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