Exploring Protein Folding Trajectories Using Geometric
SpannersDaniel Russel and Leonidas Guibas
Stanford University
Goals
● Existing work understanding protein structure– Classification– Comparison– Matching
● Qualitative understanding of proteins motions– We do not quite get there yet
Outline
● Overview of spanners● Properties of interest● Displaying trajectories● Future work
Geometric Spanners
● Vertexes are points● Edges have length● Expansion factor
– Ratio between graph distanceand Euclidean distance
Geometric Spanners
● Vertexes are points● Edges have length● Expansion factor
– Ratio between graph distanceand Euclidean distance
2CI2 Spanner
Expansion factor is 2Expansion factor is 2
backbone atom index
back
bon
e a
tom
ind
ex
spanner edges
2CI2 Spanner: Helix
helix
backbone atom index
back
bon
e a
tom
ind
ex
2CI2 Spanner: Strands
parallel strands
antiparallel strands
backbone atom index
back
bon
e a
tom
ind
ex
2CI2 Spanner: Tertiary Structure
tertiary interactions
backbone atom index
back
bon
e a
tom
ind
ex
Outline
● Overview of spanners● Properties of interest● Displaying trajectories● Future work
Combinatorializes Structure
● Picks a few pairs per set of adjacencies
Other Properties
● Regular structure of helices and strands
● Local meaning for edge
Family of Descriptors
● Vary expansion factor ● From distance matrix to sparse● Linear for many values
1.5 1.75 2.0 2.5 3.0
Outline
● Overview of spanners● Properties of interest● Displaying trajectories● Future work
Protein Folding Trajectories
● Input: Protein trajectories– Currently small proteins, later larger– Nanosecond timescales, later millisecond– Tens or hundreds of folding trajectories– Many non-folding
● Want to understand– Individual trajectories– Structure of conformation space
Processing Spanners
● Edges move slightly between frames● Tracked edge
initial frame edgesfinal frame edgesidentical edges
(identical edges colored grey or magenta)
some m
atching pairs
Another View
Initial edgesFinal edges
backbone index
Smoothing
● Birth and death events● Persistent edges● Gaps
time
pers
iste
nt
ed
ges
Tracked edge
BirthDeath
Strip Spanner Representation
start vertex
length
Strip Historyedge length
index along backbone
fram
e
brighten
Segmenting Trajectories
sample conformation
segmentdividers
Example: BBA5
Native state(1) (3)
(2)
Outline
● Overview of spanners● Properties of interest● Displaying trajectories● Future work
Sidechains
●
● Breaks the ordering of nodes● How many points?
Comparing Motions
● Compare pairs of trajectories– Partial matches
● Cluster conformations– Find bottlenecks
● Cluster trajectories– Which are similar– Which are unique
Deeper Understanding
● Proteins → spanner
● Graph → proteins
● Spanner distances vs. conformation distances
