Peter G. Bolhuis

van't Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands

TABLE OF CONTENTS

1. Abstract

2. Introduction

2.1. Defining the protein folding problem

2.2. Native state stability

2.3. Two-state behavior

2.4. Energy landscapes guide the folding mechanism

2.5. Folding rate determining factors

2.6. Investigating the transition state with phi-analysis

3. Protein simulations

3.1. Molecular simulation

3.2. Molecular models for proteins

3.3. Order parameters

3.4. What can simulation do for us?

4. Exploring the free energy landscape

4.1. Free energy of folding

4.2. Biased sampling

4.3. Metadynamics

4.4. Replica exchange/parallel tempering

5. Protein folding kinetics and mechanism

5.1. Parallel replica molecular dynamics

5.2. High temperature trajectories

5.3. Rare event methods

5.3.1. Bennett Chandler algorithm

5.3.2. The reaction coordinate problem

5.4. Path sampling

5.4.1. Sampling the transition path ensemble

5.4.2. The shooting algorithm

5.4.3. Stochastic shooting algorithm

5.4.4. Rate constants

5.5.Coarse-graining kinetics

5.5.1. Partial paths and Milestoning

5.5.2. Markovian state models and stochastic road maps

5.5.3. Mapping the kinetics on reaction coordinates

5.6. Analyzing the path ensemble

5.6.1. Committors and the Transition State Ensemble

5.6.2. Testing reaction coordinates with committor distributions

5.6.3. Genetic neural networks

5.6.4. Bayesian path statistics

5.6.5. Likelihood Maximization

6. Application of path sampling techniques on protein folding

6.1.The GB1 beta-hairpin

6.1.1. Introduction

6.1.2. TPS of GB1

6.1.3. Folding rate calculation

6.2. Trp-cage

6.2.1. Introduction

6.2.2. Order parameters

6.2.3. Replica exchange MD

6.2.4. Transition path sampling

6.2.5. Transition states

6.2.6. Summary

7. Perspective

8. References

1. ABSTRACT