Protein Planes
Bob Fraser
Protein Folding 882 Project
November, 2006
Overview
• Motivation
• Points to examine
• Preliminary 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.
• More importantly, many predictive
approaches are incremental, and begin by
producing the Cα trace.
Cα trace problem
• Possible solutions:
– De novo, CHARMM fields (Correra 90)
– Fragment matching (Levitt 92)
– Maximize hydrogen bonding (Scherega et al.
93)
• If we know the dimensions corresponding
to the peptide plane, why can’t we just fit
these to the Cα?
Cα trace problem
• Known as idealized covalent geometry
– Used by Engh & Huber (91) for X-ray
crystallography refinement
– Supplemented by including dihedral
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.
The peptide plane
NOTE!
1 plane ~=1 residue
The peptide plane
• We know that these dimensions are very
regular…
but how regular?
Can I depend on these dimensions for
predictions where accuracy is important
and errors may be cumulative?
The idea
• Cα form the connectors at the
corners of each plane.
• Given a regular length of the
plane, we could fit all the
bond lengths and angles to
be ideal.
The task
• Survey the structures in the PDB, and
determine how close the known structures
adhere to these values.
• There is a question regarding what this is
actually measuring, but this is our
standard knowledge base.
– Could think of it as verifying the PDB
structures.
– When we find irregularities, try to find why
What to measure?
•
•
•
•
•
•
Length of plane (Cα – Cα distance)
Bond lengths
Bond angles
Dihedral angles (Φ,Ψ,ω)
Angle between helix axis and plane
Beta axis and plane angle?
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.
Bond lengths
• These values should be considered
relatively fixed.
• Variance in bonds is more likely
attributable to measurement error
• Let’s measure anyhow to see what we find
• Measure for :
N-Cα , Cα-C, C-O, C-N
Bond angles
• These values should be
considered relatively fixed,
as with lengths
• Measure for :
• N-Cα-C
• Cα-C-O
• Cα-C-N
• O-C-N
• C-N-Cα
Aside: Forces equation
Dihedral Angles
• This is where it gets more
interesting!
• For the peptide plane, we
are particularly interested
in omega (ω).
• For planes, expect only
values close to 180° for
trans configuration, and 0°
for cis configuration.
• Let’s check the PDB files
to verify this
Dihedral Angle
• Given: 4 points
• To find: Determine how close the points
are to co-planarity
• Use 3 points to define a plane, the 4th
forms a vector with one of the first 3.
• cis and trans configurations are co-planar,
we’ll see how many others we find.
Omega
• Measure absolute difference from cis/trans
• We’ll call anything within 15° as in those
classes.
O
A = N-C X C-Cα
A
Cα
C
N
ω
Cα
N-C
N-C
B
B = Cα-N X N-C
Phi and Psi
• These angles can
vary widely, as shown
in the Ramachandran
plot.
• It could be interesting
to do this survey
again however if time
permits however…
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
Walther axis calculation
Plane-axis angle
• Now we have a peptide plane and the
helix axis, so we can once again find the
angle between them easily.
• This same method could be applied to
beta strands fairly easily.
• 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,
and a subset of 159 proteins for the
preliminary study.
• Several choices for the parsing method
– My previous code
– BALL
– Matlab’s pdbread() function
Preliminary Results
• Plane Length
• Quite a bit of variance…
• Why?
cis/trans
• The length of the plane is quite different
between the two!
• So, we can treat them as two cases:
cis
trans
Bond lengths
N-Cα
Cα-C
C-O
C-N
Average
1.4553
1.5214
1.2313
1.3278
Std.Dev.
0.0171
0.0184
0.0125
0.0132
Instances 38325
38325
38325
37848
Minimum
1.3453
1.3975
1.1633
1.1683
Maximum 2.7398
3.0729
2.1397
1.8167
Textbook
1.52
1.23
1.33
1.45
Bond angles
N-Cα-C Cα-C-O Cα-C-N O-C-N C-N-Cα
Average
111.31
120.8
116.33
122.79
121.42
Std.Dev.
3.374
1.4482
1.7595
1.437
2.1339
Instances 38325
38325
37848
37848
37848
Minimum
61.127
99.355
98.651
80.913
Maximum 171.09
130.04
140.04
136.46
142.59
Textbook
121
116
123
122
56.87
111
Omega
cis
trans
Other
Average
1.8748
178.17
155.74
Std.Dev.
3.234
1.8835
23.205
Instances
61
37698
89
Notes: - [Other]>[cis]
- all cis have Proline residues, though 1322 Prolines total
The most offensive residue!!!
Effects of deleting this residue
• Averages not affected, only min/max and
standard deviation, ie.:
• Cα-C-O angle: σ 1.44->1.14, min 61.1->94.6
• N-Cα-C angle: min 56.9->83.6
• C-O bond: max 2.14->1.34
• Cα-C bond: max 3.07->2.75
• Plane length: max 5.02->4.43
• It was in the trans class for ω, however.
Preliminary Results
• Data is very consistent in PDB, and
support the theoretical values.
• Using such values should be acceptable.
• Tough to predict cis configuration though!
– Pro is always involved (so far), but other
residue is mixed (19 Leu, 7 Tyr, etc.).
– The difference is in the length of the plane.
Future Work
• Incorporate secondary structure
information for determining axis/plane
angles and phi/psi angles.
• Run analysis on full PDB
• Develop algorithm for using secondary
structure to solve trace problem.
• Test on randomized Cα traces to determine
whether it is effective.
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 alphacarbon 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.