Protein Folding

1
Protein Folding

• Atlas F. Cook IV Karen Tran

2
Overview

• What is Protein Folding?
• Motivation
• Experimental Difficulties
• Simulation Models
• Configuration Spaces
• Triangular Lattice models
• Pull Moves
• Probabilistic Roadmaps
• Map-Based Master Equation (MME)
• Map-Based Monte Carlo (MMC)
• Conclusion

3
Motivation

• What is protein folding?
• Folding/Morphing process
• 1D Amino Acid Chain ? 3D Folded protein

4
Motivation

• Why study protein folding?
• Proteins regulate almost all cellular functions
• 1D chain dictates 3D shape (NP-Hard)
• 3D Shape determines proteins function

1D amino acid chain
3D folded protein
5
Motivation

• Holy grail of Protein Folding
• Build amino acid chain that
• folds into a desired shape
• and has a nice function (e.g., kill cancer cells)
• How would we do this?

6
Motivation

• Another reason to study protein folding
• Unfolded protein vulnerable protein

7
Motivation

• Misfolded proteins cause diseases
• Alzheimers
• Mad Cow
• Parkinsons
• Understand protein folding ? cure diseases!

8
Terminology

• Primary Structure
• 1D Amino Acid Chain (string)
• MGDVEKGKKIFIMKCSQCH
• Secondary Structure
• Local patterns in a global folding
• Helices and Strands
• Tertiary Structure
• Global 3D folded shape

9
Experimental Difficulties

• Levinthal Paradox
• Exponentially many ways to fold, yet
• folding occurs rapidly (milliseconds to seconds)
• Why is folding so fast?
• Unfolded protein vulnerable protein
• Experimental observation
• Too slow to capture all significant motions
• Our Goal
• Simulate protein folding on computer! ?

10
Simulation Models

• HP Lattice Model Böckenhauer08
• HP Hydrophobic-Polar
• Models forces between Hydrophobic amino acids

11
Simulation Models

• HP Lattice Model Böckenhauer08
• Amino acid ? vertex in a grid
• Protein ? self-avoiding chain in a grid

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Simulation Models

• HP Lattice Model Böckenhauer08
• Spring-like forces are modeled between
  neighboring amino acids.
• Sum of forces for a state ? Energy.

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10
2
4
5
1
2
Energy 16
0
1
3
2
2
5
4
2
1
Energy 8
1
1
2
3
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Simulation Models

• HP Lattice Model Böckenhauer08
• Global min energy
• native state final folded state
• Native state is stable.
• Global minimum is MUCH smaller than local minima.

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2
5
Global min Energy 8
4
2
1
1
1
2
3
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Simulation Models

• HP Lattice Model Böckenhauer08
• A state is defined by the position of every amino
  acid in the chain

A State
Another State
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Simulation Models

• HP Lattice Model Böckenhauer08
• Configuration space set of all possible states
• Exponential to protein length
• Protein folding simulation
• Move from start state ? goal state.

16
Simulation Models

• HP Lattice Model Böckenhauer08
• Move Properties
• Complete moves can reach all feasible states
• Reversible every move has an inverse

17
Simulation Models

• HP Lattice Model Böckenhauer08
• Forward Pull Move
• Pull vertex 5 to a new position

Before move
After move
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Simulation Models

• HP Lattice Model Böckenhauer08
• Tabu Search
• Greedy, heuristic search
• Simulates protein folding
• Pull moves transform start state ? local minimum
• Records recent moves in a Tabu list
• Fast backtracking to different paths
• Summary of HP Lattice Model
• Input Amino acid sequence
• Output Heuristically folded protein

19
Probabilistic Roadmap Model
20
Simulation Models

• Probabilistic Roadmap Song04
• 2D Graph (Configuration space)
• Each point represents an entire state (all amino
  acids).
• Obstacles are infeasible states

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Simulation Models

• Probabilistic Roadmap Song04
• Goal
• Given start goal states
• Find best path from start ? goal

22
Simulation Models

• Probabilistic Roadmap Song04
• 3 Steps
• Node generation
• Generate points randomly (dense near the goal
  state)
• Roadmap Construction
• Connect nearest neighbors ? graph
• Query roadmap
• Dijkstras algorithm ? shortest path
• Shortest path set of states
• Describes the dynamic folding process

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Simulation Models

• Probabilistic Roadmap Song04
• Node generation
• Generate random points
• Obstacles are infeasible (self-overlapping)
  states

24
Simulation Models

• Probabilistic Roadmap Song04
• Roadmap Construction
• Connect nearest neighbors ? graph

25
Simulation Models

• Probabilistic Roadmap Song04
• Query roadmap
• Dijkstras algorithm ? shortest path
• Path set of states that describes the folding
  process

26
Molecular Dynamics Model
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Simulation Models

• Molecular Dynamics Models Tapia07
• Model forces based on Newtons laws of motion
• Very accurate
• Very slow!
• Simulating one microsecond of folding for a 36
  residue protein Months of supercomputer time!
• Cannot handle full length proteins

28
Simulation Models

• Map-based Master Equation (MME) Tapia07
• Fast enough to study full length proteins
• More accurate than simplistic lattice models
• MME is an extension of a Probabilistic Roadmap
• Probabilistic roadmap Viterbi algorithm
• returns one optimal path
• MME Baum-Welch algorithm
• Maintains transition probabilities for every
  state
• Learning is executed until probabilities
  stabilize.
• Can return the probability of any state at time t.

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Simulation Models

• Map-based Monte-Carlo (MMC) Tapia07
• MMC Probabilistic Roadmap Monte-Carlo
• Monte-Carlo Wiki08_MC
• random sampling algorithms result
• Example Battleship
• Make random shots
• Apply prior knowledge
• Battleship 4 vertical/horizontal dots
• Apply algorithms to quickly sink the ship

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Simulation Models

• Map-based Monte-Carlo (MMC) Tapia07
• Fast reasonably accurate
• Models the protein as an articulated figure
• Each joint set of angles
• Movement-based (kinetic) statistics
• Results suggest that
• Local helix structures form first
• Folding occurs around hydrophobic core

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Conclusion

• Protein Folding
• 1D Amino acid chain folds into 3D structure
• Misfolding ? Alzheimers, Parkinsons, Mad Cow
  diseases
• Folding is too fast to observe experimentally
• Four Simulation Models
• Triangular Lattice model (2D Graph)
• Vertex one amino acid
• Moves transition between states

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Conclusion

• Four Simulation Models (cont.)
• Probabilistic Roadmaps
• Vertex represents state of entire protein
• Random sampling Dijkstras alg ? Best folding
  route
• Viterbi (returns one path)
• Map-Based Master Equation (MME)
• Learn probabilities
• Baum-Welch (confidence level for each state)
• Map-Based Monte Carlo (MMC)
• Articulated figures with joints model proteins

33
References

• Böckenhauer08
• Hans-Joachim Böckenhauer, Abu Zafer M. Dayem
  Ullah, Leonidas Kapsokalivas, and Kathleen
  Steinhöfel. A local move set for protein folding
  in triangular lattice models. In Keith A.
  Crandall and Jens Lagergren, editors, WABI,
  volume 5251 of Lecture Notes in Computer Science,
  pages 369381. Springer, 2008.
• Dobson99
• C. Dobson and M. Karplus. The fundamentals of
  protein folding bringing together theory and
  experiment. Current Opinion in Structural
  Biology, 9928101, 1999.

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References

• Song04
• G. Song and N. M. Amato. A motion planning
  approach to folding From paper craft to protein
  folding. Proc. IEEE Transactions on Robotics and
  Automatics, 206071, 2004.
• Tapia07
• Lydia Tapia, Xinyu Tang, Shawna Thomas, and Nancy
  M. Amato. Kinetics analysis methods for
  approximate folding landscapes. Bioinformatics,
  23(13)i539i548, 2007.

35
References

• ?Sali94
• A., E. Shakhnovich, and M. Karplus. How does a
  protein fold? Nature, 369248251, 1994.
• Wiki08
• Wikipedia. Protein folding Wikipedia, the free
  encyclopedia, 2008. http//en.wikipedia.org/wiki/P
  rotein_folding.
• Wiki08_MC
• Wikipedia. Monte-Carlo method Wikipedia, the
  free encyclopedia, 2008. http//en.wikipedia.org/w
  iki/Monte_Carlo_method

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Thank you for your attention.Questions
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Extra Slides
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Simulation Models

• Map-based Master Equation (MME) Tapia07
• MME Probabilistic roadmap Master Equation
• Master Equation set of equations defining the
  probability of a system to be in a discrete set
  of states at a given time.