Table 3. Approximations for internal loop free energy parameters at 37 °C (in kcal/mol).
| Specification | Free energy increments | |||||
|---|---|---|---|---|---|---|
| ΔG°37 initiation(n) | 0.5 ± 0.1 (2) | 1.6 ± 0.1 (3) | 1.1 ± 0.1 (4) | 2.1 ± 0.1 (5) | 1.9 ± 0.1 (6) | 1.9 + 1.08 In(n/6) (>6) |
| ΔG°37 AU/GU | 0.7 ± 0.1 | 0.7 ± 0.1 | 0.7 ± 0.1 | 0.7 ± 0.1 | 0.7 ± 0.1 | 0.7 ± 0.1 |
| ΔG°37 asym | 0.6 ± 0.1 | 0.6 ± 0.1 | 0.6 ± 0.1 | 0.6 ± 0.1 | 0.6 ± 0.1 | 0.6 ± 0.1 |
| Type of loop/first pair: | 5′RA/3′YG | 5′YA/3′RG | 5′RG/3′YA | 5′YG/3′RA | GG | UU |
| 1 × 1 | NA | NA | NA | NA | −2.6 ± 0.2 | −0.4 ± 0.1 if 5′RU/3′YU |
| 1 × 2 | 0 | −1.1 ± 0.2 | −1.1 ± 0.2 | −1.1 ± 0.2 | −1.1 ± 0.2 | −0.7 ± 0.2 |
| 1 × (n - 1), n > 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 × 3 | 0 | −0.5 ± 0.2 | −1.2 ± 0.1 | −1.1 ± 0.1 | −0.8 ± 0.2 | −0.4 ± 0.1 |
| Others, except 2 × 2 | −0.8 ± 0.1 | −0.8 ± 0.1 | −1.0 ± 0.1 | −1.0 ± 0.1 | −1.2 ± 0.1 | −0.7 ± 0.1 |
For ΔG°37 initiation, the total number of nts in the loop is n. Free energy increments for single noncanonical pairs (68, 69), i.e. 1 × 1 loops, are approximated by ΔG°37 loop(1 × 1) = ΔG°37 loop initiation(n = 2) + ΔG°37 AU/GU (per AU or GU closure) + ΔG°37 GG (1 × 1) + ΔG°37 5′RU/3′YU (1 × 1). Here, ΔG°37 loop initiation(n = 2) is the free energy of initiation for a single noncanonical pair with adjacent GC pairs; ΔG°37 AU/GU is the penalty for replacing a closing GC pair with an AU or GU pair and replaces the AU/GU terminal pair penalty used for helices (8, 44), ΔG°37 GG(1 × 1) is a bonus for a GG pair in a 1 × 1 loop; and ΔG°37 5′RU/3′YU (1 × 1) is a bonus for a 5′RU/3′YU stack in a 1 × 1 loop, where R is A or G in an AU or GC pair. Free energy increments for symmetric 2 × 2 loops lacking a measured value are approximated by interpolation of measured increments for loops of similar sequence (supporting information). Increments for nonsymmetric 2 × 2 loops are approximated by ΔG°37 loop (5′PXYS/3′ QWZT) = 0.5 [ΔG°37(5′PXWQ/3′QWXP) + ΔG°37(5′TZYS/3′SYZT)] + Δp + ΔG°37GG(2 × 2). Here, PQ and ST are canonical base pairs and XW and YZ are noncanonical pairs. The Δp term (0.6 ± 0.2 kcal/mol) is applied to loops with an AG or GA pair adjacent to a UC, CU, or CC pair and to loops with a UU pair adjacent to an AA pair. The ΔG°37 GG(2 × 2) term (−1.3 ± 0.2 kcal/mol) is applied to loops with a GG pair adjacent to an AA or any noncanonical pair with a pyrimidine. Values for Δp and ΔG°37 GG were obtained by linear regression on the 2 × 2 loop database (8, 58, 62, 64, 65, 68). Other internal loops are approximated by ΔG°37 loop(n) = ΔG°37 loop initiation(n) + ΔG°37 AU/GU +|n1 − n2| ΔG°37 asym + ΔG°37 first noncanonical pairs(except for 1 × (n − 1) for n > 3). Here, ΔG°37 loop initiation(n) is the free energy of initiation for a loop of n nucleotides, ΔG°37 asym is a penalty for loops with unequal numbers of nucleotides on each side, with n1 and n2 the number of nucleotides on each side, ΔG°37 first noncanonical pairs (except for 1 × (n − 1) for n > 3) is a parameter for the incremental free energy of the first noncanonical pair on each side of the loop; it is not applied to loops of the form 1 × (n − 1) with n > 3. Values for the parameters were obtained from a set of fits to available data for 1 × 1 (69), 1 × 2 (59, 62, 63), 1 × 3 (59, 62), 2 × 2 (8, 58, 62, 64, 65, 68), 2 × 3 (59, 61, 62), and 3 × 3 (ref. 62 and X. Jiao and D.H.T., unpublished results) loops (supporting information) and from theory (74) for n > 6. NA, not applicable to that type of loop. Identical values for adjacent parameters indicate that they were fit as a single parameter.