Exploring Protein Folding Trajectories Using Geometric Spanners Daniel 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 distance and Euclidean distance Geometric Spanners Vertexes are points Edges have length Expansion factor Ratio between graph distance and Euclidean distance 2CI2 Spanner Expansion factor is 2 backbone atom index spanner edges 2CI2 Spanner: Helix helix backbone atom index 2CI2 Spanner: Strands parallel strands antiparallel strands backbone atom index 2CI2 Spanner: Tertiary Structure tertiary interactions backbone atom index 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 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 edges final frame edges identical edges (identical edges colored grey or magenta) some matching pairs Another View Initial edges Final edges backbone index Smoothing Birth and death events Persistent edges Gaps time persistent edges Tracked edge Birth Death Strip Spanner Representation start vertex length Strip History edge length index along backbone frame brighten Segmenting Trajectories sample conformation segment dividers 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