1. Protein Planes
Bob Fraser
CSCBC 2007

2. Overview
Motivation
Points to examine
Results
Further work

3. Cα trace problem
Given: only approximate positions of the Cα atoms of a protein
Aim: Construct the entire backbone of the protein
This is an open problem!

4. Cα trace problem Why do it? Some PDB files contain only Cα atoms.
Refinement of X-ray or NMR skeletons.
More importantly, many predictive approaches are incremental, and begin by producing the Cα trace.

5. Cα trace problem Possible solutions: Idealized covalent geometry
De novo, CHARMM fields (Correa 90)
Fragment matching (Levitt 92)
Maximize hydrogen bonding (Scheraga et al. 93)
Idealized covalent geometry
Used by Engh & Huber (91) for X-ray crystallography refinement
Supplemented by including additional information (Payne 93, Blundell 03)
All methods achieve <1Å rmsd, ~0.5Å rmsd is good.
Perhaps including more information about the plane could further improve results.

6. Idealized covalent geometry

7. The task
Survey the structures in the PDB, and determine how close the known structures adhere to these values.
Next look at the relationship between the planes and secondary structures
Is this information useful?
If so, could it be used in refinement?

8. Length of plane (Cα – Cα distance)
The so-called bond distance when given a Cα trace.
If all bond angles and lengths are fixed, this distance should also be constant.
Let’s check this distance in the PDB, and determine the average, standard deviation, maximum and minimum values found.

9. cis vs. trans

10. Secondary Structure

11. Angle between helix axis and plane
It is assumed that the planar regions for amino acids in a helix are parallel to the axis of the helix.
Let’s put this to the test!
How do we measure the axis of helix?
It is a subjective measure
We’ll use the method of Walther et al. (96), it provides a local helix axis

12. Plane-axis angle
Now we have a peptide plane and the helix axis, so we can find the angle between them easily.
This same method could be applied to beta strands and 3-10 helices.
We should expect that some pattern should arise since beta strands are have regular patterns, particularly when in beta sheets.

13. Data Analysis Use the entire PDB database as a source
Compare the results obtained to the expected values for the plane lengths and alpha helices
Determine whether a preferential orientation exists for beta strands and 3-10 helices

14. Plane length
trans and cis cases need to be distinguished because they are different inherently
Plane length is composed of 5 elements of idealized covalent geometry

15. α-helix

16. 3-10 Helix

17. β-strand

18. Results

19. Future Work
Develop algorithm for using secondary structure to solve trace problem.
Test it on proteins with perfect Cα traces to verify the accuracy of reconstruction.
Test on randomized Cα traces.
Integrate this information with refinement

20. Thanks! Selected References
M.A. DePristo, P.I.W. de Bakker, R.P. Shetty, and T.L. Blundell. Discrete restraint-based protein modeling and the C -trace problem. Protein Science, 12: , 2003.
A. Liwo, M.R. Pincus, R.J. Wawak, S. Rackovsky, and H.A. Scheraga. Calculation of protein backbone geometry from alpha-carbon coordinates based on peptide-group dipole alignment. Protein Sci., 2(10): , 1993.
G.A. Petsko and D. Ringe. Protein Structure and Function. New Science Press Ltd, London, 2004.
D. Walther, F. Eisenhaber, and P. Argos. Principles of helix-helix packing in proteins: the helical lattice superimposition model. J.Mol.Biol., 255: , 1996.

21. Walther axis calculation