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Understanding protein folding with energy landscape theory Part II: Quantitative aspects
- Steven S. Plotkin, José N. Onuchic
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- Journal:
- Quarterly Reviews of Biophysics / Volume 35 / Issue 3 / August 2002
- Published online by Cambridge University Press:
- 21 January 2003, pp. 205-286
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1. Introduction 206
2. Quantifying the notions behind the energy landscape 206
2.1 Basic concepts of the Random Energy Model (REM) 206
2.2 Replica-symmetric partition functions and densities of states 209
2.3 The RHP phase diagram and avoided phase transitions 210
2.4 Basic concepts of the entropy of topologically constrained polymers 212
3. Beyond the Random Energy Model 219
3.1 The GREM and the glass transition in a finite RHP 222
4. Basics of configurational diffusion for RHPs and proteins 227
4.1 Kinetics on a correlated energy landscape 231
5. Thermodynamics and kinetics of protein folding 234
5.1 A protein Hamiltonian with cooperative interactions 234
5.2 Variance of native contact energies 235
5.3 Thermodynamics of protein folding 236
5.4 Free-energy surfaces and dynamics for a Hamiltonian with pair-wise interactions 240
5.5 The effects of cooperativity on folding 242
5.6 Transition-state drift 242
5.7 Phase diagram for a model protein 245
5.8 A non-Arrhenius folding-rate curve for proteins 246
6. Non-Markovian configurational diffusion and reaction coordinates in protein folding 247
6.1 An illustrative example 250
6.2 Non-Markovian rate theory and reaction surfaces 251
6.3 Application of non-Markovian rate theory to simulation data 257
7. Structural and energetic heterogeneity in the folding mechanism 259
7.1 The general strategy 261
7.2 An illustrative example 263
7.3 Free-energy functional 264
7.4 Dependence of the barrier height on mean loop length (contact order) and structural variance 268
7.5 Illustrations using lattice model proteins and functional theory 269
7.6 Connections of functional theory with experiments 271
8. Conclusions and future prospects 273
9. Acknowledgments 274
10. Appendices
A. Table of common symbols 275
B. GREM construction for the glass transition 276
C. Effect of a Q-dependent diffusion coefficient 279
D. A frequency-dependent Einstein relation 279
11. References 281
We have seen in Part I of this review that the energy landscape theory of protein folding is a statistical description of a protein's complex potential energy surface, where individual folding events are sampled from an ensemble of possible routes on the landscape. We found that the most likely global structure for the landscape of a protein can be described as that of a partially random heteropolymer with a rugged, yet funneled landscape towards the native structure. Here we develop some quantitative aspects of folding using tools from the statistical mechanics of disordered systems, polymers, and phase transitions in finite-sized systems. Throughout the text we will refer to concepts and equations developed in Part I of the review, and the reader is advised to at least survey its contents before proceeding here. Sections, figures or equations from Part I are often prefixed with I- [e.g. Section I-1.1, Fig. I-1, Eq. (I-1.1)].
Understanding protein folding with energy landscape theory Part I: Basic concepts
- Steven S. Plotkin, José N. Onuchic
-
- Journal:
- Quarterly Reviews of Biophysics / Volume 35 / Issue 2 / May 2002
- Published online by Cambridge University Press:
- 20 August 2002, pp. 111-167
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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.