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Protocols for the In Silico Design of RNA Nanostructures

  • Bruce A. Shapiro
  • Eckart Bindewald
  • Wojciech Kasprzak
  • Yaroslava Yingling
Protocol
Part of the Methods in Molecular Biology™ book series (MIMB, volume 474)

Summary

Recent developments in the field of nanobiology have significantly expanded the possibilities for new modalities in the treatment of many diseases, including cancer. Ribonucleic acid (RNA) represents a relatively new molecular material for the development of these biologically oriented nanodevices. In addition, RNA nanobiology presents a relatively new approach for the development of RNA-based nanoparticles that can be used as crystallization substrates and scaffolds for RNA-based nanoarrays. Presented in this chapter are some methodological shaped-based protocols for the design of such RNA nanostructures. Included are descriptions and background materials describing protocols that use a database of three-dimensional RNA structure motifs; designed RNA secondary structure motifs; and a combination of the two approaches. An example is also given illustrating one of the protocols.

Key Words

Molecular dynamics molecular mechanics RNA building blocks RNA 3D modeling RNA databases RNA motifs RNA nanostructure RNA secondary structure RNA structure 

1 1. Introduction

The field of nanobiology holds great opportunities for the development of methodologies for treatment of various diseases, including cancer, as well as for the development of tools that can be used for the diagnosis and prognosis of these diseases. RNA (ribonucleic acid) represents a relatively new molecular modality for the development of these biologically oriented nanodevices. Without associated proteins, RNA-based therapeutics have a relatively low immune response and therefore represent a safe and effective means for the delivery of multiple therapeutic agents. These include siRNAs (small interfering RNAs) for downregulation of gene expression of multiple genes in multiple cell types; RNA aptamers (RNA sequences and structure that target specified binding sites); ribozymes (RNAs with catalytic properties); antisense RNA (for binding specific sites for gene regulation); and molecular beacons and sensors. In addition, RNA nanoscale entities can be used for the development of self-assembling nanoar-rays, which may contain functional molecular entities such as biosensors or act as substrates for crystallization.

2 2. Structural and Functional Capabilities of RNA for Nanotechnology

RNA is a biopolymer that is composed of four nucleotides, two purines (adenine and guanine), and two pyrimidines (uracil and cytosine). These nucleotides are usually abbreviated as A, G, U, and C, respectively. RNA is synthesized as a single-stranded molecule that can fold on itself via complementary basepairing interactions, usually between purines and pyrimidines. The strongest basepair is G-C, followed by A-U and G-U and other possible combinations. These basepairs tend to stack and form helices, which are energetically favorable. The helical region of RNA has a well-known nanometer-scale structural geometry, approximately 2.86 nm per helical turn with 11 basepairs and an approximate 2.3-nm diameter. The unpaired nucleotides can form bulges, symmetric and asymmetric internal loops and hairpin loops (see Fig. 1 for some typical examples), single-stranded overhangs or sticky tails, and other unpaired motifs. Unpaired nucleotides usually aid in the formation of helical junctions and bends. Moreover, the unpaired nucleotides can facilitate further structural assembly into more complex structures by forming complementary basepairing or inter- and intramolecular interactions of the different single-stranded regions in the RNA. One of the most important examples of such assembly would be loop—loop contacts, such as kissing loops (see Fig. 1). Thus, even though RNA is chemically simple, involving only four nucleotides, it can form complex structures that are directly related to its complex function. However, artificial RNA structures can also be created in which the basepairing can be relatively simply controlled and predicted due to the natural tendency of RNA to form basepairs.
Fig. 1

Typical RNA motifs. Illustrated are the secondary and the associated three-dimensional (3D) structural motifs that are frequently found in RNA structures. These are representative of some of the common building blocks that can be used to construct RNA nanoparticles. Seen are (a) a hairpin loop, (b) a triple base bulge loop, (c) a symmetric internal loop, (d) a multibranch three-way junction, and (e) a kissing loop structure construct with two complementary hairpin loops.

RNAs have very versatile functionalities, and the importance and capabilities of these are still being discovered. RNA functionalities include a carrier of genetic information (messenger RNA), catalytic properties, RNA editing, gene silencing, and transcriptional and translational control, to name a few.

The versatility of RNA's function and structure makes it a very good molecule for use in nanobiology. Moreover, a protein-free RNA does not induce significant immune response and thereby makes RNA nanoparticles attractive for medicinal use. Such all-RNA nanoparticles can thus limit antibody production and cellular immune reaction. Thus, nanoparticles constructed entirely from RNA can potentially be used in long-term treatment of chronic diseases such as cancer, hepatitis B, or AIDS. However, a limiting factor for RNA nanoparticles is their stability in the bloodstream and nonspecific cellular uptake, posing a requirement for high dosage. The relative stability can be controlled by the chemical modification of the backbone; addition of proteins, lipids (1), or polymeric chains; as well as the formation of relatively compact structures (2,3). Targeting can be controlled by the use of appropriate RNA aptamers.

3 3. Building Block Approach for the Design of RNA Nanoparticles

The prediction and design of large macromolecular structures is drastically simplified if one can adopt a modular approach (4). This means designing different regions of the target structure independently. This approach works best if the target structure is separable into clearly defined domains. Ideal domains are portions of the macromolecular assembly that fold virtually independently into energetically stable units.

RNA can, in many cases, be regarded as a set of hierarchical modular objects (4,5). This is exemplified by the fact that pseudoknot-free RNA secondary structures of single sequences can be represented as tree data structures (6,7). The more interactions the RNA nanostructure possesses beyond a simple tree representation (like pseudoknots, or non-canonical tertiary interactions), the more the modularity of the RNA structure will be weakened.

Even if semi-independent domains cannot be identified, it is still possible to use fragments of RNA molecules as building blocks. Pseudoknot-free RNA structures can be separated into n-way junctions, hairpin structures, single-stranded regions, and helices. One approach is to extract from known structures unique and hard-to-predict n-way junctions as molecular building blocks. The requirements for a building block are somewhat weaker compared to a domain. Energetic stability might be desirable but is not a requirement per se. For example, the precise geometry of a three-way junction taken from a ribosome structure might be a result of interactions with the local environment of the junction. If this junction is extracted from its environment, one would expect the original geometry to be feasible, but not necessarily energetically optimal. The junction might still be a very useful building block in the target structure in which it is implanted because the inherent geometric rigidity of the target structure might supersede the orientational preference of that junction. An example of this would be an RNA tetrahedron, for which flexible three-way junctions at the corners should significantly reduce the flexibility of the tetrahedron because of the inherent overall rigidity of the structure.

Several experimental groups have shown that RNA can be used as efficient nanoparticles and scaffolds that are built from specific building blocks. Small structural fragments found in the ribosome and HIV have been used in the design of artificial RNA building blocks, called tectoRNAs (8). Each tectoRNA contains four right-angle motifs. These right-angle motifs have a structural element that forms a 90° angle between two adjacent helices, which are capped with a hairpin loop. The hairpin loops are programmed to interact with each other in a precise manner via formation of specific noncovalent loop—loop interactions, which are based on HIV kissing loops. Each right-angle motif also has an interacting single-stranded 3′ end, called a sticky tail. The sticky tails further allow the assembly of tetramers into complex nanoarrays. Thus, these tectoRNAs can be programmed to self-assemble into novel nano- and mesoscale biofabrics with controllable directionality, topology, and geometry (8,9). Moreover, such RNA—RNA interactions can guide the precise deposition of gold nanoparticles (10). For example, self-assembling tectoRNA ladders have been shown to induce a precise linear arrangement of cationic gold nanoparticles, demonstrating that RNA can control regular spacing of gold nanoparticles and can act as a nanocrown scaffold (11).

Another example is derived from the use of the bacteriophage phi29-encoded RNA (pRNA), which has been reengineered to form dimers, trimers, rods, hexamers, and three-dimensional (3D) arrays several microns in size through interactions of interlocking loops (12,13). Most prominently, a nanoparticle containing a pRNA trimer as a delivery vehicle was used to carry siRNAs to a cell. The cell targeting was accomplished with an RNA receptor-binding aptamer. This RNA nanoparticle was able to block cancer development in cell culture and living mice (14,15).

Also, H-shaped RNA molecular units were built from a portion of the group I intron domain (5,16,17). They were shown to be able to form oriented filaments (9,17). Specific RNA nanoarrangements based on HIV dimerization initiation site stem loops (18,19) were also shown to be capable of thermal isomerization to alternative structures (20).

4 4. RNA Fabrication Techniques

Two main fabrication techniques can be used for programmable self-assembly of nucleic acid nanostructures (21). Assembly may be accomplished through a single-step process, as exemplified by the building of DNA nanostructures (22,23), or in a stepwise fashion, as was used in the building of RNA nano-structures (8). In the single-step approach, all the component molecules are placed together. This mixed set of molecules is then slowly cooled. The methodology works if the building block structure that is desired is more stable than any other possible structures. Thus, through the annealing process, the building block structures should form first at higher temperatures. As the temperature is lowered, the weaker interactions associated with the nanostructure self-assembly will occur next. Sometimes it is difficult to design sequences that, when folded, have the desired structure well separated energetically from non-desirable alternatives. If this is the case, it may be necessary first to form the building blocks, then at a later stage these building blocks are mixed together to allow for their self-assembly. In addition, it may be necessary to add Mg2+ ions to stabilize tertiary interactions. The multistep approach is more time consuming, and it is also important that the melting temperatures of the populations be well separated.

5 5. Computational Design

Computer modeling is well suited for assisting the experimental community in the design of novel nanostructures. The major advantage of computational nanodesign is that it provides a relatively inexpensive and fast way to explore many structural designs and assess their properties. One can view the design process as proceeding in at least two ways: using an RNA 3D motif approach or using a RNA secondary structure motif approach. These two methodologies have their individual strengths and weaknesses. It is also possible, where appropriate, to iterate back and forth between some of the steps in either protocol at particular points. Figure 2 illustrates the basic flow associated with the two methodologies. We discuss the individual computational components concerned with computer-driven RNA nanodesign, describe some of the specifics of the protocols, and finally show how a protocol can be used in a particular example.
Fig. 2

Illustration of the two RNA nanostructure building protocols. From a user-defined shape, two basic paths can be followed. In path ‘a’, an RNA sequence and its associated secondary structure are determined. A three-dimensional (3D) model of the secondary structure is then built and later used as one of the RNA building block motifs. In path ‘b’, RNA 3D motifs are extracted from a database for the construction of the RNA nanoparticle. One can mix either of the two protocols described in the text to produce the desired structure.

5.1 5.1. RNA Databases

RNA databases are a valuable resource for finding structural motifs and characterizations that can be used in building block design. Atomic structures, derived from the application of X-ray crystallography and nuclear magnetic resonance (NMR), containing RNA can be downloaded from the Protein Data Bank (PDB) (24). The PDB home page now contains various annotations of nucleic acid structures that can be very useful, including backbone torsion angles, basepair geometry parameters, and hydrogen-bonding classification. Several databases contain RNA structures derived from the PDB, offering annotations, classifications, and substructures going beyond the information that the PDB offers.

The Nucleic Acid Database (NDB) is a repository of structural RNA and DNA data (25). It contains nucleic acid structures classified by type (for example, transfer RNAs, ribozyme structures, RNA helices) and experimental method (X-ray crystallography or NMR).

The Structural Classification of RNA (SCOR) database contains a classification of RNA internal loop and hairpin loop structures (26,27). It allows the user to search for motifs by sequence, key word, or PDB/NDB identifier. A novel motif, the extruded helical single strand has been identified with the help of the SCOR database (28).

The NCIR is a database containing structural information about noncanonical RNA basepairs (29,30). It provides access to all RNA structures in which a specified basepair has been found. This is useful for obtaining the original data corresponding to a rare (noncanonical) basepair.

For designing novel RNA structures, it is useful to have a database that contains curated and extracted fragments of RNA structures that can be used as building blocks. This prompted us to develop the RNAJunction database (30a). It provides structural and sequence information of RNA junctions that are extracted from RNA coordinate data files. As mentioned in the section introducing the RNA building block approach, it is the RNA junctions and the relative orientation of its connector helices that are most interesting for the design of RNA structures. The assumption here is that the designer knows the outline of the RNA structure to be built (for example, in the form of a 3D graph). In other words, one typical case is that one knows the number of branches in a junction (for example, a three-way junction) as well as the angles between the direction vectors of the junctions connector helices. Thus, the motivation for RNAJunction is to provide search capabilities with respect to junction order, interhelix angles, sequence, and PDB identifier. Figure 3 shows a screen shot of the database describing an example RNA junction.
Fig. 3

Screen shot illustrating the results of a three-dimensional (3D) RNA motif search. In this particular case, information associated with a two-way junction is portrayed. Seen are the Protein Data Bank (PDB) identifier from which the junction was derived, the approximate angle that the junction attachment points make with each other (angle 60°), the NC=IUBMB classification (indicating that there are two helices separated by a single strand consisting of four bases), an RNAView (102) depiction of the motif, and a 3D rendering of the actual motif.

5.2 5.2. Design From Known RNA Three-Dimensional Motifs

The main approach in 3D motif design of RNA structures starts from an abstract model of the target structure (a 3D graph). One then identifies suitable RNA n-way junctions corresponding to the vertices of order n in that graph. These junction structures are then superimposed onto the graph vertices such that their connector helices are parallel to the edges connecting the vertices. When two junctions of two adjacent vertices have been placed, one then attempts to attach the connector helices corresponding to the connecting edge with an ideal RNA double helix. While the precise order of placing junctions and connecting them with helices depends on the algorithm used, one can see that in this way, in principle, an arbitrarily complex 3D graph can be traced with RNA motifs, provided one can identify suitable junction structures corresponding to each vertex and its connecting edges.

5.3 5.3. Design From RNA Secondary Structure Motifs

In contrast to the 3D motif approach, a somewhat different and potentially more difficult and complicated approach develops the necessary structural motifs from designed RNA secondary structures, which are then used to create modeled RNA 3D motifs. To accomplish these tasks, it is necessary to be able to determine an optimal or near-optimal set of sequences that will form the necessary secondary structures of the RNA building blocks with minimal interaction between the individual building blocks. Thus, programs are needed that, when presented with a sequence, will fold the sequence into the appropriate secondary structure. Programs are also needed that will optimize the sequence so that folding proceeds with minimal interference from the other building blocks. This section describes some of the secondary structure prediction methods as well as an algorithm that can be used to do sequence optimization. Also described is a program that generates initial 3D models from the provided secondary structures.

5.3.1 5.3.1. Secondary Structure Prediction for Optimization of Building Blocks

A secondary structure of RNA can be defined as a list of primary sequence nucleotides that are paired in base—base interactions. The paired nucleotides form secondary structure helices, and the combination of these helices and the single-stranded (unpaired) nucleotides constitutes an RNA structure. The unpaired nucleotides that are totally constrained by one or more helices form the so-called loops (hairpin, bulge, internal, and multibranch). Considering helices and loops as the key motifs, a secondary structure can be represented by a tree topology in which loops form nodes and helices form edges between them. Such a topology representation is also suitable for free-energy calculations since they are based on the assumption that the total free energy of a secondary structure (a tree) is a sum of the free energies of its independent elements (branches). In most general terms, loops tend to destabilize a secondary structure (raise the free energy), while helices and coaxial stacks tend to stabilize it (lower the free energy).

Computational prediction of a secondary structure is a nontrivial task, considering that a sequence of n nucleotides can theoretically form on the order of 1.8 n secondary structures. Numerous approaches to solving the problem have been used, aiming to combine the strengths of both computational and experimental methods. Computational secondary structure prediction algorithms can be divided into two general categories. In the first category, structures of individual sequences are predicted using free-energy minimization algorithms. In the second category, information provided by multiple sequence alignments is used to predict structures. Some programs combine these approaches. A comprehensive review and evaluation of RNA secondary structure prediction programs was presented by Gardner and Giegerich in 2004 (31). Mathews and Turner presented a review of free-energy minimization methods, with an emphasis on dynamic programming-based algorithms (DPAs) (32). For nanoscale structure designs in which the inclusion of pseudoknot interactions could be beneficial, there are several programs capable of pseudoknot prediction based on empirical energy parameters (33, 34, 35, 36, 37, 38). Shapiro et al. (39) reviewed RNA structure prediction programs with an emphasis on RNA 3D modeling from secondary structure data.

5.3.1.1 5.3.1.1. RNA Secondary Structure Prediction for a Single Sequence

When only a single sequence is considered as input, that is, there is no phylo-genetically related sequence data to help (see next subheading), the method most often used for secondary structure prediction is free-energy minimization. While less accurate than the multisequence-based methods, it is a more practical approach in the majority of real-life problems.

The most widely used secondary structure prediction programs, such as Mfold (40), RNAfold (41), and RNAstructure (40,42), use the concepts associated with DPAs. These programs produce a minimum free-energy structure and a sample of energetically suboptimal structures within a requested subop-timal energy range. When it comes to the prediction of wild-type secondary structures, the functional conformation or multiple conformations of a given RNA sequence do not always correspond to a minimum free-energy structure. Therefore, the programs Sfold (43,44) and RNAshapes (45, 46, 47) narrow the search for the most likely solutions to a relatively few representative structures. Some secondary structure prediction algorithms use statistical sampling of known RNA secondary structures to create a model that can then be used to predict the secondary structure of a given new sequence (48).

In general, the DPA-based programs and their derivatives offer a fast and reasonably accurate way of testing what the dominant secondary structure of a given RNA sequence may be. In a somewhat limited way, the solution space sampling programs can indicate if more than one stable conformation for the same sequence is possible. Thus, they make good evaluators of the building blocks nanodesign.

An RNA molecule may pass through several active or inactive conformations over its lifetime. These states may be a function of the kinetics of full-sequence folding, cotranscriptional folding (i.e., folding during sequence elongation), or environmental factors, such as proteins locking a molecule in one of two or more folding states.

Programs approximating folding kinetics implement stochastic simulations (49,50) or use genetic algorithms (GAs). GAs are based on the concepts of biological evolution and the survival of the fittest individuals (51). They include intermediate folding states and are thus capable of capturing unfolding and refolding of domains in transitional structures. GA implementations include our massively parallel GA MPGAfold (52, 53, 54, 55, 56) and the smaller-scale program STAR (57,58). Because of their stochastic nature, they need to be run multiple times to produce consensus structures. We have shown that MPGAfold can capture, in a coarse-grained fashion, the dynamic folding process inherent in many RNA molecules (55,59, 60, 61, 62, 63, 64). MPGAfold and some other algorithms can simulate cotranscriptional folding and thus are capable of capturing folding kinetics unique to RNA transcription. Since the amount of information produced by programs such as MPGAfold is enormous (multiple stochastic runs), we have developed a suite of visual analysis tools, also suitable for DPA results analysis, called StructureLab (61,65).

Some of the algorithms mentioned give you the advantage of exploring folding states, which is important when multistable structural motifs or structural switches are a desired feature of the designed nanostructure. Inversely, if one wants to make sure that a structural building block does not have a likely alternate conformation one may use these folding algorithms.

5.3.1.2 5.3.1.2. Prediction of RNA Secondary Structures and Pseudoknots Using Multiple Sequence Alignments

Programs predicting RNA secondary structures based on alignments of multiple sequences produce a consensus secondary structure from both the energetic and evolutionary information provided by the alignment. This is a potentially more accurate approach than that based on free-energy minimization of single-sequence structures, but it depends on a set of well-aligned sequences with enough diversity to indicate structure-preserving mutations. Programs in this category follow the same basic two-stage paradigm. First, a matrix of scores for each basepair is computed. These scores typically incorporate information based on the thermodynamics of basepairs and covariation for a given pair of positions in the sequences considered. Second, this score matrix is mapped into one unique secondary structure. In our review paper on bridging the gap between 2D and 3D RNA structure prediction (39), we included a detailed discussion of these programs, including our own KNetFold (36,66, 67, 68, 69, 70, 71).

5.3.2 5.3.2. Optimization of Sequence Structure Design

The secondary structure prediction algorithms just described provide useful “structural surveys” of potential building blocks from various wild-type sequences. The next step in a rational structure design (although it may equally well be the first step) is determining the best sequence to fold into a desired (user-defined) secondary structure (72, 73, 74, 75). In the case of a wild-type sequence folding naturally into or close to the desired structure, we may want to check if it could be modified to match the desired structure better or made more stable in its most likely conformation. If the only known constraint is a defined secondary structure, we may want to find a sequence “from scratch” that would fold into it.

The program RNAinverse (75) works by optimizing a sequence, given a secondary structure definition and a possibly partially defined sequence. If no starting sequence is provided, the program generates a random starting sequence. Whichever starting sequence and constraints on its modification are chosen, the program iterates over modified sequences folded by RNAfold (41) until a sequence folding into a minimum free energy (MFE) structure matching the specified structural constraints is produced. Since the MFE stopping criterion may result in only a marginally stable structure, RNAinverse allows for a better approach to achieving a stronger preference for the specified secondary structure by optimizing the frequency of the specified secondary structure in the thermodynamic ensemble (refer to the subheading on suboptimal solution space sampling).

When it comes to nanoscale structure design, the approach taken by RNAinverse for the optimization of one single-stranded sequence has to be extended to multiple strands to deal with multiple building blocks. In this case, the stability of the individual building blocks has to be optimized in parallel with the optimization of the desired building block. Interactions and minimization of unwanted interference between the building blocks is a desired goal. We have developed a program that utilizes RNAinverse to produce sequences for individual building blocks (individual strands), followed by minimization of the unspecified interstrand interactions and optimization of the user-specified interstrand interactions. This procedure is iterative, with RNAfold used for comparing the designed sequence folds to the desired target structures.

5.3.3 5.3.3. Three-Dimensional Modeling of the Structure of the Building Blocks and the RNA Nanostructure

The knowledge of 3D models of RNA nanoparticles is crucial for the optimization of design and the complete understanding of their function and properties. The use of 3D RNA building blocks can be obtained from known solution structures extracted from databases, as discussed, or can be generated using specific 3D modeling software, such as MANIP (76), RNA2D3D (77), or NAB (78). The modeled fragments can then be put together via template-assisted assembly by using software such as RNA2D3D and NanoTiler.

The concept of modeling RNA building blocks by creating the starting coordinates of such an entity from a given secondary structure generated by algorithms such as those described can be done using the program RNA2D3D. This includes some special features for modeling RNA tectosquares. The use of RNA2D3D is exemplified by our modeling of the telomerase pseudoknot domain (79). RNA2D3D can generate, view, and compare 3D RNA molecules. In this software, the 3D atomic coordinates of a nucleotide are initially embedded in a planar representation of an RNA secondary structure and are generated from a reference triad of atoms. The stems are created from the reference triad of its 5′ nucleotide using helical coordinates taken from the Biosym® database. The unpaired nucleotides, bulges, hairpin loops, branching loops, and other nonhelical motifs are generated using the coordinates of their reference triad relative to the 5′ neighboring nucleotide. As a result, a first-order approximation of the actual 3D molecule is established. Structure refinement uses molecular modeling or interactive editing. The interactive editing involves a rotation and translation of a nucleotide or a group of nucleotides and is used for the removal of structural clashes, enforcing tertiary interactions, and modification of mutual stacking.

Sometimes, the structures of the building blocks can benefit from mutating one or several residues. Mutation of residues in the 3D RNA structures can be produced by replacing the original residue with the desired one in the structure using a combination of CHIMERA® and DSViewer® software.

5.4 5.4. Mixing of the Three-Dimensional Motif Protocol With the Secondary Structure Motif Protocol

Different approaches can combine the 3D motif and secondary structure motif protocols. For example, one can start with 3D information that is derived from a database of motifs. Using the assumption that similar secondary structures possess similar tertiary interactions, an algorithm maps the RNA 3D structures found in PDB to their secondary structure equivalents. Other algorithms then measure secondary structure similarity and pick 3D structure motifs from a specialized database, thus providing fragments from which an entire secondary structure and 3D structure of a given sequence can be assembled (80). This approach can be combined with or used separately from the specification of RNA secondary structure templates that will determine the sequences that will fold into some of the RNA building blocks.

Thus, the elements that comprise the final nanostructure design can be derived from database motifs, modeled motifs that may be derived from optimized secondary structures, or motifs that merge sequence and structure from both protocols. The ultimate utility of the designed nanoparticles can only be determined by understanding the structure/function relationships that exist in the underlying RNA components and by having an understanding of the properties of RNA folding. The correct assembly of RNA-based nanoparticles requires both a fundamental understanding of the role that RNA plays in biological processes and an understanding of how these processes can be designed into functional nanoparticles.

5.5 5.5. Checking Stability and Dynamic Characteristics

Once the 3D coordinates of the individual building blocks and nanoparticles have been established, we can use molecular dynamics (MD), molecular mechanics (MM), geometric structural analysis, energetic analysis, and high-temperature simulations to refine the structural characteristics and elucidate the stability, flexibility, and effect of environmental factors on the constructed entities. Described next are some of the tools for refining and determining these 3D structural features.

5.5.1 5.5.1. Molecular Dynamics

The main purpose of molecular dynamics (MD) simulations is to describe molecular motions. MD is a technique in which the time evolution of the molecular system is followed by numerical integration of the equations of motion. The MD method can provide highly detailed information not accessible by other methods, including atomically resolved conformational changes and response to environmental and chemical changes, such as concentration of ions, high temperature, pressure, mutations, and chemical modifications. We have successfully used atomistic MD simulations to model, predict, and characterize structures and dynamic behaviors of various RNA molecules, such as the minimal telomerase RNA pseudoknot domain (79,81,82) and HIV kissing loops (83), for characterization of single-bulge motifs (84), to find the characteristics of the 16s ribosomal RNA S15 binding site (85), and to determine the unfolding and folding characteristics of a tetraloop (86) and RNA nanoparticles.

Molecular dynamics makes possible the dynamic characterization and an exploration of the conformational energy landscape of biomolecules and their surroundings. Recent reviews outlined the successful use of MD simulations to characterize a wide variety of nucleic acid structures (87, 88, 89, 90, 91, 92). The limitations of MD simulations include the size of biomolecules and the relatively short simulation timescale, limited to several tens of nanoseconds. Most important, the reliability of MD depends on accurate force fields for both nucleic acids and solvent. Explicit solvent simulations are most accurate and can provide information on specific water and ion interactions; however, they are more computationally extensive. MD simulations can be significantly accelerated by treating the solvent with continuum dielectric methods. In this case, only the intrasolute electrostatics need to be evaluated (93,94). Even though implicit MD simulations are less accurate than simulations with explicit solvent, they not only permit much longer simulations and larger molecules but also provide a variety of sampled conformations. Considerable improvements in the force field have also been achieved, making simulations more reliable and accurate. The typical force field used for RNA molecules is ff99 (95). There are three major MD software packages generally used for RNA molecules: Amber (96), CHARMM (97), and NAMD (Nanoscale Molecular Dynamics) (98).

5.5.2 5.5.2. Molecular Mechanics

Molecular mechanics (MM) is a method to calculate the structure and energy of molecules based on nuclear motions. MM implements energy minimization methods to study the potential energy surfaces of different molecular systems. MM can also provide important energy-related information, such as the existence of energy barriers between different conformers or steepness of a potential energy surface around a local minimum. MD and MM are usually based on the same classical force fields and thus can be found in the same software packages. For example, the MM-PB(GB)SA module in Amber can be used to calculate the contributions of gas-phase and solvation free energies for snapshots of the MD trajectories. Total MM energies E gas; internal energies E int (i.e., bonds, angles, and dihedrals); and van der Waals E vdw and electrostatic E elec components can be determined. Moreover, the same module can help estimate the enthalpy for folding by calculating the energy difference between folded and coiled RNA structures with the same sequence. The enthalpies for folding can then estimated as ΔH = E tot folded − E tot coiled.

5.6 5.6. Structural Analysis

Groove widths, backbone torsion angles, and local basepair parameters (twist, tilt, roll, shift, slide, and rise) for each strand and stem can be analyzed by the program CURVES (99) and compared to standard A-RNA, B-DNA, and A-DNA triplex helical parameters (100). The standard A-RNA, B-DNA, and A-DNA triplex helices can be built using Insight II®.

Ptraj, a module in Amber, which can also be used as a standalone package, is useful for analyzing MD trajectories, including the calculation of bond angles; dihedral angles; the root mean square differences between various structures; displacements, including atomic positional fluctuations; correlation functions; and many other features.

The evaluation of all of these features is extremely useful for determining the 3D structural characteristics of the designed nano-building blocks and nanostructures whether they are designed using the 3D motif, the secondary structure motif, or the mixed approach. However, one has to keep in mind that the nanoconstructs can ultimately be quite large. This may require significant computing power or the use of coarse-graining techniques to reduce the combinatorics of the calculations.

6 6. Summary of the Three-Dimensional and Secondary Structure Motif Protocols for RNA Nanostructure Design

6.1 6.1. Protocol for Three-Dimensional Motif RNA Nanostructure Design as Defined by NanoTiler

  1. 1.

    Determine the shape of the RNA nanostructure desired.

     
  2. 2.

    Specify the shape in the form of a 3D graph.

     
  3. 3.

    Input the 3D graph coordinate file.

     
  4. 4.

    Read the database of available building blocks (RNA junctions).

     
  5. 5.

    For each vertex in the input graph, identify the junction from the building block database that results in the smallest fitting error.

     
  6. 6.

    Generate double-stranded helices interpolating between the fragments.

     
  7. 7.

    For randomly chosen vertices, attempt to exchange the used junction building blocks to reduce the fitting errors between the junction and the double-stranded helices that were generated to connect the neighboring junctions.

     
  8. 8.

    Optimize sequences of the generated model strands (optional).

     
  9. 9.

    Apply MM and MD to further refine the individual building blocks and the structure as a whole.

     
  10. 10.

    Analyze the structural and functional characteristics of the nanostructure to ensure that they conform to the desired attributes.

     
  11. 11.

    Iterate the procedure as necessary to optimize the desired structural characteristics.

     

Note that the user can specify the acceptable fitting errors for placing junctions and generating interpolating stems. NanoTiler is used for steps 3–8.

6.2 6.2. Secondary Structure Motif Protocol

  1. 1.

    Determine the shape of the RNA nanostructure desired.

     
  2. 2.

    Specify the shape in the form of a 3D graph.

     
  3. 3.

    Input the 3D graph coordinate file.

     
  4. 4.

    Determine the secondary structure templates for the building blocks.

     
  5. 5.

    Run the sequence optimizer to obtain the optimized sequences for the building blocks.

     
  6. 6.

    Use RNA2D3D and other molecular modeling software to obtain the 3D coordinates for the building blocks.

     
  7. 7.

    Apply MM and MD to further refine the individual building blocks and the structure as a whole.

     
  8. 8.

    Analyze the structural and functional characteristics of the nanostructure to ensure that they conform to the desired attributes.

     
  9. 9.

    Iterate the procedure as necessary to optimize the desired structural characteristics.

     

NanoTiler is used for steps 3–5.

6.3 6.3. Mixed Protocol

The mixed protocol involves the use of database structures when obtainable, and the prediction, optimization, and modeling of structural components if necessary. Molecular dynamics and mechanics should also be applied, including analysis of the structural characteristics to ensure that they conform to the desired structural and functional attributes.

6.4 6.4. Example of RNA Nanostructure Design Using the Three-Dimensional Motif Protocol With NanoTiler

Computer-assisted nanodesign can use a shape-based approach by which the desired shape guides the choice of the specific building blocks. As an example, we show how the computational methods described can be used for the design of an RNA hexagonal shape that is approximately 15 nm in diameter (101, 102). The building blocks shown here were derived from the RNAJunction database. Examples of this concept applied to the automatic model building of hexameric rings are shown in Fig. 4ac. The figure shows that kissing loops can be placed either in the corners (graph vertices) or in the middle of stem regions (corresponding to graph edges). These models have been generated with our newly developed software NanoTiler. Input to the program is a simple representation of the graph as well as a library of possible building blocks. The input graph consists of a hexagonal wire frame structure; the building block library consists of three elements: one two-way junction with a 120° angle, a kissing loop with a 120° angle, and a kissing loop (originating from the structure of the HIV dimer initiation site) corresponding roughly to a 180° angle between the connector stems. The computation time to generate these models with NanoTiler was less than 5 min in each case. Figure 5 illustrates the use of molecular dynamics on the 120° kissing-loop motif shown in Fig. 4a. The results show that the motif is quite stable.
Fig. 4

An example of the workflow in the three-dimensional (3D) motif protocol for generating computer models of RNA nanostructures with NanoTiler and the RNAJunction database (30a). From an abstract 3D graph (a hexagon in this case), an algorithm scans for suitable building blocks in the RNAJunction database. Kissing-loop building blocks (a) or two-way junctions (c) have a 120° angle and can be placed at the graph vertices. The kissing-loop building blocks with a 180° angle (b) are placed in the middle of the graph edges. The three different hexagon RNA structures were built from a library consisting of only these three building blocks. Sticky tails have been added manually by editing the molecular structures.

Fig. 5

Illustrated is a 7-ns molecular dynamics plot of the 120° kissing-loop motif shown in Fig. 4a (102). The plot depicts the root mean square deviation (RMSD) of the motif relative to its average structure. The plot is relatively flat, indicating a stable structure.

Notes

Acknowledgments

We wish to thank Robert Hayes, Christine Viets, and Calvin Grunewald for their contributions to the development of our research tools. Computational support was provided in part by the National Cancer Institute's Advanced Biomedical Computing Center. This publication was supported by the Intramural Research Program of the National Institutes of Health, National Cancer Institute, Center for Cancer Research. This publication has been funded in whole or in part with federal funds from the National Cancer Institute, National Institutes of Health, under contract N01-CO-12400. The content of this publication does not necessarily reflect the views or policies of the Department of Health and Human Services, and mention of trade names, commercial products, or organizations does not imply endorsement by the U.S. government.

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Copyright information

© Humana Press, a part of Springer Science + Business Media, LLC 2008

Authors and Affiliations

  • Bruce A. Shapiro
    • 1
  • Eckart Bindewald
    • 2
  • Wojciech Kasprzak
    • 2
  • Yaroslava Yingling
    • 1
  1. 1.Center for Cancer Research Nanobiology ProgramSAIC-Frederick National Cancer InstituteFrederick
  2. 2.Basic Research ProgramSAIC-Frederick Inc., NCI-FrederickFrederick

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