1. Background to RNA structure 200

1.1 Types of RNA 200

1.1.1 Transfer RNA (tRNA) 200

1.1.2 Messenger RNA (mRNA) 201

1.1.3 Ribosomal RNA (rRNA) 201

1.1.4 Other ribonucleoprotein particles 202

1.1.5 Viruses and viroids 202

1.1.6 Ribozymes 202

1.2 Elements of RNA secondary structure 203

1.3 Secondary structure versus tertiary structure 205

2. Theoretical and computational methods for RNA secondary structure determination 208

2.1 Dynamic programming algorithms 208

2.2 Kinetic folding algorithms 210

2.3 Genetic algorithms 212

2.4 Comparative methods 213

3. RNA thermodynamics and folding mechanisms 216

3.1 The reliability of minimum free energy structure prediction 216

3.2 The relevance of RNA folding kinetics 218

3.3 Examples of RNA folding kinetics simulations 221

3.4 RNA as a disordered system 227

4. Aspects of RNA evolution 233

4.1 The relevance of RNA for studies of molecular evolution 233

4.1.1 Molecular phylogenetics 234

4.1.2 tRNAs and the genetic code 234

4.1.3 Viruses and quasispecies 235

4.1.4 Fitness landscapes 235

4.2 The interaction between thermodynamics and sequence evolution 236

4.3 Theory of compensatory substitutions in RNA helices 238

4.4 Rates of compensatory substitutions obtained from sequence analysis 240

5. Conclusions 246

6. Acknowledgements 246

7. References 246

This article takes an inter-disciplinary approach to the study of RNA secondary structure, linking together aspects of structural biology, thermodynamics and statistical physics, bioinformatics, and molecular evolution. Since the intended audience for this review is diverse, this section gives a brief elementary level discussion of the chemistry and structure of RNA, and a rapid overview of the many types of RNA molecule known. It is intended primarily for those not already familiar with molecular biology and biochemistry.

Ribonucleic acid consists of a linear polymer with a backbone of ribose sugar rings linked by phosphate groups. Each sugar has one of the four ‘bases’ adenine, cytosine, guanine and uracil (A, C, G, and U) linked to it as a side group. The structure and function of an RNA molecule is specific to the sequence of bases. The phosphate groups link the 5′ carbon of one ribose to the 3′ carbon of the next. This imposes a directionality on the backbone. The two ends are referred to as 5′ and 3′ ends, since one end has an unlinked 5′ carbon and one has an unlinked 3′ carbon. The chemical differences between RNA and DNA (deoxyribonucleic acid) are fairly small: one of the OH groups in ribose is replaced by an H in deoxyribose, and DNA contains thymine (T) bases instead of U. However, RNA structure is very different from DNA structure. In the familiar double helical structure of DNA the two strands are perfectly complementary in sequence. RNA usually occurs as single strands, and base pairs are formed intra-molecularly, leading to a complex arrangement of short helices which is the basis of the secondary structure. Some RNA molecules have well-defined tertiary structures. In this sense, RNA structures are more akin to globular protein structures than to DNA.

The role of proteins as biochemical catalysts and the role of DNA in storage of genetic information have long been recognised. RNA has sometimes been considered as merely an intermediary between DNA and proteins. However, an increasing number of functions of RNA are now becoming apparent, and RNA is coming to be seen as an important and versatile molecule in its own right.

1. Introduction 255

1.1 General thermodynamics 256

2. Nucleic acid thermodynamics 260

2.1 DNA duplexes 261

2.2 RNA duplexes 263

2.3 Hybrid DNA–RNA duplexes 264

2.4 Hydration 267

2.5 Conformational flexibility 269

2.6 Thermodynamics 272

3. Nucleic acid–ligand interactions 277

3.1 Minor groove binders 278

3.2 DNA intercalators 284

3.3 Triple-helical systems 288

3.3.1 Structures 288

3.3.2 Hydration 291

3.3.3 Thermodynamics 291

4. Conclusions 295

5. Acknowledgements 298

6. References 298

In recent years the availability of large quantities of pure synthetic DNA and RNA has revolutionised the study of nucleic acids, such that it is now possible to study their conformations, dynamics and large-scale properties, and their interactions with small ligands, proteins and other nucleic acids in unprecedented detail. This has led to the (re)discovery of higher order structures such as triple helices and quartets, and also the catalytic activity of RNA contingent on three-dimensional folding, and the extraordinary specificity possible with DNA and RNA aptamers.

Nucleic acids are quite different from proteins, even though they are both linear polymers formed from a small number of monomeric units. The major difference reflects the nature of the linkage between the monomers. The 5′–3′ phosphodiester linkage in nucleic acids carries a permanent negative charge, and affords a relatively large number of degrees of freedom, whereas the essentially rigid planar peptide linkage in proteins is neutral and provides only two degrees of torsional freedom per backbone residue. These two properties conspire to make nucleic acids relatively flexible and less likely to form extensive folded structures. Even when true 3D folded structures are formed from nucleic acids, the topology remains simple, with the anionic phosphates forming the surface of the molecule. Nevertheless, nucleic acids do occur in a variety of structures that includes single strands and high-order duplex, triplex or tetraplex (‘quadruplex’) forms. The principles of biological recognition and the related problem of understanding the forces that stabilise such folded structures are in some respects more straightforward than for proteins, making them attractive model systems for understanding general biophysical problems. This view is aided by the relatively facile chemical synthesis of pure nucleic acids of any desired size and defined sequence, and the ease of incorporation of a wide spectrum of chemically modified bases, sugars and backbone linkers. Such modifications are considerably more difficult to achieve with oligopeptides or proteins.