Molecular Modeling of Nucleic Acid UNIT 7.5 Structure Molecular modeling, loosely defined, re- ing highly flexible systems, investigating pro- lates to the use of models to investigate the posed chemical modifications that have yet to three-dimensional structure, dynamics, and be synthesized, or to represent extremes of properties of a molecule or set of molecules. At pressure, temperature, and concentration. As the heart of this is specification of a molecular will become apparent, the methods are steadily model, which provides a molecular structure at improving to the point that reliable predictions an appropriate level of granularity, usually in are emerging. terms of three-dimensional atomic coordinates. A critical point that needs to be made at the Molecular modeling can be approached on outset is that these methods cannot be treated many levels, ranging from energy minimiza- as a “black box” or hands-off procedure; there tion (finding the set of coordinates that mini- is no standard protocol that can be applied. mizes the energy) with a complete ab initio Modeling is really more of an art. As each quantum-mechanical treatment of the energet- situation has differing requirements and needs, ics, to sampling “reasonable” conformations various choices need to be made as to what level with a simplified energy representation or po- of treatment to apply and what model to use. tential, to the manipulation of physical models These choices rely on a critical understanding where no implicit energy representation is in- of the limitations in the methods. Therefore, the cluded. These methods serve not only as tools purpose of this discussion is to open up this to aid in the interpretation of experimental data, black box a bit to allow some understanding of but to directly complement such data by pro- the options and choices a modeler makes, high- viding a relationship between the macroscropic lighting the tradeoffs that must be made in behavior observed experimentally and the mi- accuracy, system size, and time. The discussion croscopic properties represented in the model here and in UNITS 7.8 to 7.10 is not meant to provide or simulation. a complete review of nucleic acid modeling, As discussed in previous units, various mo- nor to substitute for the more complete treat- lecular modeling tools can serve as conforma- ment discussed in the primary literature. In- tional search engines for sampling conforma- stead, these units are intended to provide a tional space subject to the restraints inferred framework that describes molecular modeling from nuclear magnetic resonance (NMR; see of nucleic acids, points out common issues and UNIT 7.2) and crystallography (see UNIT 7.1) ex- limitations, and points the reader to other useful periments. This is a critical step in the refine- information sources. ment of three-dimensional atomic structure. Implicit in this discussion is a realization Inclusion of some representation of the energy, that a molecular model is more than simply a such as through the use of a specially parame- representation of the covalent connectivity or terized empirical force field, can aid in this static structure. The model may also include endeavor by limiting sampling to more realistic some representation of the energetics of the (in terms of energy) conformations. system and perhaps the dynamics over a par- As mentioned above, molecular mechanics ticular time scale. Although it increases the methods can not only be used as a tool, but can utility, supplementing static structure with a directly complement experimental data. For representation of the energy and dynamics of instance, molecular dynamics simulations can molecular motion tremendously increases the be used to aid in the interpretation of NMR cost of the modeling. For example, the simula- order parameters or to estimate anisotropic ro- tions required to accurately represent the se- tational diffusion. In addition, computer simu- quence-specific structure and molecular dy- lation techniques have the potential to give namics of a small, solvated nucleic acid duplex structural and dynamic insight into the atomic (<20 base pairs) on a nanosecond time scale interactions occurring on a time scale (<µsec) would likely require weeks to months on avail- typically not observable due to averaging in able computer workstations, even with simple crystallography and NMR experiments. Ulti- empirical energy representations. Of course, mately, as methods are proven reliable, they can this added information may not always be nec- then be applied in cases where experimentation essary. For example, to investigate whether a Biophysical Analysis of is limited, difficult, or unfeasible, such as study- proposed modification to a DNA base is steri- Nucleic Acids Contributed by Thomas E. Cheatham, III, Bernard R. Brooks, and Peter A. Kollman 7.5.1 Current Protocols in Nucleic Acid Chemistry (2000) 7.5.1-7.5.12 Copyright © 2000 by John Wiley & Sons, Inc. Supplement 6 cally feasible may only require the crude ma- nipulation of a physical model to see an effect. Therefore, it is critical to understand the appli- cability, reliability, and limitations of these methods. In other words, the choice of the model depends on the question being asked. The remainder of the discussion in this unit Figure 7.5.1 Schematic representation of introduces the simplest levels of molecular molecular modeling analysis. modeling applied to nucleic acids. These in- clude generation, evaluation, and charac- Prior to generating an initial molecular terization of the initial molecular model. At this model, it is necessary to choose its repre- simplest level, a nucleic acid model is limited sentation or level of detail. For nucleic acids, to a static representation of the structure in the the structural representation can be approached gas phase. Evaluation of this given model’s on many levels, ranging from the atomic level utility is therefore based on the chemical intui- (including electrons) to coarser levels, such as tion of the modeler, where manipulations to the those that model structure using a single point model are limited to rotation about single per base pair. The realism of the model directly bonds. To move beyond this level, supplement depends on this choice of representation and units in this series will delve more deeply into further depends on what properties one is trying the myriad of issues involved in the computer to represent. As shown in Table 7.5.1, modeling simulation of nucleic acids. These include de- can be considered a tradeoff between the accu- scribing the common energy representations racy, the size and granularity of the system, and for nucleic acids that may be applied (UNIT 7.8), the time scale to be represented. If the model and discussion of how to properly represent the only concerns a single conformation or small electrostatic interactions and solvation effects set of conformations of a molecule of <100 (UNIT 7.9). Additionally, various methods to find atoms, a very accurate energy model and a more representative structures are introduced, description that includes all the atoms and elec- with a focus on molecular dynamics simulation trons can be used (such as ab initio quantum methodologies. Finally, a description of practi- mechanics with a fairly large basis set and even cal issues in nucleic acid simulations will be correlation). However, to investigate the super- provided (UNIT 7.10), such as what force fields coiling of a small DNA plasmid over a micro- are appropriate to apply, how simulations of second time scale, the system can no longer be nucleic acid are set up with explicit solvent and represented at the atomic level, and a much counterions, and how crude relative free energy simpler description of the energetics and a differences can be estimated from molecular coarser representation of the structure must be dynamics simulations. In these discussions, the imposed. However, this may be sufficient to focus will be on the middle ground in terms of represent the properties of interest. Between a size, time scale, and accuracy—that is, the full quantum mechanical treatment appropriate simulation of small nucleic acids (typically less for small molecules and the coarse-grained sin- than ~250 base pairs), with explicit repre- gle point per base pair model appropriate for sentation of the environment (if feasible or large systems, molecular dynamics methods necessary), empirical pairwise potential func- with an empirical potential may give reliable tions, and time scales ranging from the analysis results as long as no “chemistry” is involved of individual snapshots to nanosecond-length (such as bond forming, bond breaking, or elec- simulations. For those readers more interested tron transfer) and highly polarizable metal ions in learning about the simulation of larger nu- are treated at a very approximate level. These ∼ cleic acid systems ( 1,000 to 15,000 base methods can give reliable insight into the se- pairs), a variety of reviews can be consulted quence-specific structure and dynamics of a (Vologodski and Cozzarelli, 1994; Schlick, small nucleic acid duplex in solution. 1995; Olson, 1996). MOLECULAR MODELING The Static Structure Model The practice of molecular modeling basically At the simplest level, and where the repre- Molecular involves the generation of an initial molecular sentation of the model does not include any Modeling of model, evaluation of the model’s utility, and per- reality beyond the covalent connectivity, mo- Nucleic Acid haps manipulation