Computing Missing Loops in Automatically Resolved X-Ray Structures Itay Lotan Henry van den Bedem (SSRL)

Bioinformatics core UCSD, SDSC Crystallomics core TSRI, GNF Structure Determination Core SSRL Crystal screening / X-ray data collection Structure determination Structure refinement Funding from NIH Protein Structure Initiative 10 centers Funding for five years from July 2000 Ongoing projects at SDC: Beam line automation: Sample mounting robotics, automated diffraction quality assessment Automated structure determination: Structure Solution Pipeline Joint Center for Structural Genomics : Create new technologies to drive high throughput structure determination

From Model Building to Refinement Structure Solution Pipeline Initial Model(s) Diffraction Images Final Model Mostly Automated Manual Finalizing model: Labor intensive, time consuming. Existing tools to assist in model building unsatisfactory: 1.Produce incorrect configurations 2.Lack meaningful scoring algorithm to rank configurations 3.Remain highly interactive – difficult to integrate in Structure Solution Pipeline Initial models (RESOLVE, ARP/WARP): Several chains and gaps

The Problem We are given: –A density map –A solved structure with a gap (5 – 15 res.) Goal: –Automatically compute backbone conformation for the gap region

Gaps The structure is solved automatically Gaps appear in areas of “poor” density –Signal is indistinguishable from noise –Disconnected iso-surfaces –Automatic solver bails out

Things we can use The loop-closure constraint What density there is The solved structure The sequence is known (C β atoms) Preferred backbone angles (Ramchandran plots)

Loop Closure: CCD algorithm Robot Inverse Kinematics ( Wang & Chen ’91 ) Protein loops ( Canutescu & Dunbrack ’03 ) Algorithm: 1.Fix loop at one end 2.Repeat until closure For each DOF of loop Minimize closure score for DOF

CCD for Proteins Closure score: Sum of squared distances of N, C α and C atoms of final residue from their target positions

Our Approach 1. Generate closed loops using density, Ramachandran plot bias and solved structure 2. Optimize highest scoring loops using density and solved structure

Stage 1: Generate Closed Loops Perform one big CCD run For residue i : –Compute closure moves of ( φ,ψ ) angles –Compute max density of residue i+1 –Combine and bias toward peaks in Ramachandran plot Weight of closure move is increased gradually

Stage 2: Loop Optimization Choose residue i and φ or ψ DOF at random –Apply random change –Use DOFs of residues [ i-1, i+2 ] to close loop using CCD –Compute new score Accept change using Metropolis-like criterion Slowly decrease temperature and reduce StDev of random changes

Score Density: Weighted sum of density at atom centers and points away from center along coordinate axes. Collision: Penalize overlap of loop atoms with solved structure atoms as function penetration depth. Self Collision: Penalize overlap of atoms in loop

Local Loop Changes My CCD method: –Choose DOF at random (from ALL DOFs) with biases –Compute Direction of change –Move only a little –Allowed change in N-Cα and Cα-C bond lengths, N-Cα-C angle and Ω angle decreases with distance from optimal value Repeat until closed or maximum iterations

3.7Å 0.35Å 8 Residue Loop: Example 1

8 Residue Loop: Example 2 0.3Å 2.79Å

12 Residue Loop: 1.29Å0.28Å

9 Residue Loop: 3Å0.32Å

Open Issues Many parameters that are determined arbitrarily –Annealing regimen –Weight of collision penalty –Acceptance criterion Have one set of parameters that works for all loops lengths and density qualities