1. Solving the Protein Threading Problem in Parallel Nocola Yanev, Rumen Andonov Indrajit Bhattacharya CMSC 838T Presentation

2. CMSC 838T – Presentation Motivation u Problem paper is trying to solve  3D structure prediction using threading  Is a given target sequence likely to fold to a 3D template core?  Find the alignment that minimizes some score function  NP-complete; optimal solution not possible  MAX-SNP-hard; arbitrary approximation not possible u Why do we care  3D structure determines biological function of protein  Amino acid sequence (almost) uniquely determines 3D structure  Threading is usually less accurate than comparative modeling but easier to solve

3. CMSC 838T – Presentation Talk Overview u Overview of talk  Motivation  Techniques  Evaluation  Related work  Observations

4. CMSC 838T – Presentation Techniques u Approach  Reduce the problem to some known theoretical problem of interest l In this case, network flow  Use existing tools for solving the theoretical problem efficiently l CPLEX  Explore possibilities for parallelizing the problem  Investigate the intrinsic hardness for real biological examples

5. CMSC 838T – Presentation Two structurally similar proteins Spatial adjacencies (interactions) Possible threading with a sequence Objective function Mathematical Formulation

6. CMSC 838T – Presentation Reduction to Network Flow: An Example

7. CMSC 838T – Presentation Reduction to Network Flow: Variables and Constraints u Standard Network Flow  Variable x i,t for each segment to position assignment  Restricted to [0, 1]  With standard flow conservation constraints u Additional cost for non-local interactions  Variable z i,t,i’,t’ for each non-local interaction  Restricted to {0, 1}  Constrained to sum to 1 for each non-local pair (i, i’)  Upper bounded by flow entering (i, t) and leaving (i’, t’)

8. CMSC 838T – Presentation Drawbacks of Approach u Integer programming is hard to solve!  Relax to linear programming with (0, 1) variables  Approximate to integer solution using standard heuristics  Existing tools like CPLEX u Huge number of variables  For 36 segments and 81 positions, IP problem has 741264 rows, 360945 columns and 54145231 non-zero variables!  Need to reduce number of variables and constraints  Calls for parallelization if possible

9. CMSC 838T – Presentation Parallel Solution u Utilize special flow constraints  Split into sub-problems that may be solved parallely  Split the k-th layer in the graph into r intervals  Force path for a sub-problem to pass through a particular interval in the layer  Pass best bound for objective function found so far as parameter to sub-problem  Sub-task aborts when dual objective function exceeds the current best bound

10. CMSC 838T – Presentation Improving Parallel Solution u Drawback: Hardest Sub-Problem Dominates!  Parallel strategy was found to be slower than the sequential!  Sub-problems can potentially become harder to solve  Many more difficult sub-problems than easy ones u Solution:  Break the atomicity of the tasks  Each sub-task periodically checks the current best bound and updates its cut-off  Extra overhead is still small compared to task granularity  Now the easiest executing sub-task dominates!

11. CMSC 838T – Presentation Evaluation u Experimental environment  Real protein sequences  ILOG CPLEX Callable Library  SUN Ultra-Sparc II, 450 Mhz  Objective function coefficients generated from FROST  Maximum of 7 processors and 29 sub-problems u Evaluation results  Sequential version much faster than previous branch-and- bound results for the same problem formulation  Time taken comparable to PROSPECT  Splitting and parallelization significantly improve turnaround  Really tiny gap between relaxed LP and ILP solutions  Mostly integer solutions even for relaxed LP!

12. CMSC 838T – Presentation Result Tables Comparison with branch and bound algorithm Comment: Self threading results in significantly lower scores (as should be)

13. CMSC 838T – Presentation Result Tables Gap between relaxed LP and ILP Comment: Tiny relaxation gap. (significance?)

14. CMSC 838T – Presentation Result Tables Size of the LP formulation Comment: LP problem size is still too large.

15. CMSC 838T – Presentation Result Tables Performance with parallel sub-tasks Comment: Longer times with more sub-problems??

16. CMSC 838T – Presentation Related Work u Similar / previous approaches  Lathrop and Smith, 1998 l Uses same cost function l Branch and bound algorithm for searching the space of threadings  Xu, Xu and Uberbacher, 1998 l Divide and conquer algorithm  Xu, Li, Lin, Kim and Xu, 2003 l Linear programming formulation l Solved using b&b algorithm u None of the above suggest any parallelizing scheme

17. CMSC 838T – Presentation Observations u Points of Interest  Mapping to a known problem of interest  Nicely utilizes particular constraints to break into independent subtasks  Threading of real amino acid sequences seems possible  Raises interesting questions about real-life protein threading being in P  Solver tailored for this particular problem may yield better results

18. CMSC 838T – Presentation Observations u Criticism  Not enough experiments with large number of subtasks and processors to show scaling  Prohibitively large number of variables and constraints  How accurate are the objective function coefficients?  What is the resolution of the objective function?  Threading onto multiple sequences for prediction still looks daunting  Not clear how to extend the idea for 3-way and more complex interactions u Improvements  Seems possible to break up the sub-tasks recursively

19. CMSC 838T – Presentation Thank you!