1. IMA, October 29, 2007 Slide 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 local RNA 3-D structure Jes Frellsen The Bioinformatics Centre Department of Molecular Biology University of Copenhagen

2. IMA, October 29, 2007 Slide 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. IMA, October 29, 2007 Slide 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. IMA, October 29, 2007 Slide 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. IMA, October 29, 2007 Slide 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. IMA, October 29, 2007 Slide 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 model Individual angle distributions The model captures the distribution of the individual angles E.g. the -angle and the -angle:

7. IMA, October 29, 2007 Slide 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 model Pairwise distribution The model captures the pairwise dependencies between the angles E.g. the pairwise distribution of  and  (inter-nucleotide)

8. IMA, October 29, 2007 Slide 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: 1.Sample a whole structure, S, without clashes 2.Make new structure, S’, by resampling four consecutive angles in S (randomly picked) 3.Evaluate S’ a.If it has clashed it is rejected b.If it has a better energy than S then S’ is set to be the new S c.If it has a worse energy then with probability, p, S’ is set to be the new S (otherwise it is rejected) d.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. IMA, October 29, 2007 Slide 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 Length (Bases) Decoys < 4Å Decoys < 3Å Lowest RMSD 1ZIH1258.8%21.3%1.55Å 1RNG1255.1%3.5%2.48Å 1XWP1328.3%5.8%2.03Å 1I4B1334.6%0.1%2.91Å 1PJY2210.0%1.9%1.89Å Target structureBest decoy 1ZIH

10. IMA, October 29, 2007 Slide 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. IMA, October 29, 2007 Slide 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, by Jes 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. IMA, October 29, 2007 Slide 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 and Dynamic 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: