A continuous probabilistic model of local RNA 3-D structure

1. T H E B I O I N F O R M A T I C S C E N T R E A continuous probabilistic model of localRNA 3-D structure Jes Frellsen The Bioinformatics Centre Department of Molecular Biology University of Copenhagen

2. T H E B I O I N F O R M A T I C S C E N T R E Background • 3D structure is important for understanding the function of non-coding RNA molecules • Experimental methods for determining 3D structure are time consuming and sometimes difficult • Local structure is typically modeled by using discretization • E.g. fragment libraries are used in current methods for structure prediction • Our group has recently made a continuous probabilistic model of local protein structure with great success[PLoS Comput Biol 2006, 2:1121-113] • Dynamic Bayesian Networks • Directional statistics • We have used a similar approach to model local structure of RNA

3. T H E B I O I N F O R M A T I C S C E N T R E Representation of RNA • Each nucleotide in an RNA molecule can be represented by the base type and 7 dihedrals angles • Allows for accurate conversion into coordinates of all atoms in the structure using standard values

4. T H E B I O I N F O R M A T I C S C E N T R E Angle distributions • Each variable lies on a circle • Requires directional statistics • Each variable is multi-modal • Can be described by a mixture of simple distributions • Von Mises distribution • The angles co-vary both within nucleotides and between consecutive nucleotides • We model this by a sequential model

5. T H E B I O I N F O R M A T I C S C E N T R E Our model • An DBN with 3 random variables per angle: • Discrete input variable indicating angle type (7 states) • Hidden variable with 20 states • Output variable representation the angle value and the CPDs given the hidden state is modelled by Von Mises distributions • Structure of an IOHMM with continuous output (except bookkeeping) • Does not impose a groping of the angles • Parameters are estimated by stochastic EM from experimental data

6. T H E B I O I N F O R M A T I C S C E N T R E Evaluating the modelIndividual angle distributions • The model captures the distribution of the individual angles • E.g. the -angle and the -angle:

7. T H E B I O I N F O R M A T I C S C E N T R E Evaluating the modelPairwise distribution • The model captures the pairwise dependencies between the angles • E.g. the pairwise distribution of  and  (inter-nucleotide)

8. T H E B I O I N F O R M A T I C S C E N T R E Proof of concept: generating decoys for a target structure • A simple simulated annealing scheme: • Sample a whole structure, S, without clashes • Make new structure, S’, by resampling four consecutive angles in S (randomly picked) • Evaluate S’ • If it has clashed it is rejected • If it has a better energy than S then S’ is set to be the new S • If it has a worse energy then with probability, p, S’ is set to be the new S (otherwise it is rejected) • Go to step 2 • In the scheme we used • p = e(E-E’)/T , where T decreases with time • a simple “energy function” that promotes structure with the same Watson-Crick base pair as are found in the target structure

9. T H E B I O I N F O R M A T I C S C E N T R E Results of generating 1,500 decoys for 5 different structures Target structure Best decoy 1ZIH

10. T H E B I O I N F O R M A T I C S C E N T R E Perspectives • The model assigns a probability distribution to the conformational space and describes many aspects of local RNA structure well • It has numerous applications! • It allows for fast probabilistic sampling of locally RNA-like structures • Can thus be used in RNA 3D structure prediction • The model can be used to calculate the probabilities of seeing different local structures • Can thus be used for quality validation of experimentally determined structures

11. T H E B I O I N F O R M A T I C S C E N T R E Acknowledgements • The research was conducted in the structural bioinformatics group, lead by Thomas Hamelryck, byJes Frellsen, Ida Moltke, Martin Thiim and Thomas Hamelryck • We would like to thank • Our collaborator Senior Research Professor Kanti V. Mardia from The University of Leeds for his contributions on directional statistics. • The Richardsons Lab at Duke University for making their RNA dataset available • JF thanks IMA for the invitation to the conference • JF is funded by The Danish Council for Strategic Research • TH is funded by The Danish Council for Technology and Innovation

12. T H E B I O I N F O R M A T I C S C E N T R E Bayesian Networks andDynamic Bayesian Networks • A BN is a DAG where • Nodes are random variables • Edges represent conditional dependencies in the factorization of the joint probability • The graph encodes conditional indepencies • E.g. A and D is conditional independent give C • DBNs are the time series expansion of BNs • E.g. an HMM: