©Copyright 2017 Kameron Decker Harris This Brain Is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks
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©Copyright 2017 Kameron Decker Harris This Brain Is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks Kameron Decker Harris A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2017 Reading Committee: Eric Shea-Brown, Chair Stefan Mihalas Adrienne Fairhall Program Authorized to Offer Degree: Applied Mathematics University of Washington Abstract This Brain Is a Mess: Inference, Random Graphs, and Biophysics to Disentangle Neuronal Networks Kameron Decker Harris Chair of the Supervisory Committee: Professor Eric Shea-Brown Applied Mathematics At first glance, the neuronal network seems like a tangled web in many areas through- out the nervous system. Often, our best guess is that such “messy” connections are close to random, while obeying certain statistical constraints, e.g. the number of connections per neuron. However, neuronal wiring is coordinated across larger mesoscopic distances in a way that differentiates between brain layers, areas, and groups of cells. We work across spatial scales in order to understand this hierarchy of order and disorder in brain networks. Ultimately, the goal is to understand how network structure is important for brain function. This leads to: 1. An inference technique which reconstructs mesoscopic brain networks from tracing experiments targeting spatially contiguous groups of neurons. 2. Models of networks which are random, while also having constrained average con- nectivity and group structure. 3. Comparing simulated and real respiratory rhythms, highlighting the role of in- hibitory neurons and connectivity on rhythmogenesis, in particular synchrony and irregularity. TABLE OF CONTENTS Page Notation............................................ iii Chapter 1: Connecting network theory, statistics, and physiology.........1 1.1 Introduction to networks and graph theory...................2 1.2 Finding networks in the real world........................4 1.3 Networks built from graph statistics.......................7 1.4 Biological neural network models.........................9 1.5 The role of theoretical neuroscience........................ 11 Bibliography........................................ 12 Chapter 2: High resolution neural connectivity from incomplete tracing data us- ing nonnegative spline regression..................... 16 2.1 Introduction..................................... 17 2.2 Spatial smoothness of mesoscale connectivity.................. 20 2.3 Nonnegative spline regression with incomplete tracing data......... 21 2.4 Test problem..................................... 25 2.5 Finding a voxel-scale connectivity map for mouse cortex........... 27 2.6 Conclusions..................................... 31 Bibliography........................................ 32 Chapter 3: Random graph models of communities: spectral gap and its applica- tions...................................... 37 3.1 Introduction..................................... 37 3.2 Non-backtracking matrix B ............................ 42 3.3 Main result...................................... 44 3.4 Preliminaries..................................... 45 3.5 Proof of Theorem3................................. 48 i 3.6 Application: Community detection........................ 73 3.7 Application: Low density parity check or expander codes........... 81 3.8 Application: Matrix completion.......................... 83 Bibliography........................................ 89 Chapter 4: Different roles for inhibition in the rhythm-generating respiratory net- work...................................... 95 4.1 Introduction..................................... 96 4.2 Materials and Methods............................... 98 4.3 Results........................................ 110 4.4 Discussion...................................... 132 Bibliography........................................ 139 Chapter 5: Conclusion.................................. 149 Bibliography........................................ 150 List of Figures......................................... 154 List of Tables.......................................... 160 ii NOTATION : entry-wise greater than or equal to, e.g. W 0 means every entry of W is non- negative G(V, E): graph (directed or undirected) with vertices V and edges E N: natural numbers 1, 2, 3, . R: real numbers R+: the non-negative real numbers iii ACKNOWLEDGMENTS Thanks to everyone who helped me get through this PhD. When we feel like we are toiling away alone, on something that can seem so specialized, it is our relationships and the teaching we do that make science worth it. First of all, thank you to my advisor Eric Shea-Brown for being a tireless advocate of me and the rest of his students. You bring a consistently cheerful attitude to your work and life. I am always impressed by your professionalism and drive to create a welcoming and open environment in the lab. In the Applied Mathematics department, thank you to Keshanie Dissanayake, Lauren Lederer, Derek Franz, Alan Perry, Tony Garcia, and the rest of the staff and faculty. You are the ones that keep everything running! The support of the rest of the UW computational neuroscience community was es- sential. In particular, thanks to the other members of our group (past and present): Josh Mendoza, Iris Shi, Doris Voina, Matt Farrell, Ali Weber, Kathleen Champion, Tim Oleskiw, Alex Cayco-Gajic, Guillaume Lajoie, Yu Hu, Braden Brinkman, Hannah Choi, Merav Stern, Gabrielle Gutierrez, and Joel Zylberberg. I appreciate all the help I’ve received from Adrienne Fairhall and her wonderful group of students. And the many comp neuro happy hours were another joyful release from the frustrations of graduate school life. Thanks to all of my collaborators as well, especially the committee members who co- advised me on these projects. At the Allen Institute: Stefan Mihalas, Joe Knox, Nile Grad- dis, Nick Cain, David Feng, Lydia Ng, and many others were a great help in getting me going with their data and as the source of many great ideas. In the Seattle Children’s Research Institute: Nino Ramirez, your group has been so iv welcoming, and it seems like you guys have the most fun of any lab I know! Thanks to members Tatiana Dashevskiy (sorry for demanding so many Ns), Fred Garcia, Aguan Wei, and everyone else. Thank you to Ioana Dumtriu for your patience teaching me spectral graph theory from the basics, as well as to Marina Meila.˘ Thank you to my collaborator Gerandy Brito, and congratulations on your baby! I really enjoyed all of our discussions. Thank you also to the many colleagues and friends I met at conferences and the sum- mer schools in Berkeley, Woods Hole, and Friday Harbor. In particular, Ashok Litwin- Kumar, Haim Sompolinsky, and Larry Abbott, who became my co-authors on a fun project that came from the Woods Hole course. I also must acknowledge the people who have been with me from the beginning of my foray into research: Chris Danforth and Peter Dodds of UVM. You guys have been such great role models. You were the ones who inspired me to start on this path, and I valued your encouragement highest of all. The group of friends my (now) wife and I made after moving to Seattle also deserves a huge shout out. In particular, the first friend Aaron Brooks, whom I met in Santa Fe in what feels like another life, thanks for welcoming us into your tribe of so many cool moun- tain people cross scientists. The massive ski community of Seattle has been another great source of support. There’s no better way to refresh the mind and find inspiration than glide silently through the old growth in the early morning, or thread down a glaciated volcano on a fine spring afternoon. Finally, I must thank my family: my dad, mom, and Jim, along with my grandma, who are always impressed by the scientific stuff although I am not sure you ever really want me to try and explain it. Also, I have the best and most supportive wife, Meira, and I have loved becoming part of your family. When I get frustrated, I only have to think about you and the fourth-graders to get my perspective straight. v DEDICATION To the glaciers, may you stick around. Sunrise over the Granite glacier, Adamant Range, British Colombia vi 1 Chapter 1 CONNECTING NETWORK THEORY, STATISTICS, AND PHYSIOLOGY If you look at a piece of brain under a microscope, it will probably look like a mess. Every neuron connects to thousands of others on average, in a way that appears random. If we zoom out, however, hierarchical structure reveals itself. In the cortex, for exam- ple, neurons are organized into layers and cell-types, which are furthermore organized into different areas. I study how to measure and model these “messy” networks given incomplete data, both from an inference standpoint and using “toy” random networks whose parameters are easily measureable. I also examine how that structure shapes brain dynamics, in particular synchrony and rhythms. The brain is a fascinating system which allows us to actively engage with the world through sensation, cognition, and action. Brains are both complicated—intricately com- posed of many particular parts—and complex—their behavior emerges from the interac- tions of many neurons connected in a network [Anderson, 1972]. Because of this complex- ity, reductionism alone will not solve the brain. Instead, we need constructive theories for how assemblies of networked neurons perform computations. These computations rely on network structure. Neurons are the main information processing