1.1 Assignment 2: performing rotations

"defining the connnectivity of a backbone chain"

Figure 1 provides examples of some aminoacids, from long ones such as arginine to bulky ones such as proline, and to the smallest one,glycine. Note that as we have mentioned, while different in their sidechain atoms, all these aminoacids share a common group of atoms thatincludes N, CA, C, and O. The chain that goes through this shared core is known as the backbone. For the purpose of this module, you will consideras the backbone the chain that goes through N, CA, and C for every aminoacid. Note that there are two backbone dihedrals per aminoacid,with the number of sidechain dihedrals varying depending on the aminoacid. To simplify the rotation by dihedrals, in this assignment you will onlymanipulate protein structures from which the sidechain atoms have been removed. This means that you will only deal with a backbone chain thatgoes through the N, CA, and C of every aminoacid.

You should be familiar with how aminoacids connect to each other through the peptide bond. Figure 2 illustrates the peptide bond formed between theC of an aminoacid and the N of the following aminoacid. Consecutive applications of the peptide bond create the backbone chain.Recall that due to its double covalent nature, the peptide bond is planar (illustrated with the plane in Figure 2), and unrotatable. Therefore, inyour manipulation of the backbone chain, you do not need to consider the peptide bond for rotation. You are left with two dihedral bonds peraminoacid.

Figure 3 shows four consecutive aminoacids in a polypeptide chain. Note the peptide bonds that connect the aminoacids. You need to understand thatrotation of a backbone dihedral will affect the location of all atoms following it due to the accumulation of rotations along the backbone.Therefore, it is necessary for you to define an orientation for the backbone. The easiest orientation is that used for the sequence of a protein, where thebackbone is defined as the chain starting at the N atom of the first aminoacid of the sequence and ending at the C atom of the last aminoacid ofthe sequence. For your convenience, the native conformation supplied to you later in this assignment will list the coordinates of the atoms in the orderN, CA, C for every aminoacid. So, reading in order from this file will give you the orientation of the backbone.

Before you proceed to the next section, make sure that you can answer these questions:

• If we rotate the dihedral bond between the N and CA of the last aminoacid, which atoms' locations will change in 3D space? Answering this question willhelp you answer Q1 .
• Why do we usually say that rotations by dihedrals produce large scale motions? Think of an example of a rotation by dihedral where this is true.Answering this question will help you answer Q3 .