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 protein’s 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? Kill Cancer Cells Desired Function Required Shape Required Amino Acid Chain

6 Motivation Another reason to study protein folding:  Unfolded protein = vulnerable protein

7 Motivation Misfolded proteins cause diseases:  Alzheimer’s  Mad Cow  Parkinson’s 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 Amino AcidChain

12 Simulation Models HP Lattice Model: [Böckenhauer08]  Spring-like forces are modeled between neighboring amino acids.  Sum of forces for a state  Energy Energy = Energy =

13 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 Global min Energy =

14 Simulation Models HP Lattice Model: [Böckenhauer08]  A state is defined by the position of every amino acid in the chain A StateAnother State

15 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 moveAfter move

18 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

21 Simulation Models Probabilistic Roadmap [Song04]  Goal: Given start & goal states Find “best path” from start  goal

22 Simulation Models Probabilistic Roadmap [Song04] 3 Steps: 1.Node generation: Generate points randomly (dense near the goal state) 2.Roadmap Construction Connect nearest neighbors  graph 3.Query roadmap Dijkstra’s algorithm  shortest path Shortest path = set of states Describes the dynamic folding process

23 Simulation Models Probabilistic Roadmap [Song04] 1.Node generation: Generate random points “Obstacles” are infeasible (self-overlapping) states

24 Simulation Models Probabilistic Roadmap [Song04] 2.Roadmap Construction Connect nearest neighbors  graph

25 Simulation Models Probabilistic Roadmap [Song04] 3.Query roadmap Dijkstra’s algorithm  shortest path Path = set of states that describes the folding process

26 Molecular Dynamics Model

27 Simulation Models Molecular Dynamics Models [Tapia07]  Model forces based on Newton’s 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.

29 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

30 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

31 Conclusion Protein Folding:  1D Amino acid chain folds into 3D structure  Misfolding  Alzheimer’s, Parkinson’s, Mad Cow diseases  Folding is too fast to observe experimentally Four Simulation Models: 1.Triangular Lattice model (2D Graph) Vertex = one amino acid “Moves” transition between states

32 Conclusion Four Simulation Models (cont.) 2.Probabilistic Roadmaps Vertex represents state of entire protein Random sampling + Dijkstra’s alg  Best folding route ≈ Viterbi (returns one path) 3.Map-Based Master Equation (MME)  Learn probabilities  ≈ Baum-Welch (confidence level for each state) 4.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 369–381. Springer, [Dobson99]  C. Dobson and M. Karplus. The fundamentals of protein folding: bringing together theory and experiment. Current Opinion in Structural Biology, 9:928–101, 1999.

34 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, 20:60–71, [Tapia07]  Lydia Tapia, Xinyu Tang, Shawna Thomas, and Nancy M. Amato. Kinetics analysis methods for approximate folding landscapes. Bioinformatics, 23(13):i539–i548, 2007.

35 References: [˘Sali94]  A., E. Shakhnovich, and M. Karplus. How does a protein fold? Nature, 369:248–251, [Wiki08]  Wikipedia. Protein folding — Wikipedia, the free encyclopedia, [Wiki08_MC]  Wikipedia. Monte-Carlo method — Wikipedia, the free encyclopedia,

36 Thank you for your attention. Questions

37 Extra Slides

38 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.