MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology Nov 22, 2013: Topological methods for exploring low-density states in biomolecular folding pathways. Fall 2013 course offered through the University of Iowa Division of Continuing Education Isabel K. Darcy, Department of Mathematics Applied Mathematical and Computational Sciences, University of Iowa http://www.math.uiowa.edu/~idarcy/AppliedTopology.html

You can join live lecture Wednesday and Friday either by going to or joining via regular classroom. NOTE: to ask questions, you need to joing via regular classroom.

IMA Annual Program Year Workshop, December 9-13, 2013 Topological Structures in Computational Biology http://www.ima.umn.edu/2013-2014/W12.9-13.13/ Tuesday December 10, 2013 11:30am-12:20pm Pek Lum (Ayasdi, Inc.) Friday December 13, 2013 9:00am-9:50am Monica Nicolau (Stanford University)

http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

Example: Point cloud data representing a hand. Data Set: Example: Point cloud data representing a hand. Function f : Data Set  R Example: x-coordinate f : (x, y, z)  x http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

Put data into overlapping bins. Example: f-1(ai, bi) ( ( ) ( ) ( ) ( ) ( ) ) Function f : Data Set  R Ex 1: x-coordinate f : (x, y, z)  x http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

Vertex = a cluster of a bin. Edge = nonempty intersection D) Cluster each bin & create network. Vertex = a cluster of a bin. Edge = nonempty intersection between clusters Need covering Resolution multiscale http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

Vertex = a cluster of a bin. Edge = nonempty intersection D) Cluster each bin & create network. Vertex = a cluster of a bin. Edge = nonempty intersection between clusters Need covering Resolution multiscale http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

Vertex = a cluster of a bin. Edge = nonempty intersection D) Cluster each bin & create network. Vertex = a cluster of a bin. Edge = nonempty intersection between clusters Need covering Resolution multiscale http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

Example: Point cloud data representing a hand. A) Data Set Example: Point cloud data representing a hand. B) Function f : Data Set  R Example: x-coordinate f : (x, y, z)  x Put data into overlapping bins. Example: f-1(ai, bi) Cluster each bin & create network. Vertex = a cluster of a bin. Edge = nonempty intersection between clusters http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

Chose filter http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

Chose filter http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

http://scitation. aip. org/content/aip/journal/jcp/130/14/10. 1063/1 http://scitation.aip.org/content/aip/journal/jcp/130/14/10.1063/1.3103496

Data: Contact maps from 2,800 Serial Replica Exchange Molecular Dynamics (SREMD) simulations of the GCAA tetraloop on the Folding@home distributed computing platform. 760 trajectories with a complete unfolding event 550 trajectories with a complete refolding event. Goal: To determine secondary structure pathways between folded and unfolded state

Problem: Many more folded and unfolded conformations than intermediate conformations How to distinguish intermediate conformations from noise? Solution Choose f: space of conformations  R f(conformation) = density

550 trajectories with a complete refolding event 2952 configurations

Distance = Hamming distance

550 trajectories with a complete refolding event 2952 configurations

760 trajectories with a complete refolding event 4330 configurations

An eQTL biological data visualization challenge and approaches from the visualization community, Bartlett et al. BMC Bioinformatics 2012, 13(Suppl 8):S8 Mapper applied to SNP data: http://www.biomedcentral.com/1471-2105/13/S8/S8

Monday December 09, 2013 9:00am-9:50am Visualizing and Exploring Molecular Simulation Data via Energy Landscape Metaphor Yusu Wang (The Ohio State University)

E(conformation) = energy of the conformation Motivation: Let S = set of conformations of the survivin protein Energy landscape E: S  R E(conformation) = energy of the conformation http://pubs.acs.org/doi/pdf/10.1021/jp911085d https://parasol.tamu.edu/foldingserver/FAQ_Technique.php

Data from: 20,000 conformations obtained via replica exchange molecular dynamics. The backbone = 46 alpha-carbon atoms = 1035 dimensional vector of pairwise distances describing the protein shape. Intrinsic dimensionality of the conformational manifold has been estimated at around 20.

level set = f-1(r) = { x in M | f(x) = r } http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf contour tree level set = f-1(r) = { x in M | f(x) = r } A contour = a connected component of a level set. Let Cq = the contour in M that is collapsed to q Let TopoComp(edge) = U Cq 1940’s Reeb graph How do you embed the tree? q in edge

Given f: Md  R, Find g: R2  R such that f and g share same contour tree (2) the area of TopoComp(edge) of g is the same as the volumes of the corresponding TopoComp(edge) of f for each edge in the contour tree. Expands upon Weber’s Topological Landscapes, 2007

f: M^2  R http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

Figure 8: (a) Slice-and-dice and (b) Voronoi treemap layouts of terrains in Figure 6. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf