# Model introduction

The model treats DNA as a string of rigid nucleotides, which interact through potentials which depend on the position and orientation of the nucleotides. The interactions are:

1. Sugar-phosphate backbone connectivity,
2. Excluded volume,
3. Hydrogen bonding,
4. Nearest-neighbour stacking,
5. Cross-stacking between base-pair steps in a duplex,
6. Coaxial stacking.

This interactions are illustrated below. Orientational modulations of the stacking potential encourage the bases to form coplanar stacks, the twist arising from the different length scales of the backbone separation and the optimum stacking separation. The possibility of unstacking allows single strands to be very flexible. Hydrogen bonding can occur between complementary bases when they are anti-aligned, leading to the formation of double helical structures.

(a) Model interaction sites with their interaction ranges (the typical range of an interaction is twice the radius of the sphere shown).

(b) Representation of these interaction site in a visualisation that makes the planarity of the base clear.

(c) A duplex in this representation.

Indication of the interactions which hold together a typical duplex. V(b.b.) indicates the phosphate-sugar backbone connectivity.

In the original model, all complementary base pairs and stacking partners interact with the same strength (there is no attractive interaction between non-complementary bases). A sequence-dependent parameterisation of the hydrogen-bonding and stacking interactions is included as an option in the code release: a paper discussing this parameterisation and its effects is currently in preparation. The melting temperatures of a set of short DNA oligomers in the coarse-grained model, compared to the melting temperatures as predicted by SantaLucia's nearest-neighbor model ([1]), are available here: [2]

The model does not incorporate the differentiation between the major and minor grooves of DNA double helices, and incorporates electrostatics only through the short-ranged excluded volume. For this reason, it is only appropriate for the study of systems at high salt concentration, when electrostatic interactions are strongly screened.

### Simulation units

The code uses dimensionless energy, mass, length and timescales for convenience. The relationship between simulation units (SU) and SI units is given below.

Simulation unit Physical unit
1 unit of length 8.518x10${\displaystyle ^{-10}}$ m
1 unit of energy 4.142${\displaystyle ^{-20}}$ J
1 unit of Temperature 3000 K
1 unit of Force 4.863${\displaystyle ^{-11}}$ N
1 unit of Mass 1.66${\displaystyle ^{-25}}$ kg
1 unit of Time 1.71${\displaystyle ^{-12}}$ s

The model and its performance is discussed in detail in the following references (the thesis provides the most complete analysis):

T. E. Ouldridge, D.Phil. Thesis, University of Oxford, 2011. Coarse-grained modelling of DNA and DNA self-assembly

T. E. Ouldridge, A. A. Louis and J. P. K. Doye, J. Chem. Phys, 134, 085101 (2011) Structural, mechanical and thermodynamic properties of a coarse-grained DNA model (arXiv)

P. Šulc, F. Romano, T. E. Ouldridge, L. Rovigatti, J. P. K. Doye, A. A. Louis, "arxiv" (2012) Sequence-dependent thermodynamics of a coarse-grained DNA model