Using Motion Planning to Study Protein Folding Pathways

1. Using Motion Planning to Study Protein Folding Pathways by Guang Song and Nancy M. Amato Journal of Computational Biology, April 1, 2002 Presentation by AthinaRopodi

2. outline • Introduction- Definition • Motion planning • Probabilistic Roadmap Method • Denaturation • C-space • Probabilistic Roadmap Method • Basic steps • Degrees of freedom/C-space • Node Generation • Sampling strategy • Potential Energy Computations • Results

3. Introduction- motion planning • Motion planning is a term used in robotics for the process of detailing a task into atomic robotic motions. • This issue is also known as the “navigation problem”: • Givenan environment, a start and a goal position of an object, the objective is to find a valid path (continuous sequence of validconfigurations) from start to goal.

4. PRM- Denaturation • Probabilistic Roadmap (PRM) motion planning techniques are applied to “small” proteins (up to 60 residues) in order to compute folding pathways from a denaturated state to its native fold. • Denaturate: To cause the structure to unfold, so that some of its original properties, especially its biological activity, are diminished or eliminated. Usually caused by extreme conditions, e.g. high temperature.

5. How denaturation occurs at levels of protein structure • In quaternary structuredenaturation, protein sub-units are dissociated and/or the spatial arrangement of protein subunits is disrupted. • Tertiary structuredenaturation involves the disruption of: • Covalent interactions between amino acid side chains (such as disulfide bridges between cysteine groups) • Noncovalent dipole-dipole interactions between polar amino acid side chains (and the surrounding solvent) • Van der Waals (induced dipole) interactions between nonpolar amino acid side chains. • In secondary structuredenaturation, proteins lose all regular repeating patterns such as alpha-helices and beta-pleated sheets, and adopt a random coil configuration. • Primary structure, such as the sequence of amino acids held together by covalent peptide bonds, is not disrupted by denaturation

6. Basic assumption • The article investigates the folding mechanisms of a protein assuming we know its native fold. • Results are validated by comparing the formation order to pulse-labeling experimental results. • The configuration space (C-Space) of a movable object is the space consisting of all positions and orientations of that object. • Pulse labeling is a biochemistry technique of identifying the target moleculepresence by inclusion of a pulse of a radioactive compound.

7. outline • Introduction- Definition • Motion planning • Probabilistic Roadmap Method • Denaturation • C-space • Probabilistic Roadmap Method • Basic steps • Degrees of freedom/C-space • Node Generation • Sampling strategy • Potential Energy Computations • Results

8. Probabilistic Roadmap Method for protein folding • Any complete motion planner would require time exponential in the number of degrees of freedom (dof). • Several methods such as energy minimization, molecular dynamics, Monte-Carlo and genetic algorithms have been used. • This method tries to simulate the true dynamics of the folding process using the classical Newton’s motion equations. • However, an exact simulation would depend on the start conformation and could result in local minima.

9. Probabilistic Roadmap Method for protein folding The basic steps are: • First of all, PRM samples points randomly from C-space and retains those that satisfy certain requirements. • Then, the points are connected and form a graph using a simple planning method. • Finally, paths connecting the start and goal configurations are extracted using standard graph search techniques. • [Kavraki, Svestka, Latombe,Overmars 1996] In this case, low-energy conformations are preferable.

10. Probabilistic Roadmap Method for protein folding

11. C-spaces • All atomic bond lengths and angles are considered to be constants. • We only consider 2 dofs, φ and ψ angles. • Side-chains are modeled as spheres with no dof. • Fold positions (atomic bonds) correspond to joints and atoms correspond to links. Thus, for k residues our model has 2k links and 2k revolute joints…

12. node generation • Different configurations are produced by assigning possible angle values. • But, the nodes are accepted or rejected based on their potential energy: where Emin=50000 and Emax=89000KJouls/mol A configuration with higher potential is more likely to be rejected.

13. Sampling strategy • Due to the high dimensionality of the problem, a very dense uniform sampling is required. • Since prior knowledge of the native fold is assumed, a sampling strategy biased to the native fold is applied: • Sampling is performed from a set of normal distributions around the native fold. The standard deviations used are {5, 10, 20, 40, 80,160 degrees}. Small STDs capture the detail around the goal, and larger ensure adequate roadmap coverage

14. Construction of Roadmap • For each node, the k-nearest neighbors are found(k=20 and the metric is Euclidean). • For each connection a feasibility check is performed. (two nodes are connected by a straight line) • For 2 consecutive intermediate conformations, i and i+1, we first check their potential energies and then the probability of moving from i to i+1: RMSD metric proved inferior

15. Construction of Roadmap • The total weight of the edge is: • Dijkstra’s algorithm is then used to find the smallest weight path. • Path optimization: resampling is performed around the nodes of paths with high potential.

16. Potential Energy Computations The 1st term represents constraints that favor secondary structure, hydrogen and disulphide bonds • To reduce the cost of calculations, an approximation function is used. We only consider contribution from side chains and those are modeled as spheres. • The cost is then reduced by 2 orders of magnitude. The 2nd the van der Waals interactions among atoms.

17. outline • Introduction- Definition • Motion planning • Probabilistic Roadmap Method • Denaturation • C-space • Probabilistic Roadmap Method • Basic steps • Degrees of freedom/C-space • Node Generation • Sampling strategy • Potential Energy Computations • Results

18. Results

19. results • Folding process of GB1:

20. results • Protein GB1(56 residues): 1 α-helix and 4 β-strands • Protein A (60 residues): 3 α-helices

21. Protein GB1: Phi/Psi distribution of roadmap nodes

22. Protein GB1: Potential vs RMSDdistribution of roadmap nodes

23. Protein GB1: Effect of Resolution potential profiles for different size roadmaps Peaks show where atoms are close and Van der Waals interactions dominate. Bigger roadmaps have smoother paths.

24. Effect of re-sampling around the peaks More samples around the peaks improve the path.

25. What about different start conformations? • Different pathways tend to come together and appear to have some common channels, as they approach the native fold.

26. Thank you! Bibliography: • Probabilistic roadmaps for path planning in high-dimensional configuration spacesL. Kavraki, P. Svestka, J-C. Latombe, M. H. Overmars, 1996 • Protein Folding by Restrained Energy Minimization and Molecular Dynamics Michael Levitt,1983 • http://faculty.cs.tamu.edu/amato/dsmft/research/folding/index.shtml.OLD2