Transcript Automated High-Resolution Protein Structure Determination using

Automated High-Resolution Protein
Structure Determination using
Residual Dipolar Couplings
Anna Yershova
Department of Computer Science
Duke University
February 5, 2010
1
Feb 5 2010, NC State University
Automated Protein Structure Determination using RDCs
Introduction Motivation
Protein Structure Determination is
Important
Amino acid sequences
Structures
Functions
Protein
redesign
 High-resolution structures are needed for:
 Determining protein functions
 Protein redesign
2
Introduction Motivation
What is Protein Structure: Primary
Structure
The sequence of amino acids forms the backbone.
Residues are sidechains attached to the backbone.
1
3
2
Side chain
3
Amino acid
4
Dihedral angle
Introduction Motivation
What is Protein Structure: Secondary
Structure Elements
Local folding is maintained by short distance interactions.
4
Introduction Motivation
What is Protein Structure: 3D Fold
Global 3D folding is maintained by more distant interactions.
Alpha-helix
Side chain
Beta-strands
5
Loop
Introduction Motivation
High-Throughput Structure
Determination
Is Important
The gap between
sequences and structures
6
http://www.metabolomics.ca/News/lectures/CPI2008-short.pdf
Introduction Motivation
Current Approaches for Structure
Determination
X-ray crystallography
 Difficulty: growing good quality crystals
Nuclear Magnetic Resonance (NMR) spectroscopy
 Difficulty: lengthy (expensive) time in processing and
analyzing experimental data
Both require expressing and purifying proteins.
7
Introduction Motivation
Bruce Donald’s Lab
Michael Zeng
Chittu Tripathy
Lincong Wang
Pei Zhou
Bruce Donald
Cheng-Yu Chen
John MacMaster
8
Introduction Motivation
Types of NMR Spectroscopy Data
R
133.1
4.2
Ha
NOE
172.1
8.9
B0
 Chemical shift (CS)
 Unique resonance frequency, serves as an ID
 Nuclear Overhauser effect (NOE)
 Local distance restraint between two protons
 Residual dipolar coupling (RDC)
9
 Global orientational restraint for bond vectors
Introduction Motivation
Resonance Assignment Problem
Assigning
chemical shifts
to each atom
10
http://www.pnas.org/content/102/52/18890/suppl/DC1
Bailey-Kellogg et al., 2000, 2004
Introduction Motivation
NOE Assignment Problem
Obtain local distance
restraints between protons
A famous
bottleneck
11
Bailey-Kellogg et al., 2000, 2004
Introduction Motivation
Structure Determination from NOEs
NOESY spectrum
Resonance assignments
NOE
assignment
Distance
Geometry
NP-Hard
[Saxe ’79; Hendrickson ’92, ’95]
12
Assignment Ambiguity
...
a1 a2 a 3
an
...
...
...
4 3
a1
a2 4
?
a3 3 ?
. . . .
. . . .
. . . .
an
.
.
.
Introduction Motivation
Traditional Structure Determination Protocol
Resonance assignments
NOESY spectra
SA/MD
Initial fold
NOE Assignments
XPLOR-NIH
RDCs
13
Structure
Refinement
NOE Assignments
3D Structures
A famous
bottleneck
Introduction Motivation
Traditional Structure Determination Protocol
Resonance assignments
NOESY spectra
error propagation
local minima
manual intervention
for initial fold and
for evaluation of
NOE assignments
SA/MD
Initial fold
A famous
NOE Assignments bottleneck
XPLOR-NIH
RDCs
14
Structure
Refinement
NOE Assignments
3D Structures
Can we have a polytime algorithm
using orientational
restraints?
Yes: Wang and
Donald, 2004; Wang
et al, 2006
Introduction Motivation
Types of NMR Spectroscopy Data
R
133.1
4.2
Ha
NOE
172.1
8.9
B0
 Chemical shift (CS)
 Unique resonance frequency, serves as an ID
 Nuclear Overhauser effect (NOE)
 Local distance restraint between two protons
 Residual dipolar coupling (RDC)
15
 Global orientational restraint for bond vectors
Background RDCs
RDC Equation for a Single Bond
Alignment medium
B0

b
v
a
0 a b 3 cos2   1
D
4 2 ra3,b
2
Szz
D
16
Sxx
v
Syy
S – Saupe Matrix
S is traceless and symmetric
S contains 5 dofs
Introduction Motivation
Traditional Structure Determination VS RDC-Panda
Resonance assignments
NOESY spectra
error propagation
local minima
manual intervention
for initial fold and
for evaluation of
NOE assignments
SA/MD
Initial fold
17
RDCs
Constaint number
of NOEs
RDC-ANALYTIC
PACKER
Global Fold
NOE Assignments
Sidechain Placement
XPLOR-NIH
RDCs
RDC-PANDA Protocol
NOE Assignments
Structure
Refinement
XPLOR-NIH
NOE Assignments
3D Structures
NOE Assignments
3D Structures
Zeng et al. (Jour. Biomolecular NMR,2009)
Introduction Motivation
Importance of Backbone Structure
Determination
Global orientational restraints from RDCs
Sparce data
(highthroughput,
large proteins,
membraine
proteins)
Compute initial fold
using exact solutions to RDC equations
Resolve NOE
assignment ambiguity
18
Avoid the NP-Hard
problem of structure
determination from
NOEs
Automated side-chain
resonance assignment
Introduction Motivation
Current Limitations of RDC-Panda
Because it requires only 2 RDCs per residue:
 Only SSE elements can be reliably determined,
NOEs are needed to determine structure of loops
 Difficulty in handling missing data
19
Introduction Motivation
My Current Project
 Improve current protein structure determination
techniques from our lab
 Design new algorithms for protein backbone
structure determination using orientational
restraints from RDCs
20
Introduction Motivation
Literature Overview

Distance geometry based structure determination
 Braun, 1987
 Crippen and Havel, 1988
 More and Wu, 1999

Heuristic based automated NOE
assignment
– Mumenthaler et al., 1997
– Nilges et al., 1997, 2003
– Herrmann et al., 2002
– Schwieters et al., 2003
– Kuszewski et al., 2004
– Huang et al., 2006
•
Automated NOE assignment starting with
initial fold computed from RDCs
Heuristic based structure determination





•
Brünger, 1992
Nilges et al., 1997
Güntert, 2003
Rieping et al., 2005
RDC-based structure determination











21
Tolman et al., 1995
Tjandra and Bax, 1997
Hus et al., 2001
Tian et al., 2001
Prestegard et al., 2004
Wang and Donald (CSB 2004)
Wang and Donald (Jour. Biomolecular NMR,
2004)
Wang, Mettu and Donald (JCB 2005)
Donald and Martin (Progress in NMR
Spectroscopy, 2009 )
Ruan et al., 2008
Zeng et al. (Jour. Biomolecular NMR,2009)
– Wang and Donald (CSB 2005)
– Zeng et al. (CSB 2008)
– Zeng et al. (Jour. Biomolecular NMR,2009)
•
Automated side-chain resonance
assignment
–
–
–
–
Li and Sanctuary, 1996, 1997
Marin et al., 2004
Masse et al., 2006
Zeng et al. (In submission, 2009)
Background RDCs
RDC Equation for a Single Bond
Linear in S,
A fixed v defines a hyperplane
Quadratic in v,
A fixed S defines a hyperboloid
Szz
S
22
D
Sxx
v
Syy
Background RDCs
RDC Equation for a Single Bond
1 RDC equation defines a collection of
hyperplanes, 7 variables
Linear in S,
A fixed v defines a hyperplane
S
23
Quadratic in v,
A fixed S defines a hyperboloid
Background RDCs
RDC Equations for a Protein Portion
1
24
2
3
4
Background RDCs
RDC Equations for a Protein Portion
1
v
2
3
4
u
1
1
v
2
Too few equations,
too many
variables!
25
[1] L. Wang and B. R. Donald. J.
Biomol. NMR, 29(3):223–242,
2004.
[2] J. Zeng, J. Boyles, C. Tripathy,
L. Wang, A. Yan, P. Zhou, and B.
R. Donald J. Biomol. NMR, [Epub
ahead of print] PMID:19711185,
2009.
Background RDCs
Forward Kinematics Reduces the Number of
Variables
v
Fix coordinate
system.
1
u
1
26
v
2
Background RDCs
RDC Equations for a Protein Portion
v
1
u
1
27
v
2
Background RDCs
RDC Equations for a Protein Portion
Recursive
representation
is possible!
28
Background RDCs
One Equation Per Dihedral Angle is Not
Enough!
Each equation is linear in S, and quartic in either tan() or tan()
To be able to solve this system there must be additional information:
Possible scenarios:
29
1.
2.
3.
4.
5.
Additional RDC measurement(s) for each dihedral angle.
Additional alignment media.
Additional NOE data.
Modeling (Ramachandran regions, steric clashes, energy function)
Sampling (for alignment tensors)
Background RDC-Panda
The RDC-PANDA Structure Determination
Package
Current requirements
•
•
2 RDCs per residue to obtain SSE structures
Sparse NOEs to pack the SSEs
Current bottlenecks
•
•
•
•
30
Missing data (even in long SSEs)
Long loops
Sampling for computing alignment tensor(s)
Sampling for the orientation of the first pp
[1] L. Wang and B. R.
Donald. J. Biomol.
NMR, 29(3):223–242,
2004.
[2] J. Zeng, J. Boyles,
C. Tripathy, L. Wang,
A. Yan, P. Zhou, and B.
R. Donald J. Biomol.
NMR, [Epub ahead of
print]
PMID:19711185, 2009.
Background RDC-Panda
When Saupe Matrix is Known Solution
Can Be Found Exactly!
Ellipse equations for CH bond vector
Wang & Donald, 2004;
Donald & Martin, 2009.
Background RDC-Panda
Solution Structure Deposited Using RDCPanda
Solution Structure of FF Domain 2 of human transcription
elongation factor CA150 (FF2) using RDC-PANDA
PDB ID: 2KIQ
In collaboration with
Dr. Zhou’s Lab
32
Current Project
Problem Formulation: NH, CH RDCs in 2
Media
33
We require measurements for at least 9 consecutive bond
vectors (4.5 residues) in 2 media. The goal is to handle
more equations and errors.
Current Project
Relationship to Minimization
34
Current Project
Relationship to Minimization and SVD
b
A
s
Solving an over constrained system of linear
equations is equivalent to finding a projection of the
b vector on the A hyperplane. This is also equivalent
to minimizing the least square function of the
terms.
35
Current Project
Relationship to Minimization
36
Current Project
Relationship to Minimization and SVD
b
A(i i)
s
Solving such a system of non-linear equations is not
trivial!
There are multiple local minima in the corresponding
minimization problem.
37
Current Project
Advantages
If the minimization problem is solved then
• Computation of packed SSEs and loops is possible
without additional NOE data.
• Saupe matrices for each of the alignment medium can be
computed without sampling.
• Robust handling of missing values
38
Current Project
The Algorithm: Initialization Using Helix
Initialize (i,i) for a helix
Compute initial approximation for Si using SVD
Compute (i,i) using tree search and minimization
Update Si using SVD
39
Current Project
The Algorithm: Protein Portion
Initialize Si to computed approximations
Compute (i,i) using tree search and minimization
Update Si using SVD
40
Current Project
The Algorithm: Computing Dihedrals
1
Minimize each of the
RMSD terms as a
univariate function.
ψ1
x
x
n
x
ψn
41
Compute the
list of best
solutions.
x
Iteratively
minimize the
RMSD function
Current Project
Advantages
• The algorithm is converging, since every step minimizes
RMSD function
• If the data was “perfect” then the solution to the
minimization problem would be the roots of the
polynomials in the RMSD terms, and the algorithm
would find ALL of them.
• The minima of the RMSD terms give a good collection of
initial structures for finding local and global minima
• Robust handling of missing values
42
Preliminary Results
Preliminary Results: Ubiquitin Helix
60
CH RDCs
NH RDCs
experimental RDCs
40
20
0
-60
0
-20
-40
20
40
60
-20
-40
43
Conformation of the portion [25-31]
of the helix for human ubiquitin
computed using NH and CH RDCs in
two
media
(red)
has
been
superimposed on the same portion
from high-resolution X-ray structure
(PDB Id: 1UBQ) (green). The
backbone RMSD is 0.58 Å.
-60
back-computed RDCs
Protein
RMSD (Hz)
Alignment Tensor (Syy, Szz)
Ubq :25-31
CH : 0.32
(23.66, 16.48)
NH: 0.24
(53.25, 7.65)
Preliminary Results
Preliminary Results: Ubiquitin Strand
40
NH RDCs
CH RDCs
experimental RDCs
20
0
-60
-40
-20
0
20
-20
-40
-60
back-computed RDCs
44
Conformation of the portion [2-7] of
the beta-strand for human ubiquitin
computed using NH and CH RDCs in
two media has been superimposed on
the same portion from high-resolution
X-ray structure (PDB Id: 1UBQ). The
backbone RMSD is 1.151 Å.
Protein
RMSD
(Hz)
Alignment Tensor (Syy, Szz)
Ubq: beta 2-7
CH :
(53.32, 4.83)
NH:
(48.03, 14.32)
40
Conclusions
•
Complete and exhaustive search over the space of all structures
minimizing the RDC fit function seems feasible due to
understanding the structure of the solution.
•
Possible and exiting extensions to more/different data
Funding: NIH
Thank you!
45
Comparison
Accuracy:
Sparse
Data requirements vs. Accuracy (Ubiquitin):
46