Modeling large nucleic acids Arun Malhotra, Henry A. Gabb and Stephen C. Harvey University of Alabama at Birmingham, Birmingham, USA During the past year, a variety of methods have been developed with which to investigate the structures of large nucleic acids. Modeling techniques ‘are assisting in the refinement of structures, particularly for large RNAs. Supercoiled DNA plasmids are being investigated using models that mimic the known elastic properties of the molecule. The level of detail in a particular modeling method must be appropriate to the question being posed. Current Opinion in Structural Biology 1993, 3:241-246 Introduction A variety of computer algorithms are available for build- ing, manipulating, refining and examining models of pro- teins and nucleic acids [ 11. These approaches, which are generically referred to as molecular mechanics methods, represent each atom of the molecule as a point mass, and treat both covalent and non-covalent interactions using approximations based on classical physics. They continue to be complemented by manually built all-atom models (e.g. [2]). The principal advantage of all-atom approaches - the great level of detail - is also one of their major lim- itations when treating large macromolecules, because model building then becomes cumbersome and com- puter calculations become very expensive. Although the meaning of ‘large’ is not precise, it is rare to see all-atom simulations on a DNA molecule with more than about two or three turns of the double helix, or on an RNA that is substantially larger than tRNA (76 nucleotides). Large nucleic acids are modeled using a variety of pro- cedures. The unifying feature of most of these methods is that they generally use some simplification to reduce the number of degrees of freedom. All-atom models can be built by describing the structure in terms of the internal coordinates (particularly torsion angles), in- stead of Cartesian coordinates; alternatively, they can be described by ‘helicoidal’ coordinates, derived from the generally helical nature of nucleic acid structures. An- other way to reduce the number of degrees of free- dom is to surrender the all-atom level of detail and build the molecule from ‘pseudoatoms’ that represent suitable chunks of the structure. Such reduced repre- sentations are a suitable approximation for ribosomal FUVAs, where the available data only permit the construc- tion of low-resolution models. They are also appropriate for closed circular DNAs, where the models are designed to mimic the known elastic properties of the molecule. This review describes recent advances in the modeling of nucleic acids, with an emphasis on methods other than conventional all-atom methods. Helicoidal coordinate representations All-atom models have traditionally been specified by giv- ing the Cartesian coordinates of every atom in the struc- ture [ 1,2]. For a molecule with N atoms, there are 3N degrees of freedom when the full Cartesian description is used. If we are interested primarily in the relative ener- getics of different conformations, we can, to a very good first approximation, eliminate those degrees of freedom associated with bond stretching and bond-angle bending, leaving only the torsional degrees of freedom associated with rotations about covalent bonds. This is a particu- larly advantageous approximation for nucleic acids, as each nucleotide contains -20 heavy atoms (i.e. -60 degrees of freedom), but only six free torsions (a, p, y, E, 6 and x> and only two important degrees of free- dom for puckering of the huanose ring. A different approach, which also provides about six degrees of freedom per nucleotide (or six degrees of freedom per base pair if the bas&pairing geometry is assumed to be fixed), is to focus on the translational and rotational relationships between one unit and the next. This is done using a coordinate system derived from the natural tendency of nucleic acids to adopt helical confor- mations. Helices can be specified by such terms as rise and twist per residue. These and other coordinates are often called ‘helicoidals’. An EMBO Workshop in l!%S produced a uniform nomenclature for helicoidals [3]. The position of a base pair is described intuitively in terms of three translational and three rotational degrees of freedom. Specifically, base pairs can shift towards the grooves (x displacement), the sugar-phosphate back- bone (y displacement), and/or along the helix axis. Also, Abbreviation RNP-ribonucleoprotein particles. @ Current Biology Ltd ISSN 0959-440X 241