Figure 2.

Simulating dipole vector directional distributions. (a) Definition of two spherical angles describing in-plane (θ) and out-of-plane rotation (ϕ) of a base probe in double-stranded DNA (only the nucleobases are shown). The two neighbouring base pairs are shown above and below the tC–G base pair. The strand in which the base probe is positioned has 5′ directed downwards and 3′ upwards. (b–e) Sampling dipole vectors from two marginal Boltzmann probability distributions. First, samples are drawn in spherical coordinates (b, d) and then subsequently transformed into Cartesian space where samples are located on the unit sphere representing dipole unit vectors (c, e). The form and width of the distribution in (b) and (d) is the same as in (c) and (e), respectively. In (b, c), a harmonic potential is used to describe in-plane and out-of-plane motion, corresponding to sampling a bivariate Gaussian distribution. In (d, e), a harmonic potential is used to describe out-of-plane motion, and a Lennard-Jones potential is used to describe the potential imposed by the in-plane hydrogen-bonding to the complementary base.