# 28 Coaxial Stacking

## 28.1 Introduction

Coaxial stacking is the stacking of two base pairs at the terminii of adjacent helices. This stacking aligns the two helices along a common axis. In unimolecular secondary structures, coaxial stacking occurs in multibranch and exterior loops.

This set of nearest neighbor parameters allows for two types of coaxial stacking, flush stacking of helices that are directly adjacent (no intervening unpaired nucleotides) and mismatch-mediated coaxial stacking in which a single mistmatch occurs between the stacked helices. Mismatch-mediated coaxial stacking of helices is only allowed when there is exactly one unpaired nucleotide between the helices that can form a non-canonical pair with a nucleotide on the other side of one of the two helices.

## 28.2 Flush Coaxial Stacking

In flush coaxial stacking, the free energy and enthalpy changes of the coaxial stack are approximated using the helical nearest neighbor parameters Watson-Crick-Franklin as though there is no break in the backbone.

## 28.3 Mismatch-Mediated Coaxial Stacking

In the case of mismatch-mediated coaxial stacking, there are two adjacent stacks. The stack of the mismatch on the adjacent helix, where there is no break in the backbone, is approximated using the terminal mismatch parameters. The second stack is the stack of the mismatch on the second helix, where the backbone is not continuous.

## 28.4 Examples

### Flush coaxial stacking

ΔG°_{37} _{coaxial} _{stack} = ΔG°_{37}(Watson-Crick-Franklin stack)

ΔG°_{37} _{coaxial} _{stack} = ΔG°_{37}(AT pair followed by CG pair)

ΔG°_{37} _{coaxial} _{stack} = -1.4 kcal/mol

ΔH°_{coaxial} _{stack} = ΔH°(Watson-Crick-Franklin stack)

ΔH°_{coaxial} _{stack} = ΔH°(AT pair followed by CG pair)

ΔH°_{coaxial} _{stack} = -0.8 kcal/mol

**Note** that at this interface, the terminal AT pair penalty would still apply when calculating the helix stability.

### Mismatch-mediated coaxial stacking

ΔG°_{37} _{coaxial} _{stack} = ΔG°_{37}(continuous backbone stack) + ΔG°_{37}(discontinuous backbone stack)

ΔG°_{37} _{coaxial} _{stack} = ΔG°_{37}(AT pair followed by GG mismatch) + ΔG°_{37}(discontinuous backbone stack)

ΔG°_{37} _{coaxial} _{stack} = -0.4 kcal/mol -2.1 kcal/mol

ΔG°_{37} _{coaxial} _{stack} = -2.5 kcal/mol

ΔH°_{coaxial} _{stack} = ΔH°(continuous backbone stack) + ΔH°(discontinuous backbone stack)

ΔH°_{coaxial} _{stack} = ΔH°(AT pair followed by GG mismatch) + ΔH°(discontinuous backbone stack)

ΔH°_{coaxial} _{stack} = 1.5 kcal/mol - 8.4 kcal/mol

ΔH°_{coaxial} _{stack} = -6.9 kcal/mol

**Note** that at this interface, the terminal AT pair penalty would still apply when calculating the helix stability.

## 28.5 Parameter Tables

A table summarizing the parameters is available in html format.