Turner 1999

Multibranch Loop

Example

# Free Energy Change

### Prediction of Stacking

The predicted stacking configuration is the one with lowest free energy change. There are eight relevant configurations.

Configuration 1:

Helix 1 with 3' dangling U, Helix 2 with terminal mismatch, Helix 3 with 3' dangling A, and Helix 4 with 5' dangling C

∆G°37 = ∆G°37(UA with 3' dangling U) + ∆G°37(CG followed by GA) + ∆G°37(GC with 3' dangling A) + ∆G°37(GC with 5' dangling C)

∆G°37 = –0.1 kcal/mol 1.4 kcal/mol – 1.1 kcal/mol 0.3 kcal/mol

∆G°37 = –2.9 kcal/mol

Configuration 2:

Helix 1 with 3' dangling U, Helix 2 with 5' dangling A, Helix 3 with terminal mismatch, and Helix 4 with 5' dangling C

∆G°37 = ∆G°37(UA with 3' dangling U) + ∆G°37(CG with 5' dangling A) + ∆G°37(GC followed by AG) + ∆G°37(GC with 5' dangling C)

∆G°37 = –0.1 kcal/mol 0.2 kcal/mol – 1.3 kcal/mol 0.3 kcal/mol

∆G°37 = –1.9 kcal/mol

Configuration 3:

Helix 1 in flush coaxial stack with helix 4, Helix 2 with terminal mismatch, and Helix 3 with 3' dangling A

∆G°37 = ∆G°37(GC followed by AU) + ∆G°37(CG followed by GA) + ∆G°37(GC with 3' dangling A)

∆G°37 = –2.35 kcal/mol 1.4 kcal/mol – 1.1 kcal/mol

∆G°37 = –4.9 kcal/mol

Configuration 4:

Helix 1 in flush coaxial stack with helix 4, Helix 2 with 5' dangling A, and Helix 3 with terminal mismatch

∆G°37 = ∆G°37(GC followed by AU) + ∆G°37(CG with 5' dangling A) + ∆G°37(GC followed by AG)

∆G°37 = –2.35 kcal/mol 0.2 kcal/mol – 1.3 kcal/mol

∆G°37 = –3.9 kcal/mol

Configuration 5:

Helix 1 with 3' dangling U, Helix 2 in mismatch–mediated coaxial stack with helix 3 with GA intervening mismatch, and Helix 4 with 5' dangling C

∆G°37 = ∆G°37(UA with 3' dangling U) + ∆G°37(CG followed by GA) + ∆G°37(Discontinuous Backbone Stack) + ∆G°37(GC with 5' dangling C)

∆G°37 = –0.1 kcal/mol 1.4 kcal/mol – 2.1 kcal/mol 0.3 kcal/mol

∆G°37 = –3.9 kcal/mol

Configuration 6:

Helix 1 with 3' dangling U, Helix 2 in mismatch–mediated coaxial stack with helix 3 with AG intervening mismatch, and Helix 4 with 5' dangling C

∆G°37 = ∆G°37(UA with 3' dangling U) + ∆G°37(Discontinuous Backbone Stack) + ∆G°37(GC followed by AG) + ∆G°37(GC with 5' dangling C)

∆G°37 = –0.1 kcal/mol – 2.1 kcal/mol 1.3 kcal/mol – 0.3 kcal/mol

∆G°37 = –3.8 kcal/mol

Configuration 7:

Helix 1 in flush coaxial stack with helix 4 and Helix 2 in mismatch–mediated coaxial stack with helix 3 with GA intervening mismatch

∆G°37 = ∆G°37(GC followed by AU)) + ∆G°37(CG followed by GA) + ∆G°37(Discontinuous Backbone Stack)

∆G°37 = –2.35 kcal/mol 1.4 kcal/mol – 2.1 kcal/mol

∆G°37 = –5.9 kcal/mol

Configuration 8:

Helix 1 in flush coaxial stack with helix 4 and Helix 2 in mismatch–mediated coaxial stack with helix 3 with AG intervening mismatch

∆G°37 = ∆G°37(GC followed by AU)) + ∆G°37(Discontinuous Backbone Stack) + ∆G°37(GC followed by AG)

∆G°37 = –2.35 kcal/mol – 2.1 kcal/mol 1.3 kcal/mol

∆G°37 = –5.8 kcal/mol

Configuration 7 has the lowest folding free energy change of –5.9 kcal/mol.

### Initiation Free Energy Change

ΔG°37 initiation = a + 6b + (1.1 kcal/mol)×ln([number of unpaired nucleotides]/6) + c×[number of branching helices]

ΔG°37 initiation = 10.1 kcal/mol + 6×(–0.3 kcal/mol) + (1.1 kcal/mol)×ln(8/6) + 4×(–0.3 kcal/mol)

ΔG°37 initiation = 7.4 kcal/mol

### Total Folding Free Energy Change

ΔG°37 multibranch loop = ΔG°37 initiation + ΔG°37 stacking = 7.4 kcal/mol 5.9 kcal/mol = 1.5 kcal/mol

Note that helices 1 and 2 are separated by two unpaired nucleotides and cannot stack coaxially. Similarly, helices 3 and 4 are too distant to stack coaxially. Also note that coaxial stacking is only allowed between adjacent helices and hence, for example, helices 1 and 3 cannot stack coaxially.