmax)
double precision u(3,3),t(3),rms,drms !armsd is real
data w /nmax*1.0/
ccc
data aa/ 'BCK','GLY','ALA','SER','CYS',
& 'VAL','THR','ILE','PRO','MET',
& 'ASP','ASN','LEU','LYS','GLU',
& 'GLN','ARG','HIS','PHE','TYR',
& 'TRP','CYX'/
character*1 slc(-1:20)
data slc/'X','G','A','S','C',
& 'V','T','I','P','M',
& 'D','N','L','K','E',
& 'Q','R','H','F','Y',
& 'W','C'/
*****instructions ----------------->
call getarg(1,fnam)
if(fnam.eq.' '.or.fnam.eq.'?'.or.fnam.eq.'-h')then
write(*,*)
write(*,*)'Brief instruction for running TM-score program:'
write(*,*)'(For detail: Zhang & Skolnick, Proteins, 2004',
& ' 57:702-10)'
write(*,*)
write(*,*)'1. Run TM-score to compare ''model'' and ''native',
& ':'
write(*,*)' >TMscore model native'
write(*,*)
write(*,*)'2. Run TM-score with an assigned d0, e.g. 5',
& ' Angstroms:'
write(*,*)' >TMscore model native -d 5'
write(*,*)
write(*,*)'3. Run TM-score with superposition output, e.g. ',
& '''TM.sup'':'
write(*,*)' >TMscore model native -o TM.sup'
write(*,*)' To view the superimposed structures by rasmol:'
write(*,*)' >rasmol -script TM.sup'
write(*,*)
goto 9999
endif
******* options ----------->
m_out=-1
m_fix=-1
narg=iargc()
i=0
j=0
115 continue
i=i+1
call getarg(i,fnam)
if(fnam.eq.'-o')then
m_out=1
i=i+1
call getarg(i,outname)
elseif(fnam.eq.'-d')then
m_fix=1
i=i+1
call getarg(i,fnam)
read(fnam,*)d0_fix
else
j=j+1
pdb(j)=fnam
endif
if(i.lt.narg)goto 115
ccccccccc read data from first CA file:
open(unit=10,file=pdb(1),status='old')
i=0
101 read(10,104,end=102) s
if(s(1:3).eq.'TER') goto 102
if(s(1:4).eq.'ATOM')then
if(s(13:16).eq.'CA '.or.s(13:16).eq.' CA '.or.s(13:16).
& eq.' CA')then
if(s(17:17).eq.' '.or.s(17:17).eq.'A')then
i=i+1
read(s,103)du,seqA(i),du,nresA(i),du,xa(i),ya(i),za(i)
do j=-1,20
if(seqA(i).eq.aa(j))then
seq1A(i)=slc(j)
goto 21
endif
enddo
seq1A(i)=slc(-1)
21 continue
endif
endif
endif
goto 101
102 continue
103 format(A17,A3,A2,i4,A4,3F8.3)
104 format(A100)
close(10)
nseqA=i
c^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
ccccccccc read data from first CA file:
open(unit=10,file=pdb(2),status='old')
i=0
201 read(10,204,end=202) s
if(s(1:3).eq.'TER') goto 202
if(s(1:4).eq.'ATOM')then
if(s(13:16).eq.'CA '.or.s(13:16).eq.' CA '.or.s(13:16).
& eq.' CA')then
if(s(17:17).eq.' '.or.s(17:17).eq.'A')then
i=i+1
read(s,203)du,seqB(i),du,nresB(i),du,xb(i),yb(i),zb(i)
do j=-1,20
if(seqB(i).eq.aa(j))then
seq1B(i)=slc(j)
goto 22
endif
enddo
seq1B(i)=slc(-1)
22 continue
endif
endif
endif
goto 201
202 continue
203 format(A17,A3,A2,i4,A4,3F8.3)
204 format(A100)
close(10)
nseqB=i
c^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
******************************************************************
* pickup the aligned residues:
******************************************************************
k=0
do i=1,nseqA
do j=1,nseqB
if(nresA(i).eq.nresB(j))then
k=k+1
iA(k)=i
iB(k)=j
goto 205
endif
enddo
205 continue
enddo
n_ali=k !number of aligned residues
if(n_ali.lt.1)then
write(*,*)'There is no common residues in the input structures'
goto 9999
endif
************/////
* parameters:
*****************
*** d0------------->
if(nseqB.gt.15)then
d0=1.24*(nseqB-15)**(1.0/3.0)-1.8
else
d0=0.5
endif
if(d0.lt.0.5)d0=0.5
if(m_fix.eq.1)d0=d0_fix
*** d0_search ----->
d0_search=d0
if(d0_search.gt.8)d0_search=8
if(d0_search.lt.4.5)d0_search=4.5
*** iterative parameters ----->
n_it=20 !maximum number of iterations
d_output=5 !for output alignment
if(m_fix.eq.1)d_output=d0_fix
n_init_max=6 !maximum number of L_init
n_init=0
L_ini_min=4
if(n_ali.lt.4)L_ini_min=n_ali
do i=1,n_init_max-1
n_init=n_init+1
L_ini(n_init)=n_ali/2**(n_init-1)
if(L_ini(n_init).le.L_ini_min)then
L_ini(n_init)=L_ini_min
goto 402
endif
enddo
n_init=n_init+1
L_ini(n_init)=L_ini_min
402 continue
******************************************************************
* find the maximum score starting from local structures superposition
******************************************************************
score_max=-1 !TM-score
score_maxsub_max=-1 !MaxSub-score
score10_max=-1 !TM-score10
n_GDT05_max=-1 !number of residues<0.5
n_GDT1_max=-1 !number of residues<1
n_GDT2_max=-1 !number of residues<2
n_GDT4_max=-1 !number of residues<4
n_GDT8_max=-1 !number of residues<8
do 333 i_init=1,n_init
L_init=L_ini(i_init)
iL_max=n_ali-L_init+1
do 300 iL=1,iL_max !on aligned residues, [1,nseqA]
LL=0
ka=0
do i=1,L_init
k=iL+i-1 ![1,n_ali] common aligned
r_1(1,i)=xa(iA(k))
r_1(2,i)=ya(iA(k))
r_1(3,i)=za(iA(k))
r_2(1,i)=xb(iB(k))
r_2(2,i)=yb(iB(k))
r_2(3,i)=zb(iB(k))
ka=ka+1
k_ali(ka)=k
LL=LL+1
enddo
if(i_init.eq.1)then !global superposition
call u3b(w,r_1,r_2,LL,2,rms,u,t,ier) !0:rmsd; 1:u,t; 2:rmsd,u,t
armsd=dsqrt(rms/LL)
rmsd_ali=armsd
else
call u3b(w,r_1,r_2,LL,1,rms,u,t,ier) !u rotate r_1 to r_2
endif
do j=1,nseqA
xt(j)=t(1)+u(1,1)*xa(j)+u(1,2)*ya(j)+u(1,3)*za(j)
yt(j)=t(2)+u(2,1)*xa(j)+u(2,2)*ya(j)+u(2,3)*za(j)
zt(j)=t(3)+u(3,1)*xa(j)+u(3,2)*ya(j)+u(3,3)*za(j)
enddo
d=d0_search-1
call score_fun !init, get scores, n_cut+i_ali(i) for iteration
if(score_max.lt.score)then
score_max=score
ka0=ka
do i=1,ka0
k_ali0(i)=k_ali(i)
enddo
endif
if(score10_max.lt.score10)score10_max=score10
if(score_maxsub_max.lt.score_maxsub)score_maxsub_max=
& score_maxsub
if(n_GDT05_max.lt.n_GDT05)n_GDT05_max=n_GDT05
if(n_GDT1_max.lt.n_GDT1)n_GDT1_max=n_GDT1
if(n_GDT2_max.lt.n_GDT2)n_GDT2_max=n_GDT2
if(n_GDT4_max.lt.n_GDT4)n_GDT4_max=n_GDT4
if(n_GDT8_max.lt.n_GDT8)n_GDT8_max=n_GDT8
*** iteration for extending ---------------------------------->
d=d0_search+1
do 301 it=1,n_it
LL=0
ka=0
do i=1,n_cut
m=i_ali(i) ![1,n_ali]
r_1(1,i)=xa(iA(m))
r_1(2,i)=ya(iA(m))
r_1(3,i)=za(iA(m))
r_2(1,i)=xb(iB(m))
r_2(2,i)=yb(iB(m))
r_2(3,i)=zb(iB(m))
ka=ka+1
k_ali(ka)=m
LL=LL+1
enddo
call u3b(w,r_1,r_2,LL,1,rms,u,t,ier) !u rotate r_1 to r_2
do j=1,nseqA
xt(j)=t(1)+u(1,1)*xa(j)+u(1,2)*ya(j)+u(1,3)*za(j)
yt(j)=t(2)+u(2,1)*xa(j)+u(2,2)*ya(j)+u(2,3)*za(j)
zt(j)=t(3)+u(3,1)*xa(j)+u(3,2)*ya(j)+u(3,3)*za(j)
enddo
call score_fun !get scores, n_cut+i_ali(i) for iteration
if(score_max.lt.score)then
score_max=score
ka0=ka
do i=1,ka
k_ali0(i)=k_ali(i)
enddo
endif
if(score10_max.lt.score10)score10_max=score10
if(score_maxsub_max.lt.score_maxsub)score_maxsub_max
& =score_maxsub
if(n_GDT05_max.lt.n_GDT05)n_GDT05_max=n_GDT05
if(n_GDT1_max.lt.n_GDT1)n_GDT1_max=n_GDT1
if(n_GDT2_max.lt.n_GDT2)n_GDT2_max=n_GDT2
if(n_GDT4_max.lt.n_GDT4)n_GDT4_max=n_GDT4
if(n_GDT8_max.lt.n_GDT8)n_GDT8_max=n_GDT8
if(it.eq.n_it)goto 302
if(n_cut.eq.ka)then
neq=0
do i=1,n_cut
if(i_ali(i).eq.k_ali(i))neq=neq+1
enddo
if(n_cut.eq.neq)goto 302
endif
301 continue !for iteration
302 continue
300 continue !for shift
333 continue !for initial length, L_ali/M
******************************************************************
* Output
******************************************************************
*** output TM-scale ---------------------------->
write(*,*)
write(*,*)'*****************************************************',
& '************************'
write(*,*)'* TM-SCORE ',
& ' *'
write(*,*)'* A scoring function to assess the similarity of prot',
& 'ein structures *'
write(*,*)'* Based on statistics: ',
& ' *'
write(*,*)'* 0.0 < TM-score < 0.17, random structural simi',
& 'larity *'
write(*,*)'* 0.5 < TM-score < 1.00, in about the same fold',
& ' *'
write(*,*)'* Reference: Yang Zhang and Jeffrey Skolnick, ',
& 'Proteins 2004 57: 702-710 *'
write(*,*)'* For comments, please email to: zhng@umich.edu ',
& ' *'
write(*,*)'*****************************************************',
& '************************'
write(*,*)
write(*,501)pdb(1),nseqA
501 format('Structure1: ',A10,' Length= ',I4)
write(*,502)pdb(2),nseqB
502 format('Structure2: ',A10,' Length= ',I4,
& ' (by which all scores are normalized)')
write(*,503)n_ali
503 format('Number of residues in common= ',I4)
write(*,513)rmsd_ali
513 format('RMSD of the common residues= ',F8.3)
write(*,*)
write(*,504)score_max,d0,score10_max
504 format('TM-score = ',f6.4,' (d0=',f5.2,',',' TM10= ',f6.4,')')
write(*,505)score_maxsub_max
505 format('MaxSub-score= ',f6.4,' (d0= 3.50)')
score_GDT=(n_GDT1_max+n_GDT2_max+n_GDT4_max+n_GDT8_max)
& /float(4*nseqB)
write(*,506)score_GDT,n_GDT1_max/float(nseqB),n_GDT2_max
& /float(nseqB),n_GDT4_max/float(nseqB),n_GDT8_max/float(nseqB)
506 format('GDT-TS-score= ',f6.4,' %(d<1)=',f6.4,' %(d<2)=',f6.4,
$ ' %(d<4)=',f6.4,' %(d<8)=',f6.4)
score_GDT_HA=(n_GDT05_max+n_GDT1_max+n_GDT2_max+n_GDT4_max)
& /float(4*nseqB)
write(*,507)score_GDT_HA,n_GDT05_max/float(nseqB),n_GDT1_max
& /float(nseqB),n_GDT2_max/float(nseqB),n_GDT4_max/float(nseqB)
507 format('GDT-HA-score= ',f6.4,' %(d<0.5)=',f6.4,' %(d<1)=',f6.4,
$ ' %(d<2)=',f6.4,' %(d<4)=',f6.4)
write(*,*)
*** recall and output the superposition of maxiumum TM-score:
LL=0
do i=1,ka0
m=k_ali0(i) !record of the best alignment
r_1(1,i)=xa(iA(m))
r_1(2,i)=ya(iA(m))
r_1(3,i)=za(iA(m))
r_2(1,i)=xb(iB(m))
r_2(2,i)=yb(iB(m))
r_2(3,i)=zb(iB(m))
LL=LL+1
enddo
call u3b(w,r_1,r_2,LL,1,rms,u,t,ier) !u rotate r_1 to r_2
do j=1,nseqA
xt(j)=t(1)+u(1,1)*xa(j)+u(1,2)*ya(j)+u(1,3)*za(j)
yt(j)=t(2)+u(2,1)*xa(j)+u(2,2)*ya(j)+u(2,3)*za(j)
zt(j)=t(3)+u(3,1)*xa(j)+u(3,2)*ya(j)+u(3,3)*za(j)
enddo
********* extract rotation matrix ------------>
write(*,*)'-------- rotation matrix to rotate Chain-1 to ',
& 'Chain-2 ------'
write(*,*)'i t(i) u(i,1) u(i,2) ',
& ' u(i,3)'
do i=1,3
write(*,304)i,t(i),u(i,1),u(i,2),u(i,3)
enddo
c do j=1,nseqA
c xt(j)=t(1)+u(1,1)*xa(j)+u(1,2)*ya(j)+u(1,3)*za(j)
c yt(j)=t(2)+u(2,1)*xa(j)+u(2,2)*ya(j)+u(2,3)*za(j)
c zt(j)=t(3)+u(3,1)*xa(j)+u(3,2)*ya(j)+u(3,3)*za(j)
c write(*,*)j,xt(j),yt(j),zt(j)
c enddo
write(*,*)
304 format(I2,f18.10,f15.10,f15.10,f15.10)
********* rmsd in superposed regions --------------->
d=d_output !for output
call score_fun() !give i_ali(i), score_max=score now
LL=0
do i=1,n_cut
m=i_ali(i) ![1,nseqA]
r_1(1,i)=xa(iA(m))
r_1(2,i)=ya(iA(m))
r_1(3,i)=za(iA(m))
r_2(1,i)=xb(iB(m))
r_2(2,i)=yb(iB(m))
r_2(3,i)=zb(iB(m))
LL=LL+1
enddo
call u3b(w,r_1,r_2,LL,0,rms,u,t,ier)
armsd=dsqrt(rms/LL)
rmsd=armsd
*** output rotated chain1 + chain2----->
if(m_out.ne.1)goto 999
OPEN(unit=7,file=outname,status='unknown') !pdb1.aln + pdb2.aln
900 format(A)
901 format('select ',I4)
write(7,900)'load inline'
write(7,900)'select atomno<1000'
c write(7,900)'color [255,20,147]'
write(7,900)'wireframe .45'
write(7,900)'select none'
write(7,900)'select atomno>1000'
c write(7,900)'color [100,149,237]'
write(7,900)'wireframe .15'
write(7,900)'color white'
do i=1,n_cut
write(7,901)nresA(iA(i_ali(i)))
write(7,900)'color red'
enddo
write(7,900)'select all'
write(7,900)'exit'
write(7,514)rmsd_ali
514 format('REMARK RMSD of the common residues=',F8.3)
write(7,515)score_max,d0
515 format('REMARK TM-score=',f6.4,' (d0=',f5.2,')')
do i=1,nseqA
write(7,1237)nresA(i),seqA(i),nresA(i),xt(i),yt(i),zt(i)
enddo
write(7,1238)
do i=2,nseqA
write(7,1239)nresA(i-1),nresA(i)
enddo
do i=1,nseqB
write(7,1237)2000+nresB(i),seqB(i),nresB(i),xb(i),yb(i),zb(i)
enddo
write(7,1238)
do i=2,nseqB
write(7,1239)2000+nresB(i-1),2000+nresB(i)
enddo
1237 format('ATOM ',i5,' CA ',A3,I6,4X,3F8.3)
1238 format('TER')
1239 format('CONECT',I5,I5)
999 continue
*** record aligned residues by i=[1,nseqA], for sequenceM()------------>
do i=1,nseqA
iq(i)=0
enddo
do i=1,n_cut
j=iA(i_ali(i)) ![1,nseqA]
k=iB(i_ali(i)) ![1,nseqB]
dis=sqrt((xt(j)-xb(k))**2+(yt(j)-yb(k))**2+(zt(j)-zb(k))**2)
if(dis.lt.d_output)then
iq(j)=1
endif
enddo
*******************************************************************
*** output aligned sequences
k=0
i=1
j=1
800 continue
if(i.gt.nseqA.and.j.gt.nseqB)goto 802
if(i.gt.nseqA.and.j.le.nseqB)then
k=k+1
sequenceA(k)='-'
sequenceB(k)=seq1B(j)
sequenceM(k)=' '
j=j+1
goto 800
endif
if(i.le.nseqA.and.j.gt.nseqB)then
k=k+1
sequenceA(k)=seq1A(i)
sequenceB(k)='-'
sequenceM(k)=' '
i=i+1
goto 800
endif
if(nresA(i).eq.nresB(j))then
k=k+1
sequenceA(k)=seq1A(i)
sequenceB(k)=seq1B(j)
if(iq(i).eq.1)then
sequenceM(k)=':'
else
sequenceM(k)=' '
endif
i=i+1
j=j+1
goto 800
elseif(nresA(i).lt.nresB(j))then
k=k+1
sequenceA(k)=seq1A(i)
sequenceB(k)='-'
sequenceM(k)=' '
i=i+1
goto 800
elseif(nresB(j).lt.nresA(i))then
k=k+1
sequenceA(k)='-'
sequenceB(k)=seq1B(j)
sequenceM(k)=' '
j=j+1
goto 800
endif
802 continue
write(*,600)d_output,n_cut,rmsd
600 format('Superposition in the TM-score: Length(d<',f3.1,
$ ')=',i3,' RMSD=',f6.2)
write(*,603)d_output
603 format('(":" denotes the residue pairs of distance < ',f3.1,
& ' Angstrom)')
write(*,601)(sequenceA(i),i=1,k)
write(*,601)(sequenceM(i),i=1,k)
write(*,601)(sequenceB(i),i=1,k)
write(*,602)(mod(i,10),i=1,k)
601 format(2000A1)
602 format(2000I1)
write(*,*)
c^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
9999 END
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c 1, collect those residues with dis<d;
c 2, calculate score_GDT, score_maxsub, score_TM
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine score_fun
PARAMETER(nmax=5000)
common/stru/xt(nmax),yt(nmax),zt(nmax),xb(nmax),yb(nmax),zb(nmax)
common/nres/nresA(nmax),nresB(nmax),nseqA,nseqB
common/para/d,d0,d0_fix
common/align/n_ali,iA(nmax),iB(nmax)
common/nscore/i_ali(nmax),n_cut ![1,n_ali],align residues for the score
common/scores/score,score_maxsub,score_fix,score10
common/GDT/n_GDT05,n_GDT1,n_GDT2,n_GDT4,n_GDT8
double precision score,score_max,score_fix,score_fix_max
double precision score_maxsub,score10
d_tmp=d
21 n_cut=0 !number of residue-pairs dis<d, for iteration
n_GDT05=0 !for GDT-score, # of dis<0.5
n_GDT1=0 !for GDT-score, # of dis<1
n_GDT2=0 !for GDT-score, # of dis<2
n_GDT4=0 !for GDT-score, # of dis<4
n_GDT8=0 !for GDT-score, # of dis<8
score_maxsub_sum=0 !Maxsub-score
score_sum=0 !TMscore
score_sum10=0 !TMscore10
do k=1,n_ali
i=iA(k) ![1,nseqA] reoder number of structureA
j=iB(k) ![1,nseqB]
dis=sqrt((xt(i)-xb(j))**2+(yt(i)-yb(j))**2+(zt(i)-zb(j))**2)
*** for iteration:
if(dis.lt.d_tmp)then
n_cut=n_cut+1
i_ali(n_cut)=k ![1,n_ali], mark the residue-pairs in dis<d
endif
*** for GDT-score:
if(dis.le.8)then
n_GDT8=n_GDT8+1
if(dis.le.4)then
n_GDT4=n_GDT4+1
if(dis.le.2)then
n_GDT2=n_GDT2+1
if(dis.le.1)then
n_GDT1=n_GDT1+1
if(dis.le.0.5)then
n_GDT05=n_GDT05+1
endif
endif
endif
endif
endif
*** for MAXsub-score:
if(dis.lt.3.5)then
score_maxsub_sum=score_maxsub_sum+1/(1+(dis/3.5)**2)
endif
*** for TM-score:
score_sum=score_sum+1/(1+(dis/d0)**2)
*** for TM-score10:
if(dis.lt.10)then
score_sum10=score_sum10+1/(1+(dis/d0)**2)
endif
enddo
if(n_cut.lt.3.and.n_ali.gt.3)then
d_tmp=d_tmp+.5
goto 21
endif
score_maxsub=score_maxsub_sum/float(nseqB) !MAXsub-score
score=score_sum/float(nseqB) !TM-score
score10=score_sum10/float(nseqB) !TM-score10
return
end
cccccccccccccccc Calculate sum of (r_d-r_m)^2 cccccccccccccccccccccccccc
c w - w(m) is weight for atom pair c m (given)
c x - x(i,m) are coordinates of atom c m in set x (given)
c y - y(i,m) are coordinates of atom c m in set y (given)
c n - n is number of atom pairs (given)
c mode - 0:calculate rms only (given,short)
c 1:calculate u,t only (given,medium)
c 2:calculate rms,u,t (given,longer)
c rms - sum of w*(ux+t-y)**2 over all atom pairs (result)
c u - u(i,j) is rotation matrix for best superposition (result)
c t - t(i) is translation vector for best superposition (result)
c ier - 0: a unique optimal superposition has been determined(result)
c -1: superposition is not unique but optimal
c -2: no result obtained because of negative weights w
c or all weights equal to zero.
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine u3b(w, x, y, n, mode, rms, u, t, ier)
double precision w(*), x(3,*), y(3,*)
integer n, mode
double precision rms, u(3,3), t(3)
integer ier
integer i, j, k, l, m1, m
integer ip(9), ip2312(4)
double precision r(3,3), xc(3), yc(3), wc
double precision a(3,3), b(3,3), e(3), rr(6), ss(6)
double precision e0, d, spur, det, cof, h, g
double precision cth, sth, sqrth, p, sigma
double precision c1x, c1y, c1z, c2x, c2y, c2z
double precision s1x, s1y, s1z, s2x, s2y, s2z
double precision sxx, sxy, sxz, syx, syy, syz, szx, szy, szz
double precision sqrt3, tol, zero
data sqrt3 / 1.73205080756888d+00 /
data tol / 1.0d-2 /
data zero / 0.0d+00 /
data ip / 1, 2, 4, 2, 3, 5, 4, 5, 6 /
data ip2312 / 2, 3, 1, 2 /
wc = zero
rms = zero
e0 = zero
s1x = zero
s1y = zero
s1z = zero
s2x = zero
s2y = zero
s2z = zero
sxx = zero
sxy = zero
sxz = zero
syx = zero
syy = zero
syz = zero
szx = zero
szy = zero
szz = zero
do i=1, 3
xc(i) = zero
yc(i) = zero
t(i) = zero
do j=1, 3
r(i,j) = zero
u(i,j) = zero
a(i,j) = zero
if( i .eq. j ) then
u(i,j) = 1.0
a(i,j) = 1.0
end if
end do
end do
ier = -1
if( n .lt. 1 ) return
ier = -2
do m=1, n
c1x=x(1, m)
c1y=x(2, m)
c1z=x(3, m)
c2x=y(1, m)
c2y=y(2, m)
c2z=y(3, m)
s1x = s1x + c1x
s1y = s1y + c1y;
s1z = s1z + c1z;
s2x = s2x + c2x;
s2y = s2y + c2y;
s2z = s2z + c2z;
sxx = sxx + c1x*c2x;
sxy = sxy + c1x*c2y;
sxz = sxz + c1x*c2z;
syx = syx + c1y*c2x;
syy = syy + c1y*c2y;
syz = syz + c1y*c2z;
szx = szx + c1z*c2x;
szy = szy + c1z*c2y;
szz = szz + c1z*c2z;
end do
xc(1) = s1x/n;
xc(2) = s1y/n;
xc(3) = s1z/n;
yc(1) = s2x/n;
yc(2) = s2y/n;
yc(3) = s2z/n;
if(mode.eq.2.or.mode.eq.0) then ! need rmsd
do m=1, n
do i=1, 3
e0 = e0+ (x(i, m)-xc(i))**2 + (y(i, m)-yc(i))**2
end do
end do
endif
r(1, 1) = sxx-s1x*s2x/n;
r(2, 1) = sxy-s1x*s2y/n;
r(3, 1) = sxz-s1x*s2z/n;
r(1, 2) = syx-s1y*s2x/n;
r(2, 2) = syy-s1y*s2y/n;
r(3, 2) = syz-s1y*s2z/n;
r(1, 3) = szx-s1z*s2x/n;
r(2, 3) = szy-s1z*s2y/n;
r(3, 3) = szz-s1z*s2z/n;
det = r(1,1) * ( (r(2,2)*r(3,3)) - (r(2,3)*r(3,2)) )
& - r(1,2) * ( (r(2,1)*r(3,3)) - (r(2,3)*r(3,1)) )
& + r(1,3) * ( (r(2,1)*r(3,2)) - (r(2,2)*r(3,1)) )
sigma = det
m = 0
do j=1, 3
do i=1, j
m = m+1
rr(m) = r(1,i)*r(1,j) + r(2,i)*r(2,j) + r(3,i)*r(3,j)
end do
end do
spur = (rr(1)+rr(3)+rr(6)) / 3.0
cof = (((((rr(3)*rr(6) - rr(5)*rr(5)) + rr(1)*rr(6))
& - rr(4)*rr(4)) + rr(1)*rr(3)) - rr(2)*rr(2)) / 3.0
det = det*det
do i=1, 3
e(i) = spur
end do
if( spur .le. zero ) goto 40
d = spur*spur
h = d - cof
g = (spur*cof - det)/2.0 - spur*h
if( h .le. zero ) then
if( mode .eq. 0 ) then
goto 50
else
goto 30
end if
end if
sqrth = dsqrt(h)
d = h*h*h - g*g
if( d .lt. zero ) d = zero
d = datan2( dsqrt(d), -g ) / 3.0
cth = sqrth * dcos(d)
sth = sqrth*sqrt3*dsin(d)
e(1) = (spur + cth) + cth
e(2) = (spur - cth) + sth
e(3) = (spur - cth) - sth
if( mode .eq. 0 ) then
goto 50
end if
do l=1, 3, 2
d = e(l)
ss(1) = (d-rr(3)) * (d-rr(6)) - rr(5)*rr(5)
ss(2) = (d-rr(6)) * rr(2) + rr(4)*rr(5)
ss(3) = (d-rr(1)) * (d-rr(6)) - rr(4)*rr(4)
ss(4) = (d-rr(3)) * rr(4) + rr(2)*rr(5)
ss(5) = (d-rr(1)) * rr(5) + rr(2)*rr(4)
ss(6) = (d-rr(1)) * (d-rr(3)) - rr(2)*rr(2)
if( dabs(ss(1)) .ge. dabs(ss(3)) ) then
j=1
if( dabs(ss(1)) .lt. dabs(ss(6)) ) j = 3
else if( dabs(ss(3)) .ge. dabs(ss(6)) ) then
j = 2
else
j = 3
end if
d = zero
j = 3 * (j - 1)
do i=1, 3
k = ip(i+j)
a(i,l) = ss(k)
d = d + ss(k)*ss(k)
end do
if( d .gt. zero ) d = 1.0 / dsqrt(d)
do i=1, 3
a(i,l) = a(i,l) * d
end do
end do
d = a(1,1)*a(1,3) + a(2,1)*a(2,3) + a(3,1)*a(3,3)
if ((e(1) - e(2)) .gt. (e(2) - e(3))) then
m1 = 3
m = 1
else
m1 = 1
m = 3
endif
p = zero
do i=1, 3
a(i,m1) = a(i,m1) - d*a(i,m)
p = p + a(i,m1)**2
end do
if( p .le. tol ) then
p = 1.0
do 21 i=1, 3
if (p .lt. dabs(a(i,m))) goto 21
p = dabs( a(i,m) )
j = i
21 continue
k = ip2312(j)
l = ip2312(j+1)
p = dsqrt( a(k,m)**2 + a(l,m)**2 )
if( p .le. tol ) goto 40
a(j,m1) = zero
a(k,m1) = -a(l,m)/p
a(l,m1) = a(k,m)/p
else
p = 1.0 / dsqrt(p)
do i=1, 3
a(i,m1) = a(i,m1)*p
end do
end if
a(1,2) = a(2,3)*a(3,1) - a(2,1)*a(3,3)
a(2,2) = a(3,3)*a(1,1) - a(3,1)*a(1,3)
a(3,2) = a(1,3)*a(2,1) - a(1,1)*a(2,3)
30 do l=1, 2
d = zero
do i=1, 3
b(i,l) = r(i,1)*a(1,l) + r(i,2)*a(2,l) + r(i,3)*a(3,l)
d = d + b(i,l)**2
end do
if( d .gt. zero ) d = 1.0 / dsqrt(d)
do i=1, 3
b(i,l) = b(i,l)*d
end do
end do
d = b(1,1)*b(1,2) + b(2,1)*b(2,2) + b(3,1)*b(3,2)
p = zero
do i=1, 3
b(i,2) = b(i,2) - d*b(i,1)
p = p + b(i,2)**2
end do
if( p .le. tol ) then
p = 1.0
do 22 i=1, 3
if(p.lt.dabs(b(i,1)))goto 22
p = dabs( b(i,1) )
j = i
22 continue
k = ip2312(j)
l = ip2312(j+1)
p = dsqrt( b(k,1)**2 + b(l,1)**2 )
if( p .le. tol ) goto 40
b(j,2) = zero
b(k,2) = -b(l,1)/p
b(l,2) = b(k,1)/p
else
p = 1.0 / dsqrt(p)
do i=1, 3
b(i,2) = b(i,2)*p
end do
end if
b(1,3) = b(2,1)*b(3,2) - b(2,2)*b(3,1)
b(2,3) = b(3,1)*b(1,2) - b(3,2)*b(1,1)
b(3,3) = b(1,1)*b(2,2) - b(1,2)*b(2,1)
do i=1, 3
do j=1, 3
u(i,j) = b(i,1)*a(j,1) + b(i,2)*a(j,2) + b(i,3)*a(j,3)
end do
end do
40 do i=1, 3
t(i) = ((yc(i) - u(i,1)*xc(1)) - u(i,2)*xc(2)) - u(i,3)*xc(3)
end do
50 do i=1, 3
if( e(i) .lt. zero ) e(i) = zero
e(i) = dsqrt( e(i) )
end do
ier = 0
if( e(2) .le. (e(1) * 1.0d-05) ) ier = -1
d = e(3)
if( sigma .lt. 0.0 ) then
d = - d
if( (e(2) - e(3)) .le. (e(1) * 1.0d-05) ) ier = -1
end if
d = (d + e(2)) + e(1)
if(mode .eq. 2.or.mode.eq.0) then ! need rmsd
rms = (e0 - d) - d
if( rms .lt. 0.0 ) rms = 0.0
endif
return
end
|
