Computer simulation of DNA supercoiling in a simple elastomechanical approximation

An elastic model of DNA under thermal induced stress

DNAs (deoxyribonucleic acids) have the ability to alter its conformation in response to temperature changes to relieve the internal stress. The mistakenly structured DNA can lead to diseases or deformities. The conformation also influences the binding between DNA and other molecular complexes. In the present paper, we investigate the DNA elasticity under the influence of thermal induced stress by employing Kirchhoff's model of a thin elastic rod. The problem is solved by perturbation method to find equilibrium configurations of DNA at different modes. In addition, the model is validated with existing literature in which DNA is stretched or compressed. The behaviors of the helical structure under various temperatures are investigated with the melting temperature of DNA around 80 °C. This elasticity study of DNA could be a groundwork leading to better understandings on the effects of thermal induced stress to DNA's deformation and relevant biological processes in living cells.

Local sequential minimization of double stranded B-DNA using Monte Carlo annealing

A software algorithm has been developed to investigate the folding process in B-DNA structures in vacuum under a simple and accurate force field. This algorithm models linear double stranded B-DNA sequences based on a local, sequential minimization procedure. The original B-DNA structures were modeled using initial nucleotide structures taken from the Brookhaven database. The models contain information at the atomic level allowing one to investigate as accurately as possible the structure and characteristics of the resulting DNA structures. A variety of DNA sequences and sizes were investigated containing coding and non-coding, random and real, homogeneous or heterogeneous sequences in the range of 2 to 40 base pairs. The force field contains terms such as angle bend, Lennard-Jones, electrostatic interactions and hydrogen bonding which are set up using the Dreiding II force field and defined to account for the helical parameters such as twist, tilt and rise. A close comparison was made between this local minimization algorithm and a global one (previously published) in order to find out advantages and disadvantages of the different methods. From the comparison, this algorithm gives better and faster results than the previous method, allowing one to minimize larger DNA segments. DNA segments with a length of 40 bases need approximately 4 h, while 2.5 weeks are needed with the previous method. After each minimization the angles between phosphate-oxygen-carbon A1, the oxygen-phosphate-oxygen A2 and the average helical twists were calculated. From the generated fragments it was found that the bond angles are A1=150 degrees +/-2 degrees and A2=130 degrees +/-10 degrees, while the helical twist is 36.6 degrees +/-2 degrees in the A strand and A1=150 degrees +/-6 degrees and A2=130+/-6 degrees with helical twist 39.6 degrees +/-2 degrees in the B strand for the DNA segment with the same sequence as the Dickerson dodecamer.

Modeling DNA supercoils and knots with B-spline functions

A method is offered to model the complex trajectories of closed circular DNA supercoils and knots. The trajectories are approximated by polygons and analytical expressions of the curves are generated from the polygons with B-spline functions. The resulting curves are used to evaluate the writhe and elastic energy of a series of interrelated supercoils, and to generate detailed atomic models of the deformed double helix.

Molecular mechanics model of supercoiled DNA

We describe a pseudo-atomic model of supercoiled DNA. Each base-pair of the DNA is represented in the model by three particles placed in a plane. The particle triplets are stacked to model stacked base-pairs in double-helical DNA, and closed circular conformations are generated to investigate supercoiling. This model is less detailed than all-atom models, which are too computationally demanding to be used to study supercoiling. On the other hand, this model contains details at the base-pair level and is therefore more elaborate than elastomechanical models. A potential energy function is written in terms of a set of internal co-ordinates defined to resemble a limited number of helical parameters. The modeled helical parameters, helical twist, base-roll, tilt and rise, are the most important parameters of the global shape of DNA. Experimentally measured mechanical properties of DNA are used to define the forces holding the particles together. We then use a procedure incorporating energy minimization and molecular dynamics to locate low energy conformations of the model DNA. The model was found to behave very much like rubber-tubing and elastomechanical models. The conformations and the effects of supercoiling pressure (a number proportional to the degree to which the total twist of the DNA has been altered from its natural value) on these conformations are all very similar to those observed in the latter two models. We also used this model to examine the effects of supercoiling pressure, base-sequence and mechanical properties on the conformations and energies of five sequences. The sequences studied include models of naturally straight DNA and DNA with static or natural bends.