Modeling nucleic acids

Computational methods toward accurate RNA structure prediction using coarse-grained and all-atom models

Computational methods can provide significant insights into RNA structure and dynamics, bridging the gap in our understanding of the relationship between structure and biological function. Simulations enrich and enhance our understanding of data derived on the bench, as well as provide feasible alternatives to costly or technically challenging experiments. Coarse-grained computational models of RNA are especially important in this regard, as they allow analysis of events occurring in timescales relevant to RNA biological function, which are inaccessible through experimental methods alone. We have developed a three-bead coarse-grained model of RNA for discrete molecular dynamics simulations. This model is efficient in de novo prediction of short RNA tertiary structure, starting from RNA primary sequences of less than 50 nucleotides. To complement this model, we have incorporated additional base-pairing constraints and have developed a bias potential reliant on data obtained from hydroxyl probing experiments that guide RNA folding to its correct state. By introducing experimentally derived constraints to our computer simulations, we are able to make reliable predictions of RNA tertiary structures up to a few hundred nucleotides. Our refined model exemplifies a valuable benefit achieved through integration of computation and experimental methods.

Computational modeling of peptide-aptamer binding

Evolution is the progressive process that holds each living creature in its grasp. From strands of DNA evolution shapes life with response to our ever-changing environment and time. It is the continued study of this most primitive process that has led to the advancement of modern biology. The success and failure in the reading, processing, replication, and expression of genetic code and its resulting biomolecules keep the delicate balance of life. Investigations into these fundamental processes continue to make headlines as science continues to explore smaller scale interactions with increasing complexity. New applications and advanced understanding of DNA, RNA, peptides, and proteins are pushing technology and science forward and together. Today the addition of computers and advances in science has led to the fields of computational biology and chemistry. Through these computational advances it is now possible not only to quantify the end results but also visualize, analyze, and fully understand mechanisms by gaining deeper insights. The biomolecular motion that exists governing the physical and chemical phenomena can now be analyzed with the advent of computational modeling. Ever-increasing computational power combined with efficient algorithms and components are further expanding the fidelity and scope of such modeling and simulations. This chapter discusses computational methods that apply biological processes, in particular computational modeling of peptide-aptamer binding.

A Method to Predict the 3D Structure of an RNA Scaffold

The ever increasing discoveries of noncoding RNA functions draw a strong demand for RNA structure determination from the sequence. In recently years, computational studies for RNA structures, at both the two-dimensional and the three-dimensional levels, led to several highly promising new developments. In this chapter, we describe a recently developed RNA structure prediction method based on the virtual bond-based coarse-grained folding model (Vfold). The main emphasis in the Vfold method is placed on the loop entropy calculations, the treatment of noncanonical (mismatch) interactions and the 3D structure assembly from motif-based template library. As case studies, we use the glycine riboswitch and the G310-U376 domain of MLV RNA to illustrate the Vfold-based prediction of RNA 3D structures from the sequences.

RNA pseudo-knots simulated with a one-bead coarse-grained model

We present a revised version of a Monte Carlo simulation model for RNA molecules that was introduced in a previous communication [O. Taxilaga-Zetina, P. Pliego-Pastrana, and M. D. Carbajal-Tinoco, Phys. Rev. E 81, 041914 (2010)]. The basic model consists of a series of knowledge-based pair potentials that were obtained from the statistical analysis of large RNAs belonging to the Protein Data Bank. These effective interactions are then used to dress a polymeric chain that reproduces relatively simple secondary structures (e.g., small hairpins). In order to describe more complicated three-dimensional structures such as pseudo-knots, here we include orientational information for the interaction between nucleotides forming hydrogen bonds, as in the case of the Watson-Crick base pairs. As a result, the simulated molecules obtained through the modified model are now consistent with their corresponding experimental configurations.

Topological constraints are major determinants of tRNA tertiary structure and dynamics and provide basis for tertiary folding cooperativity

Recent studies have shown that basic steric and connectivity constraints encoded at the secondary structure level are key determinants of 3D structure and dynamics in simple two-way RNA junctions. However, the role of these topological constraints in higher order RNA junctions remains poorly understood. Here, we use a specialized coarse-grained molecular dynamics model to directly probe the thermodynamic contributions of topological constraints in defining the 3D architecture and dynamics of transfer RNA (tRNA). Topological constraints alone restrict tRNA's allowed conformational space by over an order of magnitude and strongly discriminate against formation of non-native tertiary contacts, providing a sequence independent source of folding specificity. Topological constraints also give rise to long-range correlations between the relative orientation of tRNA's helices, which in turn provides a mechanism for encoding thermodynamic cooperativity between distinct tertiary interactions. These aspects of topological constraints make it such that only several tertiary interactions are needed to confine tRNA to its native global structure and specify functionally important 3D dynamics. We further show that topological constraints are conserved across tRNA's different naturally occurring secondary structures. Taken together, our results emphasize the central role of secondary-structure-encoded topological constraints in defining RNA 3D structure, dynamics and folding.

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.

Computational and experimental characterization of RNA cubic nanoscaffolds

The fast-developing field of RNA nanotechnology requires the adoption and development of novel and faster computational approaches to modeling and characterization of RNA-based nano-objects. We report the first application of Elastic Network Modeling (ENM), a structure-based dynamics model, to RNA nanotechnology. With the use of an Anisotropic Network Model (ANM), a type of ENM, we characterize the dynamic behavior of non-compact, multi-stranded RNA-based nanocubes that can be used as nano-scale scaffolds carrying different functionalities. Modeling the nanocubes with our tool NanoTiler and exploring the dynamic characteristics of the models with ANM suggested relatively minor but important structural modifications that enhanced the assembly properties and thermodynamic stabilities. In silico and in vitro, we compared nanocubes having different numbers of base pairs per side, showing with both methods that the 10 bp-long helix design leads to more efficient assembly, as predicted computationally. We also explored the impact of different numbers of single-stranded nucleotide stretches at each of the cube corners and showed that cube flexibility simulations help explain the differences in the experimental assembly yields, as well as the measured nanomolecule sizes and melting temperatures. This original work paves the way for detailed computational analysis of the dynamic behavior of artificially designed multi-stranded RNA nanoparticles.

Protein modeling: what happened to the "protein structure gap"?

Computational modeling of three-dimensional macromolecular structures and complexes from their sequence has been a long-standing vision in structural biology. Over the last 2 decades, a paradigm shift has occurred: starting from a large "structure knowledge gap" between the huge number of protein sequences and small number of known structures, today, some form of structural information, either experimental or template-based models, is available for the majority of amino acids encoded by common model organism genomes. With the scientific focus of interest moving toward larger macromolecular complexes and dynamic networks of interactions, the integration of computational modeling methods with low-resolution experimental techniques allows the study of large and complex molecular machines. One of the open challenges for computational modeling and prediction techniques is to convey the underlying assumptions, as well as the expected accuracy and structural variability of a specific model, which is crucial to understanding its limitations.

Atomistic Monte Carlo simulation of lipid membranes

Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

SMMRNA: a database of small molecule modulators of RNA

We have developed SMMRNA, an interactive database, available at http://www.smmrna.org, with special focus on small molecule ligands targeting RNA. Currently, SMMRNA consists of ∼770 unique ligands along with structural images of RNA molecules. Each ligand in the SMMRNA contains information such as Kd, Ki, IC50, ΔTm, molecular weight (MW), hydrogen donor and acceptor count, XlogP, number of rotatable bonds, number of aromatic rings and 2D and 3D structures. These parameters can be explored using text search, advanced search, substructure and similarity-based analysis tools that are embedded in SMMRNA. A structure editor is provided for 3D visualization of ligands. Advance analysis can be performed using substructure and OpenBabel-based chemical similarity fingerprints. Upload facility for both RNA and ligands is also provided. The physicochemical properties of the ligands were further examined using OpenBabel descriptors, hierarchical clustering, binning partition and multidimensional scaling. We have also generated a 3D conformation database of ligands to support the structure and ligand-based screening. SMMRNA provides comprehensive resource for further design, development and refinement of small molecule modulators for selective targeting of RNA molecules.

Advances in the determination of nucleic acid conformational ensembles

Conformational changes in nucleic acids play a key role in the way genetic information is stored, transferred, and processed in living cells. Here, we describe new approaches that employ a broad range of experimental data, including NMR-derived chemical shifts and residual dipolar couplings, small-angle X-ray scattering, and computational approaches such as molecular dynamics simulations to determine ensembles of DNA and RNA at atomic resolution. We review the complementary information that can be obtained from diverse sets of data and the various methods that have been developed to combine these data with computational methods to construct ensembles and assess their uncertainty. We conclude by surveying RNA and DNA ensembles determined using these methods, highlighting the unique physical and functional insights obtained so far.

Molecular modeling of nucleic acid structure

This unit is the first in a series of four units covering the analysis of nucleic acid structure by molecular modeling. The unit provides an overview of the computer simulation of nucleic acids. Topics include the static structure model, computational graphics and energy models, the generation of an initial model, and characterization of the overall three-dimensional structure.

Coarse-grained simulations of RNA and DNA duplexes

Although RNAs play many cellular functions, little is known about the dynamics and thermodynamics of these molecules. In principle, all-atom molecular dynamics simulations can investigate these issues, but with current computer facilities, these simulations have been limited to small RNAs and to short times. HiRe-RNA, a recently proposed high-resolution coarse-grained RNA that captures many geometric details such as base pairing and stacking, is able to fold RNA molecules to near-native structures in a short computational time. So far, it had been applied to simple hairpins, and here we present its application to duplexes of a couple dozen nucleotides and show how with replica exchange molecular dynamics (REMD) we can easily predict the correct double helix from a completely random configuration and study the dissociation curve. To show the versatility of our model, we present an application to a double stranded DNA molecule as well. A reconstruction algorithm allows us to obtain full atom structures from the coarse-grained model. Through atomistic molecular dynamics (MD), we can compare the dynamics starting from a representative structure of a low temperature replica or from the experimental structure, and show how the two are statistically identical, highlighting the validity of a coarse-grained approach for structured RNAs and DNAs.

Connecting the kinetics and energy landscape of tRNA translocation on the ribosome

Functional rearrangements in biomolecular assemblies result from diffusion across an underlying energy landscape. While bulk kinetic measurements rely on discrete state-like approximations to the energy landscape, single-molecule methods can project the free energy onto specific coordinates. With measures of the diffusion, one may establish a quantitative bridge between state-like kinetic measurements and the continuous energy landscape. We used an all-atom molecular dynamics simulation of the 70S ribosome (2.1 million atoms; 1.3 microseconds) to provide this bridge for specific conformational events associated with the process of tRNA translocation. Starting from a pre-translocation configuration, we identified sets of residues that collectively undergo rotary rearrangements implicated in ribosome function. Estimates of the diffusion coefficients along these collective coordinates for translocation were then used to interconvert between experimental rates and measures of the energy landscape. This analysis, in conjunction with previously reported experimental rates of translocation, provides an upper-bound estimate of the free-energy barriers associated with translocation. While this analysis was performed for a particular kinetic scheme of translocation, the quantitative framework is general and may be applied to energetic and kinetic descriptions that include any number of intermediates and transition states.

RNA under tension: Folding Landscapes, Kinetic partitioning Mechanism, and Molecular Tensegrity

Non-coding RNA sequences play a great role in controlling a number of cellular functions, thus raising the need to understand their complex conformational dynamics in quantitative detail. In this perspective, we first show that single molecule pulling when combined with with theory and simulations can be used to quantitatively explore the folding landscape of nucleic acid hairpins, and riboswitches with tertiary interactions. Applications to riboswitches, which are non-coding RNA elements that control gene expression by undergoing dynamical conformational changes in response to binding of metabolites, lead to an organization principle that assembly of RNA is determined by the stability of isolated helices. We also point out the limitations of single molecule pulling experiments, with molecular extension as the only accessible parameter, in extracting key parameters of the folding landscapes of RNA molecules.

Novel conformation of an RNA structural switch

The RNA duplex, (5′GACGAGUGUCA)₂, has two conformations in equilibrium. The nuclear magnetic resonance solution structure reveals that the major conformation of the loop, 5′GAGU/3′UGAG, is novel and contains two unusual Watson–Crick/Hoogsteen GG pairs with G residues in the syn conformation, two A residues stacked on each other in the center of the helix with inverted sugars, and two bulged-out U residues. The structure provides a benchmark for testing approaches for predicting local RNA structure and a sequence that allows the design of a unique arrangement of functional groups and/or a conformational switch into nucleic acids.

Structure, Stiffness and Substates of the Dickerson-Drew Dodecamer

The Dickerson-Drew dodecamer (DD) d-[CGCGAATTCGCG]₂ is a prototypic B-DNA molecule whose sequence-specific structure and dynamics have been investigated by many experimental and computational studies. Here, we present an analysis of DD properties based on extensive atomistic molecular dynamics (MD) simulations using different ionic conditions and water models. The 0.6-2.4-µs-long MD trajectories are compared to modern crystallographic and NMR data. In the simulations, the duplex ends can adopt an alternative base-pairing, which influences the oligomer structure. A clear relationship between the BI/BII backbone substates and the basepair step conformation has been identified, extending previous findings and exposing an interesting structural polymorphism in the helix. For a given end pairing, distributions of the basepair step coordinates can be decomposed into Gaussian-like components associated with the BI/BII backbone states. The nonlocal stiffness matrices for a rigid-base mechanical model of DD are reported for the first time, suggesting salient stiffness features of the central A-tract. The Riemann distance and Kullback-Leibler divergence are used for stiffness matrix comparison. The basic structural parameters converge very well within 300 ns, convergence of the BI/BII populations and stiffness matrices is less sharp. Our work presents new findings about the DD structural dynamics, mechanical properties, and the coupling between basepair and backbone configurations, including their statistical reliability. The results may also be useful for optimizing future force fields for DNA.

Molecular modeling of nucleic acid structure

This unit is the first in a series of four units covering the analysis of nucleic acid structure by molecular modeling. This unit provides an overview of computer simulation of nucleic acids. Topics include the static structure model, computational graphics and energy models, generation of an initial model, and characterization of the overall three-dimensional structure.