A Probabilistic Approach to Protein Backbone Tracing in Electron Density Maps

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A Probabilistic Approach to Protein Backbone
Tracing in Electron Density Maps

• Frank DiMaio, Jude Shavlik
• Computer Sciences Department
• George Phillips
• Biochemistry Department
• University of Wisconsin Madison
• USA

Presented at the Fourteenth Conference on
Intelligent Systems for Molecular Biology (ISMB
2006), Fortaleza, Brazil, August 7, 2006
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X-ray Crystallography
FFT
X-ray beam
ProteinCrystal
CollectionPlate
ElectronDensity Map (3D picture)
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Given Sequence Density Map
Sequence
Electron Density Map
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Find Each Atoms Coordinates
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Our Subtask Backbone Trace
Ca
Ca
Ca
Ca
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The Unit Cell

• 3D density function ?(x,y,z) provided over unit
  cell
• Unit cell may contain multiple copies of the
  protein

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The Unit Cell

• 3D density function ?(x,y,z) provided over unit
  cell
• Unit cell may contain multiple copies of the
  protein

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Density Map Resolution
2Å
4Å
3Å
ARP/wARP (Perrakis et al. 1997)
TEXTAL (Ioerger et al. 1999) Resolve (Terwilliger
2002)
Our focus
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Overview of ACMI (our method)

• Local Match
• Algorithm searches for sequence-specific 5-mers
  centered at each amino acid
• Many false positives

• Global Consistency
• Use probabilistic model to filter false positives
• Find most probable backbone trace

• Global Consistency
• Use probabilistic model to filter false positives
• Find most probable backbone trace

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5-mer Lookup and Cluster

• VKH V LVSPEKIEELIKGY

PDB
Cluster 1
Cluster 2
NOTE can be done in precompute step
wt0.67
wt0.33
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5-mer Search

• 6D search (rotation translation)
  forrepresentative structures in density map
• Compute similarity
• Computed by Fourier convolution (Cowtan 2001)
• Use tuneset to convert similarity score to
  probability

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Convert Scores to Probabilities
5-mer representative
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In This Talk

• Where we are now
• For each amino acid in the protein, we have a
  probability distribution over the unit cell

• Where we are headed
• Find the backbone layout maximizing

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Pairwise Markov Field Models

• A type of undirected graphical model
• Represent joint probabilities as product of
  vertex and edge potentials
• Similar to (but more general than) Bayesian
  networks

y
u1
u3
u2
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Protein Backbone Model
ALA
GLY
LYS
LEU

• Each vertex is an amino acid
• Each label is location
  orientation
• Evidence y is the electron density map
• Each vertex (or observational) potential
  comes from the 5-mer matching

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Protein Backbone Model
ALA
GLY
LYS
LEU

• Two types of edge (or structural) potentials
• Adjacency constraints ensure adjacent amino acids
  are 3.8Å apart and in the proper orientation

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Protein Backbone Model
ALA
GLY
LYS
LEU

• Two types of structural (edge) potentials
• Adjacency constraints ensure adjacent amino acids
  are 3.8Å apart and in the proper orientation
• Occupancy constraints ensure nonadjacent amino
  acids do not occupy same 3D space

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Backbone Model Potential
Constraints between adjacent amino acids

x
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Backbone Model Potential
Constraints between nonadjacent amino acids
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Backbone Model Potential
Observational (amino-acid-finder) probabilities
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Probabilistic Inference

• Want to find backbone layout that maximizes

• Exact methods are intractable
• Use belief propagation (BP) to approximate
  marginal distributions

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Belief Propagation (BP)

• Iterative, message-passing method (Pearl 1988)
• A message, , from amino acid i toamino
  acid j indicates where i expects to find j
• An approximation to the marginal (or belief)
  ,is given as the product of incoming messages

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Belief Propagation Example
ALA
GLY
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Technical Challenges

• Representation of potentials
• Store Fourier coefficients in Cartesian space
• At each location x, store a single orientation r
• Speeding up O(N2X2) naïve implementation
• X the unit cell size ( Fourier coefficients)
• N the number of residues in the protein

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Speeding Up O(N2X2) Implementation

• O(X2) computation for each occupancy message
• Each message must integrate over the unit cell
• O(X log X) as multiplication in Fourier space
• O(N2) messages computed stored
• Approx N-3 occupancy messages with a single
  message
• O(N) messages using a message product accumulator
• Improved implementation O(NX log X)

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1XMT at 3Å Resolution
prob(AA at location)
HIGH
0.82
0.17
1.12Å RMSd 100 coverage
LOW
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1VMO at 4Å Resolution
prob(AA at location)
HIGH
0.25
0.02
3.63Å RMSd 72 coverage
LOW
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1YDH at 3.5Å Resolution
prob(AA at location)
HIGH
0.27
0.02
1.47Å RMSd 90 coverage
LOW
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Experiments

• Tested ACMI against other map interpretation
  algorithms TEXTAL and Resolve
• Used ten model-phased maps
• Smoothly diminished reflection intensitiesyieldin
  g 2.5, 3.0, 3.5, 4.0 Å resolution maps

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RMS Deviation
ACMI
ACMI
Textal
Resolve
Ca RMS Deviation
Density Map Resolution
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Model Completeness
chain traced
residues identified
ACMI
ACMI
Textal
Resolve
Density Map Resolution
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Per-protein RMS Deviation
TEXTAL RMS Error
Resolve RMS Error
ACMI RMS Error
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Conclusions

• ACMI effectively combines weakly-matching
  templates to construct a full model
• Produces an accurate trace even with
  poor-quality density map data
• Reduces computational complexity from O(N2 X2)
  to O(N X log X)
• Inference possible for even large unit cells

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Future Work

• Improve amino-acid-finding algorithm
• Incorporate sidechain placement / refinement
• Manage missing data
• Disordered regions
• Only exterior visible (e.g., in CryoEM)

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Acknowledgements

• Ameet Soni
• Craig Bingman
• NLM grants 1R01 LM008796 and 1T15 LM007359