Protein Planes

Bob Fraser

CSCBC 2007

Overview

• Motivation

• Points to examine

• Results

• Further work

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!

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.

Cα trace problem

• Possible solutions:– 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.

Idealized covalent geometry

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?

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.

cis vs. trans

Secondary Structure

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

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.

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

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

α-helix

3-10 Helix

β-strand

Results

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

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, 12:2032-2046, 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):1697-1714, 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: 536-553, 1996.

Walther axis calculation