In Silico Examination of the Structure of Closed Naked DNA and Protein/DNA Complexes

We created a user-friendly application, called 3DNAdesigner, that allows a user to construct minimum-energy configurations of open linear and spatially confined DNA molecules. Comprehension of DNA and protein/drug-bound DNA in biological processes, such as transcription, requires an understanding of their structure. When analyzing large DNA systems the complexity of the molecular dynamics in such structures makes it necessary to simplify models of the molecules due to the vast computational requirements of all-atom based simulations. Our model consists of two primary simplifications. First, it focuses on the interactions between adjoining base pairs, not all atoms. Second, the base pairs are modeled as rectangular slabs that are subject to small elastic deformations. These assumptions allow the use of a base-pair level theory of DNA elasticity.

3DNAdesigner enables a wider audience to build models of superhelical DNA. In order to address this need we identified a core set of input variables needed to generate meaningful models, without requiring the user to modify the source code, and to satisfy a wide range of interests. The resulting set of input data include (i) the sequence of the structure, (ii) the spatial boundary conditions placed on the ends of the molecule, (iii) the decision of whether or not to bind one or more proteins or drugs to sites along the sequence, and (iv) the identities of the latter proteins or drugs. In order to create the most straightforward and user-friendly experience possible with our new modeling package, we decided to capture the capabilities of our equilibrium configuration application in a graphical user interface, or GUI.

3DNAdesigner, expertly guides the users through the process of inputting the details required to generate a meaningful model by presenting them with a series of wizards that take them through the process step by step. Once the user has provided the proper input, the model is generated. However, in order to create a structure with the ends held in a particular spatial arrangement, such as a closed circle or protein-mediated loop, initial values of moments and forces are applied to one of the ends. This set of moments and forces is and initial guess needed to kickoff the iterations of the Newton-Raphson based minimum-energy calculations, which tries to find a stable configuration.

The output of 3DNAdesigner includes the coordinates of the constituent base-pairs (in the form of the origins and local coordinate axes of each pair) and detailed data on the topology (Twist, Wr, Lk), the total elastic energy E_Total of the fragment, and the six base-pair-step parameters (Shift, Slide, Rise, Tilt, Roll, Twist). 3DNAdesigner also provides the user with a three-dimensional visualization of the resulting structure so that (s)he can investigate it in greater detail. Also included in the output is a new definition of the twist that we developed for DNA base-pair steps called the twist of supercoiling, Tw^SC. Tw^SC is related to the overall folding of the DNA molecule and is a new contribution to the field of DNA topology.

The software was used to create minimum-energy configuration of DNA mini-circles and DNA/protein complexes. The stabilities of all converged configurations are calculated and quantified through the examination of the elastic energies. We found that the binding of EcoRV endonuclease protein affected the overall fold of the DNA mini-circles and changed the Lk and energy from that of the naked structure. This type of result might be of interest to a lab performing in vitro studies of their sequences. We also found numerous minimum-energy configurations of the Lac operon bound to the Lac repressor and compared them to being in the presence of the architectural prokaryotic protein called HU.