Mesoscopic Modeling of RNA Structure and Dynamics Hin Hark Gan A. Fundamentals of RNA structure 1. Hierarchical folding 2. Folding timescales B. Issues in RNA modeling 1. Mesoscopic models of RNA structure 2. RNA energy function 3. Ribosome modeling

NSF Goal: Transformative Research Research that has the capacity to: (1) revolutionize existing fields, (2) create new subfields, (3) cause paradigm shifts, (4) support discovery, and (5) lead to radically new technologies. National Science Board

A1. Hierarchical folding 2D structure folds independently of the 3D structure Explains most of RNA fold’s free energy Brion & Westhof 1997

A2. Folding timescales Thirumalai et al s (2D) 1-10ms 50ms-100s 2D and 3D structures have distinct folding timescales. Goal: Predict 3D structure and dynamics from input 2D fold.

B1. Mesoscopic Models: RNA Stems ? beads Perfect stems Imperfect stems Small bulge in stems ? - Unpaired bases are important for tertiary interactions - How to effectively model unpaired bases in helices? Similar to DNA modeling

Can DNA elastic models be applied to RNA? Elastic constants: stretching (h), bending (g), twisting (C) Applicable to long perfect helices (typically, <10 basepairs) Imperfect helices require special considerations (e.g., varying elastic potentials and interactions) Not applicable to single strand regions (h,g,C) E (h’,g’,C’) E’ E’ - Varying constants and interactions

Mesoscopic Models: Single strands Use existing coarse-grained models Baker group: 1-bead model (considers only base, neglect sugar and phosphate, base centroid as the bead origin) Amaral group: bead-pin model Overall mesoscopic RNA model is a mixture of elastic chain for helical segments and bead-pin model for unpaired bases.

System Size Length (nt) Number of sites (S1-1, H3-1)Number of sites (S1-3, H1-1) =5040*3+30= =10080*3+60= =150120*3+90= =200160*3+120=600 - Moderate number of beads for a typical RNA – not a problem! - Chromatin modeling involves ~10,000 beads

B2. RNA Energy Function Total energy =  (H-H) +  (H-S) +  (S-S) =  (coaxial) +  (A-minor) +  (ribose zipper) +  (pseudoknots) + … + (Excluded volume) + (Van der Waals) + (Electrostatics) + … - Tertiary motif interactions (similar to -, -, etc. interactions for proteins) - Special importance of tertiary motifs for structure and dynamics? , , ,… - Parameters: , , ,… S – single strand region H – helical region Tertiary motif terms usual terms

Tertiary Interaction Networks Recurrent Structural Motifs are Key to 3D folds H: helix (ds) S: single strand (ss) By Laing, Xin S/S tRNA D-loop:T-loop Kissing hairpin Pseudoknots Chang & Tinoco 1994, Ennifar et al Shen & Tinoco 1995 Van Batenburg et al hairpins Self-comp., often 6 nt 2 intertwining regions Comp. bps D/T loop interaction Holbrook et al Holbrook and Kim 1979 H/H Coaxial helices Junction, “pseudo-stem” A (in helix bridge) Kim et al Cate et al S/H Ribose zipper Antip. stem/loop interaction 5′-CC-3′ (Stem) 3′-AA-5′ (Loop) Cate et al Tamura & Holbrook 2002 A-minor motif Clustering of A G-C preferred Nissen et al Tetraloop receptor Tetraloop/internal loop 5′- GAAA -3′ 5′-CC-UAAG-3′ Pley et al Cate et al Butcher et al. 1997

Derivation and Optimization of Energy Function Structure data -> statistical potential, E ik ~ln(P ik ) Thermodynamic data – denaturation curves from temperature and pH changes Other RNA data sources (e.g., decoy structures) Brion & Westhof, 1997

B3. Modeling the Ribosome (NDPA proposal) Goal: Model ribosome structure and dynamics using mesoscopic models for all RNA and protein components and their interactions. Steitz group, Science 2000 RNA components proteins

Impact on RNA Folding and Design Folding of larger RNAs ( nt) Millisecond folding times RNA design aided by predicted 3D folds Ribosome dynamics and antibiotic action Likely Yes/No Probable Yes/No Likely Yes May be Yes Likelihood Transformative of success Research? Challenges

Quote of the day Great chess players apply a variety of principles, they sense patterns, they hold a formidable range of models and analyses in their mind without being a slave to any of them. John Kay, FT columnist