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

Mos

tly A

utom

ated

Man

ual

• Finalizing model: Labor intensive, time consuming.

• Existing tools to assist in model building unsatisfactory:

1. Produce incorrect configurations2. Lack meaningful scoring algorithm to

rank configurations3. 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 (Cβ 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, Cα 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

0.3Å2.79Å

12 Residue Loop:

1.29Å 0.28Å

9 Residue Loop:

3Å 0.32Å

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