Date: Wed, 21 Nov 2007 15:25:58 -0600 From: Yang Zhang Subject: Re: I-TASSER potentials again Hi, >1) Are you using centroid (geometrical center) or real center >of mass taking into account the weight of each type of side chain? The latter, real center of mass. >2) How do you calculate the radius of gyration? Is it just the >estimated value of 2.2*N^0.38? If it's a real distance, is it >measured using just side chain centers of mass, C-alphas or maybe both? This depends on how you use it. For the calculation of the depth factor, it is just estimated by 2.2*N^0.38. For the calculation of principal axes, we use the side-chain center of mass (see below). >3) How the side chain coordinates from 2-rotamer library are >chosen? I know that first vector is for extended and second for compact >local structure but how extend/compact is decided? Are you using here >the secondary structure prediction (H is compact, else extended) or >maybe r(i,i+2) distance like in E13 potential? No, we calculate the angle of C-alpha of (i-1,i,i+1). If the angle>105, it is extended; otherwise, it is compact. The corresponding parameters are obtained from PDB statistics. >4) How the potential is calculated when the residue neighbourhood is >too small to follow the equations (like at the beginning/end of the >sequence)? Are the terms impossible to compute just ignored (equal to >zero) or some defaults are assumed? We calculate the terms only for the involved residues. >5) How exactly the local handedness of the three consecutive residues is >decided? Is it based on angles between CA-CA vectors being within some >range? Let a,b,c are the consecutive vectors of neighboring residues, and d=a(x)b(.)c. d>0 corresponds to right-handed and d<0 to left-handed. >6) How the length of principal axes of the protein ellipsoid are being >determined? Is it just half distance between max and min coordinates >for each dimension? The principal axes are the eigenvalues of covariance matrix. In the following I attach a program for the quick calculation of the eigenvalues from the covariance matrix. Hope this helps. Yang ************************************************************** * Subroutine for calculating eigenvalue and eignevectors * A{3,3}-covariance matrix, E{3}-eigenvalue, T{3,3}-eigenvector ************************************************************** subroutine eigenvalue common/eigen/A(3,3),E(3),T(3,3) c #### Eigenvalues ############ pi=3.1415926 p1=-1 p2=A(1,1)+A(2,2)+A(3,3) p3=-A(1,1)*A(2,2)-A(1,1)*A(3,3)-A(2,2)*A(3,3)+ & A(2,3)*A(2,3)+A(1,3)*A(1,3)+A(1,2)*A(1,2) p4=A(1,1)*A(2,2)*A(3,3)+A(1,2)*A(2,3)*A(3,1)+ & A(1,3)*A(2,1)*A(3,2)-A(1,3)*A(2,2)*A(3,1)- & A(1,1)*A(2,3)*A(3,2)-A(1,2)*A(2,1)*A(3,3) p5=(-(1.0/3)*(p2/p1)**2+p3/p1)/3 ap5=sqrt(-p5) p6=((2.0/27)*(p2/p1)**3-(1.0/3)*(p2*p3/p1**2)+p4/p1)/2 p7=acos(-p6/sqrt(-p5**3)) p8=2*ap5*cos(p7/3.0) p9=-2*ap5*cos((p7+pi)/3.0) p10=-2*ap5*cos((p7-pi)/3.0) p11=p2/(3*p1) E(1)=p8-p11 !eigenvalue E(2)=p9-p11 !eigenvalue E(3)=p10-p11 !eigenvalue c ##### normalized eigenvectors ######### do i=1,3 fnorm1=A(2,1)*A(1,2)-(A(1,1)-E(i))*(A(2,2)-E(i)) x=((A(2,2)-E(i))*A(1,3)-A(1,2)*A(2,3))/fnorm1 y=((A(1,1)-E(i))*A(2,3)-A(2,1)*A(1,3))/fnorm1 T(i,3)=1/sqrt(x*x+y*y+1) T(i,1)=x*T(i,3) T(i,2)=y*T(i,3) c write(*,*)i,E(i),T(i,1),T(i,2),T(i,3) enddo return end