*************************************************************************
* This program is to calculate the root-mean-square deviation (RMSD)
*
* To calculate RMSD of 'pdb1' and 'pdb2':
* >RMSD pdb1 pdb2
*
* To output transferred 'pdb1_tr'
* >RMSD pdb1 pdb2 -o pdb1_tr
*
* Note:
* 1. Input structure much be in PDB format
* 2. Only C-alpha RMSD is reported
*
* Please address your question and comments to zhng@umich.edu
*************************************************************************
program calRMSD
PARAMETER(nmax=3000)
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
*****instructions ----------------->
call getarg(1,fnam)
if(fnam.eq.' '.or.fnam.eq.'?'.or.fnam.eq.'-h')then
write(*,*)
write(*,*)'To calculate RMSD of ''pdb1'' and ''pdb2'':'
write(*,*)' >RMSD pdb1 pdb2'
write(*,*)
write(*,*)'To output transferred ''pdb1_tr'''
write(*,*)' >RMSD pdb1 pdb2 -o pdb1_tr'
write(*,*)
write(*,*)'Note:'
write(*,*)' 1. Input structure much be in PDB format'
write(*,*)' 2. Only C-alpha RMSD is reported'
write(*,*)
goto 9999
endif
******* options ----------->
narg=iargc()
if(narg<2)then
write(*,*)'Error, please enter two PDB files'
goto 9999
endif
i=0
j=0
m_out=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)
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)
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 second 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)
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 common 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
*** RMSD calculation ---------------------------------->
do m=1,n_ali
r_1(1,m)=xa(iA(m))
r_1(2,m)=ya(iA(m))
r_1(3,m)=za(iA(m))
r_2(1,m)=xb(iB(m))
r_2(2,m)=yb(iB(m))
r_2(3,m)=zb(iB(m))
enddo
call u3b(w,r_1,r_2,n_ali,1,rms,u,t,ier) !u rotate r_1 to r_2
rmsd=dsqrt(rms/n_ali)
call zydrmsd(r_1,r_2,n_ali,drms)
drmsd=drms
******************************************************************
* Output
******************************************************************
*** output RMSD ---------------------------->
write(*,*)
write(*,501)pdb(1),nseqA
501 format('Structure1: ',A10,' Length= ',I4)
write(*,502)pdb(2),nseqB
502 format('Structure2: ',A10,' Length= ',I4)
write(*,503)n_ali
503 format('Number of residues in common= ',I4)
write(*,513)rmsd
513 format('RMSD of the common residues= ',F8.3)
write(*,514)drmsd
514 format('Distant RMSD of the common residues= ',F8.3)
write(*,*)
*** output rotated structure of pdb1:
if(m_out.eq.1)then
OPEN(unit=7,file=outname,status='unknown') !pdb1_tr
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)
write(7,1237)nresA(j),seqA(j),nresA(j),
& xt(j),yt(j),zt(j)
enddo
write(7,1238)
close(7)
endif
1237 format('ATOM ',i5,' CA ',A3,I6,4X,3F8.3)
1238 format('TER')
***
c^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
9999 END
ccccccccccc Calculate dRMSD between 1 and CA cccccccccccccccccccccccccccccccccc
subroutine zydrmsd(r_1,r_2,nn,drms)
double precision r_1(3,1),r_2(3,1),drms,d,dp
drms=0
do i=1,nn
do j=i+1,nn
d=sqrt((r_1(1,i)-r_1(1,j))**2+(r_1(2,i)-r_1(2,j))**2
$ +(r_1(3,i)-r_1(3,j))**2)
dp=sqrt((r_2(1,i)-r_2(1,j))**2+(r_2(2,i)-r_2(2,j))**2
$ +(r_2(3,i)-r_2(3,j))**2)
drms=drms+(d-dp)**2
enddo
enddo
drms=sqrt(drms*2/(nn*(nn-1)))
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)
c 1:calculate rms,u,t (takes 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 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
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
if( w(m) .lt. 0.0 ) return
wc = wc + w(m)
do i=1, 3
xc(i) = xc(i) + w(m)*x(i,m)
yc(i) = yc(i) + w(m)*y(i,m)
end do
end do
if( wc .le. zero ) return
do i=1, 3
xc(i) = xc(i) / wc
yc(i) = yc(i) / wc
end do
do m=1, n
do i=1, 3
e0=e0+w(m)*((x(i,m)-xc(i))**2+(y(i,m)-yc(i))**2)
d = w(m) * ( y(i,m) - yc(i) )
do j=1, 3
r(i,j) = r(i,j) + d*( x(j,m) - xc(j) )
end do
end do
end do
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)
rms = (e0 - d) - d
if( rms .lt. 0.0 ) rms = 0.0
return
end