Motifs in nucleic acids: molecular mechanics restraints for base pairing and base stacking

Conformational entropy of the RNA phosphate backbone and its contribution to the folding free energy

While major contributors to the free energy of RNA tertiary structures such as basepairing, base-stacking, and charge and counterion interactions have been studied extensively, little is known about the intrinsic free energy of the backbone. To assess the magnitude of the entropic strains along the phosphate backbone and their impact on the folding free energy, we have formulated a mathematical treatment for computing the volume of the main-chain torsion-angle conformation space between every pair of nucleobases along any sequence to compute the corresponding backbone entropy. To validate this method, we have compared the computed conformational entropies against a statistical free energy analysis of structures in the crystallographic database from several-thousand backbone conformations between nearest-neighbor nucleobases as well as against extensive computer simulations. Using this calculation, we analyzed the backbone entropy of several ribozymes and riboswitches and found that their entropic strains are highly localized along their sequences. The total entropic penalty due to steric congestions in the backbone for the native fold can be as high as 2.4 cal/K/mol per nucleotide for these medium and large RNAs, producing a contribution to the overall free energy of up to 0.72 kcal/mol per nucleotide. For these RNAs, we found that low-entropy high-strain residues are predominantly located at loops with tight turns and at tertiary interaction platforms with unusual structural motifs.

Molecular modeling of nucleic acid structure: energy and sampling

An overview of computer simulation techniques as applied to nucleic acid systems is presented. This unit discusses methods used to treat energy and to sample representative configurations. Emphasis is placed on molecular mechanics and empirical force fields.

Brownian dynamics simulations of single-stranded DNA hairpins

We present a Brownian dynamics model which we use to study the kinetics and thermodynamics of single-stranded DNA hairpins, gaining insights into the role of stem mismatches and the kinetics rates underlying the melting transition. The model is a base-backbone type in which the DNA bases and sugar-phosphate backbone are represented as single units (beads) in the context of the Brownian dynamics simulations. We employ a minimal number of bead-bead interactions, leading to a simple computational scheme. To demonstrate the veracity of our model for DNA hairpins, we show that the model correctly captures the effects of base stacking, hydrogen bonding, and temperature on both the thermodynamics and the kinetics of hairpin formation and melting. When cast in dimensionless form, the thermodynamic results obtained from the present model compare favorably with default predictions of the m-fold server, although the present model is not sufficiently robust to provide dimensional results. The kinetic data at low temperatures indicate frequent but short-lived opening events, consistent with the measured chain end-to-end probability distribution. The model is also used to study the effect of base mismatches in the stem of the hairpin. With the parameters used here, the model overpredicts the relative shift in the melting temperature due to mismatches. The melting transition can be primarily attributed to a rapid increase in the hairpin opening rate rather than an equivalent decrease in the closing rate, in agreement with single-molecule experimental data.

Molecular modeling of nucleic acid structure: setup and analysis

The last in a set of units by these authors, this unit addresses some important remaining questions about molecular modeling of nucleic acids. It describes how to choose an appropriate molecular mechanics force field; how to set up and equilibrate the system for accurate simulation of a nucleic acid in an explicit solvent by molecular dynamics or Monte Carlo simulation; and how to analyze molecular dynamics trajectories.

Automated extraction and classification of RNA tertiary structure cyclic motifs

A minimum cycle basis of the tertiary structure of a large ribosomal subunit (LSU) X-ray crystal structure was analyzed. Most cycles are small, as they are composed of 3- to 5 nt, and repeated across the LSU tertiary structure. We used hierarchical clustering to quantify and classify the 4 nt cycles. One class is defined by the GNRA tetraloop motif. The inspection of the GNRA class revealed peculiar instances in sequence. First is the presence of UA, CA, UC and CC base pairs that substitute the usual sheared GA base pair. Second is the revelation of GNR(X_n)A tetraloops, where X_n is bulged out of the classical GNRA structure, and of GN/RA formed by the two strands of interior-loops. We were able to unambiguously characterize the cycle classes using base stacking and base pairing annotations. The cycles identified correspond to small and cyclic motifs that compose most of the LSU RNA tertiary structure and contribute to its thermodynamic stability. Consequently, the RNA minimum cycles could well be used as the basic elements of RNA tertiary structure prediction methods.

Ribosome Builder: A software project to simulate the ribosome

The Ribosome Builder is a software project that provides tools and techniques to create dynamic models of macromolecular systems from the rapidly growing numbers of atomic structural models. It includes a computer program that allows the user to assemble the multiple molecular components within a 3D space and to define the hypothetical interactions of these components with the initial goal of understanding protein translation at an atomic level of detail. The program employs a simplified molecular dynamics forcefield that can simulate the long time-scale events, such as docking of translation factors and mRNA translocation. An embedded scripting language and Application Programming Interface (API) enable the creation of Steered Molecular Dynamics (SMD) simulations through the programmable application of external forces and torques on atoms and bonds. A graphical interface is provided for displaying and interacting with models, recording movies of molecular dynamics movements, and creating annotated 3D simulations of complex macromolecular events. Initial applications of the project include simulation of tetraloop folding, docking of an mRNA on the 30S subunit and a schematic simulation of the translation elongation cycle. The program is an open source project released under the GNU public license.

Empirical force fields for biological macromolecules: overview and issues

Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed.

Computation of DNA backbone conformations

We present an algorithm for the computation of 2'-deoxyribose-phosphodiester backbone conformations that are stereochemically compatible with a given arrangement of nucleic acid bases in a DNA structure. The algorithm involves the sequential computation of 2'-deoxyribose and phosphodiester conformers (collectively referred to as a backbone 'segment'), beginning at the 5'-end of a DNA strand. Computation of the possible segment conformations is achieved by the initial creation of a fragment library, with each fragment representing a set of bond lengths, bond angles and torsion angles. Following exhaustive searching of sugar conformations, each segment conformation is reduced to a single vector, defined by a specific distance, angle and torsion angle, that allows calculation of the O(1)' position. A given 'allowed' conformation of a backbone segment is determined based on its compatibility with the base positions and with the position of the preceding backbone segment. Initial computation of allowable segment conformations of a strand is followed by the determination of continuous backbone solutions for the strand, beginning at the 3'-end. The algorithm is also able to detect repeating segment conformations that arise in structures containing geometrically repeating dinucleotide steps. To illustrate the utility and properties of the algorithm, we have applied it to a series of experimental DNA structures. Regardless of the conformational complexity of these structures, we are able to compute backbone conformations for each structure. Hence, the algorithm, which is currently implemented within a new computer program NASDAC (Nucleic Acids: Structure, Dynamics and Conformation), should have generally applicability to the computation of DNA structures.

Theoretical methods for the simulation of nucleic acids

Different theoretical methods for the description of nucleic acid structures are reviewed. Firstly, we introduce the concept of classical force-field in the context of nucleic acid structures, discussing their accuracy. We then examine theoretical approaches to the description of nucleic acids based on: i) a rigid or quasi-rigid description of the molecule, ii) molecular mechanics optimization, and iii) molecular dynamics. Special emphasis is made ion current state of the art molecular dynamics simulations of nucleic acids structures.