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Turner 2004

Multibranch Loop

Example

 example structure

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 + b×[average asymmetry] + c×[number of branching helices] + ΔG°37 strain(three–way branching loops with fewer than two unpaired nucleotides)

ΔG°37 initiation = 9.25 kcal/mol + (0.91 kcal/mol)×[average asymmetry] + (–0.63 kcal/mol)×[4]

Average asymmetry = min[2.0,(2+1+4+5)/4] = min[2.0,3.0] = 2.0

ΔG°37 initiation = 9.25 kcal/mol + (0.91 kcal/mol)×[2] + (–0.63 kcal/mol)×[4]

ΔG°37 initiation = 8.6 kcal/mol

Total Folding Free Energy Change

ΔG°37 multibranch loop = ΔG°37 initiation + ΔG°37 stacking = 8.6 kcal/mol 5.9 kcal/mol = 3.6 kcal/mol

Enthalpy Change

Prediction of Stacking

The stacking configuration is fixed by the prediction of folding free energy change and is configuration 7 above.

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

∆H° = –12.44 kcal/mol 8.2 kcal/mol – 8.46 kcal/mol

∆H° = –29.1 kcal/mol

Initiation Enthalpy Change

ΔH°initiation = a + b×[average asymmetry] + c×[number of branching helices] + ΔH°strain(three–way branching loops with fewer than two unpaired nucleotides)

ΔH°initiation = 38.9 kcal/mol + (12.9 kcal/mol)×[average asymmetry] + (–11.9 kcal/mol)×[4]

Average asymmetry = min[2.0,(3+2+4+5)/4] = min[2.0,3.0] = 2.0

ΔH°initiation = 38.9 kcal/mol + (12.9 kcal/mol)×[2] + (–11.9 kcal/mol)×[4]

ΔH°initiation = 17.1 kcal/mol

Total Folding Enthalpy Energy Change

ΔH°multibranch loop = ΔH°initiation + ΔH°stacking = 17.1 kcal/mol 29.1 kcal/mol = –12.0 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.