Thomas M. A. Fink

St. John's College

University of Cambridge

A Dissertation

Submitted for the Degree

of Doctor of Philosophy at the

University of Cambridge

1998

Contents

• Contents
• List of Figures
• INTRODUCTION
  • Inverse Protein Folding
  • Hierarchical Optimisation
  • Tie Knots
  • Schematic Organisation
  • Publications
• PROTEIN FOLDING, INVERSE PROTEIN
  FOLDING AND Energy LANDSCAPES
  • Protein Folding
  • Inverse Protein Folding
  • Energy Landscapes
  • Smooth vs. Rugged Landscapes
  • Folding Funnels and Free Energy Traps
• LATTICE MODELS AND
  THERMODYNAMIC SEQUENCE SELECTION
  • Lattice Models
  • Folding Dynamics
  • Analytic Representation
  • Shakhnovich Selection Scheme
  • Minimisation of E
  • Minimisation of Z
• STABILITY AND ACCESSIBILITY
  • Introduction
  • Stability and Accessibility
  • Details of Simulation
  • Shift of Pair Potential
  • Protein Folding is Many to One
  • Accessibility-Stability Phase Space
  • Conclusion
• INVERSE PROTEIN FOLDING AS AN ASSOCIATIVE MEMORY
  • Introduction
  • Proteins as Associative Networks
  • Energy Function
  • Capacity from Energetics
  • Capacity from Information Theory
  • Retrieving Memories from Proteins
  • Conclusion
• FUNNEL DESIGN BASED ON
  UNFOLDING DYNAMICS
  • Introduction
  • Generalisation to Weighted Training
  • Simple Blob Model of Unfolding
  • Training to a Funnel
  • Conclusion
• KINETICALLY ORIENTED
  SEQUENCE SELECTION
  • Introduction
  • Kinetically Oriented Sequence Selection
  • Measuring Folding Time
  • Simulated Annealing
  • Probability of Moving Downhill
  • Thermodynamic Guidance
  • Results
  • Sequential MFPT Landscape is Smooth
  • Conclusion
• HIERARCHICAL OPTIMISATION PROBLEMS
  • Traveling Salesman Problem
  • Probabilistic Traveling Salesman Problem
  • Hierarchical Optimisation Problems
  • Combinatoric and Hierarchical Complexity
  • Definition of Hierarchical Optimisation
  • General Optimality Equation
• STOCHASTIC ANNEALING
  • Introduction
  • Simulated Annealing
  • Stochastic Annealing
  • Comparison of Simulated and Stochastic Annealing
  • Probabilistic Traveling Salesman Problem
  • Conclusion
• EXACTLY SOLVABLE
  HIERARCHICAL OPTIMISATION PROBLEM
  • Introduction
  • Description of Problem
  • Optimality Equation
  • Uniform Cost Distribution
  • General Cost Distribution
  • Interpretation as a Percolation Model
  • Conclusion
  • Appendix A: Applying the
    General Optimality Equation
• TIE KNOTS AND RANDOM WALKS
  • Introduction
  • Definition of Tie Knots
  • Tie Knots as Random Walks
  • Size of Knots
  • Shape of Knots
  • Symmetry
  • Balance
  • Untying
  • Topology
  • Conclusion
  • Appendix A: Distribution of End to End
    Distance of Walks in the Class
• EPILOGUE
• References
• About this document ...