subroutine cartder *********************************************************************** * This subroutine calculates the derivatives of the consecutive virtual * bond vectors and the SC vectors in the virtual-bond angles theta and * virtual-torsional angles phi, as well as the derivatives of SC vectors * in the angles alpha and omega, describing the location of a side chain * in its local coordinate system. * * The derivatives are stored in the following arrays: * * DDCDV - the derivatives of virtual-bond vectors DC in theta and phi. * The structure is as follows: * * dDC(x,2)/dT(3),...,dDC(z,2)/dT(3),0, 0, 0 * dDC(x,3)/dT(4),...,dDC(z,3)/dT(4),dDC(x,3)/dP(4),dDC(y,4)/dP(4),dDC(z,4)/dP(4) * . . . . . . . . . . . . . . . . . . * dDC(x,N-1)/dT(4),...,dDC(z,N-1)/dT(4),dDC(x,N-1)/dP(4),dDC(y,N-1)/dP(4),dDC(z,N-1)/dP(4) * . * . * . * dDC(x,N-1)/dT(N),...,dDC(z,N-1)/dT(N),dDC(x,N-1)/dP(N),dDC(y,N-1)/dP(N),dDC(z,N-1)/dP(N) * * DXDV - the derivatives of the side-chain vectors in theta and phi. * The structure is same as above. * * DCDS - the derivatives of the side chain vectors in the local spherical * andgles alph and omega: * * dX(x,2)/dA(2),dX(y,2)/dA(2),dX(z,2)/dA(2),dX(x,2)/dO(2),dX(y,2)/dO(2),dX(z,2)/dO(2) * dX(x,3)/dA(3),dX(y,3)/dA(3),dX(z,3)/dA(3),dX(x,3)/dO(3),dX(y,3)/dO(3),dX(z,3)/dO(3) * . * . * . * dX(x,N-1)/dA(N-1),dX(y,N-1)/dA(N-1),dX(z,N-1)/dA(N-1),dX(x,N-1)/dO(N-1),dX(y,N-1)/dO(N-1),dX(z,N-1)/dO(N-1) * * Version of March '95, based on an early version of November '91. * *********************************************************************** implicit real*8 (a-h,o-z) include 'DIMENSIONS' include 'COMMON.VAR' include 'COMMON.CHAIN' include 'COMMON.DERIV' include 'COMMON.GEO' include 'COMMON.LOCAL' include 'COMMON.INTERACT' dimension drt(3,3,maxres),rdt(3,3,maxres),dp(3,3),temp(3,3), & fromto(3,3,maxdim),prordt(3,3,maxres),prodrt(3,3,maxres) dimension xx(3),xx1(3) c common /przechowalnia/ fromto * get the position of the jth ijth fragment of the chain coordinate system * in the fromto array. indmat(i,j)=((2*(nres-2)-i)*(i-1))/2+j-1 * * calculate the derivatives of transformation matrix elements in theta * do i=1,nres-2 rdt(1,1,i)=-rt(1,2,i) rdt(1,2,i)= rt(1,1,i) rdt(1,3,i)= 0.0d0 rdt(2,1,i)=-rt(2,2,i) rdt(2,2,i)= rt(2,1,i) rdt(2,3,i)= 0.0d0 rdt(3,1,i)=-rt(3,2,i) rdt(3,2,i)= rt(3,1,i) rdt(3,3,i)= 0.0d0 enddo * * derivatives in phi * do i=2,nres-2 drt(1,1,i)= 0.0d0 drt(1,2,i)= 0.0d0 drt(1,3,i)= 0.0d0 drt(2,1,i)= rt(3,1,i) drt(2,2,i)= rt(3,2,i) drt(2,3,i)= rt(3,3,i) drt(3,1,i)=-rt(2,1,i) drt(3,2,i)=-rt(2,2,i) drt(3,3,i)=-rt(2,3,i) enddo * * generate the matrix products of type r(i)t(i)...r(j)t(j) * do i=2,nres-2 ind=indmat(i,i+1) do k=1,3 do l=1,3 temp(k,l)=rt(k,l,i) enddo enddo do k=1,3 do l=1,3 fromto(k,l,ind)=temp(k,l) enddo enddo do j=i+1,nres-2 ind=indmat(i,j+1) do k=1,3 do l=1,3 dpkl=0.0d0 do m=1,3 dpkl=dpkl+temp(k,m)*rt(m,l,j) enddo dp(k,l)=dpkl fromto(k,l,ind)=dpkl enddo enddo do k=1,3 do l=1,3 temp(k,l)=dp(k,l) enddo enddo enddo enddo * * Calculate derivatives. * ind1=0 do i=1,nres-2 ind1=ind1+1 * * Derivatives of DC(i+1) in theta(i+2) * do j=1,3 do k=1,2 dpjk=0.0D0 do l=1,3 dpjk=dpjk+prod(j,l,i)*rdt(l,k,i) enddo dp(j,k)=dpjk prordt(j,k,i)=dp(j,k) enddo dp(j,3)=0.0D0 dcdv(j,ind1)=vbld(i+1)*dp(j,1) enddo * * Derivatives of SC(i+1) in theta(i+2) * xx1(1)=-0.5D0*xloc(2,i+1) xx1(2)= 0.5D0*xloc(1,i+1) do j=1,3 xj=0.0D0 do k=1,2 xj=xj+r(j,k,i)*xx1(k) enddo xx(j)=xj enddo do j=1,3 rj=0.0D0 do k=1,3 rj=rj+prod(j,k,i)*xx(k) enddo dxdv(j,ind1)=rj enddo * * Derivatives of SC(i+1) in theta(i+3). The have to be handled differently * than the other off-diagonal derivatives. * do j=1,3 dxoiij=0.0D0 do k=1,3 dxoiij=dxoiij+dp(j,k)*xrot(k,i+2) enddo dxdv(j,ind1+1)=dxoiij enddo cd print *,ind1+1,(dxdv(j,ind1+1),j=1,3) * * Derivatives of DC(i+1) in phi(i+2) * do j=1,3 do k=1,3 dpjk=0.0 do l=2,3 dpjk=dpjk+prod(j,l,i)*drt(l,k,i) enddo dp(j,k)=dpjk prodrt(j,k,i)=dp(j,k) enddo dcdv(j+3,ind1)=vbld(i+1)*dp(j,1) enddo * * Derivatives of SC(i+1) in phi(i+2) * xx(1)= 0.0D0 xx(3)= xloc(2,i+1)*r(2,2,i)+xloc(3,i+1)*r(2,3,i) xx(2)=-xloc(2,i+1)*r(3,2,i)-xloc(3,i+1)*r(3,3,i) do j=1,3 rj=0.0D0 do k=2,3 rj=rj+prod(j,k,i)*xx(k) enddo dxdv(j+3,ind1)=-rj enddo * * Derivatives of SC(i+1) in phi(i+3). * do j=1,3 dxoiij=0.0D0 do k=1,3 dxoiij=dxoiij+dp(j,k)*xrot(k,i+2) enddo dxdv(j+3,ind1+1)=dxoiij enddo * * Calculate the derivatives of DC(i+1) and SC(i+1) in theta(i+3) thru * theta(nres) and phi(i+3) thru phi(nres). * do j=i+1,nres-2 ind1=ind1+1 ind=indmat(i+1,j+1) cd print *,'i=',i,' j=',j,' ind=',ind,' ind1=',ind1 do k=1,3 do l=1,3 tempkl=0.0D0 do m=1,2 tempkl=tempkl+prordt(k,m,i)*fromto(m,l,ind) enddo temp(k,l)=tempkl enddo enddo cd print '(9f8.3)',((fromto(k,l,ind),l=1,3),k=1,3) cd print '(9f8.3)',((prod(k,l,i),l=1,3),k=1,3) cd print '(9f8.3)',((temp(k,l),l=1,3),k=1,3) * Derivatives of virtual-bond vectors in theta do k=1,3 dcdv(k,ind1)=vbld(i+1)*temp(k,1) enddo cd print '(3f8.3)',(dcdv(k,ind1),k=1,3) * Derivatives of SC vectors in theta do k=1,3 dxoijk=0.0D0 do l=1,3 dxoijk=dxoijk+temp(k,l)*xrot(l,j+2) enddo dxdv(k,ind1+1)=dxoijk enddo * *--- Calculate the derivatives in phi * do k=1,3 do l=1,3 tempkl=0.0D0 do m=1,3 tempkl=tempkl+prodrt(k,m,i)*fromto(m,l,ind) enddo temp(k,l)=tempkl enddo enddo do k=1,3 dcdv(k+3,ind1)=vbld(i+1)*temp(k,1) enddo do k=1,3 dxoijk=0.0D0 do l=1,3 dxoijk=dxoijk+temp(k,l)*xrot(l,j+2) enddo dxdv(k+3,ind1+1)=dxoijk enddo enddo enddo * * Derivatives in alpha and omega: * do i=2,nres-1 c dsci=dsc(itype(i)) dsci=vbld(i+nres) #ifdef OSF alphi=alph(i) omegi=omeg(i) if(alphi.ne.alphi) alphi=100.0 if(omegi.ne.omegi) omegi=-100.0 #else alphi=alph(i) omegi=omeg(i) #endif cd print *,'i=',i,' dsci=',dsci,' alphi=',alphi,' omegi=',omegi cosalphi=dcos(alphi) sinalphi=dsin(alphi) cosomegi=dcos(omegi) sinomegi=dsin(omegi) temp(1,1)=-dsci*sinalphi temp(2,1)= dsci*cosalphi*cosomegi temp(3,1)=-dsci*cosalphi*sinomegi temp(1,2)=0.0D0 temp(2,2)=-dsci*sinalphi*sinomegi temp(3,2)=-dsci*sinalphi*cosomegi theta2=pi-0.5D0*theta(i+1) cost2=dcos(theta2) sint2=dsin(theta2) jjj=0 cd print *,((temp(l,k),l=1,3),k=1,2) do j=1,2 xp=temp(1,j) yp=temp(2,j) xxp= xp*cost2+yp*sint2 yyp=-xp*sint2+yp*cost2 zzp=temp(3,j) xx(1)=xxp xx(2)=yyp*r(2,2,i-1)+zzp*r(2,3,i-1) xx(3)=yyp*r(3,2,i-1)+zzp*r(3,3,i-1) do k=1,3 dj=0.0D0 do l=1,3 dj=dj+prod(k,l,i-1)*xx(l) enddo dxds(jjj+k,i)=dj enddo jjj=jjj+3 enddo enddo return end