Application of Robotics

1
Application of Robotics Computational
GeometryTechniques to Proteins and other
Molecules

• Nancy M. Amato
• Parasol Lab,Texas AM University
• and
• IBM TJ Watson Research Center

2
Goal of This Talk

• Mention some Techniques in Robotics,
  Computational Geometry, etc that may have
  application to biomolecules
• Computational geometry mathematical techniques
  for studying folding problems (Streinu,
  Whitesides, Snoeyink)
• CG Robotics techniques for docking and shape
  analysis (Bereg, Amato)
• Dimensionality Reduction Techniques (Forbes
  Burkowski, Snoeyink)
• Combinatorial Rigidity (Mantler, Snoeyink,
  Streinu, Amato, Thomas)
• Robotics techniques for articulated systems,
  including systems with closed loops (Amato,
  Thomas, Brock, Ros, Whitesides)

3
Geometry for Folding and Layout (Sue Whitesides)

• Algorithms for moving linkages and hinged objects
  
• See animations of folding to polyhedra and
  knotted surfaces made by folding flat patterns
  (implemented by Francois Labelle) at
• www.cs.mcgill.ca/sqrt/unfold/unfolding.html
• Applications to micromanufacturing
• Graph Layout problems Given an abstract graph,
  determine if it has a layout in space satisfying
  geometric constraints, e.g., distance constraints
• Potential application for visualization
• GraphDrawing (GD 2004) in New York, layout
  results using semi-rigid structures as a proof
  technique

4
Single-Vertex Origami Foldsand their induced
simple motions
Ileana Streinu and Walter Whiteley
Same family of infinitesimal motions
Single-vertex origami spherical polygon, and
projects to planar polygon
5
Single-vertex origami exploration tool

• Audrey Lee and Ileana Streinu Implemented using
• CGAL (planar map data structure)
• Petsc (non-linear solver)
• QT (gui) and OpenGL
• Extendible to explore other motions

6
Protein/Protein Interactions (Sergey Bereg)

• Docking of Rigid Proteins
• Examples where can predict using only shape
  complementarity
• Approach based on motion, requires fast collision
  detection (need precise location of collisions)
• Sample space of rotations can reduce the search
  space
• Current Focus is extending to Flexible Proteins
• Challenge modeling the dynamics and how to
  exploit previous technique for rigid proteins

7
Nonlinear Dimensionality Reduction (Forbes
Burkowski Shirley Hui)

• Dimensionality reduction is a technique that may
  be used to organize high dimensional data by
  discovering a more compact representation
• used in computer vision to capture changes in a
  scene.
• Dimensionality reduction for molecules
• We are currently investigating techniques to
  represent conformational changes
• Working with protein flexibility
• Working with flexibility of ligands

8
Proteins Combinatorial Rigidity Allostery
(Mantler many others)

• Work in progress Mantler many others
• Can rigidity explain allostery?
• Examining glycogen phosphorylase (GP)

7GPB Relaxed
8GPB Tense
9
Banana Spiders(Mantler Snoeyink, CCCG 2004)

• Graphs satisfying Lamans condition in 3D can be
  highly connected yet flexible.
• Andrea and Jack hoped that this answered one of
  Bills questions, but

10
Robotics Techniques for Articulated Systems
(Amato, Brock, Ros, Thomas, Whitesides)

• Many methods have been developed in robotics for
  motion planning
• Models developed for articulated robots can be
  adapted to model molecules
• Randomized motion planning methods have been
  successful in searching high-dimensional spaces
• Applied in animation, CAD/CAM, and now molecules
• Applied to problems in Computational Biology
• Protein/Ligand Binding
• Protein structure prediction
• Protein Folding
• RNA Folding

11
Motion Planning
The Piano Movers Problem
Box Folding
Alpha Puzzle
12
Protein Structure Prediction (TJ Brunette
Oliver Brock)

• New Method for searching conformation space
• family of search techniques for high-dimensional
  spaces derived from robotics motion planning
• Application to protein structure prediction
• Use Rosettas energy function
• Outperforms Rosetta in cases studied (next slide)
• Future Directions
• Dimensionality reduction by exploiting rigidity
• Incorporation of domain knowledge to reduce
  search space

13
New Conformation Space Search Prediction Results
(Brock)
Protein 2PTL 60 (78) amino acids / 120 degrees
of freedom
Native Structure
Rosetta
Our Method
Protein 1O0U 414 amino acids / 828 degrees of
freedom
14
Configuration Space (C-Space)
C-Space

• robot maps to a point in higher
• dimensional space
• parameter for each degree of freedom
• (dof) of robot
• C-space set of all robot placements
• C-obstacle infeasible robot placements

3D C-space (x,y,z)
6D C-space (x,y,z,pitch,roll,yaw)
2n-D C-space (f1, y1, f2, y2, . . . , f n, y n)
15
Motion Planning in C-space
Simple workspace obstacle transformed Into
complicated C-obstacle!!
C-space
Workspace
C-obst
C-obst
obst
obst
C-obst
C-obst
obst
obst
y
x
robot
robot
16
Probabilistic Roadmap Methods (PRMs)Kavraki,
Svestka, Latombe,Overmars 1996
C-space
Roadmap Construction (Pre-processing)
C-obst
C-obst
C-obst
C-obst
C-obst
17
Applications of PRM-based Motion Planning (Amato
et al)
18
Applications of PRM-based Motion Planning (Amato
et al)
19
Protein Folding via Motion Planning(Amato,
Thomas, Song and K. Dill M. Scholtz)
Protein L
Protein G
20
Protein Folding

• We are interested in the folding process
• how the protein folds to its native structure

21
Why Study Folding Pathways?

• Importance of Studying Pathways
• insight into protein interactions function
• may lead to better structure prediction
  algorithms
• Diseases such as Alzheimers Mad Cow related to
  misfolded proteins
• Computational Techniques Critical
• Hard to study experimentally (happens too fast)
• Can study folding for thousands of already solved
  structures
• Help guide/design future experiments

22
Folding Landscapes

• Each conformation has a potential energy
• Native state is global minimum
• Set of all conformations forms landscape
• Shape of landscape reflects folding behavior

Native state
Different proteins ? different landscapes ?
different folding behaviors
23
Using Motion Planning to Map Folding Landscapes
RECOMB 01,02, 04 PSB 03

• Use Probabilistic Roadmap (PRM) method from
  motion planning to build roadmap
• Roadmap approximates the folding landscape
• Characterizes the main features of landscape
• Can extract multiple folding pathways from
  roadmap
• Compute population kinetics for roadmap

Native state
24
Related Work

• Other PRM-Based approaches for studying molecular
  motions
• Other work on protein folding
• (Apaydin et al, ICRA01,RECOMB02)
• Ligand binding
• (Singh, Latombe, Brutlag, ISMB99, Bayazit,
  Song, Amato, ICRA01)
• RNA Folding (Tang, Kirkpatrick, Thomas, Song,
  Amato RECOMB 04)

25
Modeling Proteins
One amino acid
26
Roadmap Construction Node Generation

• Sample using known native state
• sample around it, gradually grow out
• generate conformations by randomly selecting
  phi/psi angles
• Criterion for accepting a node
• Compute potential energy E of each node and
  retain it with probability

Native state
N
Denser distribution around native state
27
Ramachandran Plots for Different Sampling
Techniques
Uniform sampling
Gaussian sampling
Iterative Gaussian sampling
28
Distributions for different typesPotential
Energy vs. RMSD for roadmap nodes
all alpha
alpha beta
all beta
29
Roadmap ConstructionNode Connection
Edge weight w(u,v) f(E(C1), E(C2), E(Cn))
Native state
30
PRMs for Protein Folding Key Issues

• Energy Functions
• The degree to which the roadmap accurately
  reflects folding landscape depends on the quality
  of energy calculation.
• We use our own coarse potential (fast) and well
  known all atom potential (slow)
• Validation
• In ICRA01, RECOMB 01, JCB 02, results
  validated with experimental results Li
  Woodward 1999.

31
One Folding Path of Protein AA nice movie. But
so what?
Ribbon Model
Space-fill Model

• B domain of staphylococcal protein A

32
Roadmap AnalysisSecondary Structure Formation
Order
RECOMB01, JCB02, RECOMB02, JCB03, PSB03

• Order in which secondary structure forms during
  folding

hairpin 1,2
helix
Q Which forms first?
33
Formation Time Calculation

• Secondary structure has formed when x of the
  native contacts are present
• native contact less than 7 A between Ca atoms in
  native state

If we pick x as 60, then at time step 30, three
contacts present, structure considered formed
34
Contact Map

• A contact map is a triangular
• matrix which identifies all the
• native contacts among
• residues

35
Contact Maps
36
Secondary Structure Formation OrderTimed
Contact Map of a Path JCB02
residue
residue
?
Formation order ?, ? 3-4, ? 1-2, ? 1-4
Average T 142

• protein G (domain B1)

37
Secondary Structure Formation OrderValidation
Sample Summary
38
Detailed Study of Proteins G LPSB03
Protein L
Protein G
Protein G

• Protein G Protein L
• Similar structure (1 helix, 2 beta strands), but
  15 sequence identity
• Fold differently
• Protein G helix, beta 3-4, beta1-2, beta 1-4
  Kuszewski et al 1994, Orban et al. 1995
• Protein L helix, beta 1-2, beta 3-4, beta 1-4
  Yi Baker 1996, Yi et al 1997
• Can our approach detect the difference? Yes!
• 75 Protein G paths 80 Protein L paths have
  right order
• Increases to 90 100, resp., when use all atom
  potential

39
Helix and Beta StrandsCoarse Potential PSB03

• Protein G
• Protein L

(b3- b4 forms first) over 2k paths analyzed
b2
b1
b4
b3
(b1- b2 forms first) over 2k paths
b2
b1
b4
b3
40
Helix and Beta StrandsAll-atom Potential

• Protein G
• Protein L

(b3- b4 forms first)
Analyze First x Contacts
b2
Contacts
SS Formation Order
20
40
60
80
100
b1
a
b
b4
b1
b2
b1
b4
,
3-
,
-
,
-
79
79
74
82
90
all
a
b1
b2
b3
b4
b1
b4
,
-
,
-
,
-
21
21
26
18
10
b4
a
b
b4
b1
b2
b1
b4
,
3-
,
-
,
-
77
74
71
77
81
hydrophobic
a
b
b2
b3
b4
b1
b4
23
26
29
23
,
1-
,
-
,
-
19
b3
(b1- b2 forms first)
b2
b1
b4
b3
41
Summary PRM-Based Protein Folding

• PRM roadmaps approximate energy landscapes
• Efficiently produce multiple folding pathways
• Secondary structure formation order (e.g. G and
  L)
• More efficient than trajectory-based simulation
  methods, such as Monte Carlo, molecular dynamics
• Provide a good way to study folding kinetics
• multiple folding kinetics in same landscape
  (roadmap)
• more realistic than statistical models (e.g.
  Lattice models, Bakers model PNAS99, Munozs
  model, PNAS99)
• Current Future Directions
• Using rigidity to bias sampling better fewer
  samples
• Studying pathways connecting specific
  conformations, e.g., allostery, folded/misfolded
  states, etc
• Doing it in Parallel using STAPL on BlueGeneL

42
Announcing our Protein Folding Server

• http//parasol.tamu.edu/foldingserver/
• You can submit proteins and we will build a
  roadmap and analyze it and show you results
• Ramachandran plots (all conformations In roadmap)
• RMSD vs. Potential energy plots (all
  conformations in roadmap)
• Secondary structure formation order statistics
  for roadmap pathways
• Energy profiles and timed contact maps for
  particular pathways
• pathway to native (best from most common ss
  formation order group)
• between two specified conformations
• You can choose to have your protein added to a
  public database, or we can keep it private just
  for you

43
RNA Folding ResultsX. Tang, B. Kirkpatrick, S.
Thomas, G. Song RECOMB04

• RNA energy landscape can be completely described
  by huge roadmaps.

• Heuristics are used to approximate energy
  landscape using small roadmaps.

• Our roadmaps contain many folding pathways.

Energy profile
Folding Steps

• Population kinetics analysis on the roadmaps
  shows that heuristic 1 can efficiently describe
  the energy landscape using a small subset of nodes

Map2 (Heuristic 1) 15 Nodes
Map3 (Heuristic 2) 33 Nodes
Map1 (Complete) 142 Nodes
Population
Population
Population
Folding Steps
Folding Steps
Folding Steps
44
Ligand BindingIEEE ICRA01
Given an description of a ligand molecule
(robot) and a protein (obstacle).
Find a configuration of the ligand near the
protein where geometric, electro-static and
chemical constraints are satisfied.
ligand
protein
45
Ligand BindingIEEE ICRA01

• Docking Find a configuration of the ligand near
  the protein that satisfies geometric,
  electro-static and chemical constraints
• PRM Approach (Singh, Latombe, Brutlag, 1999)
• rapidly explores high dimensional space
• We use OBPRM better suited for generating
  conformations in binding site (near protein
  surface)
• Haptic User interaction
• haptics (sense of touch) helps user understand
  molecular interaction
• User assists planner by suggesting promising
  regions, and planner will post-process and
  improve

46
Contact Information

• For more information, check out our website
• http//parasol.tamu.edu/amato/
• Credits
• My students Guang Song (now Postdoc with
  Jernigan at Iowa State), Shawna Thomas, Xinyu
  Tang
• Ken Dill (UCSF) and Marty Scholtz (Texas AM)