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Q2: Protein Center of Mass Calculation - 35 pts The Protein Data Bank archive serves as a single repository of information about the 3D structures of proteins, nucleic acids and complex assemblies. Each PDB file contains various kinds of information. The type of information is indicated in the first six characters of each line, such as HEADER, SOURCE, COMPND, AUTHOR, REMARKS, etc. For this homework, you just need to concentrate on lines beginning with the word "ATOM". An example is given below, where the columns represent the atom record atom number, atom identifier, amino acid type, chain identifier, residue sequence number, x-coordinate (in A), y-coordinate (in A), z coordinate (in A), occupancy, B-factor and element symbol respectively. The symbol A denotes Angstrom (1A= 10m) HEADER CHROMOSOMAL PROTEIN 02-JAN-87 TUBO TITLE STRUCTURE OF UBIQUITIN REFINED AT 1.8 ANGSTROMS RESOLUTION COMPND MOL ID: 1; COMPND 2 MOLECULE: UBIQUITIN; COMPNO 3 CHAIN: A; COMPND 4 ENGINEERED: YES SOURCE MOL ID: 1; SOURCE 2 ORGANISM SCIENTIFIC: HOMO SAPIENS, SOURCE 3 ORGANISM COMMON: HUMAN; SOURCE 4 ORGANISM TAXID: 9606 KEYWIDS CHROMOSOMAL PROTEIN EXPDTA X-RAY DIFFRACTION AUTHOR S.VIJAY KUMAR, C.E.BUGG,W.J.COOK REVDAT 5 09-MAR-11 1UBQ REMARK REVDAT 24-FEB-29 IUBQ REVDAT OLAPR.03 BURO JRML 1 4 3 VERSN ORIGX3 SCALEI SCALEZ SCALE3 ATOM ATOM ATOM ATOM ATOM ATOM ATOM ATON ATOM ATOM ATOM ATOM ATOM ATOM ATOM ATOM ATOM ATOM 0.000000 0.000000 1.680000 0.019670 0.000000 0.000000 0.000000 0.023381 0.000000 0.000000 0.000000 0.034542 1 N MET A 1 27.340 24.438 2 1 26.266 25.413 3 C MET A 1 26.913 26.639 40 MET A 1 27.886 26.463 5 CB MET A 1 25.112 24.888 6 CG MET A 1 25.353 24.860 7 SD MET A 1 23.930 23.959 8 CE MET A 24.44723.984 9 N GLNA 2 26.335 27.770 10 CA GLNA 2 26.850 29.021 11 C GLNA 2 26.100 29.253 12 0 GLNA 2 24.865 29.024 13 CB GLNA 2 26.733 30.148 14 CG GUNA 2 26.882 31.546 15 CD GLNA 2 26.786 32.562 16 OE1 GUNA 27.783 33.160 17 NE GLNA 25,562 32.733 18 N ILE A 3 26.849 29.656 19 CA ILEA 26.235 30.058 X Y 0.00080 0.00000 0.00000 0.00000 2.614 1.00 9.67 2.842 1.00 10.38 3.531 1.00 9.62 4.263 1.00 9.62 3.649 1.00 13.77 5.134 1.00 16.29 5.964 1.00 17.17 7.620 1.00 16.11 3.258 1.00 9.27 3.898 1.80 9.07 5.202 1.00 8.72 5.338 1.00 8.22 2.985 1.00 14.46 3.409 1.00 17.01 2.270 1.00 20.10 1.870 1.00 21.89 1.866 1.00 19.49 6.217 1.60 5.87 7.497 1.005.07 0 z ELEMENT Implement the following functions: A. pdb_parser(pdb_filename): Receives one argument, pdb_filename. Opens the PDB file, reads all lines starting with ATOM and stores the X, Y, Z coordinates and the ELEMENT type of the atom in a list, atoms e.g. atoms=([27.340, 24.430, 2.614, 'N'],[26.266, 25.413, 2.842, 'C'),...) atoms list is of length N, number of atoms that make up the protein in the PDB file. The function should retum atoms B. center_of_mass(atoms): This function calculates the center of mass of the protein, as follows. Nimiri 1 Tom is coordinates of the center of mass of the protein, r, is a list containing the IX. y. 2] coordinates of the i. atom), is the mass of the latom and N is the total number of atoms. m, should be obtained from the dictionary mass={"C":12.01, 'O': 16.00, "HT:1.008, ..} by using the element type of the i, atom as key, mass dictionary is already provided in the pdb.py template. C. shift(atoms, vec): This function translates the protein by vec and returns the updated coordinates of the protein, atomsnew. vec is a list of size 3. Eg. vec=[a, b, c), atoms-[[x, y, z, 'C]]-> atomsnew=[[x+a, y+b, z+c, C']] After implementing these functions, demonstrate them as follows: 1) Read the lubq.pdb file and parse the information ii) Calculate the center of mass. MI) Shift the coordinates of the protein such that the molecule's center of mass is at the origin The sample output from the program should be: Center of mass of the protein is 30.317, 28.775, 15.353 New center of mass of the protein is 0.000, 0.000, 0.000