MATH-BIOINF-STAT-547: Mathematics of Data
Hi-C: 1M Scale
Lieberman-Aiden, Erez, et al. "Comprehensive mapping of long-range interactions reveals folding principles of the human genome." science 326.5950 (2009): 289-293.
Hi-C: 100KB Scale
Dixon, Jesse R., et al. "Topological domains in mammalian genomes identified by analysis of chromatin interactions." Nature 485.7398 (2012): 376-380.
Chen J, Hero A, and Rajapakse I. "Spectral Identification of Topological Domains." Bioinformatics 32.14 (2016): 2151-2158.
Spectral Identification of Topological Domains
Page 2154
Ng AY, Jordan MI, Weiss Y. "On spectral clustering: Analysis and an algorithm." In Advances in neural information processing systems (2002) (pp. 849-856).
Spectral Clustering
Page 2
Unnormalized Spectral Clustering
Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416. (Excellent Review!)
Page 399
Normalized Spectral Clustering: Ng et al. (2002)
Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416. (Excellent Review!)
Page 399
Normalized Spectral Clustering: Shi and Malik (2000)
Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416. (Excellent Review!)
Page 399
Chen J, Hero A, and Rajapakse I. "Spectral Identification of Topological Domains." Bioinformatics 32.14 (2016): 2151-2158.
Spectral Identification of Topological Domains
Page 2154
DATA-GUIDED CONTROL (DGC)
Cellular Reprogramming
Takahashi, Kazutoshi, Koji Tanabe, Mari Ohnuki, Megumi Narita, Tomoko Ichisaka, Kiichiro Tomoda, and Shinya Yamanaka. "Induction of pluripotent stem cells from adult human fibroblasts by defined factors." cell 131, no. 5 (2007): 861-872.
Weintraub, Harold, et al. "Activation of muscle-specific genes in pigment, nerve, fat, liver, and fibroblast cell lines by forced expression of MyoD." Proceedings of the National Academy of Sciences 86.14 (1989): 5434-5438.
4DN Data
Desired Configuration
Initial Configuration
Given an Initial Condition, Desired Configuration, and the dynamics, are there Input(s) that steer the system towards the desired configuration?
Controllability: An Engineering Perspective
Discrete model
Controllability: A genome perspective
Algorithm for Cellular Reprogramming�Control Theory
Output = New Cell State
System
Controller
Sensor
Output
Data-Guided Control (DGC)
DATA (2015)
DGC (2017)
DARPA funded projects
Ronquist S, Patterson G, Muir LA, ….., Brockett R, Rajapakse I. "Algorithm for cellular reprogramming." Proceedings of the National Academy of Sciences. 2017 Nov 7;114(45):11832-7. Data-guided Control (DGC) Supporting Information
Chen H, Chen J, Muir LA, …., Smale S, Rajapakse I. "Functional Organization of the Human 4D Nucleome. " Proceedings of the National Academy of Sciences 112.26 (2015): 8002-8007. Supporting Information
Our methods and data for the algorithm
TADs
18
Various Domains of Attraction (DOA) as suggested by Waddington
Typically when a skin cell divides the daughter cells are also skin cells. However, over the last few decades laboratory studies have shown that by the insertion of certain transcription factors the cell division process can be steered so as produce different cell lines from skin cells. this can be formulated as a controllability problem and studied by standard control theoretic methods.
Reprogramming Cells
System
TFs
DOA