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TMalign.cpp
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TMalign.cpp
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/* command line argument parsing and document of TMalign main program */
#include "TMalign.h"
using namespace std;
void print_version()
{
cout <<
"\n"
" **********************************************************************\n"
" * TM-align (Version 20220623): protein and RNA structure alignment *\n"
" * References: Y Zhang, J Skolnick. Nucl Acids Res 33, 2302-9 (2005) *\n"
" * S Gong, C Zhang, Y Zhang. Bioinformatics, bz282 (2019) *\n"
" * Please email comments and suggestions to [email protected] *\n"
" **********************************************************************"
<< endl;
}
void print_extra_help()
{
cout <<
"Additional options:\n"
" -fast Fast but slightly inaccurate alignment\n"
"\n"
" -dir Perform all-against-all alignment among the list of PDB\n"
" chains listed by 'chain_list' under 'chain_folder'. Note\n"
" that the slash is necessary.\n"
" $ TMalign -dir chain_folder/ chain_list\n"
"\n"
" -dir1 Use chain2 to search a list of PDB chains listed by 'chain1_list'\n"
" under 'chain1_folder'. Note that the slash is necessary.\n"
" $ TMalign -dir1 chain1_folder/ chain1_list chain2\n"
"\n"
" -dir2 Use chain1 to search a list of PDB chains listed by 'chain2_list'\n"
" under 'chain2_folder'\n"
" $ TMalign chain1 -dir2 chain2_folder/ chain2_list\n"
"\n"
" -pair (Only when -dir1 and -dir2 are set, default is no) whether to\n"
" perform pair alignment rather than all-against-all alignment\n"
"\n"
" -suffix (Only when -dir1 and/or -dir2 are set, default is empty)\n"
" add file name suffix to files listed by chain1_list or chain2_list\n"
"\n"
" -atom 4-character atom name used to represent a residue.\n"
" Default is \" C3'\" for RNA/DNA and \" CA \" for proteins\n"
" (note the spaces before and after CA).\n"
"\n"
" -mol Molecule type: RNA or protein\n"
" Default is detect molecule type automatically\n"
"\n"
" -ter Strings to mark the end of a chain\n"
" 3: (default) TER, ENDMDL, END or different chain ID\n"
" 2: ENDMDL, END, or different chain ID\n"
" 1: ENDMDL or END\n"
" 0: (default in the first C++ TMalign) end of file\n"
"\n"
" -split Whether to split PDB file into multiple chains\n"
" 0: (default) treat the whole structure as one single chain\n"
" 1: treat each MODEL as a separate chain (-ter should be 0)\n"
" 2: treat each chain as a seperate chain (-ter should be <=1)\n"
"\n"
" -outfmt Output format\n"
" 0: (default) full output\n"
" 1: fasta format compact output\n"
" 2: tabular format very compact output\n"
" -1: full output, but without version or citation information\n"
"\n"
" -byresi Whether to assume residue index correspondence between the\n"
" two structures. The same as -TMscore.\n"
" 0: (default) sequence independent alignment\n"
" 1: (same as TMscore program) sequence-dependent superposition,\n"
" i.e. align by residue index\n"
" 2: (same as TMscore -c, should be used with -ter <=1)\n"
" align by residue index and chain ID\n"
" 3: (similar to TMscore -c, should be used with -ter <=1)\n"
" align by residue index and order of chain\n"
//" 4: sequence dependent alignment: perform Needleman-Wunsch\n"
//" global sequence alignment, followed by TM-score superposition\n"
" 5: sequence dependent alignment: perform glocal sequence\n"
" alignment followed by TM-score superposition.\n"
" -byresi 5 is thee same as -seq\n"
"\n"
" -TMcut -1: (default) do not consider TMcut\n"
" Values in [0.5,1): Do not proceed with TM-align for this\n"
" structure pair if TM-score is unlikely to reach TMcut.\n"
" TMcut is normalized is set by -a option:\n"
" -2: normalized by longer structure length\n"
" -1: normalized by shorter structure length\n"
" 0: (default, same as F) normalized by second structure\n"
" 1: same as T, normalized by average structure length\n"
"\n"
" -cp ALignment with circular permutation\n"
"\n"
" -mirror Whether to align the mirror image of input structure\n"
" 0: (default) do not align mirrored structure\n"
" 1: align mirror of chain1 to origin chain2\n"
"\n"
" -het Whether to align residues marked as 'HETATM' in addition to 'ATOM '\n"
" 0: (default) only align 'ATOM ' residues\n"
" 1: align both 'ATOM ' and 'HETATM' residues\n"
"\n"
" -infmt1 Input format for chain1\n"
" -infmt2 Input format for chain2\n"
" -1: (default) automatically detect PDB or PDBx/mmCIF format\n"
" 0: PDB format\n"
" 1: SPICKER format\n"
" 2: xyz format\n"
" 3: PDBx/mmCIF format\n"
<<endl;
}
void print_help(bool h_opt=false)
{
print_version();
cout <<
"\n"
"Usage: TMalign PDB1.pdb PDB2.pdb [Options]\n"
"\n"
"Options:\n"
" -u TM-score normalized by user assigned length (the same as -L)\n"
" warning: it should be >= minimum length of the two structures\n"
" otherwise, TM-score may be >1\n"
"\n"
" -a TM-score normalized by the average length of two structures\n"
" T or F, (default F)\n"
"\n"
" -i Start with an alignment specified in fasta file 'align.txt'\n"
"\n"
" -I Stick to the alignment specified in 'align.txt'\n"
"\n"
" -m Output TM-align rotation matrix\n"
"\n"
" -d TM-score scaled by an assigned d0, e.g. 5 Angstroms\n"
"\n"
" -o Output the superposition of PDB1.pdb to TM_sup.pdb\n"
" $ TMalign PDB1.pdb PDB2.pdb -o TM_sup.pdb\n"
" To view superposed full-atom structures:\n"
" $ pymol TM_sup.pdb PDB2.pdb\n"
"\n"
" -v Print the version of TM-align\n"
"\n"
" -h Print the full help message, including options not available\n"
" in standard TM-align program\n"
"\n"
" (Options -u, -a, -d, -o won't change the final structure alignment)\n\n"
"Example usages:\n"
" TMalign PDB1.pdb PDB2.pdb\n"
" TMalign PDB1.pdb PDB2.pdb -u 100 -d 5.0\n"
" TMalign PDB1.pdb PDB2.pdb -a T -o PDB1.sup\n"
" TMalign PDB1.pdb PDB2.pdb -i align.txt\n"
" TMalign PDB1.pdb PDB2.pdb -m matrix.txt\n"
<<endl;
if (h_opt) print_extra_help();
exit(EXIT_SUCCESS);
}
int main(int argc, char *argv[])
{
if (argc < 2) print_help();
clock_t t1, t2;
t1 = clock();
/**********************/
/* get argument */
/**********************/
string xname = "";
string yname = "";
string fname_super = ""; // file name for superposed structure
string fname_lign = ""; // file name for user alignment
string fname_matrix= ""; // file name for output matrix
vector<string> sequence; // get value from alignment file
double Lnorm_ass, d0_scale;
bool h_opt = false; // print full help message
bool v_opt = false; // print version
bool m_opt = false; // flag for -m, output rotation matrix
int i_opt = 0; // 1 for -i, 3 for -I
bool o_opt = false; // flag for -o, output superposed structure
int a_opt = 0; // flag for -a, do not normalized by average length
bool u_opt = false; // flag for -u, normalized by user specified length
bool d_opt = false; // flag for -d, user specified d0
double TMcut =-1;
int infmt1_opt=-1; // PDB or PDBx/mmCIF format for chain_1
int infmt2_opt=-1; // PDB or PDBx/mmCIF format for chain_2
int ter_opt =3; // TER, END, or different chainID
int split_opt =0; // do not split chain
int outfmt_opt=0; // set -outfmt to full output
bool fast_opt =false; // flags for -fast, fTM-align algorithm
int cp_opt =0; // do not check circular permutation
int mirror_opt=0; // do not align mirror
int het_opt =0; // do not read HETATM residues
string atom_opt ="auto";// use C alpha atom for protein and C3' for RNA
string mol_opt ="auto";// auto-detect the molecule type as protein/RNA
string suffix_opt=""; // set -suffix to empty
string dir_opt =""; // set -dir to empty
string dir1_opt =""; // set -dir1 to empty
string dir2_opt =""; // set -dir2 to empty
bool pair_opt=false; // pair alignment
int byresi_opt=0; // set -byresi to 0
vector<string> chain1_list; // only when -dir1 is set
vector<string> chain2_list; // only when -dir2 is set
for(int i = 1; i < argc; i++)
{
if ( !strcmp(argv[i],"-o") && i < (argc-1) )
{
fname_super = argv[i + 1]; o_opt = true; i++;
}
else if ( (!strcmp(argv[i],"-u") ||
!strcmp(argv[i],"-L")) && i < (argc-1) )
{
Lnorm_ass = atof(argv[i + 1]); u_opt = true; i++;
}
else if ( !strcmp(argv[i],"-a") && i < (argc-1) )
{
if (!strcmp(argv[i + 1], "T")) a_opt=true;
else if (!strcmp(argv[i + 1], "F")) a_opt=false;
else
{
a_opt=atoi(argv[i + 1]);
if (a_opt!=-2 && a_opt!=-1 && a_opt!=1)
PrintErrorAndQuit("-a must be -2, -1, 1, T or F");
}
i++;
}
else if ( !strcmp(argv[i],"-d") && i < (argc-1) )
{
d0_scale = atof(argv[i + 1]); d_opt = true; i++;
}
else if ( !strcmp(argv[i],"-v") )
{
v_opt = true;
}
else if ( !strcmp(argv[i],"-h") )
{
h_opt = true;
}
else if ( !strcmp(argv[i],"-i") && i < (argc-1) )
{
if (i_opt==3)
PrintErrorAndQuit("ERROR! -i and -I cannot be used together");
fname_lign = argv[i + 1]; i_opt = 1; i++;
}
else if (!strcmp(argv[i], "-I") && i < (argc-1) )
{
if (i_opt==1)
PrintErrorAndQuit("ERROR! -I and -i cannot be used together");
fname_lign = argv[i + 1]; i_opt = 3; i++;
}
else if (!strcmp(argv[i], "-m") && i < (argc-1) )
{
fname_matrix = argv[i + 1]; m_opt = true; i++;
}// get filename for rotation matrix
else if (!strcmp(argv[i], "-fast"))
{
fast_opt = true;
}
else if ( !strcmp(argv[i],"-infmt1") && i < (argc-1) )
{
infmt1_opt=atoi(argv[i + 1]); i++;
}
else if ( !strcmp(argv[i],"-infmt2") && i < (argc-1) )
{
infmt2_opt=atoi(argv[i + 1]); i++;
}
else if ( !strcmp(argv[i],"-ter") && i < (argc-1) )
{
ter_opt=atoi(argv[i + 1]); i++;
}
else if ( !strcmp(argv[i],"-split") && i < (argc-1) )
{
split_opt=atoi(argv[i + 1]); i++;
}
else if ( !strcmp(argv[i],"-atom") && i < (argc-1) )
{
atom_opt=argv[i + 1]; i++;
}
else if ( !strcmp(argv[i],"-mol") && i < (argc-1) )
{
mol_opt=argv[i + 1]; i++;
}
else if ( !strcmp(argv[i],"-dir") && i < (argc-1) )
{
dir_opt=argv[i + 1]; i++;
}
else if ( !strcmp(argv[i],"-dir1") && i < (argc-1) )
{
dir1_opt=argv[i + 1]; i++;
}
else if ( !strcmp(argv[i],"-dir2") && i < (argc-1) )
{
dir2_opt=argv[i + 1]; i++;
}
else if ( !strcmp(argv[i],"-pair") )
{
pair_opt=true;
}
else if ( !strcmp(argv[i],"-suffix") && i < (argc-1) )
{
suffix_opt=argv[i + 1]; i++;
}
else if ( !strcmp(argv[i],"-outfmt") && i < (argc-1) )
{
outfmt_opt=atoi(argv[i + 1]); i++;
}
else if ( !strcmp(argv[i],"-TMcut") && i < (argc-1) )
{
TMcut=atof(argv[i + 1]); i++;
}
else if ((!strcmp(argv[i],"-byresi") || !strcmp(argv[i],"-tmscore") ||
!strcmp(argv[i],"-TMscore")) && i < (argc-1) )
{
byresi_opt=atoi(argv[i + 1]); i++;
}
else if ( !strcmp(argv[i],"-seq") )
{
byresi_opt=5;
}
else if ( !strcmp(argv[i],"-cp") )
{
cp_opt=1;
}
else if ( !strcmp(argv[i],"-mirror") && i < (argc-1) )
{
mirror_opt=atoi(argv[i + 1]); i++;
}
else if ( !strcmp(argv[i],"-het") && i < (argc-1) )
{
het_opt=atoi(argv[i + 1]); i++;
}
else if (xname.size() == 0) xname=argv[i];
else if (yname.size() == 0) yname=argv[i];
else PrintErrorAndQuit(string("ERROR! Undefined option ")+argv[i]);
}
if(xname.size()==0 || (yname.size()==0 && dir_opt.size()==0) ||
(yname.size() && dir_opt.size()))
{
if (h_opt) print_help(h_opt);
if (v_opt)
{
print_version();
exit(EXIT_FAILURE);
}
if (xname.size()==0)
PrintErrorAndQuit("Please provide input structures");
else if (yname.size()==0 && dir_opt.size()==0)
PrintErrorAndQuit("Please provide structure B");
else if (yname.size() && dir_opt.size())
PrintErrorAndQuit("Please provide only one file name if -dir is set");
}
if (suffix_opt.size() && dir_opt.size()+dir1_opt.size()+dir2_opt.size()==0)
PrintErrorAndQuit("-suffix is only valid if -dir, -dir1 or -dir2 is set");
if ((dir_opt.size() || dir1_opt.size() || dir2_opt.size()))
{
if (m_opt || o_opt)
PrintErrorAndQuit("-m or -o cannot be set with -dir, -dir1 or -dir2");
else if (dir_opt.size() && (dir1_opt.size() || dir2_opt.size()))
PrintErrorAndQuit("-dir cannot be set with -dir1 or -dir2");
}
if (atom_opt.size()!=4)
PrintErrorAndQuit("ERROR! Atom name must have 4 characters, including space.");
if (mol_opt!="auto" && mol_opt!="protein" && mol_opt!="RNA")
PrintErrorAndQuit("ERROR! Molecule type must be either RNA or protein.");
else if (mol_opt=="protein" && atom_opt=="auto")
atom_opt=" CA ";
else if (mol_opt=="RNA" && atom_opt=="auto")
atom_opt=" C3'";
if (u_opt && Lnorm_ass<=0)
PrintErrorAndQuit("Wrong value for option -u! It should be >0");
if (d_opt && d0_scale<=0)
PrintErrorAndQuit("Wrong value for option -d! It should be >0");
if (outfmt_opt>=2 && (a_opt || u_opt || d_opt))
PrintErrorAndQuit("-outfmt 2 cannot be used with -a, -u, -L, -d");
if (byresi_opt!=0)
{
if (i_opt)
PrintErrorAndQuit("-byresi >=1 cannot be used with -i or -I");
if (byresi_opt<0 || byresi_opt>5)
PrintErrorAndQuit("-byresi can only be 0, 1, 2, 3, 4, or 5");
if (byresi_opt>=2 && byresi_opt<=3 && ter_opt>=2)
PrintErrorAndQuit("-byresi 2 and -byresi 3 should be used with -ter <=1");
}
if (split_opt==1 && ter_opt!=0)
PrintErrorAndQuit("-split 1 should be used with -ter 0");
else if (split_opt==2 && ter_opt!=0 && ter_opt!=1)
PrintErrorAndQuit("-split 2 should be used with -ter 0 or 1");
if (split_opt<0 || split_opt>2)
PrintErrorAndQuit("-split can only be 0, 1 or 2");
if (cp_opt!=0 && cp_opt!=1)
PrintErrorAndQuit("-cp can only be 0 or 1");
if (cp_opt && i_opt)
PrintErrorAndQuit("-cp cannot be used with -i or -I");
/* read initial alignment file from 'align.txt' */
if (i_opt) read_user_alignment(sequence, fname_lign, i_opt);
if (byresi_opt) i_opt=3;
if (m_opt && fname_matrix == "") // Output rotation matrix: matrix.txt
PrintErrorAndQuit("ERROR! Please provide a file name for option -m!");
/* parse file list */
if (dir1_opt.size()+dir_opt.size()==0) chain1_list.push_back(xname);
else file2chainlist(chain1_list, xname, dir_opt+dir1_opt, suffix_opt);
if (dir_opt.size())
for (int i=0;i<chain1_list.size();i++)
chain2_list.push_back(chain1_list[i]);
else if (dir2_opt.size()==0) chain2_list.push_back(yname);
else file2chainlist(chain2_list, yname, dir2_opt, suffix_opt);
if (outfmt_opt==2)
cout<<"#PDBchain1\tPDBchain2\tTM1\tTM2\t"
<<"RMSD\tID1\tID2\tIDali\tL1\tL2\tLali"<<endl;
/* declare previously global variables */
vector<vector<string> >PDB_lines1; // text of chain1
vector<vector<string> >PDB_lines2; // text of chain2
vector<int> mol_vec1; // molecule type of chain1, RNA if >0
vector<int> mol_vec2; // molecule type of chain2, RNA if >0
vector<string> chainID_list1; // list of chainID1
vector<string> chainID_list2; // list of chainID2
int i,j; // file index
int chain_i,chain_j; // chain index
int r; // residue index
int xlen, ylen; // chain length
int xchainnum,ychainnum;// number of chains in a PDB file
char *seqx, *seqy; // for the protein sequence
char *secx, *secy; // for the secondary structure
double **xa, **ya; // for input vectors xa[0...xlen-1][0..2] and
// ya[0...ylen-1][0..2], in general,
// ya is regarded as native structure
// --> superpose xa onto ya
vector<string> resi_vec1; // residue index for chain1
vector<string> resi_vec2; // residue index for chain2
int read_resi=byresi_opt; // whether to read residue index
if (byresi_opt==0 && o_opt) read_resi=2;
/* loop over file names */
for (i=0;i<chain1_list.size();i++)
{
/* parse chain 1 */
xname=chain1_list[i];
xchainnum=get_PDB_lines(xname, PDB_lines1, chainID_list1, mol_vec1,
ter_opt, infmt1_opt, atom_opt, false, split_opt, het_opt);
if (!xchainnum)
{
cerr<<"Warning! Cannot parse file: "<<xname
<<". Chain number 0."<<endl;
continue;
}
for (chain_i=0;chain_i<xchainnum;chain_i++)
{
xlen=PDB_lines1[chain_i].size();
if (mol_opt=="RNA") mol_vec1[chain_i]=1;
else if (mol_opt=="protein") mol_vec1[chain_i]=-1;
if (!xlen)
{
cerr<<"Warning! Cannot parse file: "<<xname
<<". Chain length 0."<<endl;
continue;
}
else if (xlen<3)
{
cerr<<"Sequence is too short <3!: "<<xname<<endl;
continue;
}
NewArray(&xa, xlen, 3);
seqx = new char[xlen + 1];
secx = new char[xlen + 1];
xlen = read_PDB(PDB_lines1[chain_i], xa, seqx,
resi_vec1, read_resi);
if (mirror_opt) for (r=0;r<xlen;r++) xa[r][2]=-xa[r][2];
if (mol_vec1[chain_i]>0) make_sec(seqx,xa, xlen, secx,atom_opt);
else make_sec(xa, xlen, secx); // secondary structure assignment
for (j=(dir_opt.size()>0)*(i+1);j<chain2_list.size();j++)
{
if (pair_opt && j!=i) continue;
/* parse chain 2 */
if (PDB_lines2.size()==0)
{
yname=chain2_list[j];
ychainnum=get_PDB_lines(yname, PDB_lines2, chainID_list2,
mol_vec2, ter_opt, infmt2_opt, atom_opt, false,
split_opt, het_opt);
if (!ychainnum)
{
cerr<<"Warning! Cannot parse file: "<<yname
<<". Chain number 0."<<endl;
continue;
}
}
for (chain_j=0;chain_j<ychainnum;chain_j++)
{
ylen=PDB_lines2[chain_j].size();
if (mol_opt=="RNA") mol_vec2[chain_j]=1;
else if (mol_opt=="protein") mol_vec2[chain_j]=-1;
if (!ylen)
{
cerr<<"Warning! Cannot parse file: "<<yname
<<". Chain length 0."<<endl;
continue;
}
else if (ylen<3)
{
cerr<<"Sequence is too short <3!: "<<yname<<endl;
continue;
}
NewArray(&ya, ylen, 3);
seqy = new char[ylen + 1];
secy = new char[ylen + 1];
ylen = read_PDB(PDB_lines2[chain_j], ya, seqy,
resi_vec2, read_resi);
if (mol_vec2[chain_j]>0)
make_sec(seqy, ya, ylen, secy, atom_opt);
else make_sec(ya, ylen, secy);
if (byresi_opt) extract_aln_from_resi(sequence,
seqx,seqy,resi_vec1,resi_vec2,byresi_opt);
/* declare variable specific to this pair of TMalign */
double t0[3], u0[3][3];
double TM1, TM2;
double TM3, TM4, TM5; // for a_opt, u_opt, d_opt
double d0_0, TM_0;
double d0A, d0B, d0u, d0a;
double d0_out=5.0;
string seqM, seqxA, seqyA;// for output alignment
double rmsd0 = 0.0;
int L_ali; // Aligned length in standard_TMscore
double Liden=0;
double TM_ali, rmsd_ali; // TMscore and rmsd in standard_TMscore
int n_ali=0;
int n_ali8=0;
/* entry function for structure alignment */
if (cp_opt) CPalign_main(
xa, ya, seqx, seqy, secx, secy,
t0, u0, TM1, TM2, TM3, TM4, TM5,
d0_0, TM_0, d0A, d0B, d0u, d0a, d0_out,
seqM, seqxA, seqyA,
rmsd0, L_ali, Liden, TM_ali, rmsd_ali, n_ali, n_ali8,
xlen, ylen, sequence, Lnorm_ass, d0_scale,
i_opt, a_opt, u_opt, d_opt, fast_opt,
mol_vec1[chain_i]+mol_vec2[chain_j],TMcut);
else TMalign_main(
xa, ya, seqx, seqy, secx, secy,
t0, u0, TM1, TM2, TM3, TM4, TM5,
d0_0, TM_0, d0A, d0B, d0u, d0a, d0_out,
seqM, seqxA, seqyA,
rmsd0, L_ali, Liden, TM_ali, rmsd_ali, n_ali, n_ali8,
xlen, ylen, sequence, Lnorm_ass, d0_scale,
i_opt, a_opt, u_opt, d_opt, fast_opt,
mol_vec1[chain_i]+mol_vec2[chain_j],TMcut);
/* print result */
if (outfmt_opt==0) print_version();
output_results(
xname.substr(dir1_opt.size()+dir_opt.size()),
yname.substr(dir2_opt.size()+dir_opt.size()),
chainID_list1[chain_i].c_str(),
chainID_list2[chain_j].c_str(),
xlen, ylen, t0, u0, TM1, TM2,
TM3, TM4, TM5, rmsd0, d0_out,
seqM.c_str(), seqxA.c_str(), seqyA.c_str(), Liden,
n_ali8, L_ali, TM_ali, rmsd_ali,
TM_0, d0_0, d0A, d0B,
Lnorm_ass, d0_scale, d0a, d0u,
(m_opt?fname_matrix:"").c_str(),
outfmt_opt, ter_opt, 0, split_opt, o_opt,
(o_opt?fname_super:"").c_str(),
i_opt, a_opt, u_opt, d_opt,mirror_opt,
resi_vec1, resi_vec2 );
/* Done! Free memory */
seqM.clear();
seqxA.clear();
seqyA.clear();
DeleteArray(&ya, ylen);
delete [] seqy;
delete [] secy;
resi_vec2.clear();
} // chain_j
if (chain2_list.size()>1)
{
yname.clear();
for (chain_j=0;chain_j<ychainnum;chain_j++)
PDB_lines2[chain_j].clear();
PDB_lines2.clear();
chainID_list2.clear();
mol_vec2.clear();
}
} // j
PDB_lines1[chain_i].clear();
DeleteArray(&xa, xlen);
delete [] seqx;
delete [] secx;
resi_vec1.clear();
} // chain_i
xname.clear();
PDB_lines1.clear();
chainID_list1.clear();
mol_vec1.clear();
} // i
if (chain2_list.size()==1)
{
yname.clear();
for (chain_j=0;chain_j<ychainnum;chain_j++)
PDB_lines2[chain_j].clear();
PDB_lines2.clear();
resi_vec2.clear();
chainID_list2.clear();
mol_vec2.clear();
}
chain1_list.clear();
chain2_list.clear();
sequence.clear();
t2 = clock();
float diff = ((float)t2 - (float)t1)/CLOCKS_PER_SEC;
printf("#Total CPU time is %5.2f seconds\n", diff);
return 0;
}