The effect of topology on the structure and free energy landscape of DNA kissing complexes

Abstract

We use a recently developed coarse-grained model for DNA to study kissing complexes formed by hybridization of complementary hairpin loops. The binding of the loops is topologically constrained because their linking number must remain constant. By studying systems with linking numbers −1, 0, or 1 we show that the average number of interstrand base pairs is larger when the topology is more favourable for the right-handed wrapping of strands around each other. The thermodynamic stability of the kissing complex also decreases when the linking number changes from −1 to 0 to 1. The structures of the kissing complexes typically involve two intermolecular helices that coaxially stack with the hairpin stems at a parallel four-way junction.

Collective translational and rotational Monte Carlo moves for attractive particles

“…We thus conclude that although our tests confirm the validity of VMMC in the limit of small clusters, they do not provide strong numerical evidence that the algorithm is valid for large moving clusters, and in that limit we can only rely on analytical considerations deriving the VMMC. We stress that other unpublished tests [24] have been performed [14] comparing VMMC with molecular dynamics simulations in systems where collective motion is important.…”

“…The requirement (14) can be easily achieved in conventional (static) cluster algorithms because p (μ) ij only depends on the energy of (i,j ) in state μ, and p (ν) ij only depends on the energy of (i,j ) in state ν, and these energies are clearly the same for pairs outside the boundary [see the first identity in Eq. (6) which applies for (i,j ) / ∈ B].…”

“…In contrast, p (μ) ij in (dynamic) VMMC also depends on the energy of (i,j ) in state ν. To satisfy relation (14) in the dynamical linking process is not so straightforward because it is not known whether (i,j ) belongs to the boundary of C, during the construction of C. Hence, it is assumed that during the cluster selection (i,j ) does not belong to the boundary, and this assumption is corrected by a bias in the cluster move acceptance probability for pairs which end up in the boundary. Moreover, in order to apply the early rejection scheme [19], which simplifies and accelerates the algorithm, the link is formed in two link formation tests as follows.…”

“…This can make it resemble Brownian or Stokesian dynamics, if the parameters within the method are chosen with regard to physical quantities, such as size-dependent diffusion coefficients. Although VMMC has begun to be used in the simulation of various aggregation or self-assembly processes [10][11][12][13][14][15][16][17], we believe that there is a need to present the algorithm in a completely clear form, especially in its symmetrized version. For clarity, and for reasons described below, the Brownian or Stokesian dynamical aspects are not considered here.…”

“…For clarity, and for reasons described below, the Brownian or Stokesian dynamical aspects are not considered here. VMMC can, indeed, be used just to investigate the thermodynamic properties [14].…”