Computation and Visualization in Multiscale Modelling of DNA Mechanics

Amongst the substances found in any living organism one of the most central in the workings of each living cell is deoxyribonucleic acid (DNA). For that reason it has been the subject of research in many of its aspects. These range from DNA sequencing to atomistic-level structural analysis. The most well known property of DNA is its coding function – the fact that it is the carrier of genetic information. It is, however, only a small fraction of the whole DNA (1% in humans) that is responsible for coding for proteins. The other functions of DNA such as transcription, replication and recombination are apparently strongly influenced by mechanical properties of the molecule, i.e. its shape and flexibility at the length scale of several hundreds of base pairs. These, in turn, differ with the sequence. Our main goal here is to provide tools that facilitate the analysis of such sequence-dependent statistical mechanical properties of DNA. Our considerations concern two recently introduced sequence-dependent models of DNA mechanics. The first one, called cgDNA, is a discrete, rigid base, nearest neighbour model with a shifted quadratic energy depending on the internal parameters of the 3D configuration. In this context we describe a method of maximum entropy fitting that can be applied in the procedure of extracting cgDNA parameters from molecular dynamics simulation data. We also introduce a formulation within the cgDNA framework that allows modelling of long, repeating sequences as well as closed loops of DNA. We apply this formulation to analyse superhelical structures of the intrinsic shape of such repeating sequences. Finally a technique for efficiently computing persistence lengths of short (∌ 200 bp long) DNA oligomers using an optimized Monte Carlo code within the cgDNA model is presented. The second mechanics model of DNA to be considered is the continuous elastic birod. In this setting the DNA is modelled as two long, thin elastic rods with local, elastic interactions. The associated sequence-dependent birod Hamiltonian system has coefficient functions extracted from the cgDNA model. For this model we address issues concerning the use of these coefficients in numerical computation. We then describe the bBDNA software, which provides a graphical user interface for running computations within the model. We end with a presentation of example results of numerical simulations obtained using bBDNA and numerical techniques adapted from elastic rod models.