Practical GK-3

Transformations and superposition

Aims

• To reinforce the concepts of three-dimensional transformations and superposition.
• To give practice in using C libraries to construct and apply transformation matrices.
• To revise the format of ATOM records in Protein Data Bank files.

Objectives

After this practical you will:

• be able to write simple C programs that construct and apply transformation matrices.

Introduction

The source code for the transformation library is in file /chalmers/users/kemp/TDA506/src/libtransform.c

Exercises

1. Protein Data Bank entry 1CRN contains coordinates of two tyrosine (TYR) residues. Look at these residues in RasMol.

   1. Modify test_fit.c so that it finds the transformation matrix that fits the N, CA, C and CB atoms of the first of these tyrosine residues onto the corresponding atoms of the other tyrosine residue. What is the value of the RMS error of this fit?

   2. Apply the transformation found in part (a) to all of the atoms in the first tyrosine residue. Write out the transformed coordinates in Protein Data Bank format (see the format of ATOM records in section 9).

      Copy the ATOM records from 1CRN to a new file, and append the ATOM records with transformed coordinates (written by your program) to this file. View the resulting PDB file in RasMol. Have the residues been superposed?

   3. Modify your program so that it superposes the first tyrosine residue onto the second using all atoms to perform the fit. What is the value of the RMS error of this fit?

2. (Only do this exercise if you have nothing else to do! It's very similar to the first exercise, so you won't gain much by modifying the program. However, it is useful to think about this question since it shows how simple fitting can be used to compare functional and non-functional forms of a binding site. Think about how you would transform one serine protease protein so that it is fitted onto another, with their binding sites superposed. Think also how you would read the points to be superposed from a file, rather than giving the coordinates explicitly in your source code!)

   1. Protein Data Bank entry 1TLD is a high resolution structure of bovine beta-trypsin, which is a serine protease (a "protein-cutting machine"). His57, Asp102 and Ser195 are important active site residues in serine protease enzymes. Locate these three residues and draw a sketch showing the distances from the nitrogen atoms in the side chain of His57 to the oxygen atoms in the side chains of the other active site residues.

      To see the side chains of these residues more easily, display the whole structure as a wireframe model, then select the three side chains:

            RasMol> select (57, 102, 195) and sidechain
              

      Select "Ball & Stick" from the Display menu to highlight these side chains.

   2. Protein Data Bank entry 1EZX is a serpin-protease complex. The molecules present are human alpha-1-antitrypsin (a serine protease inhibitor, or serpin) and bovine trypsin (a serine protease). Locate the active site residues of the trypsin molecule (chain C) and draw a sketch showing the distances from the nitrogen atoms in the side chain of His57 to the oxygen atoms in the side chains of the other active site residues.

   3. Modify the program written in question 1 to compare the active sites (residues His57, Asp102 and Ser195) of the serine protease enzymes in Protein Data Bank entries 1TLD and 1EZX.