1. RNA Folding Kinetics Bonnie Kirkpatrick bkirk@cns.montana.edu Dr. Nancy Amato, Faculty Advisor Guang Song, Graduate Student Advisor

2. Overview Problem RNA Folding Landscapes Approach: Roadmap Techniques Future Work

3. Problem RNA is a sequence of nucleotides (A,U,G,C) After being manufactured, the primary sequence folds into some conformation of secondary structures called the native state. This native state can be predicted quite well by finding the most stable conformation, which is the one with the lowest energy. The specific path the sequence takes as it folds into the native state is not known.

6. RNA Secondary Structure Described by base pair interactions (a.k.a. contact pairs) – Watson-Crick Pairs: A, U and G, C – Wobble Pair: G, U Defn: Valid Secondary Structure Configurations Given any two contact pairs [i, j] with i < j and [i’, j’] with i’ < j’, then: 1) i = i’ if and only if j = j’ Each nucleotide can appear in only one contact pair 2) If i’ < j, then i < i’ < j’ < j No pseudo-knots are allowed

8. RNA Folding Landscapes A folding landscape contains points for every possible valid secondary structure configuration. Folding pathways can be obtained from the folding landscape. Existing techniques for mapping landscapes are limited to relatively short sequences (~200 nucleotides). A robotics motion planning technique called PRM has successfully been applied to protein folding. Our goal: to apply PRM to RNA folding landscapes.

9. Approach: Probabilistic Roadmap Methods Purpose: to find a feasible path for movement through an environment (configuration space) while avoiding obstacles. start goal C-obst 1. Generate roadmap nodes 2. Generate roadmap edges 3. Add start and goal to the map 4. Query path between start and goal

10. Node Generation Let U be the power set of every possible contact pair. Let C-space, C, be the sub-set of U containing valid combinations contact pairs. C-space is very large. – Sequence: (ACGU) 10 – Length: 40 nucleotides – C-Space: 1.6x10 8 structures Purpose: generate nodes in C-space that describe the space without covering it

11. Node Generation (cont.) Generation – Starting with an empty configuration, c, contacts are added to c one at a time. – Each step preserves the condition that c contains a valid set of base pair contacts. – Contacts are added until there are no more contacts that do not conflict with the contact set of c. Evaluation – Energy determines how good a node is. – Energy function Computed by examining the types and sizes of secondary structures Reject high energy nodes

12. Node Connection Given two nodes in C-Space, C 1 and C 2, find a path between them consisting of a sequence of nodes: { C 1 = S 1, S 2, …, S n-1, S n = C 2 } The path must have the property that for each i, 1 < i < n, the set of contact pair of S i differs from that of S i-1 by the application of one transformation operation. The allowed set of operations that perform one transformation is called the move-set. Our move-set operates on configuration by (1) opening or (2) closing a single contact pair. C 1 = S 1 S2S2 S n-1 S n = C 2 …

13. Node Connection (cont.) Given any two nodes in C-Space, there exists a path connecting them. Not just any path will do; we want a good one. Bad paths have high energy nodes in them. The best path will have connect the nodes along the lowest energy route. How do we find a good path?

14. Node Connection (cont.) The more contacts a node has, the lower its energy will be. Choose a path that contains nodes with as many contacts as possible. Heuristic: if a contact is opened by the transition from one node to another, try to close a contact in the next transition

15. Future Work Analysis of the roadmap – Finding the low energy folding pathways with a shortest path algorithm Validation – How do we know if our results agree with experimental results? Compare a fully enumerated roadmap to experimental folding rates Compare a more sparse roadmap with a fully enumerated roadmap