Define a class Atom that supports the following methods:
An initializing method __init__ to which two arguments must be given: the symbolic name of the atom (a string consisting of an uppercase letter, followed by zero or more lowercase letters) and the position of the atom (represented by a tuple $$(x, y, z)$$ that represents a point in a three-dimensional area, where $$x, y, z \in \mathbb{R}$$). The initializing method must appoint these arguments to respectively the attributes element and position of the newly made object.
A method mas without arguments that prints the atomic
mass of the atom. For the implementation of this method, make optimal
use of a predefined dictionary with the symbolic names of all elements
from the periodical system as a key, and the atomic masses as the
corresponding values.
(click
here to watch the predefined dictionary)
A method __repr__ without arguments that prints a string representation of the atom. The method __repr__ prints a syntactically correct Python expression, that — when it were to be evaluated — makes an object that is equal to the object that was originally given to __repr__. All real numbers must be given with two digits after the comma.
A method __str__ without any arguments that prints a string representation of the atom. Read the example below to determine what this string representation should look like. All real numbers must be given with three digits after the comma.
Moreover, define a class Molecule that supports the following methods:
An initializing method __init__ to which a name (string) for the molecule can be given optionally. Use the empty string as standard value for the name of the molecule. The initializing method must make sure that all object of the class molecule have two attributes: i) name, a string that contains the name of the molecule, and ii) atoms, a list of all atoms of the molecule. Initially the attribute atoms indicates an empty list.
A method addAtom that adds a given object from the class Atom (that is given to the method as an argument) to the bottom of the list of atoms.
A method readPDB that can read the positions of the
atoms of a molecule from a text file in PDB format. To the method readPDB
the location of the file is given as a string argument. For every ATOM-line
from the file, the method must add an Atom object to the
bottom of the list of atoms from the Molecule object,
with an element name and a position as it is written on that line.
The Protein Data Bank (PDB) file format describes the
three-dimensional structures of molecules like they are saved in the
international PDB data bank. A typical PDB file can consist of
hundreds of thousands of lines, ass illustrated in the example below
(shortened version of a file that describes the structure of a
synthetic collagen-like peptide).
HEADER EXTRACELLULAR MATRIX 22-JAN-98 1A3I
TITLE X-RAY CRYSTALLOGRAPHIC DETERMINATION OF A COLLAGEN-LIKE
TITLE 2 PEPTIDE WITH THE REPEATING SEQUENCE (PRO-PRO-GLY)
...
EXPDTA X-RAY DIFFRACTION
AUTHOR R.Z.KRAMER,L.VITAGLIANO,J.BELLA,R.BERISIO,L.MAZZARELLA,
AUTHOR 2 B.BRODSKY,A.ZAGARI,H.M.BERMAN
...
REMARK 350 BIOMOLECULE: 1
REMARK 350 APPLY THE FOLLOWING TO CHAINS: A, B, C
REMARK 350 BIOMT1 1 1.000000 0.000000 0.000000 0.00000
REMARK 350 BIOMT2 1 0.000000 1.000000 0.000000 0.00000
...
SEQRES 1 A 9 PRO PRO GLY PRO PRO GLY PRO PRO GLY
SEQRES 1 B 6 PRO PRO GLY PRO PRO GLY
SEQRES 1 C 6 PRO PRO GLY PRO PRO GLY
...
ATOM 1 N PRO A 1 8.316 21.206 21.530 1.00 17.44 N
ATOM 2 CA PRO A 1 7.608 20.729 20.336 1.00 17.44 C
ATOM 3 C PRO A 1 8.487 20.707 19.092 1.00 17.44 C
ATOM 4 O PRO A 1 9.466 21.457 19.005 1.00 17.44 O
ATOM 5 CB PRO A 1 6.460 21.723 20.211 1.00 22.26 C
...A method mass without any arguments that prints the total mass of the molecule as a result. This is the sum of the masses of the individual atoms from which the molecule is built.
A method masscentre without any arguments that prints
the co-ordinates of the mass centre of the molecule as a tuple
$$(x,y,z)$$. The mass centre $$(x,y,z)$$ of a molecule that consists
of $$n$$ atoms with mass $$m_i$$ ($$1 \leq i \leq n$$) and position
$$(x_i, y_i, z_i)$$ is defined by
\[ \, x = \dfrac{\displaystyle\sum_{i=1}^n
m_i\,x_i}{\displaystyle\sum_{i=1}^n m_i} \qquad \, y =
\dfrac{\displaystyle\sum_{i=1}^n m_i\,y_i}{\displaystyle\sum_{i=1}^n
m_i} \qquad \, z = \dfrac{\displaystyle\sum_{i=1}^n
m_i\,z_i}{\displaystyle\sum_{i=1}^n m_i} \]
>>> oxygen = Atom('O', (4.013, 0.831, -9.083))
>>> oxygen.element
'O'
>>> oxygen.position
(4.013, 0.831, -9.083)
>>> oxygen.mass()
15.9994
>>> print(oxygen)
O-atom with mass 15.999 on position (4.013, 0.831, -9.083)
>>> oxygen
Atom('O', (4.01, 0.83, -9.08))
>>> molecule = Molecule(name='water')
>>> molecule.readPDB('water.pdb')
>>> molecule.atoms
[Atom('O', (4.01, 0.83, -9.08)), Atom('H', (4.94, 0.84, -8.84)), Atom('H', (3.75, -0.07, -9.29))]
>>> molecule.mass()
18.01528
>>> molecule.masscentre()
(4.0502061994040615, 0.7814290335759422, -9.080985829806696)The interactive Python session above uses the PDB file water.pdb1 that describes the positions of the atoms of a water molecule. Below we give the ATOM-lines of that file, preceded by two lines that clarify on which positions the co-ordinates of the atoms are given.
1 2 3 4 5 6 7 8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
ATOM 1 OH OSP3 1 4.013 0.831 -9.083 1.00 0.00 O
ATOM 2 1HH OSP3 1 4.941 0.844 -8.837 1.00 0.00 H
ATOM 3 2HH OSP3 1 3.750 -0.068 -9.293 1.00 0.00 H