NMR Structure Refinement

1
A Knowledge-Based, Structural Bio-informatics
Approach to NMR Structure Refinement
Zhijun Wu Department of Mathematics Program on
Bioinformatics and Computational Biology Iowa
State University Ames, Iowa, USA
2
Fundamental Problem in NMR Structure Determination
Given a set of distance constraints obtained from
NMR, find the coordinates of the atoms (and hence
the structure of the protein) satisfying the
distance constraints.
3
Distance Geometry Problem
Given n atoms a1, , an and a set of distances
di,j between ai and aj
Blumenthal 1953, Torgerson 1958, Crippen and
Havel 1988
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Solutions to Various Distance Geometry Problems
problems with all distances solvable in O(n3)
using SVD
problems with all distances solvable in O(n)
using GBU
problems with sparse sets of distances NP-compl
ete (Saxe 1979)
Crippen and Havel 1988
Dong and Wu 2002
problems with distance ranges (NMR
data) NP-complete (More and Wu 1997), if the
ranges are small
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Remarks

• If the distance data is adequate and accurate,
  the problem can be solved efficiently otherwise,
  the solution may either be indefinite or
  intractable.

• If the distance ranges are all that can be
  specified, the solution will not be unique, if
  not intractable.

• The distance constraints obtained from NMR cover
  only a subset of all inter-atomic distances, and
  are given in distance ranges.

• The structures determined by NMR are not as
  detailed and accurate as those by X-ray
  crystallography.

• The structures determined by NMR are not as
  fixed as those by X-ray crystallography.

• An ensemble of structures can be determined for
  a protein based on the NMR distance data --
  structural flexibilities or modeling errors?

6
Ensemble of Structures
Representative Structure
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Issues in NMR Structure Refinement

• Inadequate Distance Constraints
• Calculation of Structures
• Interpretation of Structural Variations

8
Deriving Additional Conformational Constraints
Dipolar Coupling (Tjandra and Bax 1997, Clore and
Gronenborn 1998) Dihedral Angles in Structural
Databases (Kuszewski, Gronenborn, and Clore
1996) Distances in Structural Databases (Wall,
Subramaniam, and Phillips, Jr. 1999)
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Inter-Atomic Distances in Structural Databases
R H O
R H O R
Ca N C
Ca N C Ca
N C Ca
N C Ca N C
H O R
H O R H O
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Cross-Residue, Inter-Atomic Distances
Distances 1st Atom, 2nd Atom, 1st Residue,
2nd Residue, Separation Example N
C ALA ALA
0 Choices 5 5
20 20
2 Total 20,000 distances Ca,
Cß, C, N, O, 20 residues, separated by 0 or 1
residue
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Distributions of the Distances
PA1, A2, R1, R2, S (D)
A1 N, A2 C, R1 ALA, R2 ALA, S 0
in Databases of Known Protein Structures
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Distributions of the Distances
PA1, A2, R1, R2, S (D) Probability
Distribution of Cross-Residue Inter-Atomic
Distances in Databases of Known Protein
Structures A1 1st Atom, A2 2nd Atom, R1
1st Residue, R2 2nd Residue, S
Separation For any D in Di, Di1, PA1, A2,
R1, R2, S (D) Distances in Di, Di1 /
Total Distances
in Databases of Known Protein Structures
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Database Profiles of Distributions of Distances
2150 X-ray structures with resolution of 2 Å or
higher and sequence similarity of 90 or less
from PDB Data Bank are utilized.
The probability distributions of 20,000
short-range, cross-residue, inter-atomic
distances (S1/0) are profiled in databases.
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Inter-Atomic Distances in NMR Structures
A survey on 462 NMR structures shows that the
cross-residue, inter-atomic distances in the
structures deviate significantly (more than two
standard deviations) from their means evaluated
with their distributions in structural databases.
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Deviations of Distances in NMR-Determined
Structures
Sample atomic pairs (A1 and A2) across some of
the residues (R1 and R2) in NMR structure 2GB1
with distances (D) deviating more than twice
their standard deviations (STD) from their
average distributions (Mean) in known protein
structures.
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NMR Structure Refinement with Database Derived
Distance Constraints
Mean 2STD are used as lower and upper bounds
for distances (among Ca, Cß, C, N, O with S1/0).
A set of structures, 1EPH, 1GB1, 1IGL, 2IGG,
2SOB, 1CEY, 1CRP, 1E8L, 1ITL, 1PFL, are tested
(experimental data from BioMagResBank are
utilized).
The dynamic simulated annealing protocol in CNS
is used for the refinement.
17
Incorrectly Formed Cross-Residue Inter-Atomic
Distances
Numbers of incorrectly formed cross-residue,
inter-atomic distances versus numbers of affected
residue pairs for structures refined with and
without database distance constraints (DDD).
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Acceptance Rates of the Refined NMR Structures
The acceptance rates for two ensembles of NMR
structures, 1E8L on the left and 1IGL on the
right, refined with (green line) and without
(blue line) using database distance constraints.
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RMSD Values of the Ensembles of Refined NMR
Structures
The means and standard deviations of the RMSD
values of the structure ensembles refined with
and without database distance constraints.
20
Refined NMR Structures Compared with Their X-ray
Structures
The means and standard deviations of the RMSD
values for the ensembles of NMR structures
compared with their X-ray structures.
21
2IGG Immunoglobulin G binding domain of protein
G, a cell-surface protein from pathogenic
bacteria Streptococcus strain G148
2IGG
Number of residues 64 Number of atoms 973
Number of NOE distance constraints 445, Number
of angle constraints 31? and 9?1
1FCC
Lian, Derrick, Sutcliffe, Yang, and Roberts, 1992
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NMR and X-ray Crystal Structures of 2IGG
The NMR structures are refined with (green line)
and without (red line) using additional database
distance constraints. They are compared against
the structure determined by X-ray crystallography
(blue line).
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Residue-Residue Comparisons between Refined NMR
and X-ray Structures
The residue RMSD values for an accepted structure
(left) and an averaged and energy minimized
structure (right) of 2IGG refined with (red line)
and without database distance constraints (blue
line).
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1FO7 - E200K variant of human prion protein,
related to the study of spongiform
encephalopathies.
1FO7
Number of residues107 Number of atoms 1733
Number of NOE distance constraints 516,
J-coupling constraints 44
1FKC
Zhang, Swietnicki, Zagorski, Surewicz,
Sönnichsen 2000
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Tertiary Structure of Prion Protein
http//content.karger.com/ProdukteDB/Katalogteile/
isbn3_8055/_76/_56/prions_01.pdf
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Ramachandran Plot of Unimproved Structure
85 in most favorable regions
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Ramachandran Plot of Improved Structure
90 in most favorable regions
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Superimposed Structures of Loop Regions
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Remarks

• Distance constraints are derived based on the
  distance distributions in databases of known
  protein structures.
• NMR structures can be improved when the
  distances are confined to the most probable
  ranges according to their distributions.
• The constraints can be derived similarly for
  longer-range distances and to include other types
  of atoms as well.
• More efficient distance geometry algorithms can
  be developed for structure calculations.
• The structural fluctuations should be
  distinguished from the structural variations that
  originate from the modeling errors.

30
Acknowledgements

• Feng Cui, Program on Bioinformatics and
  Computational Biology, Iowa State University
• Robert Jernigan, Lawrence Baker Center for
  Bioinformatics and Biological Statistics, Iowa
  State University
• Kriti Mukhopadhyay, Department of Mathematics,
  Iowa State University
• Di Wu, Program on Bioinformatics and
  Computational Biology, Iowa State University
• Wonbin Young, Newlink Genetics, Inc., Iowa Sate
  University Research Park
• F. Cui, R. Jernigan, Z. Wu, J. Bioinformatics and
  Computational Biology (2005), published
• F. Cui, K. Mukhopadhyay, W. Young, R. Jernigan,
  Z. Wu, J. Applied Bioinformatics (2006), under
  review
• D. Wu, F. Cui, R. Jernigan, Z. Wu, Nucleic Acids
  Research (2006), to submit