Figure 3. The PMFs of the RNA hairpin at 300 K are shown as a function of a number of order parameters. NH is the number of native hydrogen bonds and NN the number of non-native hydrogen bonds. Rg is the radius of gyration of the hairpin and RMSD is the root mean square deviation from the hairpin crystal conformation in the ribosome. The crystal structure has 12 native hydrogen bonds: 3 belong to the U-turn sub-motif, 2 belong to the U-A trans WC/H bp and 7 belong to the helical stem. Local minima are indicated in red. The transition state is deﬁned as the barrier region between the native and non-native basins. The energy of the native and non-native basin is similar, and the energy of the transition state is at least 1.5 kcal/mol higher than the two basins. Sample transition state structures, which contain 1–3 native hydrogen bonds in the helical stem, are shown here. All RMSD and Rg values are in Angstroms units (A˚ ). PMF is plotted in units of kcal/mol, where 1 kcal roughly equals to 0.6 KT at 300 K. arrangement in order to fold correctly to state N. State U can either be more expanded or compact than state N depending on the nature of the coil structures. Structures within the non-native basin at 300 K are often stabilized by a number of non-native hydrogen bond instead of being completely random coils. Among all non-native hydrogen bonds present in the structures belonging to the non-native basin, 60% were contributed by hydrogen bond donors and acceptors present in the nucleotide base while the rest were contributed by backbone phosphate and 20OH group in the sugar (data not shown here). State I is probably the product of speciﬁc collapse events while state U is likely to be a result of the non-speciﬁc collapse events proposed by Pande and coworkers in their study of the tetraloop hairpin (40). Nucleic Acids Research, 2007, Vol. 35, No. 20 6999 A possible transition state is proposed here based on structures located in the barrier region between the two local minima referred to as the native and non- native basin (Figure 3). We deﬁne the transition state (Figure 3) as having the following parameters: Rg = 9–9.5 A˚, RMSD = 3.5–4.5 A˚ , NH = 1–3, and NN = 2–5. We found the transition state to be very much hairpin like and containing 1–3 native hydrogen bond as well as helical twist. Zipping usually initiates within the stem region or, to a lesser extent, at the U:A trans W/H base pair. The barrier height between the native and non-native basins is 1.5 kcal/mol. Temperature dependence of the RNA hairpin energy landscape To assess the ruggedness of the energy landscape, we also investigate the temperature dependence of the RNA hairpin PMF. Here, we consider a minimum to be signiﬁcant when it is separated by a barrier larger than 1.5 kcal/mol and contains at least 2% of the total population. At both low temperature (275 K) and room temperature (300 K), we observed local minima corre- sponding to state N, I and U, as deﬁned above (Figure 4). Interestingly, we found that the U state from 275 K corresponds to a speciﬁc coil-like structure, while the U state at 300 K corresponds to a more heterogeneous population of coil structures. We speculate that the particular coil conformer observed at 275 K is only marginally stable at extremely low temperatures. When the temperature is raised slightly to 300 K, this particular coil conformer quickly overcomes energy barriers and inter-convert with other coil conformers or converts to more stable N and I state. As temperature is raised further to 347 K (Figure 4), N and I are no longer viewed as separate minima. At the same time, a newly emerged extended conformer E becomes more populated (where <0.7% of the structures belongs to E at 275 K, while 8% of the structures belongs to E at 347 K). At 400 K (Figure 4), state N is no longer signiﬁcantly populated, signaling the ﬁnal loss of native population. E is populated, but it ceases to be a separated minimum due to low barrier height at 400 K. The most populated structures at 400 K are coil-like unfolded structures (U), which are entropically favored due to their great structural heterogeneity. These structures seem to be ﬂexible and rapidly inter-convert with each other due to the low barrier heights. Fully extended state E only becomes signiﬁcantly accessible when temperature is raised above 300 K, which implies that it might be isolated by a relatively high barrier that cannot be easily overcome at low temperatures. E is considered as a separate minimum, which diﬀers from unfolded coil states U for several reasons. Visual analysis shows that E is a straight extended conformer stabilized by base stacking, which is more entropically unfavorable than the coil unfolded states. In addition, E appears to be a distinct minimum separated by a 1.5 kcal/mol barrier from the coil-like unfolded states at 347 K.