ENERGY LANDSCAPES AND FOLDING KINETICS OF PAIRWISE INTERACTING RNAS - PowerPoint PPT Presentation

ENERGY LANDSCAPES AND FOLDING KINETICS OF PAIRWISE INTERACTING RNAS Stefan Badelt 1 , Christoph Flamm , Ivo L. Hofacker 2 2 (1) DNA and Natural Algorithms Group, California Institute of Technology (2) Theoretical Biochemistry Group (tbi), University of Vienna Munich, Sept, 5 , 2016 th 1

OUTLINE RNA modeling and RNA energy landscapes Coarse grained RNA folding kinetics Folding kinetics of RNA-RNA interactions Analysis of toehold-mediated interactions 2

RNA STRUCTURE GCGGAUUUAGCUCAGUUGGGAGAGCGCCAGACUGAAGAUCUGGAGGUCCUGUGUUCGAUCCACAGAAUUCGCACCA A C C 1 1 A G C 50 C G 70 G C 60 U G 60 70 U A U 20 C A A U C A G C A U A G U C G G U U U U G C U A A 10 50 10 U C C U C G G U G A G C G A G G G G C 20 G A C G 40 A U 30 G C 30 40 A U C A U G G A A A secondary structure is a list of base pairs, where: A base may participate in at most one base pair Base pairs must not cross (no pseudoknots) Only isosteric base-pairs (GC, AU, GU) are allowed. 3

THE NEAREST NEIGHBOR ENERGY MODEL A A U H A U H G A A I C G G U 20 I I C U C A U A C I I G A 10 U G C 30 H: Hairpin loop M U U M: Multi loop C G I: Interior loop I G C E: Exterior loop G G I G C C A E A U 5' 3' 5' 3' E ( s ) = e ( l ) ∑ l ∈ s 4

ENERGY LANDSCAPES An energy landscape is defined by Conformation space s ∈ Ω Neighborhood relation [Move set] M ( s ) Energy function E ( s ) o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 5

ENERGY LANDSCAPES free energy [kcal/mol] − E ( s ) P ( s ) = e − E ( s )/ kT kT Z = ∑ s ∈ Ω e G = − kT ln Z Z 6

ENERGY LANDSCAPES Free energy Christoph Flamm, Walter Fontana, Ivo L Hofacker, and Peter Schuster RNA folding at elementary step resolution. RNA, 6:325–338, 2000. Michael T. Wolfinger, Andreas Svrcek-Seiler, Christoph Flamm, Ivo L. Hofacker, and Peter F. Stadler. Efficient computation of RNA folding dynamics. Journal of Physics A: Mathematical and General, 37:4731–4741, 2004. 7

KINETICS Calculate transition rates from energy barriers G ‡ Δ = E ( ) − E ( ) s j s i G ‡ k 0 if Δ ≤ 0 k ij = { k 0 e − Δ G ‡ RT otherwise ... where is a constant to relate folding to wall-clock time k 0 N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6):1087–1092, 1953. 8

THE CHEMICAL MASTER EQUATION d P i ( t ) = ( P j ( t ) k ji − P i ( t ) k ij ) ∑ dt i ≠ j ... together with the rates of gradient basin transitions ... free energy [kcal/mol] α β k αβ = P ( i | α ) k ij ∑ i ∈ α ∑ j ∈ β 9

10 ... can be solved for 60-80 nucleotides sequence length 1.1 3.3 1.9 3.7 2.3 1.6 2 1 1.72.4 30 24 1.9 42 33 1.6 58 54 3.6 1.1 1.1 19 2.5 59 57 1.4 1.0 85 41 1.1 104 79 1.11.7 1.1 4 1.3 1.5 8 6 1.1 12 11 1.11.7 18 10 1.1 1.1 17 1.3 2.3 21 20 1.3 26 14 1.12.2 1.5 29 27 1.11.7 28 25 1.3 32 1.11.7 50 37 1.1 45 35 1.1 1.9 56 40 1.3 2.3 63 1.5 2.3 61 48 67 52 1.11.7 1.3 1.1 1.1 7 5 2.3 1.3 9 1.11.7 16 15 1.1 31 23 1.9 1.3 46 36 1.1 2.3 47 1.5 2.3 69 49 1.9 75 51 1.11.7 73 66 1.9 2.1 84 64 1.1 1.1 72 1.1 2.2 95 91 1.3 93 74 2.2 3.2 109 62 1.9 1.9 80 1.11.9 1.6 97 88 126 106 1.1 1.6 107 101 1.1 1.8 133 1.11.9 138 114 1.0 140 113 1.8 2.3 150 103 1.6 2.3 130 120 1.1 3.2 105 1.1 2.5 155 83 163 102 2.8 1.8 2.2 1.5 39 22 2.1 2.6 38 1.9 1.1 82 65 2.4 139 129 1.8 2.3 137 112 1.1 1.5 121 1.6 1.8 187 156 1.5 160 146 1.1 1.3 175 162 1.1 2.4 194 192 1.7 2.1 124 1.1 1.1 159 136 1.1 199 200 1.0 1.9 210 198 1.1 1.4 151 1.1 1.4 209 181 1.9 218 190 1.1 1.5 191 164 1.1 1.1 231 1.0 230 228 3.3 1.4 241 96 2.9 1.11.7 184 128 1.1 152 127 1.3 1.9 177 1.0 1.1 221 176 1.9 244 240 2.6 1.11.7 185 145 1.1 144 1.6 2.2 212 182 1.3 216 169 1.7 2.6 239 147 1.1 1.1 214 1.0 2.2 258 261 1.4 271 189 1.3 252 248 5.3 0.8 0.8 1.0 1.6 123 34 1.2 1.3 148 1.5 2.1 253 183 1.9 245 197 1.3 1.9 206 207 1.1 1.9 272 1.7 1.9 286 233 1.6 247 232 1.1 2.3 293 254 1.8 1.9 211 1.6 2.1 249 242 2.3 262 229 1.7 1.8 265 225 1.6 2.1 297 281 2.1 267 1.4 0.9 266 0.8 1.6 1.0 99 1.7 118 110 1.0 1.5 173 154 1.3 1.1 213 1.4 1.0 236 237 2.4 269 268 1.1 2.8 259 161 1.5 2.3 195 294 257 1.1 6.4 1.0 68 3 1.3 2.4 71 70 0.8 1.5 53 3.9 13 0.8 1.7 2.3 44 1.4 3.3 60 43 1.1 94 55 1.0 2.6 116 115 1.0 1.5 77 2.3 2.7 131 111 1.4 90 78 1.0 2.7 135 119 2.1 2.3 81 1.9 2.6 100 92 1.3 108 87 1.1 2.9 141 132 1.1 1.2 149 86 1.1 2.2 158 2.1 166 122 1.4 3.3 125 89 1.1 1.1 186 165 1.2 1.3 180 1.2 1.9 203 174 1.5 208 157 1.5 2.6 193 134 1.9 2.1 202 1.2 1.9 188 171 1.1 238 179 1.6 2.1 251 178 1.2 1.1 256 217 1.1 1.1 255 1.0 263 264 1.0 1.9 274 275 1.3 1.5 246 219 1.1 1.2 279 1.2 2.3 285 283 1.1 288 201 1.2 1.9 292 234 1.9 2.6 289 1.72.5 224 168 2.6 273 222 2.1 2.4 227 220 2.3 3.6 278 170 2.5 2.2 282 2.3 287 270 2.3 2.6 284 277 2.3 2.7 298 295 276 1.9 1.1 2.0 1.1 1.8 98 76 2.0 204 143 1.1 2.1 205 142 1.1 1.5 153 1.6 3.2 226 196 1.1 235 117 1.3 2.2 300 280 1.6 2.1 250 243 2.6 2.6 291 3.7 290 260 3.0 3.6 172 167 3.501 2.0 296 215 2.601 223 299 2.0 0.0 -2.0 -4.0 -6.0 -8.0 -10.0

RNA-RNA INTERACTIONS are concentration dependent... Z ′ [ AB ] AB = K AB = [ A ][ B ] Z A Z B A A A G G A U U G U U G C A G A G C C C A A A G G G G G G A U A G G U A A U A U U A G U G U U A C C G C C C C A G A C C A A G G G G U A A U A U U G C C G C C A 11

RNA-RNA INTERACTIONS are concentration dependent... Z ′ [ AB ] AB = K AB = [ A ][ B ] Z A Z B A L B L AB A A G G A L A U G U U U G G C A G A C C C A A A G G G G G G A U A G G U A A U A U U A L' AB G U U G U A C C G C C C C G A A C C A A G G G G U A A U A U U G C G C C C A 12

DESIGN SEQUENCE PAIRS U U C U 10 G C 10 G U U G A A A G U A switch-RNA U G A C U A G G C C A A U U U A U U C G A C G U U G C G A A C U U A U A C U G 20 G G G G C U trigger-RNA A A A U G C C G C C G C C C G U A C C trigger-RNA switch-RNA 13

DESIGN SEQUENCE PAIRS U U C U 10 G C 10 G U U G A A A G U A switch-RNA U G A C U A G G C C A A U U U A U U C G A C G U U G C G A A C U U A U A C U G 20 G G G G C U trigger-RNA A A A U G C C G C C G C C C G U A C C trigger-RNA switch-RNA 1m M switch-RNA 1m M trigge r-RNA 0.0010 switch monomers 0.0008 trigger monomers occupa ncy [m ol/l] switch/trigger dimers 0.0006 0.0004 0.0002 0.0000 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 tim e [se conds] 14

DESIGN SEQUENCE PAIRS U U C U 10 G C 10 G U U G A A A G U A switch-RNA U G A C U A G G C C A A U U U A U U C G A C G U U G C G A A C U U A U A C U G 20 G G G G C U trigger-RNA A A A U G C C G C C G C C C G U A C C trigger-RNA switch-RNA 2x random coil intramolecular equilibrium metastable state 1m M switch-RNA 1m M trigge r-RNA 0.0010 switch monomers 0.0008 trigger monomers occupa ncy [m ol/l] switch/trigger dimers 0.0006 0.0004 0.0002 0.0000 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 tim e [se conds] 15

RNA-RNA INTERACTIONS toehold interactions 16

C U U C A U Cliffhanger design Conan design Hulk design U A C U A A U C C U G U C A U A A A U U G U U A C C A A G A U A U U C U G U A A U C G C G G C A A A C G A C A G A U A U C U A C C U A G U C U U G A A U A G C C A G U G U A U U G U U G G G C C G G C G C G C U G A U G G C C G G G G A C C G C A G G C G C C U A U C C A A A refolding using a toehold refolding without a toehold refolding with or without a toehold 17

17 Cliffha nge r de sign: 1nM switch-RNA 1m M trigge r-RNA 1e 9 1.0 C A A G G G U U G G G C G U U U G C A A 0.8 U C C G C G G C A A A occupa ncy [m ol/l] U C A C G 0.6 C G C U A C A U U C A C U A A U C U G G U G U A G G U G G G U U A C A C C C U A A A C U C A G A A A A 0.4 A U C U C U A A U A C C U U C A C U U A U U C C C G G G G U U U G G G G U G U G G A A A C G C G G A C A U C A C U G U C C A G G U G C U G U A C A G G C A U C A G C 0.2 A A C 0.0 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 tim e [se conds] 18