1. Introduction 111

2. Levinthal's paradox and energy landscapes 115

2.1 Including randomness in the energy function 121

2.2 Some effects of energetic correlations between structurally similar states 126

3. Resolution of problems by funnel theory 128

3.1 Physical origin of free-energy barriers 133

4. Generic mechanisms in folding 138

4.1 Collapse, generic and specific 139

4.2 Helix formation 139

4.3 Nematic ordering 141

4.4 Microphase separation 142

5. Signatures of a funneled energy landscape 145

6. Statistical Hamiltonians and self-averaging 152

7. Conclusions and future prospects 156

8. Acknowledgments 157

9. Appendix: Glossary of terms 157

10. References 158

The current explosion of research in molecular biology was made possible by the profound discovery that hereditary information is stored and passed on in the simple, one-dimensional (1D) sequence of DNA base pairs (Watson & Crick, 1953). The connection between heredity and biological function is made through the transmission of this 1D information, through RNA, to the protein sequence of amino acids. The information contained in this sequence is now known to be sufficient to completely determine a protein's geometrical 3D structure, at least for simpler proteins which are observed to reliably refold when denatured in vitro, i.e. without the aid of any cellular machinery such as chaperones or steric (geometrical) constraints due to the presence of a ribosomal surface (for example Anfinsen, 1973) (see Fig. 1). Folding to a specific structure is typically a prerequisite for a protein to function, and structural and functional probes are both often used in the laboratory to test for the in vitro yield of folded proteins in an experiment.