RNA secondary structure: physical and computational aspects

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.