computing protein structures from electron density maps: the missing fragment problem
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Computing Protein Structures from Electron Density Maps: The Missing Fragment Problem
Itay Lotan†
Henry van den Bedem* Ashley M. Deacon*Jean-Claude Latombe†
† Computer Science Dept., Stanford University* Joint Center for Structural Genomics (JCSG) at SSRL
Structure determination
Bernhard Rupp
X-ray crystallography
Protein Structure Initiative 152K sequenced genes
(30K/year)25K determined structures
(3.6K/year)
Reduce cost and time to determine protein structure
Develop software to automatically interpret the electron density map (EDM)
EDM3-D “image” of atomic structure
High value (electron density) at atom centers
Density falls off exponentially away from center
Limited resolution, sampled on 3D grid
Automated model building ~90% built at high resolution (2Å) ~66% built at medium to low
resolution (2.5 – 2.8Å) Gaps left at noisy areas in EDM
(blurred density)
Gaps need to be resolved manually
The Fragment completion problem Input
EDM Partially resolved structure 2 Anchor residues Length of missing fragment
Output A small number of candidate structures
for missing fragmentA robotics inverse kinematics (IK) problem
Related workComputer Science Exact IK solvers
Manocha & Canny ’94 Manocha et al. ’95
Optimization IK solvers Wang & Chen ’91
Redundant manipulators Khatib ’87 Burdick ’89
Motion planning for closed loops Han & Amato ’00 Yakey et al. ’01 Cortes et al. ’02, ’04
Biology/Crystallography Exact IK solvers
Wedemeyer & Scheraga ’99 Coutsias et al. ’04
Optimization IK solvers Fine et al. ’86 Canutescu & Dunbrack Jr. ’03
Ab-initio loop closure Fiser et al. ’00 Kolodny et al. ’03
Database search loop closure Jones & Thirup ’86 Van Vlijman & Karplus ’97
Semi-automatic tools Jones & Kjeldgaard ’97 Oldfield ’01
Contributions Sampling of gap-closing fragments
biased by the EDM Refinement of fit to density without
breaking closure Fully automatic fragment completion
software for X-ray Crystallography
Novel application of a combination of inverse kinematics techniques
Torsion angle model
NN
NN
C’C’
C’C’
O
O O
O
C
C
C
C
C
C C
C
Resi Resi+1 Resi+2 Resi+3
Protein backbone is a kinematic chain
Two-stage IK method
1. Candidate generations: Optimize density fit while closing the gap
2. Refinement: Optimize closed fragments without breaking closure
Stage 1: candidate generation Generate random conformation Close using Cyclic Coordinate Descent
(CCD) (Wang & Chen ’91, Canutescu & Dunbrack Jr. ’03)
Stage 1: candidate generation Generate random conformation Close using Cyclic Coordinate Descent
(CCD) (Wang & Chen ’91, Canutescu & Dunbrack ’03)
Stage 1: candidate generation Generate random conformation Close using Cyclic Coordinate Descent
(CCD) (Wang & Chen ’91, Canutescu & Dunbrack ’03)
Stage 1: candidate generation Generate random conformation Close using Cyclic Coordinate Descent
(CCD) (Wang & Chen ’91, Canutescu & Dunbrack ’03)
Stage 1: candidate generation Generate random conformation Close using Cyclic Coordinate Descent
(CCD) (Wang & Chen ’91, Canutescu & Dunbrack ’03)
CCD moves biased toward high-density
Stage 2: refinement
1-D manifold
Target function T (goodness of fit to EDM) Minimize T while retaining closure Closed conformations lie on Self-motion
manifold of lower dimension
Stage 2: null-space minimizationJacobian: linear relation between joint velocities and end-effector linear and angular velocity .
(6 matrix)x J q q n
Compute minimizing move using:
† T T qq J q x N N
q
null | 0J q J q
qx
N – orthonormal basis of null space
Stage 2: minimization with closure1. Choose sub-fragment with n > 6 DOFs2. Compute using SVD3. Project onto 4. Move until minimum is reached or
closure is broken
( )T q q null( )Jnull( )J
Escape from local minima using Monte Carlo with simulated annealing
MC + Minimization (Li & Scheraga ’87)
Suggest large random change Random move in Exact IK solution for 3 residues
(Coutsias et al. ’04) Minimize resulting conformation Accept using Metropolis criterion:
Use simulated annealing
exp prev newT q T q
P acceptTemp
null( )J
Test: artificial gaps Completed structure (gold standard) Good density (1.6Å resolution) Remove fragment and rebuild
Length High - 2.0Å Medium - 2.5Å Low - 2.8Å4 100% (0.14Å) 100% (0.19Å) 100% (0.32Å)8 100% (0.18Å) 100% (0.23Å) 100% (0.36Å)12 91% (0.51Å) 96% (0.41Å) 91% (0.52Å)15 91% (0.53Å) 88% (0.63Å) 83% (0.76Å)
Produced by H. van den Bedem
Test: true gaps Completed structure (gold standard) OK density (2.4Å resolution) 6 gaps left by model builder (RESOLVE)
Length Error4 0.40Å4 0.22Å5 0.78Å5 0.36Å7 0.66Å10 0.43Å
Produced by H. van den Bedem
Example: TM0423PDB: 1KQ3, 376 res.2.0Å resolution12 residue gapBest: 0.3Å aaRMSD
Example: TM0813
GLU-77
GLY-90
PDB: 1J5X, 342 res.2.8Å resolution12 residue gapBest: 0.6Å aaRMSD
Example: TM0813
GLU-77
GLY-90
PDB: 1J5X, 342 res.2.8Å resolution12 residue gapBest: 0.6Å aaRMSD
Example: TM0813
GLU-77
GLY-90
PDB: 1J5X, 342 res.2.8Å resolution12 residue gapBest 0.6Å aaRMSD
Alternative conformations
AB
TM0755, 1.8Å res.
Produced by H. van den Bedem
Conclusion Sampling of gap-closing fragments
biased by the EDM Refinement of fit to density without
breaking closure Fully automatic fragment completion
software for X-ray Crystallography
Thank you
Stage 1: Density-biased CCD Compute pair that minimizes
closure distance Search square neighborhood
for density maximum and move there.
The size of is reduced with the number of iterations
,i i
, ,t t t ti i i i
Stage 2: Target function EDM - Computed (model) density -
5 2
1
expci
ii
ra b
Least-squares residuals between EDM and model density
2
i
o ci i
g V
T q S g k g
oc
Building a missing fragment1. Generate 1000 fragments using CCD2. Choose top 6 candidates3. Refine each candidate 6 times4. Save top 2 of each refinement set
12 final candidates are output
Testing: TM1621
2Å Res. 2.8Å Res.
• PDB: 1O1Z, SCOP: α/β, 234 res.• 34% helical, 19% strands • Collected at 1.6Å res.
• 2mFo-DFc EDMs calculated at 2.0Å, 2.5Å, and 2.8Å
• 103 fragments of length 4,8,12 and 15
Produced by H. van den Bedem
Testing: TM1621
2Å Res. 2.8Å Res.
Produced by H. van den Bedem
Helical fragments (>2/3 helical) account for most misses
- mean- median- %>1Å aaRMSD
xxp
Testing: TM1742• PDB: 1VJR, 271 res. • Collected at 2.4Å• Good quality density
• 88% built using RESOLVE • 5 gaps, 1 region built incorrectly
Produced by H. van den Bedem
TM1621: running timeLength High (2.0) Medium (2.5Å) Low (2.8Å)
4 40 29 28
8 92 63 58
12 134 82 73
15 178 105 95
Times reported in minutes
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